diff options
Diffstat (limited to 'src/libs/3rdparty/botan/src/lib/math')
42 files changed, 13832 insertions, 0 deletions
diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/big_code.cpp b/src/libs/3rdparty/botan/src/lib/math/bigint/big_code.cpp new file mode 100644 index 0000000000..c428199659 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/big_code.cpp @@ -0,0 +1,166 @@ +/* +* BigInt Encoding/Decoding +* (C) 1999-2010,2012 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/bigint.h> +#include <botan/divide.h> +#include <botan/charset.h> +#include <botan/hex.h> + +namespace Botan { + +/* +* Encode a BigInt +*/ +void BigInt::encode(uint8_t output[], const BigInt& n, Base base) + { + if(base == Binary) + { + n.binary_encode(output); + } + else if(base == Hexadecimal) + { + secure_vector<uint8_t> binary(n.encoded_size(Binary)); + n.binary_encode(binary.data()); + + hex_encode(cast_uint8_ptr_to_char(output), + binary.data(), binary.size()); + } + else if(base == Decimal) + { + BigInt copy = n; + BigInt remainder; + copy.set_sign(Positive); + const size_t output_size = n.encoded_size(Decimal); + for(size_t j = 0; j != output_size; ++j) + { + divide(copy, 10, copy, remainder); + output[output_size - 1 - j] = + Charset::digit2char(static_cast<uint8_t>(remainder.word_at(0))); + if(copy.is_zero()) + break; + } + } + else + throw Invalid_Argument("Unknown BigInt encoding method"); + } + +/* +* Encode a BigInt +*/ +std::vector<uint8_t> BigInt::encode(const BigInt& n, Base base) + { + std::vector<uint8_t> output(n.encoded_size(base)); + encode(output.data(), n, base); + if(base != Binary) + for(size_t j = 0; j != output.size(); ++j) + if(output[j] == 0) + output[j] = '0'; + return output; + } + +/* +* Encode a BigInt +*/ +secure_vector<uint8_t> BigInt::encode_locked(const BigInt& n, Base base) + { + secure_vector<uint8_t> output(n.encoded_size(base)); + encode(output.data(), n, base); + if(base != Binary) + for(size_t j = 0; j != output.size(); ++j) + if(output[j] == 0) + output[j] = '0'; + return output; + } + +/* +* Encode a BigInt, with leading 0s if needed +*/ +secure_vector<uint8_t> BigInt::encode_1363(const BigInt& n, size_t bytes) + { + secure_vector<uint8_t> output(bytes); + BigInt::encode_1363(output.data(), output.size(), n); + return output; + } + +//static +void BigInt::encode_1363(uint8_t output[], size_t bytes, const BigInt& n) + { + const size_t n_bytes = n.bytes(); + if(n_bytes > bytes) + throw Encoding_Error("encode_1363: n is too large to encode properly"); + + const size_t leading_0s = bytes - n_bytes; + encode(&output[leading_0s], n, Binary); + } + +/* +* Encode two BigInt, with leading 0s if needed, and concatenate +*/ +secure_vector<uint8_t> BigInt::encode_fixed_length_int_pair(const BigInt& n1, const BigInt& n2, size_t bytes) + { + secure_vector<uint8_t> output(2 * bytes); + BigInt::encode_1363(output.data(), bytes, n1); + BigInt::encode_1363(output.data() + bytes, bytes, n2); + return output; + } + +/* +* Decode a BigInt +*/ +BigInt BigInt::decode(const uint8_t buf[], size_t length, Base base) + { + BigInt r; + if(base == Binary) + r.binary_decode(buf, length); + else if(base == Hexadecimal) + { + secure_vector<uint8_t> binary; + + if(length % 2) + { + // Handle lack of leading 0 + const char buf0_with_leading_0[2] = + { '0', static_cast<char>(buf[0]) }; + + binary = hex_decode_locked(buf0_with_leading_0, 2); + + binary += hex_decode_locked(cast_uint8_ptr_to_char(&buf[1]), + length - 1, + false); + } + else + binary = hex_decode_locked(cast_uint8_ptr_to_char(buf), + length, false); + + r.binary_decode(binary.data(), binary.size()); + } + else if(base == Decimal) + { + for(size_t i = 0; i != length; ++i) + { + if(Charset::is_space(buf[i])) + continue; + + if(!Charset::is_digit(buf[i])) + throw Invalid_Argument("BigInt::decode: " + "Invalid character in decimal input"); + + const uint8_t x = Charset::char2digit(buf[i]); + + if(x >= 10) + throw Invalid_Argument("BigInt: Invalid decimal string"); + + r *= 10; + r += x; + } + } + else + throw Invalid_Argument("Unknown BigInt decoding method"); + return r; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/big_io.cpp b/src/libs/3rdparty/botan/src/lib/math/bigint/big_io.cpp new file mode 100644 index 0000000000..803e1cc4ae --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/big_io.cpp @@ -0,0 +1,56 @@ +/* +* BigInt Input/Output +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/bigint.h> +#include <istream> +#include <ostream> + +namespace Botan { + +/* +* Write the BigInt into a stream +*/ +std::ostream& operator<<(std::ostream& stream, const BigInt& n) + { + BigInt::Base base = BigInt::Decimal; + if(stream.flags() & std::ios::hex) + base = BigInt::Hexadecimal; + else if(stream.flags() & std::ios::oct) + throw Exception("Octal output of BigInt not supported"); + + if(n == 0) + stream.write("0", 1); + else + { + if(n < 0) + stream.write("-", 1); + const std::vector<uint8_t> buffer = BigInt::encode(n, base); + size_t skip = 0; + while(skip < buffer.size() && buffer[skip] == '0') + ++skip; + stream.write(cast_uint8_ptr_to_char(buffer.data()) + skip, + buffer.size() - skip); + } + if(!stream.good()) + throw Stream_IO_Error("BigInt output operator has failed"); + return stream; + } + +/* +* Read the BigInt from a stream +*/ +std::istream& operator>>(std::istream& stream, BigInt& n) + { + std::string str; + std::getline(stream, str); + if(stream.bad() || (stream.fail() && !stream.eof())) + throw Stream_IO_Error("BigInt input operator has failed"); + n = BigInt(str); + return stream; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/big_ops2.cpp b/src/libs/3rdparty/botan/src/lib/math/bigint/big_ops2.cpp new file mode 100644 index 0000000000..bd107f33ad --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/big_ops2.cpp @@ -0,0 +1,382 @@ +/* +* (C) 1999-2007,2018 Jack Lloyd +* 2016 Matthias Gierlings +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/bigint.h> +#include <botan/internal/mp_core.h> +#include <botan/internal/bit_ops.h> +#include <algorithm> + +namespace Botan { + +BigInt& BigInt::add(const word y[], size_t y_sw, Sign y_sign) + { + const size_t x_sw = sig_words(); + + if(sign() == y_sign) + { + const size_t reg_size = std::max(x_sw, y_sw) + 1; + + if(m_reg.size() < reg_size) + grow_to(reg_size); + + bigint_add2(mutable_data(), reg_size - 1, y, y_sw); + } + else + { + const int32_t relative_size = bigint_cmp(data(), x_sw, y, y_sw); + + if(relative_size < 0) + { + const size_t reg_size = std::max(x_sw, y_sw); + grow_to(reg_size); + bigint_sub2_rev(mutable_data(), y, y_sw); + set_sign(y_sign); + } + else if(relative_size == 0) + { + zeroise(m_reg); + set_sign(Positive); + } + else if(relative_size > 0) + { + bigint_sub2(mutable_data(), x_sw, y, y_sw); + } + } + + return (*this); + } + +BigInt& BigInt::operator+=(const BigInt& y) + { + return add(y.data(), y.sig_words(), y.sign()); + } + +BigInt& BigInt::operator+=(word y) + { + return add(&y, 1, Positive); + } + +BigInt& BigInt::sub(const word y[], size_t y_sw, Sign y_sign) + { + const size_t x_sw = sig_words(); + + int32_t relative_size = bigint_cmp(data(), x_sw, y, y_sw); + + const size_t reg_size = std::max(x_sw, y_sw) + 1; + grow_to(reg_size); + + if(relative_size < 0) + { + if(sign() == y_sign) + bigint_sub2_rev(mutable_data(), y, y_sw); + else + bigint_add2(mutable_data(), reg_size - 1, y, y_sw); + + set_sign(y_sign == Positive ? Negative : Positive); + } + else if(relative_size == 0) + { + if(sign() == y_sign) + { + clear(); + set_sign(Positive); + } + else + bigint_shl1(mutable_data(), x_sw, 0, 1); + } + else if(relative_size > 0) + { + if(sign() == y_sign) + bigint_sub2(mutable_data(), x_sw, y, y_sw); + else + bigint_add2(mutable_data(), reg_size - 1, y, y_sw); + } + + return (*this); + } + +BigInt& BigInt::operator-=(const BigInt& y) + { + return sub(y.data(), y.sig_words(), y.sign()); + } + +BigInt& BigInt::operator-=(word y) + { + return sub(&y, 1, Positive); + } + +BigInt& BigInt::mod_add(const BigInt& s, const BigInt& mod, secure_vector<word>& ws) + { + if(this->is_negative() || s.is_negative() || mod.is_negative()) + throw Invalid_Argument("BigInt::mod_add expects all arguments are positive"); + + // TODO add optimized version of this + *this += s; + this->reduce_below(mod, ws); + + return (*this); + } + +BigInt& BigInt::mod_sub(const BigInt& s, const BigInt& mod, secure_vector<word>& ws) + { + if(this->is_negative() || s.is_negative() || mod.is_negative()) + throw Invalid_Argument("BigInt::mod_sub expects all arguments are positive"); + + const size_t t_sw = sig_words(); + const size_t s_sw = s.sig_words(); + const size_t mod_sw = mod.sig_words(); + + if(t_sw > mod_sw || s_sw > mod_sw) + throw Invalid_Argument("BigInt::mod_sub args larger than modulus"); + + BOTAN_DEBUG_ASSERT(*this < mod); + BOTAN_DEBUG_ASSERT(s < mod); + + int32_t relative_size = bigint_cmp(data(), t_sw, s.data(), s_sw); + + if(relative_size >= 0) + { + // this >= s in which case just subtract + bigint_sub2(mutable_data(), t_sw, s.data(), s_sw); + } + else + { + // Otherwise we must sub s and then add p (or add (p - s) as here) + + if(ws.size() < mod_sw) + ws.resize(mod_sw); + + word borrow = bigint_sub3(ws.data(), mod.data(), mod_sw, s.data(), s_sw); + BOTAN_ASSERT_NOMSG(borrow == 0); + + if(m_reg.size() < mod_sw) + grow_to(mod_sw); + + word carry = bigint_add2_nc(mutable_data(), m_reg.size(), ws.data(), mod_sw); + BOTAN_ASSERT_NOMSG(carry == 0); + } + + return (*this); + } + +BigInt& BigInt::rev_sub(const word y[], size_t y_sw, secure_vector<word>& ws) + { + /* + *this = BigInt(y, y_sw) - *this; + return *this; + */ + if(this->sign() != BigInt::Positive) + throw Invalid_State("BigInt::sub_rev requires this is positive"); + + const size_t x_sw = this->sig_words(); + + const int32_t relative_size = bigint_cmp(y, y_sw, this->data(), x_sw); + + ws.resize(std::max(y_sw, x_sw) + 1); + clear_mem(ws.data(), ws.size()); + + if(relative_size < 0) + { + bigint_sub3(ws.data(), this->data(), x_sw, y, y_sw); + this->flip_sign(); + } + else if(relative_size == 0) + { + ws.clear(); + } + else if(relative_size > 0) + { + bigint_sub3(ws.data(), y, y_sw, this->data(), x_sw); + } + + m_reg.swap(ws); + + return (*this); + } + +/* +* Multiplication Operator +*/ +BigInt& BigInt::operator*=(const BigInt& y) + { + secure_vector<word> ws; + return this->mul(y, ws); + } + +BigInt& BigInt::mul(const BigInt& y, secure_vector<word>& ws) + { + const size_t x_sw = sig_words(); + const size_t y_sw = y.sig_words(); + set_sign((sign() == y.sign()) ? Positive : Negative); + + if(x_sw == 0 || y_sw == 0) + { + clear(); + set_sign(Positive); + } + else if(x_sw == 1 && y_sw) + { + grow_to(y_sw + 1); + bigint_linmul3(mutable_data(), y.data(), y_sw, word_at(0)); + } + else if(y_sw == 1 && x_sw) + { + grow_to(x_sw + 1); + bigint_linmul2(mutable_data(), x_sw, y.word_at(0)); + } + else + { + const size_t new_size = x_sw + y_sw + 1; + ws.resize(new_size); + secure_vector<word> z_reg(new_size); + + bigint_mul(z_reg.data(), z_reg.size(), + data(), size(), x_sw, + y.data(), y.size(), y_sw, + ws.data(), ws.size()); + + z_reg.swap(m_reg); + } + + return (*this); + } + +BigInt& BigInt::square(secure_vector<word>& ws) + { + const size_t sw = sig_words(); + + secure_vector<word> z(2*sw); + ws.resize(z.size()); + + bigint_sqr(z.data(), z.size(), + data(), size(), sw, + ws.data(), ws.size()); + + swap_reg(z); + set_sign(BigInt::Positive); + + return (*this); + } + +BigInt& BigInt::operator*=(word y) + { + if(y == 0) + { + clear(); + set_sign(Positive); + } + + const size_t x_sw = sig_words(); + + if(size() < x_sw + 1) + grow_to(x_sw + 1); + bigint_linmul2(mutable_data(), x_sw, y); + + return (*this); + } + +/* +* Division Operator +*/ +BigInt& BigInt::operator/=(const BigInt& y) + { + if(y.sig_words() == 1 && is_power_of_2(y.word_at(0))) + (*this) >>= (y.bits() - 1); + else + (*this) = (*this) / y; + return (*this); + } + +/* +* Modulo Operator +*/ +BigInt& BigInt::operator%=(const BigInt& mod) + { + return (*this = (*this) % mod); + } + +/* +* Modulo Operator +*/ +word BigInt::operator%=(word mod) + { + if(mod == 0) + throw BigInt::DivideByZero(); + + if(is_power_of_2(mod)) + { + word result = (word_at(0) & (mod - 1)); + clear(); + grow_to(2); + m_reg[0] = result; + return result; + } + + word remainder = 0; + + for(size_t j = sig_words(); j > 0; --j) + remainder = bigint_modop(remainder, word_at(j-1), mod); + clear(); + grow_to(2); + + if(remainder && sign() == BigInt::Negative) + m_reg[0] = mod - remainder; + else + m_reg[0] = remainder; + + set_sign(BigInt::Positive); + + return word_at(0); + } + +/* +* Left Shift Operator +*/ +BigInt& BigInt::operator<<=(size_t shift) + { + if(shift) + { + const size_t shift_words = shift / BOTAN_MP_WORD_BITS, + shift_bits = shift % BOTAN_MP_WORD_BITS, + words = sig_words(); + + /* + * FIXME - if shift_words == 0 && the top shift_bits of the top word + * are zero then we know that no additional word is needed and can + * skip the allocation. + */ + const size_t needed_size = words + shift_words + (shift_bits ? 1 : 0); + + if(m_reg.size() < needed_size) + grow_to(needed_size); + + bigint_shl1(mutable_data(), words, shift_words, shift_bits); + } + + return (*this); + } + +/* +* Right Shift Operator +*/ +BigInt& BigInt::operator>>=(size_t shift) + { + if(shift) + { + const size_t shift_words = shift / BOTAN_MP_WORD_BITS, + shift_bits = shift % BOTAN_MP_WORD_BITS; + + bigint_shr1(mutable_data(), sig_words(), shift_words, shift_bits); + + if(is_zero()) + set_sign(Positive); + } + + return (*this); + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/big_ops3.cpp b/src/libs/3rdparty/botan/src/lib/math/bigint/big_ops3.cpp new file mode 100644 index 0000000000..492a69ad05 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/big_ops3.cpp @@ -0,0 +1,219 @@ +/* +* BigInt Binary Operators +* (C) 1999-2007 Jack Lloyd +* 2016 Matthias Gierlings +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/bigint.h> +#include <botan/divide.h> +#include <botan/internal/mp_core.h> +#include <botan/internal/bit_ops.h> +#include <algorithm> + +namespace Botan { + +namespace { + +BigInt bigint_add(const BigInt& x, const word y[], size_t y_sw, BigInt::Sign y_sign) + { + const size_t x_sw = x.sig_words(); + + BigInt z(x.sign(), std::max(x_sw, y_sw) + 1); + + if(x.sign() == y_sign) + bigint_add3(z.mutable_data(), x.data(), x_sw, y, y_sw); + else + { + int32_t relative_size = bigint_cmp(x.data(), x_sw, y, y_sw); + + if(relative_size < 0) + { + bigint_sub3(z.mutable_data(), y, y_sw, x.data(), x_sw); + z.set_sign(y_sign); + } + else if(relative_size == 0) + z.set_sign(BigInt::Positive); + else if(relative_size > 0) + bigint_sub3(z.mutable_data(), x.data(), x_sw, y, y_sw); + } + + return z; + } + +BigInt bigint_sub(const BigInt& x, const word y[], size_t y_sw, BigInt::Sign y_sign) + { + const size_t x_sw = x.sig_words(); + + int32_t relative_size = bigint_cmp(x.data(), x_sw, y, y_sw); + + BigInt z(BigInt::Positive, std::max(x_sw, y_sw) + 1); + + if(relative_size < 0) + { + if(x.sign() == y_sign) + bigint_sub3(z.mutable_data(), y, y_sw, x.data(), x_sw); + else + bigint_add3(z.mutable_data(), x.data(), x_sw, y, y_sw); + z.set_sign(y_sign == BigInt::Positive ? BigInt::Negative : BigInt::Positive); + } + else if(relative_size == 0) + { + if(x.sign() != y_sign) + bigint_shl2(z.mutable_data(), x.data(), x_sw, 0, 1); + z.set_sign(y_sign == BigInt::Positive ? BigInt::Negative : BigInt::Positive); + } + else if(relative_size > 0) + { + if(x.sign() == y_sign) + bigint_sub3(z.mutable_data(), x.data(), x_sw, y, y_sw); + else + bigint_add3(z.mutable_data(), x.data(), x_sw, y, y_sw); + z.set_sign(x.sign()); + } + return z; + } + +} + +BigInt operator+(const BigInt& x, const BigInt& y) + { + return bigint_add(x, y.data(), y.sig_words(), y.sign()); + } + +BigInt operator+(const BigInt& x, word y) + { + return bigint_add(x, &y, 1, BigInt::Positive); + } + +BigInt operator-(const BigInt& x, const BigInt& y) + { + return bigint_sub(x, y.data(), y.sig_words(), y.sign()); + } + +BigInt operator-(const BigInt& x, word y) + { + return bigint_sub(x, &y, 1, BigInt::Positive); + } + +/* +* Multiplication Operator +*/ +BigInt operator*(const BigInt& x, const BigInt& y) + { + const size_t x_sw = x.sig_words(), y_sw = y.sig_words(); + + BigInt z(BigInt::Positive, x.size() + y.size()); + + if(x_sw == 1 && y_sw) + bigint_linmul3(z.mutable_data(), y.data(), y_sw, x.word_at(0)); + else if(y_sw == 1 && x_sw) + bigint_linmul3(z.mutable_data(), x.data(), x_sw, y.word_at(0)); + else if(x_sw && y_sw) + { + secure_vector<word> workspace(z.size()); + + bigint_mul(z.mutable_data(), z.size(), + x.data(), x.size(), x_sw, + y.data(), y.size(), y_sw, + workspace.data(), workspace.size()); + } + + if(x_sw && y_sw && x.sign() != y.sign()) + z.flip_sign(); + return z; + } + +/* +* Division Operator +*/ +BigInt operator/(const BigInt& x, const BigInt& y) + { + if(y.sig_words() == 1 && is_power_of_2(y.word_at(0))) + return (x >> (y.bits() - 1)); + + BigInt q, r; + divide(x, y, q, r); + return q; + } + +/* +* Modulo Operator +*/ +BigInt operator%(const BigInt& n, const BigInt& mod) + { + if(mod.is_zero()) + throw BigInt::DivideByZero(); + if(mod.is_negative()) + throw Invalid_Argument("BigInt::operator%: modulus must be > 0"); + if(n.is_positive() && mod.is_positive() && n < mod) + return n; + + BigInt q, r; + divide(n, mod, q, r); + return r; + } + +/* +* Modulo Operator +*/ +word operator%(const BigInt& n, word mod) + { + if(mod == 0) + throw BigInt::DivideByZero(); + + if(mod == 1) + return 0; + + if(is_power_of_2(mod)) + return (n.word_at(0) & (mod - 1)); + + word remainder = 0; + + for(size_t j = n.sig_words(); j > 0; --j) + remainder = bigint_modop(remainder, n.word_at(j-1), mod); + + if(remainder && n.sign() == BigInt::Negative) + return mod - remainder; + return remainder; + } + +/* +* Left Shift Operator +*/ +BigInt operator<<(const BigInt& x, size_t shift) + { + if(shift == 0) + return x; + + const size_t shift_words = shift / BOTAN_MP_WORD_BITS, + shift_bits = shift % BOTAN_MP_WORD_BITS; + + const size_t x_sw = x.sig_words(); + + BigInt y(x.sign(), x_sw + shift_words + (shift_bits ? 1 : 0)); + bigint_shl2(y.mutable_data(), x.data(), x_sw, shift_words, shift_bits); + return y; + } + +/* +* Right Shift Operator +*/ +BigInt operator>>(const BigInt& x, size_t shift) + { + if(shift == 0) + return x; + if(x.bits() <= shift) + return 0; + + const size_t shift_words = shift / BOTAN_MP_WORD_BITS, + shift_bits = shift % BOTAN_MP_WORD_BITS, + x_sw = x.sig_words(); + + BigInt y(x.sign(), x_sw - shift_words); + bigint_shr2(y.mutable_data(), x.data(), x_sw, shift_words, shift_bits); + return y; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/big_rand.cpp b/src/libs/3rdparty/botan/src/lib/math/bigint/big_rand.cpp new file mode 100644 index 0000000000..dd4cb5eaba --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/big_rand.cpp @@ -0,0 +1,64 @@ +/* +* BigInt Random Generation +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/bigint.h> +#include <botan/rng.h> +#include <botan/internal/rounding.h> + +namespace Botan { + +/* +* Randomize this number +*/ +void BigInt::randomize(RandomNumberGenerator& rng, + size_t bitsize, bool set_high_bit) + { + set_sign(Positive); + + if(bitsize == 0) + { + clear(); + } + else + { + secure_vector<uint8_t> array = rng.random_vec(round_up(bitsize, 8) / 8); + + // Always cut unwanted bits + if(bitsize % 8) + array[0] &= 0xFF >> (8 - (bitsize % 8)); + + // Set the highest bit if wanted + if (set_high_bit) + array[0] |= 0x80 >> ((bitsize % 8) ? (8 - bitsize % 8) : 0); + + binary_decode(array); + } + } + +/* +* Generate a random integer within given range +*/ +BigInt BigInt::random_integer(RandomNumberGenerator& rng, + const BigInt& min, const BigInt& max) + { + if(min.is_negative() || max.is_negative() || max <= min) + throw Invalid_Argument("BigInt::random_integer invalid range"); + + BigInt r; + + const size_t bits = max.bits(); + + do + { + r.randomize(rng, bits, false); + } + while(r < min || r >= max); + + return r; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/bigint.cpp b/src/libs/3rdparty/botan/src/lib/math/bigint/bigint.cpp new file mode 100644 index 0000000000..495907d1ab --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/bigint.cpp @@ -0,0 +1,381 @@ +/* +* BigInt Base +* (C) 1999-2011,2012,2014 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/bigint.h> +#include <botan/internal/mp_core.h> +#include <botan/internal/rounding.h> +#include <botan/internal/bit_ops.h> +#include <botan/internal/ct_utils.h> + +namespace Botan { + +BigInt::BigInt(const word words[], size_t length) + { + m_reg.assign(words, words + length); + } + +/* +* Construct a BigInt from a regular number +*/ +BigInt::BigInt(uint64_t n) + { + if(n == 0) + return; + + const size_t limbs_needed = sizeof(uint64_t) / sizeof(word); + + m_reg.resize(limbs_needed); + for(size_t i = 0; i != limbs_needed; ++i) + m_reg[i] = ((n >> (i*BOTAN_MP_WORD_BITS)) & MP_WORD_MASK); + } + +/* +* Construct a BigInt of the specified size +*/ +BigInt::BigInt(Sign s, size_t size) + { + m_reg.resize(round_up(size, 8)); + m_signedness = s; + } + +/* +* Copy constructor +*/ +BigInt::BigInt(const BigInt& other) + { + m_reg = other.m_reg; + m_signedness = other.m_signedness; + } + +/* +* Construct a BigInt from a string +*/ +BigInt::BigInt(const std::string& str) + { + Base base = Decimal; + size_t markers = 0; + bool negative = false; + + if(str.length() > 0 && str[0] == '-') + { + markers += 1; + negative = true; + } + + if(str.length() > markers + 2 && str[markers ] == '0' && + str[markers + 1] == 'x') + { + markers += 2; + base = Hexadecimal; + } + + *this = decode(cast_char_ptr_to_uint8(str.data()) + markers, + str.length() - markers, base); + + if(negative) set_sign(Negative); + else set_sign(Positive); + } + +BigInt::BigInt(const uint8_t input[], size_t length) + { + binary_decode(input, length); + } + +/* +* Construct a BigInt from an encoded BigInt +*/ +BigInt::BigInt(const uint8_t input[], size_t length, Base base) + { + *this = decode(input, length, base); + } + +BigInt::BigInt(const uint8_t buf[], size_t length, size_t max_bits) + { + const size_t max_bytes = std::min(length, (max_bits + 7) / 8); + *this = decode(buf, max_bytes); + + const size_t b = this->bits(); + if(b > max_bits) + { + *this >>= (b - max_bits); + } + } + +/* +* Construct a BigInt from an encoded BigInt +*/ +BigInt::BigInt(RandomNumberGenerator& rng, size_t bits, bool set_high_bit) + { + randomize(rng, bits, set_high_bit); + } + +int32_t BigInt::cmp_word(word other) const + { + if(is_negative()) + return -1; // other is positive ... + + const size_t sw = this->sig_words(); + if(sw > 1) + return 1; // must be larger since other is just one word ... + + return bigint_cmp(this->data(), sw, &other, 1); + } + +/* +* Comparison Function +*/ +int32_t BigInt::cmp(const BigInt& other, bool check_signs) const + { + if(check_signs) + { + if(other.is_positive() && this->is_negative()) + return -1; + + if(other.is_negative() && this->is_positive()) + return 1; + + if(other.is_negative() && this->is_negative()) + return (-bigint_cmp(this->data(), this->sig_words(), + other.data(), other.sig_words())); + } + + return bigint_cmp(this->data(), this->sig_words(), + other.data(), other.sig_words()); + } + +void BigInt::encode_words(word out[], size_t size) const + { + const size_t words = sig_words(); + + if(words > size) + throw Encoding_Error("BigInt::encode_words value too large to encode"); + + clear_mem(out, size); + copy_mem(out, data(), words); + } + +/* +* Return bits {offset...offset+length} +*/ +uint32_t BigInt::get_substring(size_t offset, size_t length) const + { + if(length > 32) + throw Invalid_Argument("BigInt::get_substring: Substring size " + std::to_string(length) + " too big"); + + uint64_t piece = 0; + for(size_t i = 0; i != 8; ++i) + { + const uint8_t part = byte_at((offset / 8) + (7-i)); + piece = (piece << 8) | part; + } + + const uint64_t mask = (static_cast<uint64_t>(1) << length) - 1; + const size_t shift = (offset % 8); + + return static_cast<uint32_t>((piece >> shift) & mask); + } + +/* +* Convert this number to a uint32_t, if possible +*/ +uint32_t BigInt::to_u32bit() const + { + if(is_negative()) + throw Encoding_Error("BigInt::to_u32bit: Number is negative"); + if(bits() > 32) + throw Encoding_Error("BigInt::to_u32bit: Number is too big to convert"); + + uint32_t out = 0; + for(size_t i = 0; i != 4; ++i) + out = (out << 8) | byte_at(3-i); + return out; + } + +/* +* Set bit number n +*/ +void BigInt::set_bit(size_t n) + { + const size_t which = n / BOTAN_MP_WORD_BITS; + const word mask = static_cast<word>(1) << (n % BOTAN_MP_WORD_BITS); + if(which >= size()) grow_to(which + 1); + m_reg[which] |= mask; + } + +/* +* Clear bit number n +*/ +void BigInt::clear_bit(size_t n) + { + const size_t which = n / BOTAN_MP_WORD_BITS; + const word mask = static_cast<word>(1) << (n % BOTAN_MP_WORD_BITS); + if(which < size()) + m_reg[which] &= ~mask; + } + +size_t BigInt::bytes() const + { + return round_up(bits(), 8) / 8; + } + +/* +* Count how many bits are being used +*/ +size_t BigInt::bits() const + { + const size_t words = sig_words(); + + if(words == 0) + return 0; + + const size_t full_words = words - 1; + return (full_words * BOTAN_MP_WORD_BITS + high_bit(word_at(full_words))); + } + +/* +* Calcluate the size in a certain base +*/ +size_t BigInt::encoded_size(Base base) const + { + static const double LOG_2_BASE_10 = 0.30102999566; + + if(base == Binary) + return bytes(); + else if(base == Hexadecimal) + return 2*bytes(); + else if(base == Decimal) + return static_cast<size_t>((bits() * LOG_2_BASE_10) + 1); + else + throw Invalid_Argument("Unknown base for BigInt encoding"); + } + +/* +* Return the negation of this number +*/ +BigInt BigInt::operator-() const + { + BigInt x = (*this); + x.flip_sign(); + return x; + } + +void BigInt::reduce_below(const BigInt& p, secure_vector<word>& ws) + { + if(p.is_negative()) + throw Invalid_Argument("BigInt::reduce_below mod must be positive"); + + const size_t p_words = p.sig_words(); + + if(size() < p_words + 1) + grow_to(p_words + 1); + + if(ws.size() < p_words + 1) + ws.resize(p_words + 1); + + clear_mem(ws.data(), ws.size()); + + for(;;) + { + word borrow = bigint_sub3(ws.data(), data(), p_words + 1, p.data(), p_words); + + if(borrow) + break; + + m_reg.swap(ws); + } + } + +/* +* Return the absolute value of this number +*/ +BigInt BigInt::abs() const + { + BigInt x = (*this); + x.set_sign(Positive); + return x; + } + +void BigInt::grow_to(size_t n) + { + if(n > size()) + { + if(n <= m_reg.capacity()) + m_reg.resize(m_reg.capacity()); + else + m_reg.resize(round_up(n, 8)); + } + } + +/* +* Encode this number into bytes +*/ +void BigInt::binary_encode(uint8_t output[]) const + { + const size_t sig_bytes = bytes(); + for(size_t i = 0; i != sig_bytes; ++i) + output[sig_bytes-i-1] = byte_at(i); + } + +/* +* Set this number to the value in buf +*/ +void BigInt::binary_decode(const uint8_t buf[], size_t length) + { + const size_t WORD_BYTES = sizeof(word); + + clear(); + m_reg.resize(round_up((length / WORD_BYTES) + 1, 8)); + + for(size_t i = 0; i != length / WORD_BYTES; ++i) + { + const size_t top = length - WORD_BYTES*i; + for(size_t j = WORD_BYTES; j > 0; --j) + m_reg[i] = (m_reg[i] << 8) | buf[top - j]; + } + + for(size_t i = 0; i != length % WORD_BYTES; ++i) + m_reg[length / WORD_BYTES] = (m_reg[length / WORD_BYTES] << 8) | buf[i]; + } + +#if defined(BOTAN_HAS_VALGRIND) +void BigInt::const_time_poison() const + { + CT::poison(m_reg.data(), m_reg.size()); + } + +void BigInt::const_time_unpoison() const + { + CT::unpoison(m_reg.data(), m_reg.size()); + } +#endif + +void BigInt::const_time_lookup(secure_vector<word>& output, + const std::vector<BigInt>& vec, + size_t idx) + { + const size_t words = output.size(); + + clear_mem(output.data(), output.size()); + + CT::poison(&idx, sizeof(idx)); + + for(size_t i = 0; i != vec.size(); ++i) + { + BOTAN_ASSERT(vec[i].size() >= words, + "Word size as expected in const_time_lookup"); + + const word mask = CT::is_equal(i, idx); + + for(size_t w = 0; w != words; ++w) + output[w] |= CT::select<word>(mask, vec[i].word_at(w), 0); + } + + CT::unpoison(idx); + CT::unpoison(output.data(), output.size()); + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/bigint.h b/src/libs/3rdparty/botan/src/lib/math/bigint/bigint.h new file mode 100644 index 0000000000..4a07723b77 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/bigint.h @@ -0,0 +1,806 @@ +/* +* BigInt +* (C) 1999-2008,2012 Jack Lloyd +* 2007 FlexSecure +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_BIGINT_H_ +#define BOTAN_BIGINT_H_ + +#include <botan/types.h> +#include <botan/secmem.h> +#include <botan/exceptn.h> +#include <botan/loadstor.h> +#include <iosfwd> + +namespace Botan { + +class RandomNumberGenerator; + +/** +* Arbitrary precision integer +*/ +class BOTAN_PUBLIC_API(2,0) BigInt final + { + public: + /** + * Base enumerator for encoding and decoding + */ + enum Base { Decimal = 10, Hexadecimal = 16, Binary = 256 }; + + /** + * Sign symbol definitions for positive and negative numbers + */ + enum Sign { Negative = 0, Positive = 1 }; + + /** + * DivideByZero Exception + */ + class BOTAN_PUBLIC_API(2,0) DivideByZero final : public Exception + { + public: + DivideByZero() : Exception("BigInt divide by zero") {} + }; + + /** + * Create empty BigInt + */ + BigInt() = default; + + /** + * Create BigInt from 64 bit integer + * @param n initial value of this BigInt + */ + BigInt(uint64_t n); + + /** + * Copy Constructor + * @param other the BigInt to copy + */ + BigInt(const BigInt& other); + + /** + * Create BigInt from a string. If the string starts with 0x the + * rest of the string will be interpreted as hexadecimal digits. + * Otherwise, it will be interpreted as a decimal number. + * + * @param str the string to parse for an integer value + */ + explicit BigInt(const std::string& str); + + /** + * Create a BigInt from an integer in a byte array + * @param buf the byte array holding the value + * @param length size of buf + */ + BigInt(const uint8_t buf[], size_t length); + + /** + * Create a BigInt from an integer in a byte array + * @param buf the byte array holding the value + * @param length size of buf + * @param base is the number base of the integer in buf + */ + BigInt(const uint8_t buf[], size_t length, Base base); + + /** + * Create a BigInt from an integer in a byte array + * @param buf the byte array holding the value + * @param length size of buf + * @param max_bits if the resulting integer is more than max_bits, + * it will be shifted so it is at most max_bits in length. + */ + BigInt(const uint8_t buf[], size_t length, size_t max_bits); + + /** + * Create a BigInt from an array of words + * @param words the words + * @param length number of words + */ + BigInt(const word words[], size_t length); + + /** + * \brief Create a random BigInt of the specified size + * + * @param rng random number generator + * @param bits size in bits + * @param set_high_bit if true, the highest bit is always set + * + * @see randomize + */ + BigInt(RandomNumberGenerator& rng, size_t bits, bool set_high_bit = true); + + /** + * Create BigInt of specified size, all zeros + * @param sign the sign + * @param n size of the internal register in words + */ + BigInt(Sign sign, size_t n); + + /** + * Move constructor + */ + BigInt(BigInt&& other) + { + this->swap(other); + } + + /** + * Move assignment + */ + BigInt& operator=(BigInt&& other) + { + if(this != &other) + this->swap(other); + + return (*this); + } + + /** + * Copy assignment + */ + BigInt& operator=(const BigInt&) = default; + + /** + * Swap this value with another + * @param other BigInt to swap values with + */ + void swap(BigInt& other) + { + m_reg.swap(other.m_reg); + std::swap(m_signedness, other.m_signedness); + } + + void swap_reg(secure_vector<word>& reg) + { + m_reg.swap(reg); + } + + /** + * += operator + * @param y the BigInt to add to this + */ + BigInt& operator+=(const BigInt& y); + + /** + * += operator + * @param y the word to add to this + */ + BigInt& operator+=(word y); + + /** + * -= operator + * @param y the BigInt to subtract from this + */ + BigInt& operator-=(const BigInt& y); + + /** + * -= operator + * @param y the word to subtract from this + */ + BigInt& operator-=(word y); + + /** + * *= operator + * @param y the BigInt to multiply with this + */ + BigInt& operator*=(const BigInt& y); + + /** + * *= operator + * @param y the word to multiply with this + */ + BigInt& operator*=(word y); + + /** + * /= operator + * @param y the BigInt to divide this by + */ + BigInt& operator/=(const BigInt& y); + + /** + * Modulo operator + * @param y the modulus to reduce this by + */ + BigInt& operator%=(const BigInt& y); + + /** + * Modulo operator + * @param y the modulus (word) to reduce this by + */ + word operator%=(word y); + + /** + * Left shift operator + * @param shift the number of bits to shift this left by + */ + BigInt& operator<<=(size_t shift); + + /** + * Right shift operator + * @param shift the number of bits to shift this right by + */ + BigInt& operator>>=(size_t shift); + + /** + * Increment operator + */ + BigInt& operator++() { return (*this += 1); } + + /** + * Decrement operator + */ + BigInt& operator--() { return (*this -= 1); } + + /** + * Postfix increment operator + */ + BigInt operator++(int) { BigInt x = (*this); ++(*this); return x; } + + /** + * Postfix decrement operator + */ + BigInt operator--(int) { BigInt x = (*this); --(*this); return x; } + + /** + * Unary negation operator + * @return negative this + */ + BigInt operator-() const; + + /** + * ! operator + * @return true iff this is zero, otherwise false + */ + bool operator !() const { return (!is_nonzero()); } + + BigInt& add(const word y[], size_t y_words, Sign sign); + BigInt& sub(const word y[], size_t y_words, Sign sign); + + /** + * Multiply this with y + * @param y the BigInt to multiply with this + * @param ws a temp workspace + */ + BigInt& mul(const BigInt& y, secure_vector<word>& ws); + + /** + * Square value of *this + * @param ws a temp workspace + */ + BigInt& square(secure_vector<word>& ws); + + /** + * Set *this to y - *this + * @param y the BigInt to subtract from as a sequence of words + * @param y_size length of y in words + * @param ws a temp workspace + */ + BigInt& rev_sub(const word y[], size_t y_size, secure_vector<word>& ws); + + /** + * Set *this to (*this + y) % mod + * This function assumes *this is >= 0 && < mod + * @param y the BigInt to add - assumed y >= 0 and y < mod + * @param mod the positive modulus + * @param ws a temp workspace + */ + BigInt& mod_add(const BigInt& y, const BigInt& mod, secure_vector<word>& ws); + + /** + * Set *this to (*this - y) % mod + * This function assumes *this is >= 0 && < mod + * @param y the BigInt to subtract - assumed y >= 0 and y < mod + * @param mod the positive modulus + * @param ws a temp workspace + */ + BigInt& mod_sub(const BigInt& y, const BigInt& mod, secure_vector<word>& ws); + + /** + * Return *this below mod + * + * Assumes that *this is (if anything) only slightly larger than + * mod and performs repeated subtractions. It should not be used if + * *this is much larger than mod, instead of modulo operator. + */ + void reduce_below(const BigInt& mod, secure_vector<word> &ws); + + /** + * Zeroize the BigInt. The size of the underlying register is not + * modified. + */ + void clear() { zeroise(m_reg); } + + /** + * Compare this to another BigInt + * @param n the BigInt value to compare with + * @param check_signs include sign in comparison? + * @result if (this<n) return -1, if (this>n) return 1, if both + * values are identical return 0 [like Perl's <=> operator] + */ + int32_t cmp(const BigInt& n, bool check_signs = true) const; + + /** + * Compare this to an integer + * @param n the value to compare with + * @result if (this<n) return -1, if (this>n) return 1, if both + * values are identical return 0 [like Perl's <=> operator] + */ + int32_t cmp_word(word n) const; + + /** + * Test if the integer has an even value + * @result true if the integer is even, false otherwise + */ + bool is_even() const { return (get_bit(0) == 0); } + + /** + * Test if the integer has an odd value + * @result true if the integer is odd, false otherwise + */ + bool is_odd() const { return (get_bit(0) == 1); } + + /** + * Test if the integer is not zero + * @result true if the integer is non-zero, false otherwise + */ + bool is_nonzero() const { return (!is_zero()); } + + /** + * Test if the integer is zero + * @result true if the integer is zero, false otherwise + */ + bool is_zero() const + { + const size_t sw = sig_words(); + + for(size_t i = 0; i != sw; ++i) + if(m_reg[i]) + return false; + return true; + } + + /** + * Set bit at specified position + * @param n bit position to set + */ + void set_bit(size_t n); + + /** + * Clear bit at specified position + * @param n bit position to clear + */ + void clear_bit(size_t n); + + /** + * Clear all but the lowest n bits + * @param n amount of bits to keep + */ + void mask_bits(size_t n) + { + if(n == 0) { clear(); return; } + + const size_t top_word = n / BOTAN_MP_WORD_BITS; + const word mask = (static_cast<word>(1) << (n % BOTAN_MP_WORD_BITS)) - 1; + + if(top_word < size()) + { + const size_t len = size() - (top_word + 1); + if (len > 0) + { + clear_mem(&m_reg[top_word+1], len); + } + m_reg[top_word] &= mask; + } + } + + /** + * Return bit value at specified position + * @param n the bit offset to test + * @result true, if the bit at position n is set, false otherwise + */ + bool get_bit(size_t n) const + { + return ((word_at(n / BOTAN_MP_WORD_BITS) >> (n % BOTAN_MP_WORD_BITS)) & 1); + } + + /** + * Return (a maximum of) 32 bits of the complete value + * @param offset the offset to start extracting + * @param length amount of bits to extract (starting at offset) + * @result the integer extracted from the register starting at + * offset with specified length + */ + uint32_t get_substring(size_t offset, size_t length) const; + + /** + * Convert this value into a uint32_t, if it is in the range + * [0 ... 2**32-1], or otherwise throw an exception. + * @result the value as a uint32_t if conversion is possible + */ + uint32_t to_u32bit() const; + + /** + * @param n the offset to get a byte from + * @result byte at offset n + */ + uint8_t byte_at(size_t n) const + { + return get_byte(sizeof(word) - (n % sizeof(word)) - 1, + word_at(n / sizeof(word))); + } + + /** + * Return the word at a specified position of the internal register + * @param n position in the register + * @return value at position n + */ + word word_at(size_t n) const + { return ((n < size()) ? m_reg[n] : 0); } + + void set_word_at(size_t i, word w) + { + if(i >= m_reg.size()) + grow_to(i + 1); + m_reg[i] = w; + } + + void set_words(const word w[], size_t len) + { + m_reg.resize(len); + copy_mem(mutable_data(), w, len); + } + + /** + * Tests if the sign of the integer is negative + * @result true, iff the integer has a negative sign + */ + bool is_negative() const { return (sign() == Negative); } + + /** + * Tests if the sign of the integer is positive + * @result true, iff the integer has a positive sign + */ + bool is_positive() const { return (sign() == Positive); } + + /** + * Return the sign of the integer + * @result the sign of the integer + */ + Sign sign() const { return (m_signedness); } + + /** + * @result the opposite sign of the represented integer value + */ + Sign reverse_sign() const + { + if(sign() == Positive) + return Negative; + return Positive; + } + + /** + * Flip the sign of this BigInt + */ + void flip_sign() + { + set_sign(reverse_sign()); + } + + /** + * Set sign of the integer + * @param sign new Sign to set + */ + void set_sign(Sign sign) + { + if(is_zero()) + m_signedness = Positive; + else + m_signedness = sign; + } + + /** + * @result absolute (positive) value of this + */ + BigInt abs() const; + + /** + * Give size of internal register + * @result size of internal register in words + */ + size_t size() const { return m_reg.size(); } + + /** + * Return how many words we need to hold this value + * @result significant words of the represented integer value + */ + size_t sig_words() const + { + const word* x = m_reg.data(); + size_t sig = m_reg.size(); + + while(sig && (x[sig-1] == 0)) + sig--; + return sig; + } + + /** + * Give byte length of the integer + * @result byte length of the represented integer value + */ + size_t bytes() const; + + /** + * Get the bit length of the integer + * @result bit length of the represented integer value + */ + size_t bits() const; + + /** + * Return a mutable pointer to the register + * @result a pointer to the start of the internal register + */ + word* mutable_data() { return m_reg.data(); } + + /** + * Return a const pointer to the register + * @result a pointer to the start of the internal register + */ + const word* data() const { return m_reg.data(); } + + secure_vector<word>& get_word_vector() { return m_reg; } + const secure_vector<word>& get_word_vector() const { return m_reg; } + + /** + * Increase internal register buffer to at least n words + * @param n new size of register + */ + void grow_to(size_t n); + + /** + * Resize the vector to the minimum word size to hold the integer, or + * min_size words, whichever is larger + */ + void shrink_to_fit(size_t min_size = 0) + { + const size_t words = std::max(min_size, sig_words()); + m_reg.resize(words); + } + + /** + * Fill BigInt with a random number with size of bitsize + * + * If \p set_high_bit is true, the highest bit will be set, which causes + * the entropy to be \a bits-1. Otherwise the highest bit is randomly chosen + * by the rng, causing the entropy to be \a bits. + * + * @param rng the random number generator to use + * @param bitsize number of bits the created random value should have + * @param set_high_bit if true, the highest bit is always set + */ + void randomize(RandomNumberGenerator& rng, size_t bitsize, bool set_high_bit = true); + + /** + * Store BigInt-value in a given byte array + * @param buf destination byte array for the integer value + */ + void binary_encode(uint8_t buf[]) const; + + /** + * Read integer value from a byte array with given size + * @param buf byte array buffer containing the integer + * @param length size of buf + */ + void binary_decode(const uint8_t buf[], size_t length); + + /** + * Read integer value from a byte array (secure_vector<uint8_t>) + * @param buf the array to load from + */ + void binary_decode(const secure_vector<uint8_t>& buf) + { + binary_decode(buf.data(), buf.size()); + } + + /** + * @param base the base to measure the size for + * @return size of this integer in base base + */ + size_t encoded_size(Base base = Binary) const; + + /** + * Place the value into out, zero-padding up to size words + * Throw if *this cannot be represented in size words + */ + void encode_words(word out[], size_t size) const; + +#if defined(BOTAN_HAS_VALGRIND) + void const_time_poison() const; + void const_time_unpoison() const; +#else + void const_time_poison() const {} + void const_time_unpoison() const {} +#endif + + /** + * @param rng a random number generator + * @param min the minimum value (must be non-negative) + * @param max the maximum value (must be non-negative and > min) + * @return random integer in [min,max) + */ + static BigInt random_integer(RandomNumberGenerator& rng, + const BigInt& min, + const BigInt& max); + + /** + * Create a power of two + * @param n the power of two to create + * @return bigint representing 2^n + */ + static BigInt power_of_2(size_t n) + { + BigInt b; + b.set_bit(n); + return b; + } + + /** + * Encode the integer value from a BigInt to a std::vector of bytes + * @param n the BigInt to use as integer source + * @param base number-base of resulting byte array representation + * @result secure_vector of bytes containing the integer with given base + */ + static std::vector<uint8_t> encode(const BigInt& n, Base base = Binary); + + /** + * Encode the integer value from a BigInt to a secure_vector of bytes + * @param n the BigInt to use as integer source + * @param base number-base of resulting byte array representation + * @result secure_vector of bytes containing the integer with given base + */ + static secure_vector<uint8_t> encode_locked(const BigInt& n, + Base base = Binary); + + /** + * Encode the integer value from a BigInt to a byte array + * @param buf destination byte array for the encoded integer + * value with given base + * @param n the BigInt to use as integer source + * @param base number-base of resulting byte array representation + */ + static void encode(uint8_t buf[], const BigInt& n, Base base = Binary); + + /** + * Create a BigInt from an integer in a byte array + * @param buf the binary value to load + * @param length size of buf + * @param base number-base of the integer in buf + * @result BigInt representing the integer in the byte array + */ + static BigInt decode(const uint8_t buf[], size_t length, + Base base = Binary); + + /** + * Create a BigInt from an integer in a byte array + * @param buf the binary value to load + * @param base number-base of the integer in buf + * @result BigInt representing the integer in the byte array + */ + static BigInt decode(const secure_vector<uint8_t>& buf, + Base base = Binary) + { + return BigInt::decode(buf.data(), buf.size(), base); + } + + /** + * Create a BigInt from an integer in a byte array + * @param buf the binary value to load + * @param base number-base of the integer in buf + * @result BigInt representing the integer in the byte array + */ + static BigInt decode(const std::vector<uint8_t>& buf, + Base base = Binary) + { + return BigInt::decode(buf.data(), buf.size(), base); + } + + /** + * Encode a BigInt to a byte array according to IEEE 1363 + * @param n the BigInt to encode + * @param bytes the length of the resulting secure_vector<uint8_t> + * @result a secure_vector<uint8_t> containing the encoded BigInt + */ + static secure_vector<uint8_t> encode_1363(const BigInt& n, size_t bytes); + + static void encode_1363(uint8_t out[], size_t bytes, const BigInt& n); + + /** + * Encode two BigInt to a byte array according to IEEE 1363 + * @param n1 the first BigInt to encode + * @param n2 the second BigInt to encode + * @param bytes the length of the encoding of each single BigInt + * @result a secure_vector<uint8_t> containing the concatenation of the two encoded BigInt + */ + static secure_vector<uint8_t> encode_fixed_length_int_pair(const BigInt& n1, const BigInt& n2, size_t bytes); + + /** + * Set output = vec[idx].m_reg in constant time + * All words of vec must have the same size + */ + static void const_time_lookup( + secure_vector<word>& output, + const std::vector<BigInt>& vec, + size_t idx); + + private: + secure_vector<word> m_reg; + Sign m_signedness = Positive; + }; + +/* +* Arithmetic Operators +*/ +BigInt BOTAN_PUBLIC_API(2,0) operator+(const BigInt& x, const BigInt& y); +BigInt BOTAN_PUBLIC_API(2,7) operator+(const BigInt& x, word y); +inline BigInt operator+(word x, const BigInt& y) { return y + x; } + +BigInt BOTAN_PUBLIC_API(2,0) operator-(const BigInt& x, const BigInt& y); +BigInt BOTAN_PUBLIC_API(2,7) operator-(const BigInt& x, word y); + +BigInt BOTAN_PUBLIC_API(2,0) operator*(const BigInt& x, const BigInt& y); +BigInt BOTAN_PUBLIC_API(2,0) operator/(const BigInt& x, const BigInt& d); +BigInt BOTAN_PUBLIC_API(2,0) operator%(const BigInt& x, const BigInt& m); +word BOTAN_PUBLIC_API(2,0) operator%(const BigInt& x, word m); +BigInt BOTAN_PUBLIC_API(2,0) operator<<(const BigInt& x, size_t n); +BigInt BOTAN_PUBLIC_API(2,0) operator>>(const BigInt& x, size_t n); + +/* +* Comparison Operators +*/ +inline bool operator==(const BigInt& a, const BigInt& b) + { return (a.cmp(b) == 0); } +inline bool operator!=(const BigInt& a, const BigInt& b) + { return (a.cmp(b) != 0); } +inline bool operator<=(const BigInt& a, const BigInt& b) + { return (a.cmp(b) <= 0); } +inline bool operator>=(const BigInt& a, const BigInt& b) + { return (a.cmp(b) >= 0); } +inline bool operator<(const BigInt& a, const BigInt& b) + { return (a.cmp(b) < 0); } +inline bool operator>(const BigInt& a, const BigInt& b) + { return (a.cmp(b) > 0); } + +inline bool operator==(const BigInt& a, word b) + { return (a.cmp_word(b) == 0); } +inline bool operator!=(const BigInt& a, word b) + { return (a.cmp_word(b) != 0); } +inline bool operator<=(const BigInt& a, word b) + { return (a.cmp_word(b) <= 0); } +inline bool operator>=(const BigInt& a, word b) + { return (a.cmp_word(b) >= 0); } +inline bool operator<(const BigInt& a, word b) + { return (a.cmp_word(b) < 0); } +inline bool operator>(const BigInt& a, word b) + { return (a.cmp_word(b) > 0); } + +/* +* I/O Operators +*/ +BOTAN_PUBLIC_API(2,0) std::ostream& operator<<(std::ostream&, const BigInt&); +BOTAN_PUBLIC_API(2,0) std::istream& operator>>(std::istream&, BigInt&); + +} + +namespace std { + +template<> +inline void swap<Botan::BigInt>(Botan::BigInt& x, Botan::BigInt& y) + { + x.swap(y); + } + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/divide.cpp b/src/libs/3rdparty/botan/src/lib/math/bigint/divide.cpp new file mode 100644 index 0000000000..63326d6552 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/divide.cpp @@ -0,0 +1,140 @@ +/* +* Division Algorithm +* (C) 1999-2007,2012 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/divide.h> +#include <botan/internal/mp_core.h> +#include <botan/internal/mp_madd.h> + +namespace Botan { + +namespace { + +/* +* Handle signed operands, if necessary +*/ +void sign_fixup(const BigInt& x, const BigInt& y, BigInt& q, BigInt& r) + { + if(x.sign() == BigInt::Negative) + { + q.flip_sign(); + if(r.is_nonzero()) { --q; r = y.abs() - r; } + } + if(y.sign() == BigInt::Negative) + q.flip_sign(); + } + +bool division_check(word q, word y2, word y1, + word x3, word x2, word x1) + { + // Compute (y3,y2,y1) = (y2,y1) * q + + word y3 = 0; + y1 = word_madd2(q, y1, &y3); + y2 = word_madd2(q, y2, &y3); + + // Return (y3,y2,y1) >? (x3,x2,x1) + + if(y3 > x3) return true; + if(y3 < x3) return false; + + if(y2 > x2) return true; + if(y2 < x2) return false; + + if(y1 > x1) return true; + if(y1 < x1) return false; + + return false; + } + +} + +/* +* Solve x = q * y + r +*/ +void divide(const BigInt& x, const BigInt& y_arg, BigInt& q, BigInt& r) + { + if(y_arg.is_zero()) + throw BigInt::DivideByZero(); + + BigInt y = y_arg; + const size_t y_words = y.sig_words(); + + r = x; + q = 0; + + r.set_sign(BigInt::Positive); + y.set_sign(BigInt::Positive); + + int32_t compare = r.cmp(y); + + if(compare == 0) + { + q = 1; + r = 0; + } + else if(compare > 0) + { + size_t shifts = 0; + word y_top = y.word_at(y.sig_words()-1); + while(y_top < MP_WORD_TOP_BIT) { y_top <<= 1; ++shifts; } + y <<= shifts; + r <<= shifts; + + const size_t n = r.sig_words() - 1, t = y_words - 1; + + if(n < t) + throw Internal_Error("BigInt division word sizes"); + + q.grow_to(n - t + 1); + + word* q_words = q.mutable_data(); + + if(n <= t) + { + while(r > y) { r -= y; ++q; } + r >>= shifts; + sign_fixup(x, y_arg, q, r); + return; + } + + BigInt temp = y << (BOTAN_MP_WORD_BITS * (n-t)); + + while(r >= temp) { r -= temp; q_words[n-t] += 1; } + + for(size_t j = n; j != t; --j) + { + const word x_j0 = r.word_at(j); + const word x_j1 = r.word_at(j-1); + const word y_t = y.word_at(t); + + if(x_j0 == y_t) + q_words[j-t-1] = MP_WORD_MAX; + else + q_words[j-t-1] = bigint_divop(x_j0, x_j1, y_t); + + while(division_check(q_words[j-t-1], + y_t, y.word_at(t-1), + x_j0, x_j1, r.word_at(j-2))) + { + q_words[j-t-1] -= 1; + } + + r -= (q_words[j-t-1] * y) << (BOTAN_MP_WORD_BITS * (j-t-1)); + + if(r.is_negative()) + { + r += y << (BOTAN_MP_WORD_BITS * (j-t-1)); + q_words[j-t-1] -= 1; + } + } + r >>= shifts; + } + + sign_fixup(x, y_arg, q, r); + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/divide.h b/src/libs/3rdparty/botan/src/lib/math/bigint/divide.h new file mode 100644 index 0000000000..03e5ff7c14 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/divide.h @@ -0,0 +1,29 @@ +/* +* Division +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_DIVISON_ALGORITHM_H_ +#define BOTAN_DIVISON_ALGORITHM_H_ + +#include <botan/bigint.h> + +namespace Botan { + +/** +* BigInt Division +* @param x an integer +* @param y a non-zero integer +* @param q will be set to x / y +* @param r will be set to x % y +*/ +void BOTAN_PUBLIC_API(2,0) divide(const BigInt& x, + const BigInt& y, + BigInt& q, + BigInt& r); + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/bigint/info.txt b/src/libs/3rdparty/botan/src/lib/math/bigint/info.txt new file mode 100644 index 0000000000..e84061bb6d --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/bigint/info.txt @@ -0,0 +1,16 @@ +<defines> +BIGINT -> 20131128 +</defines> + +load_on auto + +<header:public> +bigint.h +divide.h +</header:public> + +<requires> +mp +hex +rng +</requires> diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/info.txt b/src/libs/3rdparty/botan/src/lib/math/mp/info.txt new file mode 100644 index 0000000000..cee4325ed8 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/info.txt @@ -0,0 +1,10 @@ +<defines> +BIGINT_MP -> 20151225 +</defines> + +<header:internal> +mp_core.h +mp_madd.h +mp_asmi.h +mp_monty.h +</header:internal> diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_asmi.h b/src/libs/3rdparty/botan/src/lib/math/mp/mp_asmi.h new file mode 100644 index 0000000000..1b332811f8 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_asmi.h @@ -0,0 +1,875 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2010 Jack Lloyd +* 2006 Luca Piccarreta +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_MP_ASM_INTERNAL_H_ +#define BOTAN_MP_ASM_INTERNAL_H_ + +#include <botan/internal/mp_madd.h> + +namespace Botan { + +#if defined(BOTAN_MP_USE_X86_32_ASM) + +#define ADDSUB2_OP(OPERATION, INDEX) \ + ASM("movl 4*" #INDEX "(%[y]), %[carry]") \ + ASM(OPERATION " %[carry], 4*" #INDEX "(%[x])") \ + +#define ADDSUB3_OP(OPERATION, INDEX) \ + ASM("movl 4*" #INDEX "(%[x]), %[carry]") \ + ASM(OPERATION " 4*" #INDEX "(%[y]), %[carry]") \ + ASM("movl %[carry], 4*" #INDEX "(%[z])") \ + +#define LINMUL_OP(WRITE_TO, INDEX) \ + ASM("movl 4*" #INDEX "(%[x]),%%eax") \ + ASM("mull %[y]") \ + ASM("addl %[carry],%%eax") \ + ASM("adcl $0,%%edx") \ + ASM("movl %%edx,%[carry]") \ + ASM("movl %%eax, 4*" #INDEX "(%[" WRITE_TO "])") + +#define MULADD_OP(IGNORED, INDEX) \ + ASM("movl 4*" #INDEX "(%[x]),%%eax") \ + ASM("mull %[y]") \ + ASM("addl %[carry],%%eax") \ + ASM("adcl $0,%%edx") \ + ASM("addl 4*" #INDEX "(%[z]),%%eax") \ + ASM("adcl $0,%%edx") \ + ASM("movl %%edx,%[carry]") \ + ASM("movl %%eax, 4*" #INDEX " (%[z])") + +#define ADD_OR_SUBTRACT(CORE_CODE) \ + ASM("rorl %[carry]") \ + CORE_CODE \ + ASM("sbbl %[carry],%[carry]") \ + ASM("negl %[carry]") + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + +#define ADDSUB2_OP(OPERATION, INDEX) \ + ASM("movq 8*" #INDEX "(%[y]), %[carry]") \ + ASM(OPERATION " %[carry], 8*" #INDEX "(%[x])") \ + +#define ADDSUB3_OP(OPERATION, INDEX) \ + ASM("movq 8*" #INDEX "(%[x]), %[carry]") \ + ASM(OPERATION " 8*" #INDEX "(%[y]), %[carry]") \ + ASM("movq %[carry], 8*" #INDEX "(%[z])") \ + +#define LINMUL_OP(WRITE_TO, INDEX) \ + ASM("movq 8*" #INDEX "(%[x]),%%rax") \ + ASM("mulq %[y]") \ + ASM("addq %[carry],%%rax") \ + ASM("adcq $0,%%rdx") \ + ASM("movq %%rdx,%[carry]") \ + ASM("movq %%rax, 8*" #INDEX "(%[" WRITE_TO "])") + +#define MULADD_OP(IGNORED, INDEX) \ + ASM("movq 8*" #INDEX "(%[x]),%%rax") \ + ASM("mulq %[y]") \ + ASM("addq %[carry],%%rax") \ + ASM("adcq $0,%%rdx") \ + ASM("addq 8*" #INDEX "(%[z]),%%rax") \ + ASM("adcq $0,%%rdx") \ + ASM("movq %%rdx,%[carry]") \ + ASM("movq %%rax, 8*" #INDEX " (%[z])") + +#define ADD_OR_SUBTRACT(CORE_CODE) \ + ASM("rorq %[carry]") \ + CORE_CODE \ + ASM("sbbq %[carry],%[carry]") \ + ASM("negq %[carry]") + +#endif + +#if defined(ADD_OR_SUBTRACT) + +#define ASM(x) x "\n\t" + +#define DO_8_TIMES(MACRO, ARG) \ + MACRO(ARG, 0) \ + MACRO(ARG, 1) \ + MACRO(ARG, 2) \ + MACRO(ARG, 3) \ + MACRO(ARG, 4) \ + MACRO(ARG, 5) \ + MACRO(ARG, 6) \ + MACRO(ARG, 7) + +#endif + +/* +* Word Addition +*/ +inline word word_add(word x, word y, word* carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ADD_OR_SUBTRACT(ASM("adcl %[y],%[x]")) + : [x]"=r"(x), [carry]"=r"(*carry) + : "0"(x), [y]"rm"(y), "1"(*carry) + : "cc"); + return x; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + ADD_OR_SUBTRACT(ASM("adcq %[y],%[x]")) + : [x]"=r"(x), [carry]"=r"(*carry) + : "0"(x), [y]"rm"(y), "1"(*carry) + : "cc"); + return x; + +#else + word z = x + y; + word c1 = (z < x); + z += *carry; + *carry = c1 | (z < *carry); + return z; +#endif + } + +/* +* Eight Word Block Addition, Two Argument +*/ +inline word word8_add2(word x[8], const word y[8], word carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB2_OP, "adcl")) + : [carry]"=r"(carry) + : [x]"r"(x), [y]"r"(y), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB2_OP, "adcq")) + : [carry]"=r"(carry) + : [x]"r"(x), [y]"r"(y), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_32_MSVC_ASM) + + __asm { + mov edx,[x] + mov esi,[y] + xor eax,eax + sub eax,[carry] //force CF=1 iff *carry==1 + mov eax,[esi] + adc [edx],eax + mov eax,[esi+4] + adc [edx+4],eax + mov eax,[esi+8] + adc [edx+8],eax + mov eax,[esi+12] + adc [edx+12],eax + mov eax,[esi+16] + adc [edx+16],eax + mov eax,[esi+20] + adc [edx+20],eax + mov eax,[esi+24] + adc [edx+24],eax + mov eax,[esi+28] + adc [edx+28],eax + sbb eax,eax + neg eax + } + +#else + x[0] = word_add(x[0], y[0], &carry); + x[1] = word_add(x[1], y[1], &carry); + x[2] = word_add(x[2], y[2], &carry); + x[3] = word_add(x[3], y[3], &carry); + x[4] = word_add(x[4], y[4], &carry); + x[5] = word_add(x[5], y[5], &carry); + x[6] = word_add(x[6], y[6], &carry); + x[7] = word_add(x[7], y[7], &carry); + return carry; +#endif + } + +/* +* Eight Word Block Addition, Three Argument +*/ +inline word word8_add3(word z[8], const word x[8], + const word y[8], word carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "adcl")) + : [carry]"=r"(carry) + : [x]"r"(x), [y]"r"(y), [z]"r"(z), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "adcq")) + : [carry]"=r"(carry) + : [x]"r"(x), [y]"r"(y), [z]"r"(z), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_32_MSVC_ASM) + + __asm { + mov edi,[x] + mov esi,[y] + mov ebx,[z] + xor eax,eax + sub eax,[carry] //force CF=1 iff *carry==1 + mov eax,[edi] + adc eax,[esi] + mov [ebx],eax + + mov eax,[edi+4] + adc eax,[esi+4] + mov [ebx+4],eax + + mov eax,[edi+8] + adc eax,[esi+8] + mov [ebx+8],eax + + mov eax,[edi+12] + adc eax,[esi+12] + mov [ebx+12],eax + + mov eax,[edi+16] + adc eax,[esi+16] + mov [ebx+16],eax + + mov eax,[edi+20] + adc eax,[esi+20] + mov [ebx+20],eax + + mov eax,[edi+24] + adc eax,[esi+24] + mov [ebx+24],eax + + mov eax,[edi+28] + adc eax,[esi+28] + mov [ebx+28],eax + + sbb eax,eax + neg eax + } + +#else + z[0] = word_add(x[0], y[0], &carry); + z[1] = word_add(x[1], y[1], &carry); + z[2] = word_add(x[2], y[2], &carry); + z[3] = word_add(x[3], y[3], &carry); + z[4] = word_add(x[4], y[4], &carry); + z[5] = word_add(x[5], y[5], &carry); + z[6] = word_add(x[6], y[6], &carry); + z[7] = word_add(x[7], y[7], &carry); + return carry; +#endif + } + +/* +* Word Subtraction +*/ +inline word word_sub(word x, word y, word* carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ADD_OR_SUBTRACT(ASM("sbbl %[y],%[x]")) + : [x]"=r"(x), [carry]"=r"(*carry) + : "0"(x), [y]"rm"(y), "1"(*carry) + : "cc"); + return x; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + ADD_OR_SUBTRACT(ASM("sbbq %[y],%[x]")) + : [x]"=r"(x), [carry]"=r"(*carry) + : "0"(x), [y]"rm"(y), "1"(*carry) + : "cc"); + return x; + +#else + word t0 = x - y; + word c1 = (t0 > x); + word z = t0 - *carry; + *carry = c1 | (z > t0); + return z; +#endif + } + +/* +* Eight Word Block Subtraction, Two Argument +*/ +inline word word8_sub2(word x[8], const word y[8], word carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB2_OP, "sbbl")) + : [carry]"=r"(carry) + : [x]"r"(x), [y]"r"(y), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB2_OP, "sbbq")) + : [carry]"=r"(carry) + : [x]"r"(x), [y]"r"(y), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_32_MSVC_ASM) + + __asm { + mov edi,[x] + mov esi,[y] + xor eax,eax + sub eax,[carry] //force CF=1 iff *carry==1 + mov eax,[edi] + sbb eax,[esi] + mov [edi],eax + mov eax,[edi+4] + sbb eax,[esi+4] + mov [edi+4],eax + mov eax,[edi+8] + sbb eax,[esi+8] + mov [edi+8],eax + mov eax,[edi+12] + sbb eax,[esi+12] + mov [edi+12],eax + mov eax,[edi+16] + sbb eax,[esi+16] + mov [edi+16],eax + mov eax,[edi+20] + sbb eax,[esi+20] + mov [edi+20],eax + mov eax,[edi+24] + sbb eax,[esi+24] + mov [edi+24],eax + mov eax,[edi+28] + sbb eax,[esi+28] + mov [edi+28],eax + sbb eax,eax + neg eax + } + +#else + x[0] = word_sub(x[0], y[0], &carry); + x[1] = word_sub(x[1], y[1], &carry); + x[2] = word_sub(x[2], y[2], &carry); + x[3] = word_sub(x[3], y[3], &carry); + x[4] = word_sub(x[4], y[4], &carry); + x[5] = word_sub(x[5], y[5], &carry); + x[6] = word_sub(x[6], y[6], &carry); + x[7] = word_sub(x[7], y[7], &carry); + return carry; +#endif + } + +/* +* Eight Word Block Subtraction, Two Argument +*/ +inline word word8_sub2_rev(word x[8], const word y[8], word carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "sbbl")) + : [carry]"=r"(carry) + : [x]"r"(y), [y]"r"(x), [z]"r"(x), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "sbbq")) + : [carry]"=r"(carry) + : [x]"r"(y), [y]"r"(x), [z]"r"(x), "0"(carry) + : "cc", "memory"); + return carry; + +#else + x[0] = word_sub(y[0], x[0], &carry); + x[1] = word_sub(y[1], x[1], &carry); + x[2] = word_sub(y[2], x[2], &carry); + x[3] = word_sub(y[3], x[3], &carry); + x[4] = word_sub(y[4], x[4], &carry); + x[5] = word_sub(y[5], x[5], &carry); + x[6] = word_sub(y[6], x[6], &carry); + x[7] = word_sub(y[7], x[7], &carry); + return carry; +#endif + } + +/* +* Eight Word Block Subtraction, Three Argument +*/ +inline word word8_sub3(word z[8], const word x[8], + const word y[8], word carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "sbbl")) + : [carry]"=r"(carry) + : [x]"r"(x), [y]"r"(y), [z]"r"(z), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "sbbq")) + : [carry]"=r"(carry) + : [x]"r"(x), [y]"r"(y), [z]"r"(z), "0"(carry) + : "cc", "memory"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_32_MSVC_ASM) + + __asm { + mov edi,[x] + mov esi,[y] + xor eax,eax + sub eax,[carry] //force CF=1 iff *carry==1 + mov ebx,[z] + mov eax,[edi] + sbb eax,[esi] + mov [ebx],eax + mov eax,[edi+4] + sbb eax,[esi+4] + mov [ebx+4],eax + mov eax,[edi+8] + sbb eax,[esi+8] + mov [ebx+8],eax + mov eax,[edi+12] + sbb eax,[esi+12] + mov [ebx+12],eax + mov eax,[edi+16] + sbb eax,[esi+16] + mov [ebx+16],eax + mov eax,[edi+20] + sbb eax,[esi+20] + mov [ebx+20],eax + mov eax,[edi+24] + sbb eax,[esi+24] + mov [ebx+24],eax + mov eax,[edi+28] + sbb eax,[esi+28] + mov [ebx+28],eax + sbb eax,eax + neg eax + } + +#else + z[0] = word_sub(x[0], y[0], &carry); + z[1] = word_sub(x[1], y[1], &carry); + z[2] = word_sub(x[2], y[2], &carry); + z[3] = word_sub(x[3], y[3], &carry); + z[4] = word_sub(x[4], y[4], &carry); + z[5] = word_sub(x[5], y[5], &carry); + z[6] = word_sub(x[6], y[6], &carry); + z[7] = word_sub(x[7], y[7], &carry); + return carry; +#endif + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul2(word x[8], word y, word carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + DO_8_TIMES(LINMUL_OP, "x") + : [carry]"=r"(carry) + : [x]"r"(x), [y]"rm"(y), "0"(carry) + : "cc", "%eax", "%edx"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + DO_8_TIMES(LINMUL_OP, "x") + : [carry]"=r"(carry) + : [x]"r"(x), [y]"rm"(y), "0"(carry) + : "cc", "%rax", "%rdx"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_32_MSVC_ASM) + + __asm { + mov esi,[x] + mov eax,[esi] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,[carry] //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [esi],eax //load a + + mov eax,[esi+4] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [esi+4],eax //load a + + mov eax,[esi+8] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [esi+8],eax //load a + + mov eax,[esi+12] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [esi+12],eax //load a + + mov eax,[esi+16] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [esi+16],eax //load a + + mov eax,[esi+20] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [esi+20],eax //load a + + mov eax,[esi+24] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [esi+24],eax //load a + + mov eax,[esi+28] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov [esi+28],eax //load a + + mov eax,edx //store carry + } + +#else + x[0] = word_madd2(x[0], y, &carry); + x[1] = word_madd2(x[1], y, &carry); + x[2] = word_madd2(x[2], y, &carry); + x[3] = word_madd2(x[3], y, &carry); + x[4] = word_madd2(x[4], y, &carry); + x[5] = word_madd2(x[5], y, &carry); + x[6] = word_madd2(x[6], y, &carry); + x[7] = word_madd2(x[7], y, &carry); + return carry; +#endif + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul3(word z[8], const word x[8], word y, word carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + DO_8_TIMES(LINMUL_OP, "z") + : [carry]"=r"(carry) + : [z]"r"(z), [x]"r"(x), [y]"rm"(y), "0"(carry) + : "cc", "%eax", "%edx"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + asm( + DO_8_TIMES(LINMUL_OP, "z") + : [carry]"=r"(carry) + : [z]"r"(z), [x]"r"(x), [y]"rm"(y), "0"(carry) + : "cc", "%rax", "%rdx"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_32_MSVC_ASM) + + __asm { + mov edi,[z] + mov esi,[x] + mov eax,[esi] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,[carry] //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [edi],eax //load a + + mov eax,[esi+4] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [edi+4],eax //load a + + mov eax,[esi+8] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [edi+8],eax //load a + + mov eax,[esi+12] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [edi+12],eax //load a + + mov eax,[esi+16] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [edi+16],eax //load a + + mov eax,[esi+20] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [edi+20],eax //load a + + mov eax,[esi+24] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov ecx,edx //store carry + mov [edi+24],eax //load a + + mov eax,[esi+28] //load a + mul [y] //edx(hi):eax(lo)=a*b + add eax,ecx //sum lo carry + adc edx,0 //sum hi carry + mov [edi+28],eax //load a + mov eax,edx //store carry + } + +#else + z[0] = word_madd2(x[0], y, &carry); + z[1] = word_madd2(x[1], y, &carry); + z[2] = word_madd2(x[2], y, &carry); + z[3] = word_madd2(x[3], y, &carry); + z[4] = word_madd2(x[4], y, &carry); + z[5] = word_madd2(x[5], y, &carry); + z[6] = word_madd2(x[6], y, &carry); + z[7] = word_madd2(x[7], y, &carry); + return carry; +#endif + } + +/* +* Eight Word Block Multiply/Add +*/ +inline word word8_madd3(word z[8], const word x[8], word y, word carry) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + DO_8_TIMES(MULADD_OP, "") + : [carry]"=r"(carry) + : [z]"r"(z), [x]"r"(x), [y]"rm"(y), "0"(carry) + : "cc", "%eax", "%edx"); + return carry; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + DO_8_TIMES(MULADD_OP, "") + : [carry]"=r"(carry) + : [z]"r"(z), [x]"r"(x), [y]"rm"(y), "0"(carry) + : "cc", "%rax", "%rdx"); + return carry; + +#else + z[0] = word_madd3(x[0], y, z[0], &carry); + z[1] = word_madd3(x[1], y, z[1], &carry); + z[2] = word_madd3(x[2], y, z[2], &carry); + z[3] = word_madd3(x[3], y, z[3], &carry); + z[4] = word_madd3(x[4], y, z[4], &carry); + z[5] = word_madd3(x[5], y, z[5], &carry); + z[6] = word_madd3(x[6], y, z[6], &carry); + z[7] = word_madd3(x[7], y, z[7], &carry); + return carry; +#endif + } + +/* +* Multiply-Add Accumulator +* (w2,w1,w0) += x * y +*/ +inline void word3_muladd(word* w2, word* w1, word* w0, word x, word y) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + word z0 = 0, z1 = 0; + + asm ("mull %[y]" + : "=a"(z0),"=d"(z1) + : "a"(x), [y]"rm"(y) + : "cc"); + + asm(ASM("addl %[z0],%[w0]") + ASM("adcl %[z1],%[w1]") + ASM("adcl $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [z0]"r"(z0), [z1]"r"(z1), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + word z0 = 0, z1 = 0; + + asm ("mulq %[y]" + : "=a"(z0),"=d"(z1) + : "a"(x), [y]"rm"(y) + : "cc"); + + asm(ASM("addq %[z0],%[w0]") + ASM("adcq %[z1],%[w1]") + ASM("adcq $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [z0]"r"(z0), [z1]"r"(z1), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + +#else + word carry = *w0; + *w0 = word_madd2(x, y, &carry); + *w1 += carry; + *w2 += (*w1 < carry); +#endif + } + +/* +* 3-word addition +* (w2,w1,w0) += x +*/ +inline void word3_add(word* w2, word* w1, word* w0, word x) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ASM("addl %[x],%[w0]") + ASM("adcl $0,%[w1]") + ASM("adcl $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [x]"r"(x), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + asm( + ASM("addq %[x],%[w0]") + ASM("adcq $0,%[w1]") + ASM("adcq $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [x]"r"(x), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + +#else + *w0 += x; + word c1 = (*w0 < x); + *w1 += c1; + word c2 = (*w1 < c1); + *w2 += c2; +#endif + } + +/* +* Multiply-Add Accumulator +* (w2,w1,w0) += 2 * x * y +*/ +inline void word3_muladd_2(word* w2, word* w1, word* w0, word x, word y) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + + word z0 = 0, z1 = 0; + + asm ("mull %[y]" + : "=a"(z0),"=d"(z1) + : "a"(x), [y]"rm"(y) + : "cc"); + + asm( + ASM("addl %[z0],%[w0]") + ASM("adcl %[z1],%[w1]") + ASM("adcl $0,%[w2]") + + ASM("addl %[z0],%[w0]") + ASM("adcl %[z1],%[w1]") + ASM("adcl $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [z0]"r"(z0), [z1]"r"(z1), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + + word z0 = 0, z1 = 0; + + asm ("mulq %[y]" + : "=a"(z0),"=d"(z1) + : "a"(x), [y]"rm"(y) + : "cc"); + + asm( + ASM("addq %[z0],%[w0]") + ASM("adcq %[z1],%[w1]") + ASM("adcq $0,%[w2]") + + ASM("addq %[z0],%[w0]") + ASM("adcq %[z1],%[w1]") + ASM("adcq $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [z0]"r"(z0), [z1]"r"(z1), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + +#else + word carry = 0; + x = word_madd2(x, y, &carry); + y = carry; + + word top = (y >> (BOTAN_MP_WORD_BITS-1)); + y <<= 1; + y |= (x >> (BOTAN_MP_WORD_BITS-1)); + x <<= 1; + + carry = 0; + *w0 = word_add(*w0, x, &carry); + *w1 = word_add(*w1, y, &carry); + *w2 = word_add(*w2, top, &carry); +#endif + } + +#if defined(ASM) + #undef ASM + #undef DO_8_TIMES + #undef ADD_OR_SUBTRACT + #undef ADDSUB2_OP + #undef ADDSUB3_OP + #undef LINMUL_OP + #undef MULADD_OP +#endif + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_comba.cpp b/src/libs/3rdparty/botan/src/lib/math/mp/mp_comba.cpp new file mode 100644 index 0000000000..ec527224c8 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_comba.cpp @@ -0,0 +1,2211 @@ +/* +* Comba Multiplication and Squaring +* +* This file was automatically generated by ./src/scripts/comba.py on 2018-05-08 +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/mp_core.h> +#include <botan/internal/mp_asmi.h> + +namespace Botan { + +/* +* Comba 4x4 Squaring +*/ +void bigint_comba_sqr4(word z[8], const word x[4]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd (&w2, &w1, &w0, x[ 0], x[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); + z[ 1] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); + word3_muladd (&w1, &w0, &w2, x[ 1], x[ 1]); + z[ 2] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); + z[ 3] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); + word3_muladd (&w0, &w2, &w1, x[ 2], x[ 2]); + z[ 4] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); + z[ 5] = w2; w2 = 0; + + word3_muladd (&w2, &w1, &w0, x[ 3], x[ 3]); + z[ 6] = w0; + z[ 7] = w1; + } + +/* +* Comba 4x4 Multiplication +*/ +void bigint_comba_mul4(word z[8], const word x[4], const word y[4]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); + z[ 1] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); + z[ 2] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); + z[ 3] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); + z[ 4] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); + z[ 5] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); + z[ 6] = w0; + z[ 7] = w1; + } + +/* +* Comba 6x6 Squaring +*/ +void bigint_comba_sqr6(word z[12], const word x[6]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd (&w2, &w1, &w0, x[ 0], x[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); + z[ 1] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); + word3_muladd (&w1, &w0, &w2, x[ 1], x[ 1]); + z[ 2] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); + z[ 3] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 4]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); + word3_muladd (&w0, &w2, &w1, x[ 2], x[ 2]); + z[ 4] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 5]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 4]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); + z[ 5] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 5]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 4]); + word3_muladd (&w2, &w1, &w0, x[ 3], x[ 3]); + z[ 6] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 5]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 4]); + z[ 7] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 5]); + word3_muladd (&w1, &w0, &w2, x[ 4], x[ 4]); + z[ 8] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 5]); + z[ 9] = w0; w0 = 0; + + word3_muladd (&w0, &w2, &w1, x[ 5], x[ 5]); + z[10] = w1; + z[11] = w2; + } + +/* +* Comba 6x6 Multiplication +*/ +void bigint_comba_mul6(word z[12], const word x[6], const word y[6]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); + z[ 1] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); + z[ 2] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); + z[ 3] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 0]); + z[ 4] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 0]); + z[ 5] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 1]); + z[ 6] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 2]); + z[ 7] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 3]); + z[ 8] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 4]); + z[ 9] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 5]); + z[10] = w1; + z[11] = w2; + } + +/* +* Comba 8x8 Squaring +*/ +void bigint_comba_sqr8(word z[16], const word x[8]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd (&w2, &w1, &w0, x[ 0], x[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); + z[ 1] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); + word3_muladd (&w1, &w0, &w2, x[ 1], x[ 1]); + z[ 2] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); + z[ 3] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 4]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); + word3_muladd (&w0, &w2, &w1, x[ 2], x[ 2]); + z[ 4] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 5]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 4]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); + z[ 5] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 5]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 4]); + word3_muladd (&w2, &w1, &w0, x[ 3], x[ 3]); + z[ 6] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 7]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 6]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 5]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 4]); + z[ 7] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 7]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 6]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 5]); + word3_muladd (&w1, &w0, &w2, x[ 4], x[ 4]); + z[ 8] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 7]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 5]); + z[ 9] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 7]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 6]); + word3_muladd (&w0, &w2, &w1, x[ 5], x[ 5]); + z[10] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[ 7]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 6]); + z[11] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 7]); + word3_muladd (&w2, &w1, &w0, x[ 6], x[ 6]); + z[12] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[ 7]); + z[13] = w1; w1 = 0; + + word3_muladd (&w1, &w0, &w2, x[ 7], x[ 7]); + z[14] = w2; + z[15] = w0; + } + +/* +* Comba 8x8 Multiplication +*/ +void bigint_comba_mul8(word z[16], const word x[8], const word y[8]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); + z[ 1] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); + z[ 2] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); + z[ 3] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 0]); + z[ 4] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 0]); + z[ 5] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 0]); + z[ 6] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 0]); + z[ 7] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 1]); + z[ 8] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 2]); + z[ 9] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 3]); + z[10] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 4]); + z[11] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 5]); + z[12] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 6]); + z[13] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 7]); + z[14] = w2; + z[15] = w0; + } + +/* +* Comba 9x9 Squaring +*/ +void bigint_comba_sqr9(word z[18], const word x[9]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd (&w2, &w1, &w0, x[ 0], x[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); + z[ 1] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); + word3_muladd (&w1, &w0, &w2, x[ 1], x[ 1]); + z[ 2] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); + z[ 3] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 4]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); + word3_muladd (&w0, &w2, &w1, x[ 2], x[ 2]); + z[ 4] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 5]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 4]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); + z[ 5] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 5]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 4]); + word3_muladd (&w2, &w1, &w0, x[ 3], x[ 3]); + z[ 6] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 7]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 6]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 5]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 4]); + z[ 7] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 8]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 7]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 6]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 5]); + word3_muladd (&w1, &w0, &w2, x[ 4], x[ 4]); + z[ 8] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 7]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 5]); + z[ 9] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 8]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 7]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 6]); + word3_muladd (&w0, &w2, &w1, x[ 5], x[ 5]); + z[10] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 8]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[ 7]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 6]); + z[11] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 7]); + word3_muladd (&w2, &w1, &w0, x[ 6], x[ 6]); + z[12] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[ 8]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[ 7]); + z[13] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[ 8]); + word3_muladd (&w1, &w0, &w2, x[ 7], x[ 7]); + z[14] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[ 8]); + z[15] = w0; w0 = 0; + + word3_muladd (&w0, &w2, &w1, x[ 8], x[ 8]); + z[16] = w1; + z[17] = w2; + } + +/* +* Comba 9x9 Multiplication +*/ +void bigint_comba_mul9(word z[18], const word x[9], const word y[9]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); + z[ 1] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); + z[ 2] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); + z[ 3] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 0]); + z[ 4] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 0]); + z[ 5] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 0]); + z[ 6] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 0]); + z[ 7] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 0]); + z[ 8] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 1]); + z[ 9] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 2]); + z[10] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 3]); + z[11] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 4]); + z[12] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 5]); + z[13] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 6]); + z[14] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 7]); + z[15] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 8]); + z[16] = w1; + z[17] = w2; + } + +/* +* Comba 16x16 Squaring +*/ +void bigint_comba_sqr16(word z[32], const word x[16]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd (&w2, &w1, &w0, x[ 0], x[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); + z[ 1] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); + word3_muladd (&w1, &w0, &w2, x[ 1], x[ 1]); + z[ 2] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); + z[ 3] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 4]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); + word3_muladd (&w0, &w2, &w1, x[ 2], x[ 2]); + z[ 4] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 5]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 4]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); + z[ 5] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 5]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 4]); + word3_muladd (&w2, &w1, &w0, x[ 3], x[ 3]); + z[ 6] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 7]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 6]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 5]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 4]); + z[ 7] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 8]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 7]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 6]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 5]); + word3_muladd (&w1, &w0, &w2, x[ 4], x[ 4]); + z[ 8] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 7]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 5]); + z[ 9] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[10]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 9]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 8]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 7]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 6]); + word3_muladd (&w0, &w2, &w1, x[ 5], x[ 5]); + z[10] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[11]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[10]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 9]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 8]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[ 7]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 6]); + z[11] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 7]); + word3_muladd (&w2, &w1, &w0, x[ 6], x[ 6]); + z[12] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[13]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[12]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[11]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[10]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 9]); + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[ 8]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[ 7]); + z[13] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[14]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[13]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[12]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[11]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[10]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 9]); + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[ 8]); + word3_muladd (&w1, &w0, &w2, x[ 7], x[ 7]); + z[14] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[ 8]); + z[15] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[15]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[14]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[13]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[12]); + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[11]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[10]); + word3_muladd_2(&w0, &w2, &w1, x[ 7], x[ 9]); + word3_muladd (&w0, &w2, &w1, x[ 8], x[ 8]); + z[16] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[15]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[14]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[13]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[12]); + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[11]); + word3_muladd_2(&w1, &w0, &w2, x[ 7], x[10]); + word3_muladd_2(&w1, &w0, &w2, x[ 8], x[ 9]); + z[17] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[10]); + word3_muladd (&w2, &w1, &w0, x[ 9], x[ 9]); + z[18] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[15]); + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[14]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[13]); + word3_muladd_2(&w0, &w2, &w1, x[ 7], x[12]); + word3_muladd_2(&w0, &w2, &w1, x[ 8], x[11]); + word3_muladd_2(&w0, &w2, &w1, x[ 9], x[10]); + z[19] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[15]); + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[14]); + word3_muladd_2(&w1, &w0, &w2, x[ 7], x[13]); + word3_muladd_2(&w1, &w0, &w2, x[ 8], x[12]); + word3_muladd_2(&w1, &w0, &w2, x[ 9], x[11]); + word3_muladd (&w1, &w0, &w2, x[10], x[10]); + z[20] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[10], x[11]); + z[21] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 7], x[15]); + word3_muladd_2(&w0, &w2, &w1, x[ 8], x[14]); + word3_muladd_2(&w0, &w2, &w1, x[ 9], x[13]); + word3_muladd_2(&w0, &w2, &w1, x[10], x[12]); + word3_muladd (&w0, &w2, &w1, x[11], x[11]); + z[22] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 8], x[15]); + word3_muladd_2(&w1, &w0, &w2, x[ 9], x[14]); + word3_muladd_2(&w1, &w0, &w2, x[10], x[13]); + word3_muladd_2(&w1, &w0, &w2, x[11], x[12]); + z[23] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[10], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[11], x[13]); + word3_muladd (&w2, &w1, &w0, x[12], x[12]); + z[24] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[10], x[15]); + word3_muladd_2(&w0, &w2, &w1, x[11], x[14]); + word3_muladd_2(&w0, &w2, &w1, x[12], x[13]); + z[25] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[11], x[15]); + word3_muladd_2(&w1, &w0, &w2, x[12], x[14]); + word3_muladd (&w1, &w0, &w2, x[13], x[13]); + z[26] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[12], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[13], x[14]); + z[27] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[13], x[15]); + word3_muladd (&w0, &w2, &w1, x[14], x[14]); + z[28] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[14], x[15]); + z[29] = w2; w2 = 0; + + word3_muladd (&w2, &w1, &w0, x[15], x[15]); + z[30] = w0; + z[31] = w1; + } + +/* +* Comba 16x16 Multiplication +*/ +void bigint_comba_mul16(word z[32], const word x[16], const word y[16]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); + z[ 1] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); + z[ 2] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); + z[ 3] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 0]); + z[ 4] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 0]); + z[ 5] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 0]); + z[ 6] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 0]); + z[ 7] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 0]); + z[ 8] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 0]); + z[ 9] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[10]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[10], y[ 0]); + z[10] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[11]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[10]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[10], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[11], y[ 0]); + z[11] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 0]); + z[12] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[13]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[12]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[11]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[10]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[10], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[11], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[12], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[13], y[ 0]); + z[13] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[14]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[13]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[12]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[11]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[10]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[10], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[11], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[12], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[13], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[14], y[ 0]); + z[14] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 0]); + z[15] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 1], y[15]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[14]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[13]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[12]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[11]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[10]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[10], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[11], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[12], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[13], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[14], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[15], y[ 1]); + z[16] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 2], y[15]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[14]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[13]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[12]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[11]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[10]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[10], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[11], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[12], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[13], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[14], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[15], y[ 2]); + z[17] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 3], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 3]); + z[18] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 4], y[15]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[14]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[13]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[12]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[11]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[10]); + word3_muladd(&w0, &w2, &w1, x[10], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[11], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[12], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[13], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[14], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[15], y[ 4]); + z[19] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 5], y[15]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[14]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[13]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[12]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[11]); + word3_muladd(&w1, &w0, &w2, x[10], y[10]); + word3_muladd(&w1, &w0, &w2, x[11], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[12], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[13], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[14], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[15], y[ 5]); + z[20] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 6], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[12]); + word3_muladd(&w2, &w1, &w0, x[10], y[11]); + word3_muladd(&w2, &w1, &w0, x[11], y[10]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 6]); + z[21] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 7], y[15]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[14]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[13]); + word3_muladd(&w0, &w2, &w1, x[10], y[12]); + word3_muladd(&w0, &w2, &w1, x[11], y[11]); + word3_muladd(&w0, &w2, &w1, x[12], y[10]); + word3_muladd(&w0, &w2, &w1, x[13], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[14], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[15], y[ 7]); + z[22] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 8], y[15]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[14]); + word3_muladd(&w1, &w0, &w2, x[10], y[13]); + word3_muladd(&w1, &w0, &w2, x[11], y[12]); + word3_muladd(&w1, &w0, &w2, x[12], y[11]); + word3_muladd(&w1, &w0, &w2, x[13], y[10]); + word3_muladd(&w1, &w0, &w2, x[14], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[15], y[ 8]); + z[23] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 9], y[15]); + word3_muladd(&w2, &w1, &w0, x[10], y[14]); + word3_muladd(&w2, &w1, &w0, x[11], y[13]); + word3_muladd(&w2, &w1, &w0, x[12], y[12]); + word3_muladd(&w2, &w1, &w0, x[13], y[11]); + word3_muladd(&w2, &w1, &w0, x[14], y[10]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 9]); + z[24] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[10], y[15]); + word3_muladd(&w0, &w2, &w1, x[11], y[14]); + word3_muladd(&w0, &w2, &w1, x[12], y[13]); + word3_muladd(&w0, &w2, &w1, x[13], y[12]); + word3_muladd(&w0, &w2, &w1, x[14], y[11]); + word3_muladd(&w0, &w2, &w1, x[15], y[10]); + z[25] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[11], y[15]); + word3_muladd(&w1, &w0, &w2, x[12], y[14]); + word3_muladd(&w1, &w0, &w2, x[13], y[13]); + word3_muladd(&w1, &w0, &w2, x[14], y[12]); + word3_muladd(&w1, &w0, &w2, x[15], y[11]); + z[26] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[12], y[15]); + word3_muladd(&w2, &w1, &w0, x[13], y[14]); + word3_muladd(&w2, &w1, &w0, x[14], y[13]); + word3_muladd(&w2, &w1, &w0, x[15], y[12]); + z[27] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[13], y[15]); + word3_muladd(&w0, &w2, &w1, x[14], y[14]); + word3_muladd(&w0, &w2, &w1, x[15], y[13]); + z[28] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[14], y[15]); + word3_muladd(&w1, &w0, &w2, x[15], y[14]); + z[29] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[15], y[15]); + z[30] = w0; + z[31] = w1; + } + +/* +* Comba 24x24 Squaring +*/ +void bigint_comba_sqr24(word z[48], const word x[24]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd (&w2, &w1, &w0, x[ 0], x[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); + z[ 1] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); + word3_muladd (&w1, &w0, &w2, x[ 1], x[ 1]); + z[ 2] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); + z[ 3] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 4]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); + word3_muladd (&w0, &w2, &w1, x[ 2], x[ 2]); + z[ 4] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 5]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 4]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); + z[ 5] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 5]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 4]); + word3_muladd (&w2, &w1, &w0, x[ 3], x[ 3]); + z[ 6] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 7]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 6]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 5]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 4]); + z[ 7] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 8]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 7]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 6]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 5]); + word3_muladd (&w1, &w0, &w2, x[ 4], x[ 4]); + z[ 8] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 7]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 5]); + z[ 9] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[10]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 9]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 8]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 7]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 6]); + word3_muladd (&w0, &w2, &w1, x[ 5], x[ 5]); + z[10] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[11]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[10]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 9]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 8]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[ 7]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 6]); + z[11] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 7]); + word3_muladd (&w2, &w1, &w0, x[ 6], x[ 6]); + z[12] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[13]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[12]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[11]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[10]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 9]); + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[ 8]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[ 7]); + z[13] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[14]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[13]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[12]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[11]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[10]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 9]); + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[ 8]); + word3_muladd (&w1, &w0, &w2, x[ 7], x[ 7]); + z[14] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[ 8]); + z[15] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[16]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[15]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[14]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[13]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[12]); + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[11]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[10]); + word3_muladd_2(&w0, &w2, &w1, x[ 7], x[ 9]); + word3_muladd (&w0, &w2, &w1, x[ 8], x[ 8]); + z[16] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[17]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[16]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[15]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[14]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[13]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[12]); + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[11]); + word3_muladd_2(&w1, &w0, &w2, x[ 7], x[10]); + word3_muladd_2(&w1, &w0, &w2, x[ 8], x[ 9]); + z[17] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[18]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[17]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[16]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[10]); + word3_muladd (&w2, &w1, &w0, x[ 9], x[ 9]); + z[18] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[19]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[18]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[17]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[16]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[15]); + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[14]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[13]); + word3_muladd_2(&w0, &w2, &w1, x[ 7], x[12]); + word3_muladd_2(&w0, &w2, &w1, x[ 8], x[11]); + word3_muladd_2(&w0, &w2, &w1, x[ 9], x[10]); + z[19] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[20]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[19]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[18]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[17]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[16]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[15]); + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[14]); + word3_muladd_2(&w1, &w0, &w2, x[ 7], x[13]); + word3_muladd_2(&w1, &w0, &w2, x[ 8], x[12]); + word3_muladd_2(&w1, &w0, &w2, x[ 9], x[11]); + word3_muladd (&w1, &w0, &w2, x[10], x[10]); + z[20] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[21]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[20]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[19]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[18]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[17]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[16]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[10], x[11]); + z[21] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 0], x[22]); + word3_muladd_2(&w0, &w2, &w1, x[ 1], x[21]); + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[20]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[19]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[18]); + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[17]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[16]); + word3_muladd_2(&w0, &w2, &w1, x[ 7], x[15]); + word3_muladd_2(&w0, &w2, &w1, x[ 8], x[14]); + word3_muladd_2(&w0, &w2, &w1, x[ 9], x[13]); + word3_muladd_2(&w0, &w2, &w1, x[10], x[12]); + word3_muladd (&w0, &w2, &w1, x[11], x[11]); + z[22] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 0], x[23]); + word3_muladd_2(&w1, &w0, &w2, x[ 1], x[22]); + word3_muladd_2(&w1, &w0, &w2, x[ 2], x[21]); + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[20]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[19]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[18]); + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[17]); + word3_muladd_2(&w1, &w0, &w2, x[ 7], x[16]); + word3_muladd_2(&w1, &w0, &w2, x[ 8], x[15]); + word3_muladd_2(&w1, &w0, &w2, x[ 9], x[14]); + word3_muladd_2(&w1, &w0, &w2, x[10], x[13]); + word3_muladd_2(&w1, &w0, &w2, x[11], x[12]); + z[23] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[23]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[22]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[21]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[20]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[19]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[18]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[17]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[16]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[10], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[11], x[13]); + word3_muladd (&w2, &w1, &w0, x[12], x[12]); + z[24] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 2], x[23]); + word3_muladd_2(&w0, &w2, &w1, x[ 3], x[22]); + word3_muladd_2(&w0, &w2, &w1, x[ 4], x[21]); + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[20]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[19]); + word3_muladd_2(&w0, &w2, &w1, x[ 7], x[18]); + word3_muladd_2(&w0, &w2, &w1, x[ 8], x[17]); + word3_muladd_2(&w0, &w2, &w1, x[ 9], x[16]); + word3_muladd_2(&w0, &w2, &w1, x[10], x[15]); + word3_muladd_2(&w0, &w2, &w1, x[11], x[14]); + word3_muladd_2(&w0, &w2, &w1, x[12], x[13]); + z[25] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 3], x[23]); + word3_muladd_2(&w1, &w0, &w2, x[ 4], x[22]); + word3_muladd_2(&w1, &w0, &w2, x[ 5], x[21]); + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[20]); + word3_muladd_2(&w1, &w0, &w2, x[ 7], x[19]); + word3_muladd_2(&w1, &w0, &w2, x[ 8], x[18]); + word3_muladd_2(&w1, &w0, &w2, x[ 9], x[17]); + word3_muladd_2(&w1, &w0, &w2, x[10], x[16]); + word3_muladd_2(&w1, &w0, &w2, x[11], x[15]); + word3_muladd_2(&w1, &w0, &w2, x[12], x[14]); + word3_muladd (&w1, &w0, &w2, x[13], x[13]); + z[26] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[23]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[22]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[21]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[20]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[19]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[18]); + word3_muladd_2(&w2, &w1, &w0, x[10], x[17]); + word3_muladd_2(&w2, &w1, &w0, x[11], x[16]); + word3_muladd_2(&w2, &w1, &w0, x[12], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[13], x[14]); + z[27] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 5], x[23]); + word3_muladd_2(&w0, &w2, &w1, x[ 6], x[22]); + word3_muladd_2(&w0, &w2, &w1, x[ 7], x[21]); + word3_muladd_2(&w0, &w2, &w1, x[ 8], x[20]); + word3_muladd_2(&w0, &w2, &w1, x[ 9], x[19]); + word3_muladd_2(&w0, &w2, &w1, x[10], x[18]); + word3_muladd_2(&w0, &w2, &w1, x[11], x[17]); + word3_muladd_2(&w0, &w2, &w1, x[12], x[16]); + word3_muladd_2(&w0, &w2, &w1, x[13], x[15]); + word3_muladd (&w0, &w2, &w1, x[14], x[14]); + z[28] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 6], x[23]); + word3_muladd_2(&w1, &w0, &w2, x[ 7], x[22]); + word3_muladd_2(&w1, &w0, &w2, x[ 8], x[21]); + word3_muladd_2(&w1, &w0, &w2, x[ 9], x[20]); + word3_muladd_2(&w1, &w0, &w2, x[10], x[19]); + word3_muladd_2(&w1, &w0, &w2, x[11], x[18]); + word3_muladd_2(&w1, &w0, &w2, x[12], x[17]); + word3_muladd_2(&w1, &w0, &w2, x[13], x[16]); + word3_muladd_2(&w1, &w0, &w2, x[14], x[15]); + z[29] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[23]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[22]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[21]); + word3_muladd_2(&w2, &w1, &w0, x[10], x[20]); + word3_muladd_2(&w2, &w1, &w0, x[11], x[19]); + word3_muladd_2(&w2, &w1, &w0, x[12], x[18]); + word3_muladd_2(&w2, &w1, &w0, x[13], x[17]); + word3_muladd_2(&w2, &w1, &w0, x[14], x[16]); + word3_muladd (&w2, &w1, &w0, x[15], x[15]); + z[30] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[ 8], x[23]); + word3_muladd_2(&w0, &w2, &w1, x[ 9], x[22]); + word3_muladd_2(&w0, &w2, &w1, x[10], x[21]); + word3_muladd_2(&w0, &w2, &w1, x[11], x[20]); + word3_muladd_2(&w0, &w2, &w1, x[12], x[19]); + word3_muladd_2(&w0, &w2, &w1, x[13], x[18]); + word3_muladd_2(&w0, &w2, &w1, x[14], x[17]); + word3_muladd_2(&w0, &w2, &w1, x[15], x[16]); + z[31] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[ 9], x[23]); + word3_muladd_2(&w1, &w0, &w2, x[10], x[22]); + word3_muladd_2(&w1, &w0, &w2, x[11], x[21]); + word3_muladd_2(&w1, &w0, &w2, x[12], x[20]); + word3_muladd_2(&w1, &w0, &w2, x[13], x[19]); + word3_muladd_2(&w1, &w0, &w2, x[14], x[18]); + word3_muladd_2(&w1, &w0, &w2, x[15], x[17]); + word3_muladd (&w1, &w0, &w2, x[16], x[16]); + z[32] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[10], x[23]); + word3_muladd_2(&w2, &w1, &w0, x[11], x[22]); + word3_muladd_2(&w2, &w1, &w0, x[12], x[21]); + word3_muladd_2(&w2, &w1, &w0, x[13], x[20]); + word3_muladd_2(&w2, &w1, &w0, x[14], x[19]); + word3_muladd_2(&w2, &w1, &w0, x[15], x[18]); + word3_muladd_2(&w2, &w1, &w0, x[16], x[17]); + z[33] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[11], x[23]); + word3_muladd_2(&w0, &w2, &w1, x[12], x[22]); + word3_muladd_2(&w0, &w2, &w1, x[13], x[21]); + word3_muladd_2(&w0, &w2, &w1, x[14], x[20]); + word3_muladd_2(&w0, &w2, &w1, x[15], x[19]); + word3_muladd_2(&w0, &w2, &w1, x[16], x[18]); + word3_muladd (&w0, &w2, &w1, x[17], x[17]); + z[34] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[12], x[23]); + word3_muladd_2(&w1, &w0, &w2, x[13], x[22]); + word3_muladd_2(&w1, &w0, &w2, x[14], x[21]); + word3_muladd_2(&w1, &w0, &w2, x[15], x[20]); + word3_muladd_2(&w1, &w0, &w2, x[16], x[19]); + word3_muladd_2(&w1, &w0, &w2, x[17], x[18]); + z[35] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[13], x[23]); + word3_muladd_2(&w2, &w1, &w0, x[14], x[22]); + word3_muladd_2(&w2, &w1, &w0, x[15], x[21]); + word3_muladd_2(&w2, &w1, &w0, x[16], x[20]); + word3_muladd_2(&w2, &w1, &w0, x[17], x[19]); + word3_muladd (&w2, &w1, &w0, x[18], x[18]); + z[36] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[14], x[23]); + word3_muladd_2(&w0, &w2, &w1, x[15], x[22]); + word3_muladd_2(&w0, &w2, &w1, x[16], x[21]); + word3_muladd_2(&w0, &w2, &w1, x[17], x[20]); + word3_muladd_2(&w0, &w2, &w1, x[18], x[19]); + z[37] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[15], x[23]); + word3_muladd_2(&w1, &w0, &w2, x[16], x[22]); + word3_muladd_2(&w1, &w0, &w2, x[17], x[21]); + word3_muladd_2(&w1, &w0, &w2, x[18], x[20]); + word3_muladd (&w1, &w0, &w2, x[19], x[19]); + z[38] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[16], x[23]); + word3_muladd_2(&w2, &w1, &w0, x[17], x[22]); + word3_muladd_2(&w2, &w1, &w0, x[18], x[21]); + word3_muladd_2(&w2, &w1, &w0, x[19], x[20]); + z[39] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[17], x[23]); + word3_muladd_2(&w0, &w2, &w1, x[18], x[22]); + word3_muladd_2(&w0, &w2, &w1, x[19], x[21]); + word3_muladd (&w0, &w2, &w1, x[20], x[20]); + z[40] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[18], x[23]); + word3_muladd_2(&w1, &w0, &w2, x[19], x[22]); + word3_muladd_2(&w1, &w0, &w2, x[20], x[21]); + z[41] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[19], x[23]); + word3_muladd_2(&w2, &w1, &w0, x[20], x[22]); + word3_muladd (&w2, &w1, &w0, x[21], x[21]); + z[42] = w0; w0 = 0; + + word3_muladd_2(&w0, &w2, &w1, x[20], x[23]); + word3_muladd_2(&w0, &w2, &w1, x[21], x[22]); + z[43] = w1; w1 = 0; + + word3_muladd_2(&w1, &w0, &w2, x[21], x[23]); + word3_muladd (&w1, &w0, &w2, x[22], x[22]); + z[44] = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[22], x[23]); + z[45] = w0; w0 = 0; + + word3_muladd (&w0, &w2, &w1, x[23], x[23]); + z[46] = w1; + z[47] = w2; + } + +/* +* Comba 24x24 Multiplication +*/ +void bigint_comba_mul24(word z[48], const word x[24], const word y[24]) + { + word w2 = 0, w1 = 0, w0 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); + z[ 0] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); + z[ 1] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); + z[ 2] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); + z[ 3] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 0]); + z[ 4] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 0]); + z[ 5] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 0]); + z[ 6] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 0]); + z[ 7] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 0]); + z[ 8] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 0]); + z[ 9] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[10]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[10], y[ 0]); + z[10] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[11]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[10]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[10], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[11], y[ 0]); + z[11] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 0]); + z[12] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[13]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[12]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[11]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[10]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[10], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[11], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[12], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[13], y[ 0]); + z[13] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[14]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[13]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[12]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[11]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[10]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[10], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[11], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[12], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[13], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[14], y[ 0]); + z[14] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 0]); + z[15] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[16]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[15]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[14]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[13]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[12]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[11]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[10]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[10], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[11], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[12], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[13], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[14], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[15], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[16], y[ 0]); + z[16] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[17]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[16]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[15]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[14]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[13]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[12]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[11]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[10]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[10], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[11], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[12], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[13], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[14], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[15], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[16], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[17], y[ 0]); + z[17] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[18]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[17]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[16]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[16], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[17], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[18], y[ 0]); + z[18] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[19]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[18]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[17]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[16]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[15]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[14]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[13]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[12]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[11]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[10]); + word3_muladd(&w0, &w2, &w1, x[10], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[11], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[12], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[13], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[14], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[15], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[16], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[17], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[18], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[19], y[ 0]); + z[19] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[20]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[19]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[18]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[17]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[16]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[15]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[14]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[13]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[12]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[11]); + word3_muladd(&w1, &w0, &w2, x[10], y[10]); + word3_muladd(&w1, &w0, &w2, x[11], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[12], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[13], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[14], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[15], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[16], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[17], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[18], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[19], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[20], y[ 0]); + z[20] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[21]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[20]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[19]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[18]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[17]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[16]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[12]); + word3_muladd(&w2, &w1, &w0, x[10], y[11]); + word3_muladd(&w2, &w1, &w0, x[11], y[10]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[16], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[17], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[18], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[19], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[20], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[21], y[ 0]); + z[21] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 0], y[22]); + word3_muladd(&w0, &w2, &w1, x[ 1], y[21]); + word3_muladd(&w0, &w2, &w1, x[ 2], y[20]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[19]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[18]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[17]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[16]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[15]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[14]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[13]); + word3_muladd(&w0, &w2, &w1, x[10], y[12]); + word3_muladd(&w0, &w2, &w1, x[11], y[11]); + word3_muladd(&w0, &w2, &w1, x[12], y[10]); + word3_muladd(&w0, &w2, &w1, x[13], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[14], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[15], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[16], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[17], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[18], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[19], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[20], y[ 2]); + word3_muladd(&w0, &w2, &w1, x[21], y[ 1]); + word3_muladd(&w0, &w2, &w1, x[22], y[ 0]); + z[22] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 0], y[23]); + word3_muladd(&w1, &w0, &w2, x[ 1], y[22]); + word3_muladd(&w1, &w0, &w2, x[ 2], y[21]); + word3_muladd(&w1, &w0, &w2, x[ 3], y[20]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[19]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[18]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[17]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[16]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[15]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[14]); + word3_muladd(&w1, &w0, &w2, x[10], y[13]); + word3_muladd(&w1, &w0, &w2, x[11], y[12]); + word3_muladd(&w1, &w0, &w2, x[12], y[11]); + word3_muladd(&w1, &w0, &w2, x[13], y[10]); + word3_muladd(&w1, &w0, &w2, x[14], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[15], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[16], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[17], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[18], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[19], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[20], y[ 3]); + word3_muladd(&w1, &w0, &w2, x[21], y[ 2]); + word3_muladd(&w1, &w0, &w2, x[22], y[ 1]); + word3_muladd(&w1, &w0, &w2, x[23], y[ 0]); + z[23] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 1], y[23]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[22]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[21]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[20]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[19]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[18]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[17]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[16]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[15]); + word3_muladd(&w2, &w1, &w0, x[10], y[14]); + word3_muladd(&w2, &w1, &w0, x[11], y[13]); + word3_muladd(&w2, &w1, &w0, x[12], y[12]); + word3_muladd(&w2, &w1, &w0, x[13], y[11]); + word3_muladd(&w2, &w1, &w0, x[14], y[10]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[16], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[17], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[18], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[19], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[20], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[21], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[22], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[23], y[ 1]); + z[24] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 2], y[23]); + word3_muladd(&w0, &w2, &w1, x[ 3], y[22]); + word3_muladd(&w0, &w2, &w1, x[ 4], y[21]); + word3_muladd(&w0, &w2, &w1, x[ 5], y[20]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[19]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[18]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[17]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[16]); + word3_muladd(&w0, &w2, &w1, x[10], y[15]); + word3_muladd(&w0, &w2, &w1, x[11], y[14]); + word3_muladd(&w0, &w2, &w1, x[12], y[13]); + word3_muladd(&w0, &w2, &w1, x[13], y[12]); + word3_muladd(&w0, &w2, &w1, x[14], y[11]); + word3_muladd(&w0, &w2, &w1, x[15], y[10]); + word3_muladd(&w0, &w2, &w1, x[16], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[17], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[18], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[19], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[20], y[ 5]); + word3_muladd(&w0, &w2, &w1, x[21], y[ 4]); + word3_muladd(&w0, &w2, &w1, x[22], y[ 3]); + word3_muladd(&w0, &w2, &w1, x[23], y[ 2]); + z[25] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 3], y[23]); + word3_muladd(&w1, &w0, &w2, x[ 4], y[22]); + word3_muladd(&w1, &w0, &w2, x[ 5], y[21]); + word3_muladd(&w1, &w0, &w2, x[ 6], y[20]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[19]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[18]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[17]); + word3_muladd(&w1, &w0, &w2, x[10], y[16]); + word3_muladd(&w1, &w0, &w2, x[11], y[15]); + word3_muladd(&w1, &w0, &w2, x[12], y[14]); + word3_muladd(&w1, &w0, &w2, x[13], y[13]); + word3_muladd(&w1, &w0, &w2, x[14], y[12]); + word3_muladd(&w1, &w0, &w2, x[15], y[11]); + word3_muladd(&w1, &w0, &w2, x[16], y[10]); + word3_muladd(&w1, &w0, &w2, x[17], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[18], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[19], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[20], y[ 6]); + word3_muladd(&w1, &w0, &w2, x[21], y[ 5]); + word3_muladd(&w1, &w0, &w2, x[22], y[ 4]); + word3_muladd(&w1, &w0, &w2, x[23], y[ 3]); + z[26] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 4], y[23]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[22]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[21]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[20]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[19]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[18]); + word3_muladd(&w2, &w1, &w0, x[10], y[17]); + word3_muladd(&w2, &w1, &w0, x[11], y[16]); + word3_muladd(&w2, &w1, &w0, x[12], y[15]); + word3_muladd(&w2, &w1, &w0, x[13], y[14]); + word3_muladd(&w2, &w1, &w0, x[14], y[13]); + word3_muladd(&w2, &w1, &w0, x[15], y[12]); + word3_muladd(&w2, &w1, &w0, x[16], y[11]); + word3_muladd(&w2, &w1, &w0, x[17], y[10]); + word3_muladd(&w2, &w1, &w0, x[18], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[19], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[20], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[21], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[22], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[23], y[ 4]); + z[27] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 5], y[23]); + word3_muladd(&w0, &w2, &w1, x[ 6], y[22]); + word3_muladd(&w0, &w2, &w1, x[ 7], y[21]); + word3_muladd(&w0, &w2, &w1, x[ 8], y[20]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[19]); + word3_muladd(&w0, &w2, &w1, x[10], y[18]); + word3_muladd(&w0, &w2, &w1, x[11], y[17]); + word3_muladd(&w0, &w2, &w1, x[12], y[16]); + word3_muladd(&w0, &w2, &w1, x[13], y[15]); + word3_muladd(&w0, &w2, &w1, x[14], y[14]); + word3_muladd(&w0, &w2, &w1, x[15], y[13]); + word3_muladd(&w0, &w2, &w1, x[16], y[12]); + word3_muladd(&w0, &w2, &w1, x[17], y[11]); + word3_muladd(&w0, &w2, &w1, x[18], y[10]); + word3_muladd(&w0, &w2, &w1, x[19], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[20], y[ 8]); + word3_muladd(&w0, &w2, &w1, x[21], y[ 7]); + word3_muladd(&w0, &w2, &w1, x[22], y[ 6]); + word3_muladd(&w0, &w2, &w1, x[23], y[ 5]); + z[28] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 6], y[23]); + word3_muladd(&w1, &w0, &w2, x[ 7], y[22]); + word3_muladd(&w1, &w0, &w2, x[ 8], y[21]); + word3_muladd(&w1, &w0, &w2, x[ 9], y[20]); + word3_muladd(&w1, &w0, &w2, x[10], y[19]); + word3_muladd(&w1, &w0, &w2, x[11], y[18]); + word3_muladd(&w1, &w0, &w2, x[12], y[17]); + word3_muladd(&w1, &w0, &w2, x[13], y[16]); + word3_muladd(&w1, &w0, &w2, x[14], y[15]); + word3_muladd(&w1, &w0, &w2, x[15], y[14]); + word3_muladd(&w1, &w0, &w2, x[16], y[13]); + word3_muladd(&w1, &w0, &w2, x[17], y[12]); + word3_muladd(&w1, &w0, &w2, x[18], y[11]); + word3_muladd(&w1, &w0, &w2, x[19], y[10]); + word3_muladd(&w1, &w0, &w2, x[20], y[ 9]); + word3_muladd(&w1, &w0, &w2, x[21], y[ 8]); + word3_muladd(&w1, &w0, &w2, x[22], y[ 7]); + word3_muladd(&w1, &w0, &w2, x[23], y[ 6]); + z[29] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 7], y[23]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[22]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[21]); + word3_muladd(&w2, &w1, &w0, x[10], y[20]); + word3_muladd(&w2, &w1, &w0, x[11], y[19]); + word3_muladd(&w2, &w1, &w0, x[12], y[18]); + word3_muladd(&w2, &w1, &w0, x[13], y[17]); + word3_muladd(&w2, &w1, &w0, x[14], y[16]); + word3_muladd(&w2, &w1, &w0, x[15], y[15]); + word3_muladd(&w2, &w1, &w0, x[16], y[14]); + word3_muladd(&w2, &w1, &w0, x[17], y[13]); + word3_muladd(&w2, &w1, &w0, x[18], y[12]); + word3_muladd(&w2, &w1, &w0, x[19], y[11]); + word3_muladd(&w2, &w1, &w0, x[20], y[10]); + word3_muladd(&w2, &w1, &w0, x[21], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[22], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[23], y[ 7]); + z[30] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[ 8], y[23]); + word3_muladd(&w0, &w2, &w1, x[ 9], y[22]); + word3_muladd(&w0, &w2, &w1, x[10], y[21]); + word3_muladd(&w0, &w2, &w1, x[11], y[20]); + word3_muladd(&w0, &w2, &w1, x[12], y[19]); + word3_muladd(&w0, &w2, &w1, x[13], y[18]); + word3_muladd(&w0, &w2, &w1, x[14], y[17]); + word3_muladd(&w0, &w2, &w1, x[15], y[16]); + word3_muladd(&w0, &w2, &w1, x[16], y[15]); + word3_muladd(&w0, &w2, &w1, x[17], y[14]); + word3_muladd(&w0, &w2, &w1, x[18], y[13]); + word3_muladd(&w0, &w2, &w1, x[19], y[12]); + word3_muladd(&w0, &w2, &w1, x[20], y[11]); + word3_muladd(&w0, &w2, &w1, x[21], y[10]); + word3_muladd(&w0, &w2, &w1, x[22], y[ 9]); + word3_muladd(&w0, &w2, &w1, x[23], y[ 8]); + z[31] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[ 9], y[23]); + word3_muladd(&w1, &w0, &w2, x[10], y[22]); + word3_muladd(&w1, &w0, &w2, x[11], y[21]); + word3_muladd(&w1, &w0, &w2, x[12], y[20]); + word3_muladd(&w1, &w0, &w2, x[13], y[19]); + word3_muladd(&w1, &w0, &w2, x[14], y[18]); + word3_muladd(&w1, &w0, &w2, x[15], y[17]); + word3_muladd(&w1, &w0, &w2, x[16], y[16]); + word3_muladd(&w1, &w0, &w2, x[17], y[15]); + word3_muladd(&w1, &w0, &w2, x[18], y[14]); + word3_muladd(&w1, &w0, &w2, x[19], y[13]); + word3_muladd(&w1, &w0, &w2, x[20], y[12]); + word3_muladd(&w1, &w0, &w2, x[21], y[11]); + word3_muladd(&w1, &w0, &w2, x[22], y[10]); + word3_muladd(&w1, &w0, &w2, x[23], y[ 9]); + z[32] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[10], y[23]); + word3_muladd(&w2, &w1, &w0, x[11], y[22]); + word3_muladd(&w2, &w1, &w0, x[12], y[21]); + word3_muladd(&w2, &w1, &w0, x[13], y[20]); + word3_muladd(&w2, &w1, &w0, x[14], y[19]); + word3_muladd(&w2, &w1, &w0, x[15], y[18]); + word3_muladd(&w2, &w1, &w0, x[16], y[17]); + word3_muladd(&w2, &w1, &w0, x[17], y[16]); + word3_muladd(&w2, &w1, &w0, x[18], y[15]); + word3_muladd(&w2, &w1, &w0, x[19], y[14]); + word3_muladd(&w2, &w1, &w0, x[20], y[13]); + word3_muladd(&w2, &w1, &w0, x[21], y[12]); + word3_muladd(&w2, &w1, &w0, x[22], y[11]); + word3_muladd(&w2, &w1, &w0, x[23], y[10]); + z[33] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[11], y[23]); + word3_muladd(&w0, &w2, &w1, x[12], y[22]); + word3_muladd(&w0, &w2, &w1, x[13], y[21]); + word3_muladd(&w0, &w2, &w1, x[14], y[20]); + word3_muladd(&w0, &w2, &w1, x[15], y[19]); + word3_muladd(&w0, &w2, &w1, x[16], y[18]); + word3_muladd(&w0, &w2, &w1, x[17], y[17]); + word3_muladd(&w0, &w2, &w1, x[18], y[16]); + word3_muladd(&w0, &w2, &w1, x[19], y[15]); + word3_muladd(&w0, &w2, &w1, x[20], y[14]); + word3_muladd(&w0, &w2, &w1, x[21], y[13]); + word3_muladd(&w0, &w2, &w1, x[22], y[12]); + word3_muladd(&w0, &w2, &w1, x[23], y[11]); + z[34] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[12], y[23]); + word3_muladd(&w1, &w0, &w2, x[13], y[22]); + word3_muladd(&w1, &w0, &w2, x[14], y[21]); + word3_muladd(&w1, &w0, &w2, x[15], y[20]); + word3_muladd(&w1, &w0, &w2, x[16], y[19]); + word3_muladd(&w1, &w0, &w2, x[17], y[18]); + word3_muladd(&w1, &w0, &w2, x[18], y[17]); + word3_muladd(&w1, &w0, &w2, x[19], y[16]); + word3_muladd(&w1, &w0, &w2, x[20], y[15]); + word3_muladd(&w1, &w0, &w2, x[21], y[14]); + word3_muladd(&w1, &w0, &w2, x[22], y[13]); + word3_muladd(&w1, &w0, &w2, x[23], y[12]); + z[35] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[13], y[23]); + word3_muladd(&w2, &w1, &w0, x[14], y[22]); + word3_muladd(&w2, &w1, &w0, x[15], y[21]); + word3_muladd(&w2, &w1, &w0, x[16], y[20]); + word3_muladd(&w2, &w1, &w0, x[17], y[19]); + word3_muladd(&w2, &w1, &w0, x[18], y[18]); + word3_muladd(&w2, &w1, &w0, x[19], y[17]); + word3_muladd(&w2, &w1, &w0, x[20], y[16]); + word3_muladd(&w2, &w1, &w0, x[21], y[15]); + word3_muladd(&w2, &w1, &w0, x[22], y[14]); + word3_muladd(&w2, &w1, &w0, x[23], y[13]); + z[36] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[14], y[23]); + word3_muladd(&w0, &w2, &w1, x[15], y[22]); + word3_muladd(&w0, &w2, &w1, x[16], y[21]); + word3_muladd(&w0, &w2, &w1, x[17], y[20]); + word3_muladd(&w0, &w2, &w1, x[18], y[19]); + word3_muladd(&w0, &w2, &w1, x[19], y[18]); + word3_muladd(&w0, &w2, &w1, x[20], y[17]); + word3_muladd(&w0, &w2, &w1, x[21], y[16]); + word3_muladd(&w0, &w2, &w1, x[22], y[15]); + word3_muladd(&w0, &w2, &w1, x[23], y[14]); + z[37] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[15], y[23]); + word3_muladd(&w1, &w0, &w2, x[16], y[22]); + word3_muladd(&w1, &w0, &w2, x[17], y[21]); + word3_muladd(&w1, &w0, &w2, x[18], y[20]); + word3_muladd(&w1, &w0, &w2, x[19], y[19]); + word3_muladd(&w1, &w0, &w2, x[20], y[18]); + word3_muladd(&w1, &w0, &w2, x[21], y[17]); + word3_muladd(&w1, &w0, &w2, x[22], y[16]); + word3_muladd(&w1, &w0, &w2, x[23], y[15]); + z[38] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[16], y[23]); + word3_muladd(&w2, &w1, &w0, x[17], y[22]); + word3_muladd(&w2, &w1, &w0, x[18], y[21]); + word3_muladd(&w2, &w1, &w0, x[19], y[20]); + word3_muladd(&w2, &w1, &w0, x[20], y[19]); + word3_muladd(&w2, &w1, &w0, x[21], y[18]); + word3_muladd(&w2, &w1, &w0, x[22], y[17]); + word3_muladd(&w2, &w1, &w0, x[23], y[16]); + z[39] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[17], y[23]); + word3_muladd(&w0, &w2, &w1, x[18], y[22]); + word3_muladd(&w0, &w2, &w1, x[19], y[21]); + word3_muladd(&w0, &w2, &w1, x[20], y[20]); + word3_muladd(&w0, &w2, &w1, x[21], y[19]); + word3_muladd(&w0, &w2, &w1, x[22], y[18]); + word3_muladd(&w0, &w2, &w1, x[23], y[17]); + z[40] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[18], y[23]); + word3_muladd(&w1, &w0, &w2, x[19], y[22]); + word3_muladd(&w1, &w0, &w2, x[20], y[21]); + word3_muladd(&w1, &w0, &w2, x[21], y[20]); + word3_muladd(&w1, &w0, &w2, x[22], y[19]); + word3_muladd(&w1, &w0, &w2, x[23], y[18]); + z[41] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[19], y[23]); + word3_muladd(&w2, &w1, &w0, x[20], y[22]); + word3_muladd(&w2, &w1, &w0, x[21], y[21]); + word3_muladd(&w2, &w1, &w0, x[22], y[20]); + word3_muladd(&w2, &w1, &w0, x[23], y[19]); + z[42] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[20], y[23]); + word3_muladd(&w0, &w2, &w1, x[21], y[22]); + word3_muladd(&w0, &w2, &w1, x[22], y[21]); + word3_muladd(&w0, &w2, &w1, x[23], y[20]); + z[43] = w1; w1 = 0; + + word3_muladd(&w1, &w0, &w2, x[21], y[23]); + word3_muladd(&w1, &w0, &w2, x[22], y[22]); + word3_muladd(&w1, &w0, &w2, x[23], y[21]); + z[44] = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[22], y[23]); + word3_muladd(&w2, &w1, &w0, x[23], y[22]); + z[45] = w0; w0 = 0; + + word3_muladd(&w0, &w2, &w1, x[23], y[23]); + z[46] = w1; + z[47] = w2; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_core.cpp b/src/libs/3rdparty/botan/src/lib/math/mp/mp_core.cpp new file mode 100644 index 0000000000..2ae65e508f --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_core.cpp @@ -0,0 +1,527 @@ +/* +* MPI Add, Subtract, Word Multiply +* (C) 1999-2010,2016 Jack Lloyd +* 2006 Luca Piccarreta +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/mp_core.h> +#include <botan/internal/mp_asmi.h> +#include <botan/internal/ct_utils.h> +#include <botan/exceptn.h> +#include <botan/mem_ops.h> + +namespace Botan { + +/* +* If cond == 0, does nothing. +* If cond > 0, swaps x[0:size] with y[0:size] +* Runs in constant time +*/ +void bigint_cnd_swap(word cnd, word x[], word y[], size_t size) + { + const word mask = CT::expand_mask(cnd); + + for(size_t i = 0; i != size; ++i) + { + const word a = x[i]; + const word b = y[i]; + x[i] = CT::select(mask, b, a); + y[i] = CT::select(mask, a, b); + } + } + +/* +* If cond > 0 adds x[0:size] to y[0:size] and returns carry +* Runs in constant time +*/ +word bigint_cnd_add(word cnd, word x[], const word y[], size_t size) + { + const word mask = CT::expand_mask(cnd); + + word carry = 0; + + const size_t blocks = size - (size % 8); + word z[8] = { 0 }; + + for(size_t i = 0; i != blocks; i += 8) + { + carry = word8_add3(z, x + i, y + i, carry); + + for(size_t j = 0; j != 8; ++j) + x[i+j] = CT::select(mask, z[j], x[i+j]); + } + + for(size_t i = blocks; i != size; ++i) + { + z[0] = word_add(x[i], y[i], &carry); + x[i] = CT::select(mask, z[0], x[i]); + } + + return carry & mask; + } + +/* +* If cond > 0 subs x[0:size] to y[0:size] and returns borrow +* Runs in constant time +*/ +word bigint_cnd_sub(word cnd, word x[], const word y[], size_t size) + { + const word mask = CT::expand_mask(cnd); + + word carry = 0; + + const size_t blocks = size - (size % 8); + word z[8] = { 0 }; + + for(size_t i = 0; i != blocks; i += 8) + { + carry = word8_sub3(z, x + i, y + i, carry); + + for(size_t j = 0; j != 8; ++j) + x[i+j] = CT::select(mask, z[j], x[i+j]); + } + + for(size_t i = blocks; i != size; ++i) + { + z[0] = word_sub(x[i], y[i], &carry); + x[i] = CT::select(mask, z[0], x[i]); + } + + return carry & mask; + } + +void bigint_cnd_addsub(word mask, word x[], const word y[], size_t size) + { + const size_t blocks = size - (size % 8); + + word carry = 0; + word borrow = 0; + + word t0[8] = { 0 }; + word t1[8] = { 0 }; + + for(size_t i = 0; i != blocks; i += 8) + { + carry = word8_add3(t0, x + i, y + i, carry); + borrow = word8_sub3(t1, x + i, y + i, borrow); + + for(size_t j = 0; j != 8; ++j) + x[i+j] = CT::select(mask, t0[j], t1[j]); + } + + for(size_t i = blocks; i != size; ++i) + { + const word a = word_add(x[i], y[i], &carry); + const word s = word_sub(x[i], y[i], &borrow); + + x[i] = CT::select(mask, a, s); + } + } + +void bigint_cnd_abs(word cnd, word x[], size_t size) + { + const word mask = CT::expand_mask(cnd); + + word carry = mask & 1; + for(size_t i = 0; i != size; ++i) + { + const word z = word_add(~x[i], 0, &carry); + x[i] = CT::select(mask, z, x[i]); + } + } + +/* +* Two Operand Addition, No Carry +*/ +word bigint_add2_nc(word x[], size_t x_size, const word y[], size_t y_size) + { + word carry = 0; + + BOTAN_ASSERT(x_size >= y_size, "Expected sizes"); + + const size_t blocks = y_size - (y_size % 8); + + for(size_t i = 0; i != blocks; i += 8) + carry = word8_add2(x + i, y + i, carry); + + for(size_t i = blocks; i != y_size; ++i) + x[i] = word_add(x[i], y[i], &carry); + + for(size_t i = y_size; i != x_size; ++i) + x[i] = word_add(x[i], 0, &carry); + + return carry; + } + +/* +* Three Operand Addition, No Carry +*/ +word bigint_add3_nc(word z[], const word x[], size_t x_size, + const word y[], size_t y_size) + { + if(x_size < y_size) + { return bigint_add3_nc(z, y, y_size, x, x_size); } + + word carry = 0; + + const size_t blocks = y_size - (y_size % 8); + + for(size_t i = 0; i != blocks; i += 8) + carry = word8_add3(z + i, x + i, y + i, carry); + + for(size_t i = blocks; i != y_size; ++i) + z[i] = word_add(x[i], y[i], &carry); + + for(size_t i = y_size; i != x_size; ++i) + z[i] = word_add(x[i], 0, &carry); + + return carry; + } + +/* +* Two Operand Addition +*/ +void bigint_add2(word x[], size_t x_size, const word y[], size_t y_size) + { + x[x_size] += bigint_add2_nc(x, x_size, y, y_size); + } + +/* +* Three Operand Addition +*/ +void bigint_add3(word z[], const word x[], size_t x_size, + const word y[], size_t y_size) + { + z[x_size > y_size ? x_size : y_size] += + bigint_add3_nc(z, x, x_size, y, y_size); + } + +/* +* Two Operand Subtraction +*/ +word bigint_sub2(word x[], size_t x_size, const word y[], size_t y_size) + { + word borrow = 0; + + BOTAN_ASSERT(x_size >= y_size, "Expected sizes"); + + const size_t blocks = y_size - (y_size % 8); + + for(size_t i = 0; i != blocks; i += 8) + borrow = word8_sub2(x + i, y + i, borrow); + + for(size_t i = blocks; i != y_size; ++i) + x[i] = word_sub(x[i], y[i], &borrow); + + for(size_t i = y_size; i != x_size; ++i) + x[i] = word_sub(x[i], 0, &borrow); + + return borrow; + } + +/* +* Two Operand Subtraction x = y - x +*/ +void bigint_sub2_rev(word x[], const word y[], size_t y_size) + { + word borrow = 0; + + const size_t blocks = y_size - (y_size % 8); + + for(size_t i = 0; i != blocks; i += 8) + borrow = word8_sub2_rev(x + i, y + i, borrow); + + for(size_t i = blocks; i != y_size; ++i) + x[i] = word_sub(y[i], x[i], &borrow); + + BOTAN_ASSERT(!borrow, "y must be greater than x"); + } + +word bigint_sub_abs(word z[], + const word x[], const word y[], size_t N, + word ws[]) + { + // Subtract in both direction then conditional copy out the result + + word* ws0 = ws; + word* ws1 = ws + N; + + word borrow0 = 0; + word borrow1 = 0; + + const size_t blocks = N - (N % 8); + + for(size_t i = 0; i != blocks; i += 8) + { + borrow0 = word8_sub3(ws0 + i, x + i, y + i, borrow0); + borrow1 = word8_sub3(ws1 + i, y + i, x + i, borrow1); + } + + for(size_t i = blocks; i != N; ++i) + { + ws0[i] = word_sub(x[i], y[i], &borrow0); + ws1[i] = word_sub(y[i], x[i], &borrow1); + } + + word mask = CT::conditional_copy_mem(borrow1, z, ws0, ws1, N); + + return CT::select<word>(mask, 0, 1); + } + +/* +* Three Operand Subtraction +*/ +word bigint_sub3(word z[], const word x[], size_t x_size, + const word y[], size_t y_size) + { + word borrow = 0; + + BOTAN_ASSERT(x_size >= y_size, "Expected sizes"); + + const size_t blocks = y_size - (y_size % 8); + + for(size_t i = 0; i != blocks; i += 8) + borrow = word8_sub3(z + i, x + i, y + i, borrow); + + for(size_t i = blocks; i != y_size; ++i) + z[i] = word_sub(x[i], y[i], &borrow); + + for(size_t i = y_size; i != x_size; ++i) + z[i] = word_sub(x[i], 0, &borrow); + + return borrow; + } + +/* +* Two Operand Linear Multiply +*/ +void bigint_linmul2(word x[], size_t x_size, word y) + { + const size_t blocks = x_size - (x_size % 8); + + word carry = 0; + + for(size_t i = 0; i != blocks; i += 8) + carry = word8_linmul2(x + i, y, carry); + + for(size_t i = blocks; i != x_size; ++i) + x[i] = word_madd2(x[i], y, &carry); + + x[x_size] = carry; + } + +/* +* Three Operand Linear Multiply +*/ +void bigint_linmul3(word z[], const word x[], size_t x_size, word y) + { + const size_t blocks = x_size - (x_size % 8); + + word carry = 0; + + for(size_t i = 0; i != blocks; i += 8) + carry = word8_linmul3(z + i, x + i, y, carry); + + for(size_t i = blocks; i != x_size; ++i) + z[i] = word_madd2(x[i], y, &carry); + + z[x_size] = carry; + } + +/* +* Single Operand Left Shift +*/ +void bigint_shl1(word x[], size_t x_size, size_t word_shift, size_t bit_shift) + { + if(word_shift) + { + copy_mem(x + word_shift, x, x_size); + clear_mem(x, word_shift); + } + + if(bit_shift) + { + word carry = 0; + for(size_t j = word_shift; j != x_size + word_shift + 1; ++j) + { + word temp = x[j]; + x[j] = (temp << bit_shift) | carry; + carry = (temp >> (BOTAN_MP_WORD_BITS - bit_shift)); + } + } + } + +/* +* Single Operand Right Shift +*/ +void bigint_shr1(word x[], size_t x_size, size_t word_shift, size_t bit_shift) + { + if(x_size < word_shift) + { + clear_mem(x, x_size); + return; + } + + if(word_shift) + { + copy_mem(x, x + word_shift, x_size - word_shift); + clear_mem(x + x_size - word_shift, word_shift); + } + + if(bit_shift) + { + word carry = 0; + + size_t top = x_size - word_shift; + + while(top >= 4) + { + word w = x[top-1]; + x[top-1] = (w >> bit_shift) | carry; + carry = (w << (BOTAN_MP_WORD_BITS - bit_shift)); + + w = x[top-2]; + x[top-2] = (w >> bit_shift) | carry; + carry = (w << (BOTAN_MP_WORD_BITS - bit_shift)); + + w = x[top-3]; + x[top-3] = (w >> bit_shift) | carry; + carry = (w << (BOTAN_MP_WORD_BITS - bit_shift)); + + w = x[top-4]; + x[top-4] = (w >> bit_shift) | carry; + carry = (w << (BOTAN_MP_WORD_BITS - bit_shift)); + + top -= 4; + } + + while(top) + { + word w = x[top-1]; + x[top-1] = (w >> bit_shift) | carry; + carry = (w << (BOTAN_MP_WORD_BITS - bit_shift)); + + top--; + } + } + } + +/* +* Two Operand Left Shift +*/ +void bigint_shl2(word y[], const word x[], size_t x_size, + size_t word_shift, size_t bit_shift) + { + for(size_t j = 0; j != x_size; ++j) + y[j + word_shift] = x[j]; + if(bit_shift) + { + word carry = 0; + for(size_t j = word_shift; j != x_size + word_shift + 1; ++j) + { + word w = y[j]; + y[j] = (w << bit_shift) | carry; + carry = (w >> (BOTAN_MP_WORD_BITS - bit_shift)); + } + } + } + +/* +* Two Operand Right Shift +*/ +void bigint_shr2(word y[], const word x[], size_t x_size, + size_t word_shift, size_t bit_shift) + { + if(x_size < word_shift) return; + + for(size_t j = 0; j != x_size - word_shift; ++j) + y[j] = x[j + word_shift]; + if(bit_shift) + { + word carry = 0; + for(size_t j = x_size - word_shift; j > 0; --j) + { + word w = y[j-1]; + y[j-1] = (w >> bit_shift) | carry; + carry = (w << (BOTAN_MP_WORD_BITS - bit_shift)); + } + } + } + +/* +* Compare two MP integers +*/ +int32_t bigint_cmp(const word x[], size_t x_size, + const word y[], size_t y_size) + { + if(x_size < y_size) { return (-bigint_cmp(y, y_size, x, x_size)); } + + while(x_size > y_size) + { + if(x[x_size-1]) + return 1; + x_size--; + } + + for(size_t i = x_size; i > 0; --i) + { + if(x[i-1] > y[i-1]) + return 1; + if(x[i-1] < y[i-1]) + return -1; + } + + return 0; + } + +/* +* Do a 2-word/1-word Division +*/ +word bigint_divop(word n1, word n0, word d) + { + if(d == 0) + throw Invalid_Argument("bigint_divop divide by zero"); + +#if defined(BOTAN_HAS_MP_DWORD) + return ((static_cast<dword>(n1) << BOTAN_MP_WORD_BITS) | n0) / d; +#else + + word high = n1 % d, quotient = 0; + + for(size_t i = 0; i != BOTAN_MP_WORD_BITS; ++i) + { + word high_top_bit = (high & MP_WORD_TOP_BIT); + + high <<= 1; + high |= (n0 >> (BOTAN_MP_WORD_BITS-1-i)) & 1; + quotient <<= 1; + + if(high_top_bit || high >= d) + { + high -= d; + quotient |= 1; + } + } + + return quotient; +#endif + } + +/* +* Do a 2-word/1-word Modulo +*/ +word bigint_modop(word n1, word n0, word d) + { +#if defined(BOTAN_HAS_MP_DWORD) + return ((static_cast<dword>(n1) << BOTAN_MP_WORD_BITS) | n0) % d; +#else + word z = bigint_divop(n1, n0, d); + word dummy = 0; + z = word_madd2(z, d, &dummy); + return (n0-z); +#endif + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_core.h b/src/libs/3rdparty/botan/src/lib/math/mp/mp_core.h new file mode 100644 index 0000000000..9430c3753f --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_core.h @@ -0,0 +1,209 @@ +/* +* MPI Algorithms +* (C) 1999-2010 Jack Lloyd +* 2006 Luca Piccarreta +* 2016 Matthias Gierlings +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_MP_CORE_OPS_H_ +#define BOTAN_MP_CORE_OPS_H_ + +#include <botan/types.h> + +namespace Botan { + +const word MP_WORD_MASK = ~static_cast<word>(0); +const word MP_WORD_TOP_BIT = static_cast<word>(1) << (8*sizeof(word) - 1); +const word MP_WORD_MAX = MP_WORD_MASK; + +/* +* If cond == 0, does nothing. +* If cond > 0, swaps x[0:size] with y[0:size] +* Runs in constant time +*/ +BOTAN_TEST_API +void bigint_cnd_swap(word cnd, word x[], word y[], size_t size); + +/* +* If cond > 0 adds x[0:size] and y[0:size] and returns carry +* Runs in constant time +*/ +BOTAN_TEST_API +word bigint_cnd_add(word cnd, word x[], const word y[], size_t size); + +/* +* If cond > 0 subtracts x[0:size] and y[0:size] and returns borrow +* Runs in constant time +*/ +BOTAN_TEST_API +word bigint_cnd_sub(word cnd, word x[], const word y[], size_t size); + +/* +* Equivalent to +* bigint_cnd_add( mask, x, y, size); +* bigint_cnd_sub(~mask, x, y, size); +* +* Mask must be either 0 or all 1 bits +*/ +void bigint_cnd_addsub(word mask, word x[], const word y[], size_t size); + +/* +* 2s complement absolute value +* If cond > 0 sets x to ~x + 1 +* Runs in constant time +*/ +BOTAN_TEST_API +void bigint_cnd_abs(word cnd, word x[], size_t size); + +/** +* Two operand addition +* @param x the first operand (and output) +* @param x_size size of x +* @param y the second operand +* @param y_size size of y (must be >= x_size) +*/ +void bigint_add2(word x[], size_t x_size, + const word y[], size_t y_size); + +/** +* Three operand addition +*/ +void bigint_add3(word z[], + const word x[], size_t x_size, + const word y[], size_t y_size); + +/** +* Two operand addition with carry out +*/ +word bigint_add2_nc(word x[], size_t x_size, const word y[], size_t y_size); + +/** +* Three operand addition with carry out +*/ +word bigint_add3_nc(word z[], + const word x[], size_t x_size, + const word y[], size_t y_size); + +/** +* Two operand subtraction +*/ +word bigint_sub2(word x[], size_t x_size, + const word y[], size_t y_size); + +/** +* Two operand subtraction, x = y - x; assumes y >= x +*/ +void bigint_sub2_rev(word x[], const word y[], size_t y_size); + +/** +* Three operand subtraction +*/ +word bigint_sub3(word z[], + const word x[], size_t x_size, + const word y[], size_t y_size); + +/** +* Return abs(x-y), ie if x >= y, then compute z = x - y +* Otherwise compute z = y - x +* No borrow is possible since the result is always >= 0 +* +* Returns 1 if x >= y or 0 if x < y +* @param z output array of at least N words +* @param x input array of N words +* @param y input array of N words +* @param N length of x and y +* @param ws array of at least 2*N words +*/ +word bigint_sub_abs(word z[], + const word x[], const word y[], size_t N, + word ws[]); + +/* +* Shift Operations +*/ +void bigint_shl1(word x[], size_t x_size, + size_t word_shift, size_t bit_shift); + +void bigint_shr1(word x[], size_t x_size, + size_t word_shift, size_t bit_shift); + +void bigint_shl2(word y[], const word x[], size_t x_size, + size_t word_shift, size_t bit_shift); + +void bigint_shr2(word y[], const word x[], size_t x_size, + size_t word_shift, size_t bit_shift); + +/* +* Linear Multiply +*/ +void bigint_linmul2(word x[], size_t x_size, word y); +void bigint_linmul3(word z[], const word x[], size_t x_size, word y); + +/** +* Montgomery Reduction +* @param z integer to reduce, of size exactly 2*(p_size+1). + Output is in the first p_size+1 words, higher + words are set to zero. +* @param p modulus +* @param p_size size of p +* @param p_dash Montgomery value +* @param workspace array of at least 2*(p_size+1) words +* @param ws_size size of workspace in words +*/ +void bigint_monty_redc(word z[], + const word p[], size_t p_size, + word p_dash, + word workspace[], + size_t ws_size); + +/** +* Compare x and y returning early +*/ +int32_t bigint_cmp(const word x[], size_t x_size, + const word y[], size_t y_size); + +/** +* Compute ((n1<<bits) + n0) / d +*/ +word bigint_divop(word n1, word n0, word d); + +/** +* Compute ((n1<<bits) + n0) % d +*/ +word bigint_modop(word n1, word n0, word d); + +/* +* Comba Multiplication / Squaring +*/ +void bigint_comba_mul4(word z[8], const word x[4], const word y[4]); +void bigint_comba_mul6(word z[12], const word x[6], const word y[6]); +void bigint_comba_mul8(word z[16], const word x[8], const word y[8]); +void bigint_comba_mul9(word z[18], const word x[9], const word y[9]); +void bigint_comba_mul16(word z[32], const word x[16], const word y[16]); +void bigint_comba_mul24(word z[48], const word x[24], const word y[24]); + +void bigint_comba_sqr4(word out[8], const word in[4]); +void bigint_comba_sqr6(word out[12], const word in[6]); +void bigint_comba_sqr8(word out[16], const word in[8]); +void bigint_comba_sqr9(word out[18], const word in[9]); +void bigint_comba_sqr16(word out[32], const word in[16]); +void bigint_comba_sqr24(word out[48], const word in[24]); + +/* +* High Level Multiplication/Squaring Interfaces +*/ + +void bigint_mul(word z[], size_t z_size, + const word x[], size_t x_size, size_t x_sw, + const word y[], size_t y_size, size_t y_sw, + word workspace[], size_t ws_size); + +void bigint_sqr(word z[], size_t z_size, + const word x[], size_t x_size, size_t x_sw, + word workspace[], size_t ws_size); + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_karat.cpp b/src/libs/3rdparty/botan/src/lib/math/mp/mp_karat.cpp new file mode 100644 index 0000000000..69e2ae6656 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_karat.cpp @@ -0,0 +1,403 @@ +/* +* Multiplication and Squaring +* (C) 1999-2010,2018 Jack Lloyd +* 2016 Matthias Gierlings +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/mp_core.h> +#include <botan/internal/mp_asmi.h> +#include <botan/internal/ct_utils.h> +#include <botan/mem_ops.h> +#include <botan/exceptn.h> + +namespace Botan { + +namespace { + +const size_t KARATSUBA_MULTIPLY_THRESHOLD = 32; +const size_t KARATSUBA_SQUARE_THRESHOLD = 32; + +/* +* Simple O(N^2) Multiplication +*/ +void basecase_mul(word z[], size_t z_size, + const word x[], size_t x_size, + const word y[], size_t y_size) + { + if(z_size < x_size + y_size) + throw Invalid_Argument("basecase_mul z_size too small"); + + const size_t x_size_8 = x_size - (x_size % 8); + + clear_mem(z, z_size); + + for(size_t i = 0; i != y_size; ++i) + { + const word y_i = y[i]; + + word carry = 0; + + for(size_t j = 0; j != x_size_8; j += 8) + carry = word8_madd3(z + i + j, x + j, y_i, carry); + + for(size_t j = x_size_8; j != x_size; ++j) + z[i+j] = word_madd3(x[j], y_i, z[i+j], &carry); + + z[x_size+i] = carry; + } + } + +void basecase_sqr(word z[], size_t z_size, + const word x[], size_t x_size) + { + if(z_size < 2*x_size) + throw Invalid_Argument("basecase_sqr z_size too small"); + + const size_t x_size_8 = x_size - (x_size % 8); + + clear_mem(z, z_size); + + for(size_t i = 0; i != x_size; ++i) + { + const word x_i = x[i]; + + word carry = 0; + + for(size_t j = 0; j != x_size_8; j += 8) + carry = word8_madd3(z + i + j, x + j, x_i, carry); + + for(size_t j = x_size_8; j != x_size; ++j) + z[i+j] = word_madd3(x[j], x_i, z[i+j], &carry); + + z[x_size+i] = carry; + } + } + +/* +* Karatsuba Multiplication Operation +*/ +void karatsuba_mul(word z[], const word x[], const word y[], size_t N, + word workspace[]) + { + if(N < KARATSUBA_MULTIPLY_THRESHOLD || N % 2) + { + if(N == 6) + return bigint_comba_mul6(z, x, y); + else if(N == 8) + return bigint_comba_mul8(z, x, y); + else if(N == 9) + return bigint_comba_mul9(z, x, y); + else if(N == 16) + return bigint_comba_mul16(z, x, y); + else if(N == 24) + return bigint_comba_mul24(z, x, y); + else + return basecase_mul(z, 2*N, x, N, y, N); + } + + const size_t N2 = N / 2; + + const word* x0 = x; + const word* x1 = x + N2; + const word* y0 = y; + const word* y1 = y + N2; + word* z0 = z; + word* z1 = z + N; + + word* ws0 = workspace; + word* ws1 = workspace + N; + + clear_mem(workspace, 2*N); + + /* + * If either of cmp0 or cmp1 is zero then z0 or z1 resp is zero here, + * resulting in a no-op - z0*z1 will be equal to zero so we don't need to do + * anything, clear_mem above already set the correct result. + * + * However we ignore the result of the comparisons and always perform the + * subtractions and recursively multiply to avoid the timing channel. + */ + + // First compute (X_lo - X_hi)*(Y_hi - Y_lo) + const word cmp0 = bigint_sub_abs(z0, x0, x1, N2, workspace); + const word cmp1 = bigint_sub_abs(z1, y1, y0, N2, workspace); + + karatsuba_mul(ws0, z0, z1, N2, ws1); + + // Compute X_lo * Y_lo + karatsuba_mul(z0, x0, y0, N2, ws1); + + // Compute X_hi * Y_hi + karatsuba_mul(z1, x1, y1, N2, ws1); + + const word ws_carry = bigint_add3_nc(ws1, z0, N, z1, N); + word z_carry = bigint_add2_nc(z + N2, N, ws1, N); + + z_carry += bigint_add2_nc(z + N + N2, N2, &ws_carry, 1); + bigint_add2_nc(z + N + N2, N2, &z_carry, 1); + + clear_mem(workspace + N, N2); + + const word neg_mask = CT::is_equal<word>(cmp0, cmp1); + + bigint_cnd_addsub(neg_mask, z + N2, workspace, 2*N-N2); + } + +/* +* Karatsuba Squaring Operation +*/ +void karatsuba_sqr(word z[], const word x[], size_t N, word workspace[]) + { + if(N < KARATSUBA_SQUARE_THRESHOLD || N % 2) + { + if(N == 6) + return bigint_comba_sqr6(z, x); + else if(N == 8) + return bigint_comba_sqr8(z, x); + else if(N == 9) + return bigint_comba_sqr9(z, x); + else if(N == 16) + return bigint_comba_sqr16(z, x); + else if(N == 24) + return bigint_comba_sqr24(z, x); + else + return basecase_sqr(z, 2*N, x, N); + } + + const size_t N2 = N / 2; + + const word* x0 = x; + const word* x1 = x + N2; + word* z0 = z; + word* z1 = z + N; + + word* ws0 = workspace; + word* ws1 = workspace + N; + + clear_mem(workspace, 2*N); + + // See comment in karatsuba_mul + bigint_sub_abs(z0, x0, x1, N2, workspace); + karatsuba_sqr(ws0, z0, N2, ws1); + + karatsuba_sqr(z0, x0, N2, ws1); + karatsuba_sqr(z1, x1, N2, ws1); + + const word ws_carry = bigint_add3_nc(ws1, z0, N, z1, N); + word z_carry = bigint_add2_nc(z + N2, N, ws1, N); + + z_carry += bigint_add2_nc(z + N + N2, N2, &ws_carry, 1); + bigint_add2_nc(z + N + N2, N2, &z_carry, 1); + + /* + * This is only actually required if cmp (result of bigint_sub_abs) is != 0, + * however if cmp==0 then ws0[0:N] == 0 and avoiding the jump hides a + * timing channel. + */ + bigint_sub2(z + N2, 2*N-N2, ws0, N); + } + +/* +* Pick a good size for the Karatsuba multiply +*/ +size_t karatsuba_size(size_t z_size, + size_t x_size, size_t x_sw, + size_t y_size, size_t y_sw) + { + if(x_sw > x_size || x_sw > y_size || y_sw > x_size || y_sw > y_size) + return 0; + + if(((x_size == x_sw) && (x_size % 2)) || + ((y_size == y_sw) && (y_size % 2))) + return 0; + + const size_t start = (x_sw > y_sw) ? x_sw : y_sw; + const size_t end = (x_size < y_size) ? x_size : y_size; + + if(start == end) + { + if(start % 2) + return 0; + return start; + } + + for(size_t j = start; j <= end; ++j) + { + if(j % 2) + continue; + + if(2*j > z_size) + return 0; + + if(x_sw <= j && j <= x_size && y_sw <= j && j <= y_size) + { + if(j % 4 == 2 && + (j+2) <= x_size && (j+2) <= y_size && 2*(j+2) <= z_size) + return j+2; + return j; + } + } + + return 0; + } + +/* +* Pick a good size for the Karatsuba squaring +*/ +size_t karatsuba_size(size_t z_size, size_t x_size, size_t x_sw) + { + if(x_sw == x_size) + { + if(x_sw % 2) + return 0; + return x_sw; + } + + for(size_t j = x_sw; j <= x_size; ++j) + { + if(j % 2) + continue; + + if(2*j > z_size) + return 0; + + if(j % 4 == 2 && (j+2) <= x_size && 2*(j+2) <= z_size) + return j+2; + return j; + } + + return 0; + } + +template<size_t SZ> +inline bool sized_for_comba_mul(size_t x_sw, size_t x_size, + size_t y_sw, size_t y_size, + size_t z_size) + { + return (x_sw <= SZ && x_size >= SZ && + y_sw <= SZ && y_size >= SZ && + z_size >= 2*SZ); + } + +template<size_t SZ> +inline bool sized_for_comba_sqr(size_t x_sw, size_t x_size, + size_t z_size) + { + return (x_sw <= SZ && x_size >= SZ && z_size >= 2*SZ); + } + +} + +void bigint_mul(word z[], size_t z_size, + const word x[], size_t x_size, size_t x_sw, + const word y[], size_t y_size, size_t y_sw, + word workspace[], size_t ws_size) + { + clear_mem(z, z_size); + + if(x_sw == 1) + { + bigint_linmul3(z, y, y_sw, x[0]); + } + else if(y_sw == 1) + { + bigint_linmul3(z, x, x_sw, y[0]); + } + else if(sized_for_comba_mul<4>(x_sw, x_size, y_sw, y_size, z_size)) + { + bigint_comba_mul4(z, x, y); + } + else if(sized_for_comba_mul<6>(x_sw, x_size, y_sw, y_size, z_size)) + { + bigint_comba_mul6(z, x, y); + } + else if(sized_for_comba_mul<8>(x_sw, x_size, y_sw, y_size, z_size)) + { + bigint_comba_mul8(z, x, y); + } + else if(sized_for_comba_mul<9>(x_sw, x_size, y_sw, y_size, z_size)) + { + bigint_comba_mul9(z, x, y); + } + else if(sized_for_comba_mul<16>(x_sw, x_size, y_sw, y_size, z_size)) + { + bigint_comba_mul16(z, x, y); + } + else if(sized_for_comba_mul<24>(x_sw, x_size, y_sw, y_size, z_size)) + { + bigint_comba_mul24(z, x, y); + } + else if(x_sw < KARATSUBA_MULTIPLY_THRESHOLD || + y_sw < KARATSUBA_MULTIPLY_THRESHOLD || + !workspace) + { + basecase_mul(z, z_size, x, x_sw, y, y_sw); + } + else + { + const size_t N = karatsuba_size(z_size, x_size, x_sw, y_size, y_sw); + + if(N && z_size >= 2*N && ws_size >= 2*N) + karatsuba_mul(z, x, y, N, workspace); + else + basecase_mul(z, z_size, x, x_sw, y, y_sw); + } + } + +/* +* Squaring Algorithm Dispatcher +*/ +void bigint_sqr(word z[], size_t z_size, + const word x[], size_t x_size, size_t x_sw, + word workspace[], size_t ws_size) + { + clear_mem(z, z_size); + + BOTAN_ASSERT(z_size/2 >= x_sw, "Output size is sufficient"); + + if(x_sw == 1) + { + bigint_linmul3(z, x, x_sw, x[0]); + } + else if(sized_for_comba_sqr<4>(x_sw, x_size, z_size)) + { + bigint_comba_sqr4(z, x); + } + else if(sized_for_comba_sqr<6>(x_sw, x_size, z_size)) + { + bigint_comba_sqr6(z, x); + } + else if(sized_for_comba_sqr<8>(x_sw, x_size, z_size)) + { + bigint_comba_sqr8(z, x); + } + else if(sized_for_comba_sqr<9>(x_sw, x_size, z_size)) + { + bigint_comba_sqr9(z, x); + } + else if(sized_for_comba_sqr<16>(x_sw, x_size, z_size)) + { + bigint_comba_sqr16(z, x); + } + else if(sized_for_comba_sqr<24>(x_sw, x_size, z_size)) + { + bigint_comba_sqr24(z, x); + } + else if(x_size < KARATSUBA_SQUARE_THRESHOLD || !workspace) + { + basecase_sqr(z, z_size, x, x_sw); + } + else + { + const size_t N = karatsuba_size(z_size, x_size, x_sw); + + if(N && z_size >= 2*N && ws_size >= 2*N) + karatsuba_sqr(z, x, N, workspace); + else + basecase_sqr(z, z_size, x, x_sw); + } + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_madd.h b/src/libs/3rdparty/botan/src/lib/math/mp/mp_madd.h new file mode 100644 index 0000000000..4807fcd040 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_madd.h @@ -0,0 +1,165 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2008,2013 Jack Lloyd +* 2006 Luca Piccarreta +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_MP_WORD_MULADD_H_ +#define BOTAN_MP_WORD_MULADD_H_ + +#include <botan/types.h> +#include <botan/mul128.h> + +namespace Botan { + +#if (BOTAN_MP_WORD_BITS == 8) + typedef uint16_t dword; + #define BOTAN_HAS_MP_DWORD +#elif (BOTAN_MP_WORD_BITS == 16) + typedef uint32_t dword; + #define BOTAN_HAS_MP_DWORD +#elif (BOTAN_MP_WORD_BITS == 32) + typedef uint64_t dword; + #define BOTAN_HAS_MP_DWORD +#elif (BOTAN_MP_WORD_BITS == 64) + #if defined(BOTAN_TARGET_HAS_NATIVE_UINT128) + typedef uint128_t dword; + #define BOTAN_HAS_MP_DWORD + #else + // No native 128 bit integer type; use mul64x64_128 instead + #endif + +#else + #error BOTAN_MP_WORD_BITS must be 8, 16, 32, or 64 +#endif + +#if defined(BOTAN_TARGET_ARCH_IS_X86_32) && (BOTAN_MP_WORD_BITS == 32) + + #if defined(BOTAN_USE_GCC_INLINE_ASM) + #define BOTAN_MP_USE_X86_32_ASM + #define ASM(x) x "\n\t" + #elif defined(BOTAN_BUILD_COMPILER_IS_MSVC) + #define BOTAN_MP_USE_X86_32_MSVC_ASM + #endif + +#elif defined(BOTAN_TARGET_ARCH_IS_X86_64) && (BOTAN_MP_WORD_BITS == 64) && (BOTAN_USE_GCC_INLINE_ASM) + #define BOTAN_MP_USE_X86_64_ASM + #define ASM(x) x "\n\t" +#endif + +#if defined(BOTAN_MP_USE_X86_32_ASM) || defined(BOTAN_MP_USE_X86_64_ASM) + #define ASM(x) x "\n\t" +#endif + +/* +* Word Multiply/Add +*/ +inline word word_madd2(word a, word b, word* c) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ASM("mull %[b]") + ASM("addl %[c],%[a]") + ASM("adcl $0,%[carry]") + + : [a]"=a"(a), [b]"=rm"(b), [carry]"=&d"(*c) + : "0"(a), "1"(b), [c]"g"(*c) : "cc"); + + return a; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + asm( + ASM("mulq %[b]") + ASM("addq %[c],%[a]") + ASM("adcq $0,%[carry]") + + : [a]"=a"(a), [b]"=rm"(b), [carry]"=&d"(*c) + : "0"(a), "1"(b), [c]"g"(*c) : "cc"); + + return a; + +#elif defined(BOTAN_HAS_MP_DWORD) + const dword s = static_cast<dword>(a) * b + *c; + *c = static_cast<word>(s >> BOTAN_MP_WORD_BITS); + return static_cast<word>(s); +#else + static_assert(BOTAN_MP_WORD_BITS == 64, "Unexpected word size"); + + word hi = 0, lo = 0; + + mul64x64_128(a, b, &lo, &hi); + + lo += *c; + hi += (lo < *c); // carry? + + *c = hi; + return lo; +#endif + } + +/* +* Word Multiply/Add +*/ +inline word word_madd3(word a, word b, word c, word* d) + { +#if defined(BOTAN_MP_USE_X86_32_ASM) + asm( + ASM("mull %[b]") + + ASM("addl %[c],%[a]") + ASM("adcl $0,%[carry]") + + ASM("addl %[d],%[a]") + ASM("adcl $0,%[carry]") + + : [a]"=a"(a), [b]"=rm"(b), [carry]"=&d"(*d) + : "0"(a), "1"(b), [c]"g"(c), [d]"g"(*d) : "cc"); + + return a; + +#elif defined(BOTAN_MP_USE_X86_64_ASM) + asm( + ASM("mulq %[b]") + + ASM("addq %[c],%[a]") + ASM("adcq $0,%[carry]") + + ASM("addq %[d],%[a]") + ASM("adcq $0,%[carry]") + + : [a]"=a"(a), [b]"=rm"(b), [carry]"=&d"(*d) + : "0"(a), "1"(b), [c]"g"(c), [d]"g"(*d) : "cc"); + + return a; + +#elif defined(BOTAN_HAS_MP_DWORD) + const dword s = static_cast<dword>(a) * b + c + *d; + *d = static_cast<word>(s >> BOTAN_MP_WORD_BITS); + return static_cast<word>(s); +#else + static_assert(BOTAN_MP_WORD_BITS == 64, "Unexpected word size"); + + word hi = 0, lo = 0; + + mul64x64_128(a, b, &lo, &hi); + + lo += c; + hi += (lo < c); // carry? + + lo += *d; + hi += (lo < *d); // carry? + + *d = hi; + return lo; +#endif + } + +#if defined(ASM) + #undef ASM +#endif + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty.cpp b/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty.cpp new file mode 100644 index 0000000000..e5dda705ce --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty.cpp @@ -0,0 +1,135 @@ +/* +* Montgomery Reduction +* (C) 1999-2011 Jack Lloyd +* 2006 Luca Piccarreta +* 2016 Matthias Gierlings +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/mp_core.h> +#include <botan/internal/mp_monty.h> +#include <botan/internal/mp_madd.h> +#include <botan/internal/mp_asmi.h> +#include <botan/internal/ct_utils.h> +#include <botan/mem_ops.h> +#include <botan/exceptn.h> + +namespace Botan { + +namespace { + +/* +* Montgomery reduction - product scanning form +* +* https://www.iacr.org/archive/ches2005/006.pdf +* https://eprint.iacr.org/2013/882.pdf +* https://www.microsoft.com/en-us/research/wp-content/uploads/1996/01/j37acmon.pdf +*/ +void bigint_monty_redc_generic(word z[], size_t z_size, + const word p[], size_t p_size, word p_dash, + word ws[]) + { + word w2 = 0, w1 = 0, w0 = 0; + + w0 = z[0]; + + ws[0] = w0 * p_dash; + + word3_muladd(&w2, &w1, &w0, ws[0], p[0]); + + w0 = w1; + w1 = w2; + w2 = 0; + + for(size_t i = 1; i != p_size; ++i) + { + for(size_t j = 0; j < i; ++j) + { + word3_muladd(&w2, &w1, &w0, ws[j], p[i-j]); + } + + word3_add(&w2, &w1, &w0, z[i]); + + ws[i] = w0 * p_dash; + + word3_muladd(&w2, &w1, &w0, ws[i], p[0]); + + w0 = w1; + w1 = w2; + w2 = 0; + } + + for(size_t i = 0; i != p_size; ++i) + { + for(size_t j = i + 1; j != p_size; ++j) + { + word3_muladd(&w2, &w1, &w0, ws[j], p[p_size + i-j]); + } + + word3_add(&w2, &w1, &w0, z[p_size+i]); + + ws[i] = w0; + w0 = w1; + w1 = w2; + w2 = 0; + } + + word3_add(&w2, &w1, &w0, z[z_size-1]); + + ws[p_size] = w0; + ws[p_size+1] = w1; + + /* + * The result might need to be reduced mod p. To avoid a timing + * channel, always perform the subtraction. If in the compution + * of x - p a borrow is required then x was already < p. + * + * x starts at ws[0] and is p_size+1 bytes long. + * x - p starts at ws[p_size+1] and is also p_size+1 bytes log + * + * Select which address to copy from indexing off of the final + * borrow. + */ + + // word borrow = bigint_sub3(ws + p_size + 1, ws, p_size + 1, p, p_size); + word borrow = 0; + for(size_t i = 0; i != p_size; ++i) + ws[p_size + 1 + i] = word_sub(ws[i], p[i], &borrow); + ws[2*p_size+1] = word_sub(ws[p_size], 0, &borrow); + + CT::conditional_copy_mem(borrow, z, ws, ws + (p_size + 1), (p_size + 1)); + clear_mem(z + p_size, z_size - p_size - 2); + + // This check comes after we've used it but that's ok here + CT::unpoison(&borrow, 1); + BOTAN_ASSERT(borrow == 0 || borrow == 1, "Expected borrow"); + } + +} + +void bigint_monty_redc(word z[], + const word p[], size_t p_size, word p_dash, + word ws[], size_t ws_size) + { + const size_t z_size = 2*(p_size+1); + + BOTAN_ARG_CHECK(ws_size >= z_size, "workspace too small"); + + if(p_size == 4) + bigint_monty_redc_4(z, p, p_dash, ws); + else if(p_size == 6) + bigint_monty_redc_6(z, p, p_dash, ws); + else if(p_size == 8) + bigint_monty_redc_8(z, p, p_dash, ws); + else if(p_size == 16) + bigint_monty_redc_16(z, p, p_dash, ws); + else if(p_size == 24) + bigint_monty_redc_24(z, p, p_dash, ws); + else if(p_size == 32) + bigint_monty_redc_32(z, p, p_dash, ws); + else + bigint_monty_redc_generic(z, z_size, p, p_size, p_dash, ws); + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty.h b/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty.h new file mode 100644 index 0000000000..7462272d5c --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty.h @@ -0,0 +1,31 @@ +/* +* (C) 2018 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_MP_MONTY_H_ +#define BOTAN_MP_MONTY_H_ + +#include <botan/types.h> + +namespace Botan { + +/* +* Each of these functions makes the following assumptions: +* +* z_size >= 2*(p_size + 1) +* ws_size >= z_size +*/ + +void bigint_monty_redc_4(word z[], const word p[], word p_dash, word ws[]); +void bigint_monty_redc_6(word z[], const word p[], word p_dash, word ws[]); +void bigint_monty_redc_8(word z[], const word p[], word p_dash, word ws[]); +void bigint_monty_redc_16(word z[], const word p[], word p_dash, word ws[]); +void bigint_monty_redc_24(word z[], const word p[], word p_dash, word ws[]); +void bigint_monty_redc_32(word z[], const word p[], word p_dash, word ws[]); + + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty_n.cpp b/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty_n.cpp new file mode 100644 index 0000000000..0331d4a073 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/mp/mp_monty_n.cpp @@ -0,0 +1,2614 @@ +/* +* This file was automatically generated by ./src/scripts/monty.py on 2018-06-11 +* All manual changes will be lost. Edit the script instead. +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/mp_monty.h> +#include <botan/internal/mp_core.h> +#include <botan/internal/mp_asmi.h> +#include <botan/internal/ct_utils.h> + +namespace Botan { + +void bigint_monty_redc_4(word z[], const word p[4], word p_dash, word ws[]) + { + word w2 = 0, w1 = 0, w0 = 0; + w0 = z[0]; + ws[0] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[0], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[1]); + word3_add(&w2, &w1, &w0, z[1]); + ws[1] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[1], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[2]); + word3_muladd(&w2, &w1, &w0, ws[1], p[1]); + word3_add(&w2, &w1, &w0, z[2]); + ws[2] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[2], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[3]); + word3_muladd(&w2, &w1, &w0, ws[1], p[2]); + word3_muladd(&w2, &w1, &w0, ws[2], p[1]); + word3_add(&w2, &w1, &w0, z[3]); + ws[3] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[3], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[1], p[3]); + word3_muladd(&w2, &w1, &w0, ws[2], p[2]); + word3_muladd(&w2, &w1, &w0, ws[3], p[1]); + word3_add(&w2, &w1, &w0, z[4]); + ws[0] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[2], p[3]); + word3_muladd(&w2, &w1, &w0, ws[3], p[2]); + word3_add(&w2, &w1, &w0, z[5]); + ws[1] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[3], p[3]); + word3_add(&w2, &w1, &w0, z[6]); + ws[2] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[7]); + ws[3] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[9]); + ws[4] = w0; + ws[5] = w1; + word borrow = 0; + ws[5] = word_sub(ws[0], p[0], &borrow); + ws[6] = word_sub(ws[1], p[1], &borrow); + ws[7] = word_sub(ws[2], p[2], &borrow); + ws[8] = word_sub(ws[3], p[3], &borrow); + ws[9] = word_sub(ws[4], 0, &borrow); + CT::conditional_copy_mem(borrow, z, ws, ws + 5, 5); + clear_mem(z + 4, 2*(4+1) - 4); + } + +void bigint_monty_redc_6(word z[], const word p[6], word p_dash, word ws[]) + { + word w2 = 0, w1 = 0, w0 = 0; + w0 = z[0]; + ws[0] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[0], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[1]); + word3_add(&w2, &w1, &w0, z[1]); + ws[1] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[1], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[2]); + word3_muladd(&w2, &w1, &w0, ws[1], p[1]); + word3_add(&w2, &w1, &w0, z[2]); + ws[2] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[2], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[3]); + word3_muladd(&w2, &w1, &w0, ws[1], p[2]); + word3_muladd(&w2, &w1, &w0, ws[2], p[1]); + word3_add(&w2, &w1, &w0, z[3]); + ws[3] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[3], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[4]); + word3_muladd(&w2, &w1, &w0, ws[1], p[3]); + word3_muladd(&w2, &w1, &w0, ws[2], p[2]); + word3_muladd(&w2, &w1, &w0, ws[3], p[1]); + word3_add(&w2, &w1, &w0, z[4]); + ws[4] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[4], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[5]); + word3_muladd(&w2, &w1, &w0, ws[1], p[4]); + word3_muladd(&w2, &w1, &w0, ws[2], p[3]); + word3_muladd(&w2, &w1, &w0, ws[3], p[2]); + word3_muladd(&w2, &w1, &w0, ws[4], p[1]); + word3_add(&w2, &w1, &w0, z[5]); + ws[5] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[5], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[1], p[5]); + word3_muladd(&w2, &w1, &w0, ws[2], p[4]); + word3_muladd(&w2, &w1, &w0, ws[3], p[3]); + word3_muladd(&w2, &w1, &w0, ws[4], p[2]); + word3_muladd(&w2, &w1, &w0, ws[5], p[1]); + word3_add(&w2, &w1, &w0, z[6]); + ws[0] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[2], p[5]); + word3_muladd(&w2, &w1, &w0, ws[3], p[4]); + word3_muladd(&w2, &w1, &w0, ws[4], p[3]); + word3_muladd(&w2, &w1, &w0, ws[5], p[2]); + word3_add(&w2, &w1, &w0, z[7]); + ws[1] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[3], p[5]); + word3_muladd(&w2, &w1, &w0, ws[4], p[4]); + word3_muladd(&w2, &w1, &w0, ws[5], p[3]); + word3_add(&w2, &w1, &w0, z[8]); + ws[2] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[4], p[5]); + word3_muladd(&w2, &w1, &w0, ws[5], p[4]); + word3_add(&w2, &w1, &w0, z[9]); + ws[3] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[5], p[5]); + word3_add(&w2, &w1, &w0, z[10]); + ws[4] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[11]); + ws[5] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[13]); + ws[6] = w0; + ws[7] = w1; + word borrow = 0; + ws[7] = word_sub(ws[0], p[0], &borrow); + ws[8] = word_sub(ws[1], p[1], &borrow); + ws[9] = word_sub(ws[2], p[2], &borrow); + ws[10] = word_sub(ws[3], p[3], &borrow); + ws[11] = word_sub(ws[4], p[4], &borrow); + ws[12] = word_sub(ws[5], p[5], &borrow); + ws[13] = word_sub(ws[6], 0, &borrow); + CT::conditional_copy_mem(borrow, z, ws, ws + 7, 7); + clear_mem(z + 6, 2*(6+1) - 6); + } + +void bigint_monty_redc_8(word z[], const word p[8], word p_dash, word ws[]) + { + word w2 = 0, w1 = 0, w0 = 0; + w0 = z[0]; + ws[0] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[0], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[1]); + word3_add(&w2, &w1, &w0, z[1]); + ws[1] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[1], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[2]); + word3_muladd(&w2, &w1, &w0, ws[1], p[1]); + word3_add(&w2, &w1, &w0, z[2]); + ws[2] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[2], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[3]); + word3_muladd(&w2, &w1, &w0, ws[1], p[2]); + word3_muladd(&w2, &w1, &w0, ws[2], p[1]); + word3_add(&w2, &w1, &w0, z[3]); + ws[3] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[3], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[4]); + word3_muladd(&w2, &w1, &w0, ws[1], p[3]); + word3_muladd(&w2, &w1, &w0, ws[2], p[2]); + word3_muladd(&w2, &w1, &w0, ws[3], p[1]); + word3_add(&w2, &w1, &w0, z[4]); + ws[4] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[4], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[5]); + word3_muladd(&w2, &w1, &w0, ws[1], p[4]); + word3_muladd(&w2, &w1, &w0, ws[2], p[3]); + word3_muladd(&w2, &w1, &w0, ws[3], p[2]); + word3_muladd(&w2, &w1, &w0, ws[4], p[1]); + word3_add(&w2, &w1, &w0, z[5]); + ws[5] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[5], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[6]); + word3_muladd(&w2, &w1, &w0, ws[1], p[5]); + word3_muladd(&w2, &w1, &w0, ws[2], p[4]); + word3_muladd(&w2, &w1, &w0, ws[3], p[3]); + word3_muladd(&w2, &w1, &w0, ws[4], p[2]); + word3_muladd(&w2, &w1, &w0, ws[5], p[1]); + word3_add(&w2, &w1, &w0, z[6]); + ws[6] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[6], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[7]); + word3_muladd(&w2, &w1, &w0, ws[1], p[6]); + word3_muladd(&w2, &w1, &w0, ws[2], p[5]); + word3_muladd(&w2, &w1, &w0, ws[3], p[4]); + word3_muladd(&w2, &w1, &w0, ws[4], p[3]); + word3_muladd(&w2, &w1, &w0, ws[5], p[2]); + word3_muladd(&w2, &w1, &w0, ws[6], p[1]); + word3_add(&w2, &w1, &w0, z[7]); + ws[7] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[7], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[1], p[7]); + word3_muladd(&w2, &w1, &w0, ws[2], p[6]); + word3_muladd(&w2, &w1, &w0, ws[3], p[5]); + word3_muladd(&w2, &w1, &w0, ws[4], p[4]); + word3_muladd(&w2, &w1, &w0, ws[5], p[3]); + word3_muladd(&w2, &w1, &w0, ws[6], p[2]); + word3_muladd(&w2, &w1, &w0, ws[7], p[1]); + word3_add(&w2, &w1, &w0, z[8]); + ws[0] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[2], p[7]); + word3_muladd(&w2, &w1, &w0, ws[3], p[6]); + word3_muladd(&w2, &w1, &w0, ws[4], p[5]); + word3_muladd(&w2, &w1, &w0, ws[5], p[4]); + word3_muladd(&w2, &w1, &w0, ws[6], p[3]); + word3_muladd(&w2, &w1, &w0, ws[7], p[2]); + word3_add(&w2, &w1, &w0, z[9]); + ws[1] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[3], p[7]); + word3_muladd(&w2, &w1, &w0, ws[4], p[6]); + word3_muladd(&w2, &w1, &w0, ws[5], p[5]); + word3_muladd(&w2, &w1, &w0, ws[6], p[4]); + word3_muladd(&w2, &w1, &w0, ws[7], p[3]); + word3_add(&w2, &w1, &w0, z[10]); + ws[2] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[4], p[7]); + word3_muladd(&w2, &w1, &w0, ws[5], p[6]); + word3_muladd(&w2, &w1, &w0, ws[6], p[5]); + word3_muladd(&w2, &w1, &w0, ws[7], p[4]); + word3_add(&w2, &w1, &w0, z[11]); + ws[3] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[5], p[7]); + word3_muladd(&w2, &w1, &w0, ws[6], p[6]); + word3_muladd(&w2, &w1, &w0, ws[7], p[5]); + word3_add(&w2, &w1, &w0, z[12]); + ws[4] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[6], p[7]); + word3_muladd(&w2, &w1, &w0, ws[7], p[6]); + word3_add(&w2, &w1, &w0, z[13]); + ws[5] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[7], p[7]); + word3_add(&w2, &w1, &w0, z[14]); + ws[6] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[15]); + ws[7] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[17]); + ws[8] = w0; + ws[9] = w1; + word borrow = 0; + ws[9] = word_sub(ws[0], p[0], &borrow); + ws[10] = word_sub(ws[1], p[1], &borrow); + ws[11] = word_sub(ws[2], p[2], &borrow); + ws[12] = word_sub(ws[3], p[3], &borrow); + ws[13] = word_sub(ws[4], p[4], &borrow); + ws[14] = word_sub(ws[5], p[5], &borrow); + ws[15] = word_sub(ws[6], p[6], &borrow); + ws[16] = word_sub(ws[7], p[7], &borrow); + ws[17] = word_sub(ws[8], 0, &borrow); + CT::conditional_copy_mem(borrow, z, ws, ws + 9, 9); + clear_mem(z + 8, 2*(8+1) - 8); + } + +void bigint_monty_redc_16(word z[], const word p[16], word p_dash, word ws[]) + { + word w2 = 0, w1 = 0, w0 = 0; + w0 = z[0]; + ws[0] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[0], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[1]); + word3_add(&w2, &w1, &w0, z[1]); + ws[1] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[1], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[2]); + word3_muladd(&w2, &w1, &w0, ws[1], p[1]); + word3_add(&w2, &w1, &w0, z[2]); + ws[2] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[2], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[3]); + word3_muladd(&w2, &w1, &w0, ws[1], p[2]); + word3_muladd(&w2, &w1, &w0, ws[2], p[1]); + word3_add(&w2, &w1, &w0, z[3]); + ws[3] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[3], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[4]); + word3_muladd(&w2, &w1, &w0, ws[1], p[3]); + word3_muladd(&w2, &w1, &w0, ws[2], p[2]); + word3_muladd(&w2, &w1, &w0, ws[3], p[1]); + word3_add(&w2, &w1, &w0, z[4]); + ws[4] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[4], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[5]); + word3_muladd(&w2, &w1, &w0, ws[1], p[4]); + word3_muladd(&w2, &w1, &w0, ws[2], p[3]); + word3_muladd(&w2, &w1, &w0, ws[3], p[2]); + word3_muladd(&w2, &w1, &w0, ws[4], p[1]); + word3_add(&w2, &w1, &w0, z[5]); + ws[5] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[5], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[6]); + word3_muladd(&w2, &w1, &w0, ws[1], p[5]); + word3_muladd(&w2, &w1, &w0, ws[2], p[4]); + word3_muladd(&w2, &w1, &w0, ws[3], p[3]); + word3_muladd(&w2, &w1, &w0, ws[4], p[2]); + word3_muladd(&w2, &w1, &w0, ws[5], p[1]); + word3_add(&w2, &w1, &w0, z[6]); + ws[6] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[6], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[7]); + word3_muladd(&w2, &w1, &w0, ws[1], p[6]); + word3_muladd(&w2, &w1, &w0, ws[2], p[5]); + word3_muladd(&w2, &w1, &w0, ws[3], p[4]); + word3_muladd(&w2, &w1, &w0, ws[4], p[3]); + word3_muladd(&w2, &w1, &w0, ws[5], p[2]); + word3_muladd(&w2, &w1, &w0, ws[6], p[1]); + word3_add(&w2, &w1, &w0, z[7]); + ws[7] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[7], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[8]); + word3_muladd(&w2, &w1, &w0, ws[1], p[7]); + word3_muladd(&w2, &w1, &w0, ws[2], p[6]); + word3_muladd(&w2, &w1, &w0, ws[3], p[5]); + word3_muladd(&w2, &w1, &w0, ws[4], p[4]); + word3_muladd(&w2, &w1, &w0, ws[5], p[3]); + word3_muladd(&w2, &w1, &w0, ws[6], p[2]); + word3_muladd(&w2, &w1, &w0, ws[7], p[1]); + word3_add(&w2, &w1, &w0, z[8]); + ws[8] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[8], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[9]); + word3_muladd(&w2, &w1, &w0, ws[1], p[8]); + word3_muladd(&w2, &w1, &w0, ws[2], p[7]); + word3_muladd(&w2, &w1, &w0, ws[3], p[6]); + word3_muladd(&w2, &w1, &w0, ws[4], p[5]); + word3_muladd(&w2, &w1, &w0, ws[5], p[4]); + word3_muladd(&w2, &w1, &w0, ws[6], p[3]); + word3_muladd(&w2, &w1, &w0, ws[7], p[2]); + word3_muladd(&w2, &w1, &w0, ws[8], p[1]); + word3_add(&w2, &w1, &w0, z[9]); + ws[9] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[9], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[10]); + word3_muladd(&w2, &w1, &w0, ws[1], p[9]); + word3_muladd(&w2, &w1, &w0, ws[2], p[8]); + word3_muladd(&w2, &w1, &w0, ws[3], p[7]); + word3_muladd(&w2, &w1, &w0, ws[4], p[6]); + word3_muladd(&w2, &w1, &w0, ws[5], p[5]); + word3_muladd(&w2, &w1, &w0, ws[6], p[4]); + word3_muladd(&w2, &w1, &w0, ws[7], p[3]); + word3_muladd(&w2, &w1, &w0, ws[8], p[2]); + word3_muladd(&w2, &w1, &w0, ws[9], p[1]); + word3_add(&w2, &w1, &w0, z[10]); + ws[10] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[10], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[11]); + word3_muladd(&w2, &w1, &w0, ws[1], p[10]); + word3_muladd(&w2, &w1, &w0, ws[2], p[9]); + word3_muladd(&w2, &w1, &w0, ws[3], p[8]); + word3_muladd(&w2, &w1, &w0, ws[4], p[7]); + word3_muladd(&w2, &w1, &w0, ws[5], p[6]); + word3_muladd(&w2, &w1, &w0, ws[6], p[5]); + word3_muladd(&w2, &w1, &w0, ws[7], p[4]); + word3_muladd(&w2, &w1, &w0, ws[8], p[3]); + word3_muladd(&w2, &w1, &w0, ws[9], p[2]); + word3_muladd(&w2, &w1, &w0, ws[10], p[1]); + word3_add(&w2, &w1, &w0, z[11]); + ws[11] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[11], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[12]); + word3_muladd(&w2, &w1, &w0, ws[1], p[11]); + word3_muladd(&w2, &w1, &w0, ws[2], p[10]); + word3_muladd(&w2, &w1, &w0, ws[3], p[9]); + word3_muladd(&w2, &w1, &w0, ws[4], p[8]); + word3_muladd(&w2, &w1, &w0, ws[5], p[7]); + word3_muladd(&w2, &w1, &w0, ws[6], p[6]); + word3_muladd(&w2, &w1, &w0, ws[7], p[5]); + word3_muladd(&w2, &w1, &w0, ws[8], p[4]); + word3_muladd(&w2, &w1, &w0, ws[9], p[3]); + word3_muladd(&w2, &w1, &w0, ws[10], p[2]); + word3_muladd(&w2, &w1, &w0, ws[11], p[1]); + word3_add(&w2, &w1, &w0, z[12]); + ws[12] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[12], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[13]); + word3_muladd(&w2, &w1, &w0, ws[1], p[12]); + word3_muladd(&w2, &w1, &w0, ws[2], p[11]); + word3_muladd(&w2, &w1, &w0, ws[3], p[10]); + word3_muladd(&w2, &w1, &w0, ws[4], p[9]); + word3_muladd(&w2, &w1, &w0, ws[5], p[8]); + word3_muladd(&w2, &w1, &w0, ws[6], p[7]); + word3_muladd(&w2, &w1, &w0, ws[7], p[6]); + word3_muladd(&w2, &w1, &w0, ws[8], p[5]); + word3_muladd(&w2, &w1, &w0, ws[9], p[4]); + word3_muladd(&w2, &w1, &w0, ws[10], p[3]); + word3_muladd(&w2, &w1, &w0, ws[11], p[2]); + word3_muladd(&w2, &w1, &w0, ws[12], p[1]); + word3_add(&w2, &w1, &w0, z[13]); + ws[13] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[13], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[14]); + word3_muladd(&w2, &w1, &w0, ws[1], p[13]); + word3_muladd(&w2, &w1, &w0, ws[2], p[12]); + word3_muladd(&w2, &w1, &w0, ws[3], p[11]); + word3_muladd(&w2, &w1, &w0, ws[4], p[10]); + word3_muladd(&w2, &w1, &w0, ws[5], p[9]); + word3_muladd(&w2, &w1, &w0, ws[6], p[8]); + word3_muladd(&w2, &w1, &w0, ws[7], p[7]); + word3_muladd(&w2, &w1, &w0, ws[8], p[6]); + word3_muladd(&w2, &w1, &w0, ws[9], p[5]); + word3_muladd(&w2, &w1, &w0, ws[10], p[4]); + word3_muladd(&w2, &w1, &w0, ws[11], p[3]); + word3_muladd(&w2, &w1, &w0, ws[12], p[2]); + word3_muladd(&w2, &w1, &w0, ws[13], p[1]); + word3_add(&w2, &w1, &w0, z[14]); + ws[14] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[14], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[15]); + word3_muladd(&w2, &w1, &w0, ws[1], p[14]); + word3_muladd(&w2, &w1, &w0, ws[2], p[13]); + word3_muladd(&w2, &w1, &w0, ws[3], p[12]); + word3_muladd(&w2, &w1, &w0, ws[4], p[11]); + word3_muladd(&w2, &w1, &w0, ws[5], p[10]); + word3_muladd(&w2, &w1, &w0, ws[6], p[9]); + word3_muladd(&w2, &w1, &w0, ws[7], p[8]); + word3_muladd(&w2, &w1, &w0, ws[8], p[7]); + word3_muladd(&w2, &w1, &w0, ws[9], p[6]); + word3_muladd(&w2, &w1, &w0, ws[10], p[5]); + word3_muladd(&w2, &w1, &w0, ws[11], p[4]); + word3_muladd(&w2, &w1, &w0, ws[12], p[3]); + word3_muladd(&w2, &w1, &w0, ws[13], p[2]); + word3_muladd(&w2, &w1, &w0, ws[14], p[1]); + word3_add(&w2, &w1, &w0, z[15]); + ws[15] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[15], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[1], p[15]); + word3_muladd(&w2, &w1, &w0, ws[2], p[14]); + word3_muladd(&w2, &w1, &w0, ws[3], p[13]); + word3_muladd(&w2, &w1, &w0, ws[4], p[12]); + word3_muladd(&w2, &w1, &w0, ws[5], p[11]); + word3_muladd(&w2, &w1, &w0, ws[6], p[10]); + word3_muladd(&w2, &w1, &w0, ws[7], p[9]); + word3_muladd(&w2, &w1, &w0, ws[8], p[8]); + word3_muladd(&w2, &w1, &w0, ws[9], p[7]); + word3_muladd(&w2, &w1, &w0, ws[10], p[6]); + word3_muladd(&w2, &w1, &w0, ws[11], p[5]); + word3_muladd(&w2, &w1, &w0, ws[12], p[4]); + word3_muladd(&w2, &w1, &w0, ws[13], p[3]); + word3_muladd(&w2, &w1, &w0, ws[14], p[2]); + word3_muladd(&w2, &w1, &w0, ws[15], p[1]); + word3_add(&w2, &w1, &w0, z[16]); + ws[0] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[2], p[15]); + word3_muladd(&w2, &w1, &w0, ws[3], p[14]); + word3_muladd(&w2, &w1, &w0, ws[4], p[13]); + word3_muladd(&w2, &w1, &w0, ws[5], p[12]); + word3_muladd(&w2, &w1, &w0, ws[6], p[11]); + word3_muladd(&w2, &w1, &w0, ws[7], p[10]); + word3_muladd(&w2, &w1, &w0, ws[8], p[9]); + word3_muladd(&w2, &w1, &w0, ws[9], p[8]); + word3_muladd(&w2, &w1, &w0, ws[10], p[7]); + word3_muladd(&w2, &w1, &w0, ws[11], p[6]); + word3_muladd(&w2, &w1, &w0, ws[12], p[5]); + word3_muladd(&w2, &w1, &w0, ws[13], p[4]); + word3_muladd(&w2, &w1, &w0, ws[14], p[3]); + word3_muladd(&w2, &w1, &w0, ws[15], p[2]); + word3_add(&w2, &w1, &w0, z[17]); + ws[1] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[3], p[15]); + word3_muladd(&w2, &w1, &w0, ws[4], p[14]); + word3_muladd(&w2, &w1, &w0, ws[5], p[13]); + word3_muladd(&w2, &w1, &w0, ws[6], p[12]); + word3_muladd(&w2, &w1, &w0, ws[7], p[11]); + word3_muladd(&w2, &w1, &w0, ws[8], p[10]); + word3_muladd(&w2, &w1, &w0, ws[9], p[9]); + word3_muladd(&w2, &w1, &w0, ws[10], p[8]); + word3_muladd(&w2, &w1, &w0, ws[11], p[7]); + word3_muladd(&w2, &w1, &w0, ws[12], p[6]); + word3_muladd(&w2, &w1, &w0, ws[13], p[5]); + word3_muladd(&w2, &w1, &w0, ws[14], p[4]); + word3_muladd(&w2, &w1, &w0, ws[15], p[3]); + word3_add(&w2, &w1, &w0, z[18]); + ws[2] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[4], p[15]); + word3_muladd(&w2, &w1, &w0, ws[5], p[14]); + word3_muladd(&w2, &w1, &w0, ws[6], p[13]); + word3_muladd(&w2, &w1, &w0, ws[7], p[12]); + word3_muladd(&w2, &w1, &w0, ws[8], p[11]); + word3_muladd(&w2, &w1, &w0, ws[9], p[10]); + word3_muladd(&w2, &w1, &w0, ws[10], p[9]); + word3_muladd(&w2, &w1, &w0, ws[11], p[8]); + word3_muladd(&w2, &w1, &w0, ws[12], p[7]); + word3_muladd(&w2, &w1, &w0, ws[13], p[6]); + word3_muladd(&w2, &w1, &w0, ws[14], p[5]); + word3_muladd(&w2, &w1, &w0, ws[15], p[4]); + word3_add(&w2, &w1, &w0, z[19]); + ws[3] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[5], p[15]); + word3_muladd(&w2, &w1, &w0, ws[6], p[14]); + word3_muladd(&w2, &w1, &w0, ws[7], p[13]); + word3_muladd(&w2, &w1, &w0, ws[8], p[12]); + word3_muladd(&w2, &w1, &w0, ws[9], p[11]); + word3_muladd(&w2, &w1, &w0, ws[10], p[10]); + word3_muladd(&w2, &w1, &w0, ws[11], p[9]); + word3_muladd(&w2, &w1, &w0, ws[12], p[8]); + word3_muladd(&w2, &w1, &w0, ws[13], p[7]); + word3_muladd(&w2, &w1, &w0, ws[14], p[6]); + word3_muladd(&w2, &w1, &w0, ws[15], p[5]); + word3_add(&w2, &w1, &w0, z[20]); + ws[4] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[6], p[15]); + word3_muladd(&w2, &w1, &w0, ws[7], p[14]); + word3_muladd(&w2, &w1, &w0, ws[8], p[13]); + word3_muladd(&w2, &w1, &w0, ws[9], p[12]); + word3_muladd(&w2, &w1, &w0, ws[10], p[11]); + word3_muladd(&w2, &w1, &w0, ws[11], p[10]); + word3_muladd(&w2, &w1, &w0, ws[12], p[9]); + word3_muladd(&w2, &w1, &w0, ws[13], p[8]); + word3_muladd(&w2, &w1, &w0, ws[14], p[7]); + word3_muladd(&w2, &w1, &w0, ws[15], p[6]); + word3_add(&w2, &w1, &w0, z[21]); + ws[5] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[7], p[15]); + word3_muladd(&w2, &w1, &w0, ws[8], p[14]); + word3_muladd(&w2, &w1, &w0, ws[9], p[13]); + word3_muladd(&w2, &w1, &w0, ws[10], p[12]); + word3_muladd(&w2, &w1, &w0, ws[11], p[11]); + word3_muladd(&w2, &w1, &w0, ws[12], p[10]); + word3_muladd(&w2, &w1, &w0, ws[13], p[9]); + word3_muladd(&w2, &w1, &w0, ws[14], p[8]); + word3_muladd(&w2, &w1, &w0, ws[15], p[7]); + word3_add(&w2, &w1, &w0, z[22]); + ws[6] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[8], p[15]); + word3_muladd(&w2, &w1, &w0, ws[9], p[14]); + word3_muladd(&w2, &w1, &w0, ws[10], p[13]); + word3_muladd(&w2, &w1, &w0, ws[11], p[12]); + word3_muladd(&w2, &w1, &w0, ws[12], p[11]); + word3_muladd(&w2, &w1, &w0, ws[13], p[10]); + word3_muladd(&w2, &w1, &w0, ws[14], p[9]); + word3_muladd(&w2, &w1, &w0, ws[15], p[8]); + word3_add(&w2, &w1, &w0, z[23]); + ws[7] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[9], p[15]); + word3_muladd(&w2, &w1, &w0, ws[10], p[14]); + word3_muladd(&w2, &w1, &w0, ws[11], p[13]); + word3_muladd(&w2, &w1, &w0, ws[12], p[12]); + word3_muladd(&w2, &w1, &w0, ws[13], p[11]); + word3_muladd(&w2, &w1, &w0, ws[14], p[10]); + word3_muladd(&w2, &w1, &w0, ws[15], p[9]); + word3_add(&w2, &w1, &w0, z[24]); + ws[8] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[10], p[15]); + word3_muladd(&w2, &w1, &w0, ws[11], p[14]); + word3_muladd(&w2, &w1, &w0, ws[12], p[13]); + word3_muladd(&w2, &w1, &w0, ws[13], p[12]); + word3_muladd(&w2, &w1, &w0, ws[14], p[11]); + word3_muladd(&w2, &w1, &w0, ws[15], p[10]); + word3_add(&w2, &w1, &w0, z[25]); + ws[9] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[11], p[15]); + word3_muladd(&w2, &w1, &w0, ws[12], p[14]); + word3_muladd(&w2, &w1, &w0, ws[13], p[13]); + word3_muladd(&w2, &w1, &w0, ws[14], p[12]); + word3_muladd(&w2, &w1, &w0, ws[15], p[11]); + word3_add(&w2, &w1, &w0, z[26]); + ws[10] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[12], p[15]); + word3_muladd(&w2, &w1, &w0, ws[13], p[14]); + word3_muladd(&w2, &w1, &w0, ws[14], p[13]); + word3_muladd(&w2, &w1, &w0, ws[15], p[12]); + word3_add(&w2, &w1, &w0, z[27]); + ws[11] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[13], p[15]); + word3_muladd(&w2, &w1, &w0, ws[14], p[14]); + word3_muladd(&w2, &w1, &w0, ws[15], p[13]); + word3_add(&w2, &w1, &w0, z[28]); + ws[12] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[14], p[15]); + word3_muladd(&w2, &w1, &w0, ws[15], p[14]); + word3_add(&w2, &w1, &w0, z[29]); + ws[13] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[15], p[15]); + word3_add(&w2, &w1, &w0, z[30]); + ws[14] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[31]); + ws[15] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[33]); + ws[16] = w0; + ws[17] = w1; + word borrow = bigint_sub3(ws + 16 + 1, ws, 16 + 1, p, 16); + CT::conditional_copy_mem(borrow, z, ws, ws + 17, 17); + clear_mem(z + 16, 2*(16+1) - 16); + } + +void bigint_monty_redc_24(word z[], const word p[24], word p_dash, word ws[]) + { + word w2 = 0, w1 = 0, w0 = 0; + w0 = z[0]; + ws[0] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[0], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[1]); + word3_add(&w2, &w1, &w0, z[1]); + ws[1] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[1], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[2]); + word3_muladd(&w2, &w1, &w0, ws[1], p[1]); + word3_add(&w2, &w1, &w0, z[2]); + ws[2] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[2], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[3]); + word3_muladd(&w2, &w1, &w0, ws[1], p[2]); + word3_muladd(&w2, &w1, &w0, ws[2], p[1]); + word3_add(&w2, &w1, &w0, z[3]); + ws[3] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[3], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[4]); + word3_muladd(&w2, &w1, &w0, ws[1], p[3]); + word3_muladd(&w2, &w1, &w0, ws[2], p[2]); + word3_muladd(&w2, &w1, &w0, ws[3], p[1]); + word3_add(&w2, &w1, &w0, z[4]); + ws[4] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[4], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[5]); + word3_muladd(&w2, &w1, &w0, ws[1], p[4]); + word3_muladd(&w2, &w1, &w0, ws[2], p[3]); + word3_muladd(&w2, &w1, &w0, ws[3], p[2]); + word3_muladd(&w2, &w1, &w0, ws[4], p[1]); + word3_add(&w2, &w1, &w0, z[5]); + ws[5] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[5], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[6]); + word3_muladd(&w2, &w1, &w0, ws[1], p[5]); + word3_muladd(&w2, &w1, &w0, ws[2], p[4]); + word3_muladd(&w2, &w1, &w0, ws[3], p[3]); + word3_muladd(&w2, &w1, &w0, ws[4], p[2]); + word3_muladd(&w2, &w1, &w0, ws[5], p[1]); + word3_add(&w2, &w1, &w0, z[6]); + ws[6] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[6], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[7]); + word3_muladd(&w2, &w1, &w0, ws[1], p[6]); + word3_muladd(&w2, &w1, &w0, ws[2], p[5]); + word3_muladd(&w2, &w1, &w0, ws[3], p[4]); + word3_muladd(&w2, &w1, &w0, ws[4], p[3]); + word3_muladd(&w2, &w1, &w0, ws[5], p[2]); + word3_muladd(&w2, &w1, &w0, ws[6], p[1]); + word3_add(&w2, &w1, &w0, z[7]); + ws[7] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[7], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[8]); + word3_muladd(&w2, &w1, &w0, ws[1], p[7]); + word3_muladd(&w2, &w1, &w0, ws[2], p[6]); + word3_muladd(&w2, &w1, &w0, ws[3], p[5]); + word3_muladd(&w2, &w1, &w0, ws[4], p[4]); + word3_muladd(&w2, &w1, &w0, ws[5], p[3]); + word3_muladd(&w2, &w1, &w0, ws[6], p[2]); + word3_muladd(&w2, &w1, &w0, ws[7], p[1]); + word3_add(&w2, &w1, &w0, z[8]); + ws[8] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[8], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[9]); + word3_muladd(&w2, &w1, &w0, ws[1], p[8]); + word3_muladd(&w2, &w1, &w0, ws[2], p[7]); + word3_muladd(&w2, &w1, &w0, ws[3], p[6]); + word3_muladd(&w2, &w1, &w0, ws[4], p[5]); + word3_muladd(&w2, &w1, &w0, ws[5], p[4]); + word3_muladd(&w2, &w1, &w0, ws[6], p[3]); + word3_muladd(&w2, &w1, &w0, ws[7], p[2]); + word3_muladd(&w2, &w1, &w0, ws[8], p[1]); + word3_add(&w2, &w1, &w0, z[9]); + ws[9] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[9], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[10]); + word3_muladd(&w2, &w1, &w0, ws[1], p[9]); + word3_muladd(&w2, &w1, &w0, ws[2], p[8]); + word3_muladd(&w2, &w1, &w0, ws[3], p[7]); + word3_muladd(&w2, &w1, &w0, ws[4], p[6]); + word3_muladd(&w2, &w1, &w0, ws[5], p[5]); + word3_muladd(&w2, &w1, &w0, ws[6], p[4]); + word3_muladd(&w2, &w1, &w0, ws[7], p[3]); + word3_muladd(&w2, &w1, &w0, ws[8], p[2]); + word3_muladd(&w2, &w1, &w0, ws[9], p[1]); + word3_add(&w2, &w1, &w0, z[10]); + ws[10] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[10], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[11]); + word3_muladd(&w2, &w1, &w0, ws[1], p[10]); + word3_muladd(&w2, &w1, &w0, ws[2], p[9]); + word3_muladd(&w2, &w1, &w0, ws[3], p[8]); + word3_muladd(&w2, &w1, &w0, ws[4], p[7]); + word3_muladd(&w2, &w1, &w0, ws[5], p[6]); + word3_muladd(&w2, &w1, &w0, ws[6], p[5]); + word3_muladd(&w2, &w1, &w0, ws[7], p[4]); + word3_muladd(&w2, &w1, &w0, ws[8], p[3]); + word3_muladd(&w2, &w1, &w0, ws[9], p[2]); + word3_muladd(&w2, &w1, &w0, ws[10], p[1]); + word3_add(&w2, &w1, &w0, z[11]); + ws[11] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[11], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[12]); + word3_muladd(&w2, &w1, &w0, ws[1], p[11]); + word3_muladd(&w2, &w1, &w0, ws[2], p[10]); + word3_muladd(&w2, &w1, &w0, ws[3], p[9]); + word3_muladd(&w2, &w1, &w0, ws[4], p[8]); + word3_muladd(&w2, &w1, &w0, ws[5], p[7]); + word3_muladd(&w2, &w1, &w0, ws[6], p[6]); + word3_muladd(&w2, &w1, &w0, ws[7], p[5]); + word3_muladd(&w2, &w1, &w0, ws[8], p[4]); + word3_muladd(&w2, &w1, &w0, ws[9], p[3]); + word3_muladd(&w2, &w1, &w0, ws[10], p[2]); + word3_muladd(&w2, &w1, &w0, ws[11], p[1]); + word3_add(&w2, &w1, &w0, z[12]); + ws[12] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[12], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[13]); + word3_muladd(&w2, &w1, &w0, ws[1], p[12]); + word3_muladd(&w2, &w1, &w0, ws[2], p[11]); + word3_muladd(&w2, &w1, &w0, ws[3], p[10]); + word3_muladd(&w2, &w1, &w0, ws[4], p[9]); + word3_muladd(&w2, &w1, &w0, ws[5], p[8]); + word3_muladd(&w2, &w1, &w0, ws[6], p[7]); + word3_muladd(&w2, &w1, &w0, ws[7], p[6]); + word3_muladd(&w2, &w1, &w0, ws[8], p[5]); + word3_muladd(&w2, &w1, &w0, ws[9], p[4]); + word3_muladd(&w2, &w1, &w0, ws[10], p[3]); + word3_muladd(&w2, &w1, &w0, ws[11], p[2]); + word3_muladd(&w2, &w1, &w0, ws[12], p[1]); + word3_add(&w2, &w1, &w0, z[13]); + ws[13] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[13], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[14]); + word3_muladd(&w2, &w1, &w0, ws[1], p[13]); + word3_muladd(&w2, &w1, &w0, ws[2], p[12]); + word3_muladd(&w2, &w1, &w0, ws[3], p[11]); + word3_muladd(&w2, &w1, &w0, ws[4], p[10]); + word3_muladd(&w2, &w1, &w0, ws[5], p[9]); + word3_muladd(&w2, &w1, &w0, ws[6], p[8]); + word3_muladd(&w2, &w1, &w0, ws[7], p[7]); + word3_muladd(&w2, &w1, &w0, ws[8], p[6]); + word3_muladd(&w2, &w1, &w0, ws[9], p[5]); + word3_muladd(&w2, &w1, &w0, ws[10], p[4]); + word3_muladd(&w2, &w1, &w0, ws[11], p[3]); + word3_muladd(&w2, &w1, &w0, ws[12], p[2]); + word3_muladd(&w2, &w1, &w0, ws[13], p[1]); + word3_add(&w2, &w1, &w0, z[14]); + ws[14] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[14], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[15]); + word3_muladd(&w2, &w1, &w0, ws[1], p[14]); + word3_muladd(&w2, &w1, &w0, ws[2], p[13]); + word3_muladd(&w2, &w1, &w0, ws[3], p[12]); + word3_muladd(&w2, &w1, &w0, ws[4], p[11]); + word3_muladd(&w2, &w1, &w0, ws[5], p[10]); + word3_muladd(&w2, &w1, &w0, ws[6], p[9]); + word3_muladd(&w2, &w1, &w0, ws[7], p[8]); + word3_muladd(&w2, &w1, &w0, ws[8], p[7]); + word3_muladd(&w2, &w1, &w0, ws[9], p[6]); + word3_muladd(&w2, &w1, &w0, ws[10], p[5]); + word3_muladd(&w2, &w1, &w0, ws[11], p[4]); + word3_muladd(&w2, &w1, &w0, ws[12], p[3]); + word3_muladd(&w2, &w1, &w0, ws[13], p[2]); + word3_muladd(&w2, &w1, &w0, ws[14], p[1]); + word3_add(&w2, &w1, &w0, z[15]); + ws[15] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[15], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[16]); + word3_muladd(&w2, &w1, &w0, ws[1], p[15]); + word3_muladd(&w2, &w1, &w0, ws[2], p[14]); + word3_muladd(&w2, &w1, &w0, ws[3], p[13]); + word3_muladd(&w2, &w1, &w0, ws[4], p[12]); + word3_muladd(&w2, &w1, &w0, ws[5], p[11]); + word3_muladd(&w2, &w1, &w0, ws[6], p[10]); + word3_muladd(&w2, &w1, &w0, ws[7], p[9]); + word3_muladd(&w2, &w1, &w0, ws[8], p[8]); + word3_muladd(&w2, &w1, &w0, ws[9], p[7]); + word3_muladd(&w2, &w1, &w0, ws[10], p[6]); + word3_muladd(&w2, &w1, &w0, ws[11], p[5]); + word3_muladd(&w2, &w1, &w0, ws[12], p[4]); + word3_muladd(&w2, &w1, &w0, ws[13], p[3]); + word3_muladd(&w2, &w1, &w0, ws[14], p[2]); + word3_muladd(&w2, &w1, &w0, ws[15], p[1]); + word3_add(&w2, &w1, &w0, z[16]); + ws[16] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[16], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[17]); + word3_muladd(&w2, &w1, &w0, ws[1], p[16]); + word3_muladd(&w2, &w1, &w0, ws[2], p[15]); + word3_muladd(&w2, &w1, &w0, ws[3], p[14]); + word3_muladd(&w2, &w1, &w0, ws[4], p[13]); + word3_muladd(&w2, &w1, &w0, ws[5], p[12]); + word3_muladd(&w2, &w1, &w0, ws[6], p[11]); + word3_muladd(&w2, &w1, &w0, ws[7], p[10]); + word3_muladd(&w2, &w1, &w0, ws[8], p[9]); + word3_muladd(&w2, &w1, &w0, ws[9], p[8]); + word3_muladd(&w2, &w1, &w0, ws[10], p[7]); + word3_muladd(&w2, &w1, &w0, ws[11], p[6]); + word3_muladd(&w2, &w1, &w0, ws[12], p[5]); + word3_muladd(&w2, &w1, &w0, ws[13], p[4]); + word3_muladd(&w2, &w1, &w0, ws[14], p[3]); + word3_muladd(&w2, &w1, &w0, ws[15], p[2]); + word3_muladd(&w2, &w1, &w0, ws[16], p[1]); + word3_add(&w2, &w1, &w0, z[17]); + ws[17] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[17], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[18]); + word3_muladd(&w2, &w1, &w0, ws[1], p[17]); + word3_muladd(&w2, &w1, &w0, ws[2], p[16]); + word3_muladd(&w2, &w1, &w0, ws[3], p[15]); + word3_muladd(&w2, &w1, &w0, ws[4], p[14]); + word3_muladd(&w2, &w1, &w0, ws[5], p[13]); + word3_muladd(&w2, &w1, &w0, ws[6], p[12]); + word3_muladd(&w2, &w1, &w0, ws[7], p[11]); + word3_muladd(&w2, &w1, &w0, ws[8], p[10]); + word3_muladd(&w2, &w1, &w0, ws[9], p[9]); + word3_muladd(&w2, &w1, &w0, ws[10], p[8]); + word3_muladd(&w2, &w1, &w0, ws[11], p[7]); + word3_muladd(&w2, &w1, &w0, ws[12], p[6]); + word3_muladd(&w2, &w1, &w0, ws[13], p[5]); + word3_muladd(&w2, &w1, &w0, ws[14], p[4]); + word3_muladd(&w2, &w1, &w0, ws[15], p[3]); + word3_muladd(&w2, &w1, &w0, ws[16], p[2]); + word3_muladd(&w2, &w1, &w0, ws[17], p[1]); + word3_add(&w2, &w1, &w0, z[18]); + ws[18] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[18], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[19]); + word3_muladd(&w2, &w1, &w0, ws[1], p[18]); + word3_muladd(&w2, &w1, &w0, ws[2], p[17]); + word3_muladd(&w2, &w1, &w0, ws[3], p[16]); + word3_muladd(&w2, &w1, &w0, ws[4], p[15]); + word3_muladd(&w2, &w1, &w0, ws[5], p[14]); + word3_muladd(&w2, &w1, &w0, ws[6], p[13]); + word3_muladd(&w2, &w1, &w0, ws[7], p[12]); + word3_muladd(&w2, &w1, &w0, ws[8], p[11]); + word3_muladd(&w2, &w1, &w0, ws[9], p[10]); + word3_muladd(&w2, &w1, &w0, ws[10], p[9]); + word3_muladd(&w2, &w1, &w0, ws[11], p[8]); + word3_muladd(&w2, &w1, &w0, ws[12], p[7]); + word3_muladd(&w2, &w1, &w0, ws[13], p[6]); + word3_muladd(&w2, &w1, &w0, ws[14], p[5]); + word3_muladd(&w2, &w1, &w0, ws[15], p[4]); + word3_muladd(&w2, &w1, &w0, ws[16], p[3]); + word3_muladd(&w2, &w1, &w0, ws[17], p[2]); + word3_muladd(&w2, &w1, &w0, ws[18], p[1]); + word3_add(&w2, &w1, &w0, z[19]); + ws[19] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[19], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[20]); + word3_muladd(&w2, &w1, &w0, ws[1], p[19]); + word3_muladd(&w2, &w1, &w0, ws[2], p[18]); + word3_muladd(&w2, &w1, &w0, ws[3], p[17]); + word3_muladd(&w2, &w1, &w0, ws[4], p[16]); + word3_muladd(&w2, &w1, &w0, ws[5], p[15]); + word3_muladd(&w2, &w1, &w0, ws[6], p[14]); + word3_muladd(&w2, &w1, &w0, ws[7], p[13]); + word3_muladd(&w2, &w1, &w0, ws[8], p[12]); + word3_muladd(&w2, &w1, &w0, ws[9], p[11]); + word3_muladd(&w2, &w1, &w0, ws[10], p[10]); + word3_muladd(&w2, &w1, &w0, ws[11], p[9]); + word3_muladd(&w2, &w1, &w0, ws[12], p[8]); + word3_muladd(&w2, &w1, &w0, ws[13], p[7]); + word3_muladd(&w2, &w1, &w0, ws[14], p[6]); + word3_muladd(&w2, &w1, &w0, ws[15], p[5]); + word3_muladd(&w2, &w1, &w0, ws[16], p[4]); + word3_muladd(&w2, &w1, &w0, ws[17], p[3]); + word3_muladd(&w2, &w1, &w0, ws[18], p[2]); + word3_muladd(&w2, &w1, &w0, ws[19], p[1]); + word3_add(&w2, &w1, &w0, z[20]); + ws[20] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[20], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[21]); + word3_muladd(&w2, &w1, &w0, ws[1], p[20]); + word3_muladd(&w2, &w1, &w0, ws[2], p[19]); + word3_muladd(&w2, &w1, &w0, ws[3], p[18]); + word3_muladd(&w2, &w1, &w0, ws[4], p[17]); + word3_muladd(&w2, &w1, &w0, ws[5], p[16]); + word3_muladd(&w2, &w1, &w0, ws[6], p[15]); + word3_muladd(&w2, &w1, &w0, ws[7], p[14]); + word3_muladd(&w2, &w1, &w0, ws[8], p[13]); + word3_muladd(&w2, &w1, &w0, ws[9], p[12]); + word3_muladd(&w2, &w1, &w0, ws[10], p[11]); + word3_muladd(&w2, &w1, &w0, ws[11], p[10]); + word3_muladd(&w2, &w1, &w0, ws[12], p[9]); + word3_muladd(&w2, &w1, &w0, ws[13], p[8]); + word3_muladd(&w2, &w1, &w0, ws[14], p[7]); + word3_muladd(&w2, &w1, &w0, ws[15], p[6]); + word3_muladd(&w2, &w1, &w0, ws[16], p[5]); + word3_muladd(&w2, &w1, &w0, ws[17], p[4]); + word3_muladd(&w2, &w1, &w0, ws[18], p[3]); + word3_muladd(&w2, &w1, &w0, ws[19], p[2]); + word3_muladd(&w2, &w1, &w0, ws[20], p[1]); + word3_add(&w2, &w1, &w0, z[21]); + ws[21] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[21], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[22]); + word3_muladd(&w2, &w1, &w0, ws[1], p[21]); + word3_muladd(&w2, &w1, &w0, ws[2], p[20]); + word3_muladd(&w2, &w1, &w0, ws[3], p[19]); + word3_muladd(&w2, &w1, &w0, ws[4], p[18]); + word3_muladd(&w2, &w1, &w0, ws[5], p[17]); + word3_muladd(&w2, &w1, &w0, ws[6], p[16]); + word3_muladd(&w2, &w1, &w0, ws[7], p[15]); + word3_muladd(&w2, &w1, &w0, ws[8], p[14]); + word3_muladd(&w2, &w1, &w0, ws[9], p[13]); + word3_muladd(&w2, &w1, &w0, ws[10], p[12]); + word3_muladd(&w2, &w1, &w0, ws[11], p[11]); + word3_muladd(&w2, &w1, &w0, ws[12], p[10]); + word3_muladd(&w2, &w1, &w0, ws[13], p[9]); + word3_muladd(&w2, &w1, &w0, ws[14], p[8]); + word3_muladd(&w2, &w1, &w0, ws[15], p[7]); + word3_muladd(&w2, &w1, &w0, ws[16], p[6]); + word3_muladd(&w2, &w1, &w0, ws[17], p[5]); + word3_muladd(&w2, &w1, &w0, ws[18], p[4]); + word3_muladd(&w2, &w1, &w0, ws[19], p[3]); + word3_muladd(&w2, &w1, &w0, ws[20], p[2]); + word3_muladd(&w2, &w1, &w0, ws[21], p[1]); + word3_add(&w2, &w1, &w0, z[22]); + ws[22] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[22], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[23]); + word3_muladd(&w2, &w1, &w0, ws[1], p[22]); + word3_muladd(&w2, &w1, &w0, ws[2], p[21]); + word3_muladd(&w2, &w1, &w0, ws[3], p[20]); + word3_muladd(&w2, &w1, &w0, ws[4], p[19]); + word3_muladd(&w2, &w1, &w0, ws[5], p[18]); + word3_muladd(&w2, &w1, &w0, ws[6], p[17]); + word3_muladd(&w2, &w1, &w0, ws[7], p[16]); + word3_muladd(&w2, &w1, &w0, ws[8], p[15]); + word3_muladd(&w2, &w1, &w0, ws[9], p[14]); + word3_muladd(&w2, &w1, &w0, ws[10], p[13]); + word3_muladd(&w2, &w1, &w0, ws[11], p[12]); + word3_muladd(&w2, &w1, &w0, ws[12], p[11]); + word3_muladd(&w2, &w1, &w0, ws[13], p[10]); + word3_muladd(&w2, &w1, &w0, ws[14], p[9]); + word3_muladd(&w2, &w1, &w0, ws[15], p[8]); + word3_muladd(&w2, &w1, &w0, ws[16], p[7]); + word3_muladd(&w2, &w1, &w0, ws[17], p[6]); + word3_muladd(&w2, &w1, &w0, ws[18], p[5]); + word3_muladd(&w2, &w1, &w0, ws[19], p[4]); + word3_muladd(&w2, &w1, &w0, ws[20], p[3]); + word3_muladd(&w2, &w1, &w0, ws[21], p[2]); + word3_muladd(&w2, &w1, &w0, ws[22], p[1]); + word3_add(&w2, &w1, &w0, z[23]); + ws[23] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[23], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[1], p[23]); + word3_muladd(&w2, &w1, &w0, ws[2], p[22]); + word3_muladd(&w2, &w1, &w0, ws[3], p[21]); + word3_muladd(&w2, &w1, &w0, ws[4], p[20]); + word3_muladd(&w2, &w1, &w0, ws[5], p[19]); + word3_muladd(&w2, &w1, &w0, ws[6], p[18]); + word3_muladd(&w2, &w1, &w0, ws[7], p[17]); + word3_muladd(&w2, &w1, &w0, ws[8], p[16]); + word3_muladd(&w2, &w1, &w0, ws[9], p[15]); + word3_muladd(&w2, &w1, &w0, ws[10], p[14]); + word3_muladd(&w2, &w1, &w0, ws[11], p[13]); + word3_muladd(&w2, &w1, &w0, ws[12], p[12]); + word3_muladd(&w2, &w1, &w0, ws[13], p[11]); + word3_muladd(&w2, &w1, &w0, ws[14], p[10]); + word3_muladd(&w2, &w1, &w0, ws[15], p[9]); + word3_muladd(&w2, &w1, &w0, ws[16], p[8]); + word3_muladd(&w2, &w1, &w0, ws[17], p[7]); + word3_muladd(&w2, &w1, &w0, ws[18], p[6]); + word3_muladd(&w2, &w1, &w0, ws[19], p[5]); + word3_muladd(&w2, &w1, &w0, ws[20], p[4]); + word3_muladd(&w2, &w1, &w0, ws[21], p[3]); + word3_muladd(&w2, &w1, &w0, ws[22], p[2]); + word3_muladd(&w2, &w1, &w0, ws[23], p[1]); + word3_add(&w2, &w1, &w0, z[24]); + ws[0] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[2], p[23]); + word3_muladd(&w2, &w1, &w0, ws[3], p[22]); + word3_muladd(&w2, &w1, &w0, ws[4], p[21]); + word3_muladd(&w2, &w1, &w0, ws[5], p[20]); + word3_muladd(&w2, &w1, &w0, ws[6], p[19]); + word3_muladd(&w2, &w1, &w0, ws[7], p[18]); + word3_muladd(&w2, &w1, &w0, ws[8], p[17]); + word3_muladd(&w2, &w1, &w0, ws[9], p[16]); + word3_muladd(&w2, &w1, &w0, ws[10], p[15]); + word3_muladd(&w2, &w1, &w0, ws[11], p[14]); + word3_muladd(&w2, &w1, &w0, ws[12], p[13]); + word3_muladd(&w2, &w1, &w0, ws[13], p[12]); + word3_muladd(&w2, &w1, &w0, ws[14], p[11]); + word3_muladd(&w2, &w1, &w0, ws[15], p[10]); + word3_muladd(&w2, &w1, &w0, ws[16], p[9]); + word3_muladd(&w2, &w1, &w0, ws[17], p[8]); + word3_muladd(&w2, &w1, &w0, ws[18], p[7]); + word3_muladd(&w2, &w1, &w0, ws[19], p[6]); + word3_muladd(&w2, &w1, &w0, ws[20], p[5]); + word3_muladd(&w2, &w1, &w0, ws[21], p[4]); + word3_muladd(&w2, &w1, &w0, ws[22], p[3]); + word3_muladd(&w2, &w1, &w0, ws[23], p[2]); + word3_add(&w2, &w1, &w0, z[25]); + ws[1] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[3], p[23]); + word3_muladd(&w2, &w1, &w0, ws[4], p[22]); + word3_muladd(&w2, &w1, &w0, ws[5], p[21]); + word3_muladd(&w2, &w1, &w0, ws[6], p[20]); + word3_muladd(&w2, &w1, &w0, ws[7], p[19]); + word3_muladd(&w2, &w1, &w0, ws[8], p[18]); + word3_muladd(&w2, &w1, &w0, ws[9], p[17]); + word3_muladd(&w2, &w1, &w0, ws[10], p[16]); + word3_muladd(&w2, &w1, &w0, ws[11], p[15]); + word3_muladd(&w2, &w1, &w0, ws[12], p[14]); + word3_muladd(&w2, &w1, &w0, ws[13], p[13]); + word3_muladd(&w2, &w1, &w0, ws[14], p[12]); + word3_muladd(&w2, &w1, &w0, ws[15], p[11]); + word3_muladd(&w2, &w1, &w0, ws[16], p[10]); + word3_muladd(&w2, &w1, &w0, ws[17], p[9]); + word3_muladd(&w2, &w1, &w0, ws[18], p[8]); + word3_muladd(&w2, &w1, &w0, ws[19], p[7]); + word3_muladd(&w2, &w1, &w0, ws[20], p[6]); + word3_muladd(&w2, &w1, &w0, ws[21], p[5]); + word3_muladd(&w2, &w1, &w0, ws[22], p[4]); + word3_muladd(&w2, &w1, &w0, ws[23], p[3]); + word3_add(&w2, &w1, &w0, z[26]); + ws[2] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[4], p[23]); + word3_muladd(&w2, &w1, &w0, ws[5], p[22]); + word3_muladd(&w2, &w1, &w0, ws[6], p[21]); + word3_muladd(&w2, &w1, &w0, ws[7], p[20]); + word3_muladd(&w2, &w1, &w0, ws[8], p[19]); + word3_muladd(&w2, &w1, &w0, ws[9], p[18]); + word3_muladd(&w2, &w1, &w0, ws[10], p[17]); + word3_muladd(&w2, &w1, &w0, ws[11], p[16]); + word3_muladd(&w2, &w1, &w0, ws[12], p[15]); + word3_muladd(&w2, &w1, &w0, ws[13], p[14]); + word3_muladd(&w2, &w1, &w0, ws[14], p[13]); + word3_muladd(&w2, &w1, &w0, ws[15], p[12]); + word3_muladd(&w2, &w1, &w0, ws[16], p[11]); + word3_muladd(&w2, &w1, &w0, ws[17], p[10]); + word3_muladd(&w2, &w1, &w0, ws[18], p[9]); + word3_muladd(&w2, &w1, &w0, ws[19], p[8]); + word3_muladd(&w2, &w1, &w0, ws[20], p[7]); + word3_muladd(&w2, &w1, &w0, ws[21], p[6]); + word3_muladd(&w2, &w1, &w0, ws[22], p[5]); + word3_muladd(&w2, &w1, &w0, ws[23], p[4]); + word3_add(&w2, &w1, &w0, z[27]); + ws[3] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[5], p[23]); + word3_muladd(&w2, &w1, &w0, ws[6], p[22]); + word3_muladd(&w2, &w1, &w0, ws[7], p[21]); + word3_muladd(&w2, &w1, &w0, ws[8], p[20]); + word3_muladd(&w2, &w1, &w0, ws[9], p[19]); + word3_muladd(&w2, &w1, &w0, ws[10], p[18]); + word3_muladd(&w2, &w1, &w0, ws[11], p[17]); + word3_muladd(&w2, &w1, &w0, ws[12], p[16]); + word3_muladd(&w2, &w1, &w0, ws[13], p[15]); + word3_muladd(&w2, &w1, &w0, ws[14], p[14]); + word3_muladd(&w2, &w1, &w0, ws[15], p[13]); + word3_muladd(&w2, &w1, &w0, ws[16], p[12]); + word3_muladd(&w2, &w1, &w0, ws[17], p[11]); + word3_muladd(&w2, &w1, &w0, ws[18], p[10]); + word3_muladd(&w2, &w1, &w0, ws[19], p[9]); + word3_muladd(&w2, &w1, &w0, ws[20], p[8]); + word3_muladd(&w2, &w1, &w0, ws[21], p[7]); + word3_muladd(&w2, &w1, &w0, ws[22], p[6]); + word3_muladd(&w2, &w1, &w0, ws[23], p[5]); + word3_add(&w2, &w1, &w0, z[28]); + ws[4] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[6], p[23]); + word3_muladd(&w2, &w1, &w0, ws[7], p[22]); + word3_muladd(&w2, &w1, &w0, ws[8], p[21]); + word3_muladd(&w2, &w1, &w0, ws[9], p[20]); + word3_muladd(&w2, &w1, &w0, ws[10], p[19]); + word3_muladd(&w2, &w1, &w0, ws[11], p[18]); + word3_muladd(&w2, &w1, &w0, ws[12], p[17]); + word3_muladd(&w2, &w1, &w0, ws[13], p[16]); + word3_muladd(&w2, &w1, &w0, ws[14], p[15]); + word3_muladd(&w2, &w1, &w0, ws[15], p[14]); + word3_muladd(&w2, &w1, &w0, ws[16], p[13]); + word3_muladd(&w2, &w1, &w0, ws[17], p[12]); + word3_muladd(&w2, &w1, &w0, ws[18], p[11]); + word3_muladd(&w2, &w1, &w0, ws[19], p[10]); + word3_muladd(&w2, &w1, &w0, ws[20], p[9]); + word3_muladd(&w2, &w1, &w0, ws[21], p[8]); + word3_muladd(&w2, &w1, &w0, ws[22], p[7]); + word3_muladd(&w2, &w1, &w0, ws[23], p[6]); + word3_add(&w2, &w1, &w0, z[29]); + ws[5] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[7], p[23]); + word3_muladd(&w2, &w1, &w0, ws[8], p[22]); + word3_muladd(&w2, &w1, &w0, ws[9], p[21]); + word3_muladd(&w2, &w1, &w0, ws[10], p[20]); + word3_muladd(&w2, &w1, &w0, ws[11], p[19]); + word3_muladd(&w2, &w1, &w0, ws[12], p[18]); + word3_muladd(&w2, &w1, &w0, ws[13], p[17]); + word3_muladd(&w2, &w1, &w0, ws[14], p[16]); + word3_muladd(&w2, &w1, &w0, ws[15], p[15]); + word3_muladd(&w2, &w1, &w0, ws[16], p[14]); + word3_muladd(&w2, &w1, &w0, ws[17], p[13]); + word3_muladd(&w2, &w1, &w0, ws[18], p[12]); + word3_muladd(&w2, &w1, &w0, ws[19], p[11]); + word3_muladd(&w2, &w1, &w0, ws[20], p[10]); + word3_muladd(&w2, &w1, &w0, ws[21], p[9]); + word3_muladd(&w2, &w1, &w0, ws[22], p[8]); + word3_muladd(&w2, &w1, &w0, ws[23], p[7]); + word3_add(&w2, &w1, &w0, z[30]); + ws[6] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[8], p[23]); + word3_muladd(&w2, &w1, &w0, ws[9], p[22]); + word3_muladd(&w2, &w1, &w0, ws[10], p[21]); + word3_muladd(&w2, &w1, &w0, ws[11], p[20]); + word3_muladd(&w2, &w1, &w0, ws[12], p[19]); + word3_muladd(&w2, &w1, &w0, ws[13], p[18]); + word3_muladd(&w2, &w1, &w0, ws[14], p[17]); + word3_muladd(&w2, &w1, &w0, ws[15], p[16]); + word3_muladd(&w2, &w1, &w0, ws[16], p[15]); + word3_muladd(&w2, &w1, &w0, ws[17], p[14]); + word3_muladd(&w2, &w1, &w0, ws[18], p[13]); + word3_muladd(&w2, &w1, &w0, ws[19], p[12]); + word3_muladd(&w2, &w1, &w0, ws[20], p[11]); + word3_muladd(&w2, &w1, &w0, ws[21], p[10]); + word3_muladd(&w2, &w1, &w0, ws[22], p[9]); + word3_muladd(&w2, &w1, &w0, ws[23], p[8]); + word3_add(&w2, &w1, &w0, z[31]); + ws[7] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[9], p[23]); + word3_muladd(&w2, &w1, &w0, ws[10], p[22]); + word3_muladd(&w2, &w1, &w0, ws[11], p[21]); + word3_muladd(&w2, &w1, &w0, ws[12], p[20]); + word3_muladd(&w2, &w1, &w0, ws[13], p[19]); + word3_muladd(&w2, &w1, &w0, ws[14], p[18]); + word3_muladd(&w2, &w1, &w0, ws[15], p[17]); + word3_muladd(&w2, &w1, &w0, ws[16], p[16]); + word3_muladd(&w2, &w1, &w0, ws[17], p[15]); + word3_muladd(&w2, &w1, &w0, ws[18], p[14]); + word3_muladd(&w2, &w1, &w0, ws[19], p[13]); + word3_muladd(&w2, &w1, &w0, ws[20], p[12]); + word3_muladd(&w2, &w1, &w0, ws[21], p[11]); + word3_muladd(&w2, &w1, &w0, ws[22], p[10]); + word3_muladd(&w2, &w1, &w0, ws[23], p[9]); + word3_add(&w2, &w1, &w0, z[32]); + ws[8] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[10], p[23]); + word3_muladd(&w2, &w1, &w0, ws[11], p[22]); + word3_muladd(&w2, &w1, &w0, ws[12], p[21]); + word3_muladd(&w2, &w1, &w0, ws[13], p[20]); + word3_muladd(&w2, &w1, &w0, ws[14], p[19]); + word3_muladd(&w2, &w1, &w0, ws[15], p[18]); + word3_muladd(&w2, &w1, &w0, ws[16], p[17]); + word3_muladd(&w2, &w1, &w0, ws[17], p[16]); + word3_muladd(&w2, &w1, &w0, ws[18], p[15]); + word3_muladd(&w2, &w1, &w0, ws[19], p[14]); + word3_muladd(&w2, &w1, &w0, ws[20], p[13]); + word3_muladd(&w2, &w1, &w0, ws[21], p[12]); + word3_muladd(&w2, &w1, &w0, ws[22], p[11]); + word3_muladd(&w2, &w1, &w0, ws[23], p[10]); + word3_add(&w2, &w1, &w0, z[33]); + ws[9] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[11], p[23]); + word3_muladd(&w2, &w1, &w0, ws[12], p[22]); + word3_muladd(&w2, &w1, &w0, ws[13], p[21]); + word3_muladd(&w2, &w1, &w0, ws[14], p[20]); + word3_muladd(&w2, &w1, &w0, ws[15], p[19]); + word3_muladd(&w2, &w1, &w0, ws[16], p[18]); + word3_muladd(&w2, &w1, &w0, ws[17], p[17]); + word3_muladd(&w2, &w1, &w0, ws[18], p[16]); + word3_muladd(&w2, &w1, &w0, ws[19], p[15]); + word3_muladd(&w2, &w1, &w0, ws[20], p[14]); + word3_muladd(&w2, &w1, &w0, ws[21], p[13]); + word3_muladd(&w2, &w1, &w0, ws[22], p[12]); + word3_muladd(&w2, &w1, &w0, ws[23], p[11]); + word3_add(&w2, &w1, &w0, z[34]); + ws[10] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[12], p[23]); + word3_muladd(&w2, &w1, &w0, ws[13], p[22]); + word3_muladd(&w2, &w1, &w0, ws[14], p[21]); + word3_muladd(&w2, &w1, &w0, ws[15], p[20]); + word3_muladd(&w2, &w1, &w0, ws[16], p[19]); + word3_muladd(&w2, &w1, &w0, ws[17], p[18]); + word3_muladd(&w2, &w1, &w0, ws[18], p[17]); + word3_muladd(&w2, &w1, &w0, ws[19], p[16]); + word3_muladd(&w2, &w1, &w0, ws[20], p[15]); + word3_muladd(&w2, &w1, &w0, ws[21], p[14]); + word3_muladd(&w2, &w1, &w0, ws[22], p[13]); + word3_muladd(&w2, &w1, &w0, ws[23], p[12]); + word3_add(&w2, &w1, &w0, z[35]); + ws[11] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[13], p[23]); + word3_muladd(&w2, &w1, &w0, ws[14], p[22]); + word3_muladd(&w2, &w1, &w0, ws[15], p[21]); + word3_muladd(&w2, &w1, &w0, ws[16], p[20]); + word3_muladd(&w2, &w1, &w0, ws[17], p[19]); + word3_muladd(&w2, &w1, &w0, ws[18], p[18]); + word3_muladd(&w2, &w1, &w0, ws[19], p[17]); + word3_muladd(&w2, &w1, &w0, ws[20], p[16]); + word3_muladd(&w2, &w1, &w0, ws[21], p[15]); + word3_muladd(&w2, &w1, &w0, ws[22], p[14]); + word3_muladd(&w2, &w1, &w0, ws[23], p[13]); + word3_add(&w2, &w1, &w0, z[36]); + ws[12] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[14], p[23]); + word3_muladd(&w2, &w1, &w0, ws[15], p[22]); + word3_muladd(&w2, &w1, &w0, ws[16], p[21]); + word3_muladd(&w2, &w1, &w0, ws[17], p[20]); + word3_muladd(&w2, &w1, &w0, ws[18], p[19]); + word3_muladd(&w2, &w1, &w0, ws[19], p[18]); + word3_muladd(&w2, &w1, &w0, ws[20], p[17]); + word3_muladd(&w2, &w1, &w0, ws[21], p[16]); + word3_muladd(&w2, &w1, &w0, ws[22], p[15]); + word3_muladd(&w2, &w1, &w0, ws[23], p[14]); + word3_add(&w2, &w1, &w0, z[37]); + ws[13] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[15], p[23]); + word3_muladd(&w2, &w1, &w0, ws[16], p[22]); + word3_muladd(&w2, &w1, &w0, ws[17], p[21]); + word3_muladd(&w2, &w1, &w0, ws[18], p[20]); + word3_muladd(&w2, &w1, &w0, ws[19], p[19]); + word3_muladd(&w2, &w1, &w0, ws[20], p[18]); + word3_muladd(&w2, &w1, &w0, ws[21], p[17]); + word3_muladd(&w2, &w1, &w0, ws[22], p[16]); + word3_muladd(&w2, &w1, &w0, ws[23], p[15]); + word3_add(&w2, &w1, &w0, z[38]); + ws[14] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[16], p[23]); + word3_muladd(&w2, &w1, &w0, ws[17], p[22]); + word3_muladd(&w2, &w1, &w0, ws[18], p[21]); + word3_muladd(&w2, &w1, &w0, ws[19], p[20]); + word3_muladd(&w2, &w1, &w0, ws[20], p[19]); + word3_muladd(&w2, &w1, &w0, ws[21], p[18]); + word3_muladd(&w2, &w1, &w0, ws[22], p[17]); + word3_muladd(&w2, &w1, &w0, ws[23], p[16]); + word3_add(&w2, &w1, &w0, z[39]); + ws[15] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[17], p[23]); + word3_muladd(&w2, &w1, &w0, ws[18], p[22]); + word3_muladd(&w2, &w1, &w0, ws[19], p[21]); + word3_muladd(&w2, &w1, &w0, ws[20], p[20]); + word3_muladd(&w2, &w1, &w0, ws[21], p[19]); + word3_muladd(&w2, &w1, &w0, ws[22], p[18]); + word3_muladd(&w2, &w1, &w0, ws[23], p[17]); + word3_add(&w2, &w1, &w0, z[40]); + ws[16] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[18], p[23]); + word3_muladd(&w2, &w1, &w0, ws[19], p[22]); + word3_muladd(&w2, &w1, &w0, ws[20], p[21]); + word3_muladd(&w2, &w1, &w0, ws[21], p[20]); + word3_muladd(&w2, &w1, &w0, ws[22], p[19]); + word3_muladd(&w2, &w1, &w0, ws[23], p[18]); + word3_add(&w2, &w1, &w0, z[41]); + ws[17] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[19], p[23]); + word3_muladd(&w2, &w1, &w0, ws[20], p[22]); + word3_muladd(&w2, &w1, &w0, ws[21], p[21]); + word3_muladd(&w2, &w1, &w0, ws[22], p[20]); + word3_muladd(&w2, &w1, &w0, ws[23], p[19]); + word3_add(&w2, &w1, &w0, z[42]); + ws[18] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[20], p[23]); + word3_muladd(&w2, &w1, &w0, ws[21], p[22]); + word3_muladd(&w2, &w1, &w0, ws[22], p[21]); + word3_muladd(&w2, &w1, &w0, ws[23], p[20]); + word3_add(&w2, &w1, &w0, z[43]); + ws[19] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[21], p[23]); + word3_muladd(&w2, &w1, &w0, ws[22], p[22]); + word3_muladd(&w2, &w1, &w0, ws[23], p[21]); + word3_add(&w2, &w1, &w0, z[44]); + ws[20] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[22], p[23]); + word3_muladd(&w2, &w1, &w0, ws[23], p[22]); + word3_add(&w2, &w1, &w0, z[45]); + ws[21] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[23], p[23]); + word3_add(&w2, &w1, &w0, z[46]); + ws[22] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[47]); + ws[23] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[49]); + ws[24] = w0; + ws[25] = w1; + word borrow = bigint_sub3(ws + 24 + 1, ws, 24 + 1, p, 24); + CT::conditional_copy_mem(borrow, z, ws, ws + 25, 25); + clear_mem(z + 24, 2*(24+1) - 24); + } + +void bigint_monty_redc_32(word z[], const word p[32], word p_dash, word ws[]) + { + word w2 = 0, w1 = 0, w0 = 0; + w0 = z[0]; + ws[0] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[0], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[1]); + word3_add(&w2, &w1, &w0, z[1]); + ws[1] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[1], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[2]); + word3_muladd(&w2, &w1, &w0, ws[1], p[1]); + word3_add(&w2, &w1, &w0, z[2]); + ws[2] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[2], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[3]); + word3_muladd(&w2, &w1, &w0, ws[1], p[2]); + word3_muladd(&w2, &w1, &w0, ws[2], p[1]); + word3_add(&w2, &w1, &w0, z[3]); + ws[3] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[3], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[4]); + word3_muladd(&w2, &w1, &w0, ws[1], p[3]); + word3_muladd(&w2, &w1, &w0, ws[2], p[2]); + word3_muladd(&w2, &w1, &w0, ws[3], p[1]); + word3_add(&w2, &w1, &w0, z[4]); + ws[4] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[4], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[5]); + word3_muladd(&w2, &w1, &w0, ws[1], p[4]); + word3_muladd(&w2, &w1, &w0, ws[2], p[3]); + word3_muladd(&w2, &w1, &w0, ws[3], p[2]); + word3_muladd(&w2, &w1, &w0, ws[4], p[1]); + word3_add(&w2, &w1, &w0, z[5]); + ws[5] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[5], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[6]); + word3_muladd(&w2, &w1, &w0, ws[1], p[5]); + word3_muladd(&w2, &w1, &w0, ws[2], p[4]); + word3_muladd(&w2, &w1, &w0, ws[3], p[3]); + word3_muladd(&w2, &w1, &w0, ws[4], p[2]); + word3_muladd(&w2, &w1, &w0, ws[5], p[1]); + word3_add(&w2, &w1, &w0, z[6]); + ws[6] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[6], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[7]); + word3_muladd(&w2, &w1, &w0, ws[1], p[6]); + word3_muladd(&w2, &w1, &w0, ws[2], p[5]); + word3_muladd(&w2, &w1, &w0, ws[3], p[4]); + word3_muladd(&w2, &w1, &w0, ws[4], p[3]); + word3_muladd(&w2, &w1, &w0, ws[5], p[2]); + word3_muladd(&w2, &w1, &w0, ws[6], p[1]); + word3_add(&w2, &w1, &w0, z[7]); + ws[7] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[7], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[8]); + word3_muladd(&w2, &w1, &w0, ws[1], p[7]); + word3_muladd(&w2, &w1, &w0, ws[2], p[6]); + word3_muladd(&w2, &w1, &w0, ws[3], p[5]); + word3_muladd(&w2, &w1, &w0, ws[4], p[4]); + word3_muladd(&w2, &w1, &w0, ws[5], p[3]); + word3_muladd(&w2, &w1, &w0, ws[6], p[2]); + word3_muladd(&w2, &w1, &w0, ws[7], p[1]); + word3_add(&w2, &w1, &w0, z[8]); + ws[8] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[8], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[9]); + word3_muladd(&w2, &w1, &w0, ws[1], p[8]); + word3_muladd(&w2, &w1, &w0, ws[2], p[7]); + word3_muladd(&w2, &w1, &w0, ws[3], p[6]); + word3_muladd(&w2, &w1, &w0, ws[4], p[5]); + word3_muladd(&w2, &w1, &w0, ws[5], p[4]); + word3_muladd(&w2, &w1, &w0, ws[6], p[3]); + word3_muladd(&w2, &w1, &w0, ws[7], p[2]); + word3_muladd(&w2, &w1, &w0, ws[8], p[1]); + word3_add(&w2, &w1, &w0, z[9]); + ws[9] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[9], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[10]); + word3_muladd(&w2, &w1, &w0, ws[1], p[9]); + word3_muladd(&w2, &w1, &w0, ws[2], p[8]); + word3_muladd(&w2, &w1, &w0, ws[3], p[7]); + word3_muladd(&w2, &w1, &w0, ws[4], p[6]); + word3_muladd(&w2, &w1, &w0, ws[5], p[5]); + word3_muladd(&w2, &w1, &w0, ws[6], p[4]); + word3_muladd(&w2, &w1, &w0, ws[7], p[3]); + word3_muladd(&w2, &w1, &w0, ws[8], p[2]); + word3_muladd(&w2, &w1, &w0, ws[9], p[1]); + word3_add(&w2, &w1, &w0, z[10]); + ws[10] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[10], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[11]); + word3_muladd(&w2, &w1, &w0, ws[1], p[10]); + word3_muladd(&w2, &w1, &w0, ws[2], p[9]); + word3_muladd(&w2, &w1, &w0, ws[3], p[8]); + word3_muladd(&w2, &w1, &w0, ws[4], p[7]); + word3_muladd(&w2, &w1, &w0, ws[5], p[6]); + word3_muladd(&w2, &w1, &w0, ws[6], p[5]); + word3_muladd(&w2, &w1, &w0, ws[7], p[4]); + word3_muladd(&w2, &w1, &w0, ws[8], p[3]); + word3_muladd(&w2, &w1, &w0, ws[9], p[2]); + word3_muladd(&w2, &w1, &w0, ws[10], p[1]); + word3_add(&w2, &w1, &w0, z[11]); + ws[11] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[11], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[12]); + word3_muladd(&w2, &w1, &w0, ws[1], p[11]); + word3_muladd(&w2, &w1, &w0, ws[2], p[10]); + word3_muladd(&w2, &w1, &w0, ws[3], p[9]); + word3_muladd(&w2, &w1, &w0, ws[4], p[8]); + word3_muladd(&w2, &w1, &w0, ws[5], p[7]); + word3_muladd(&w2, &w1, &w0, ws[6], p[6]); + word3_muladd(&w2, &w1, &w0, ws[7], p[5]); + word3_muladd(&w2, &w1, &w0, ws[8], p[4]); + word3_muladd(&w2, &w1, &w0, ws[9], p[3]); + word3_muladd(&w2, &w1, &w0, ws[10], p[2]); + word3_muladd(&w2, &w1, &w0, ws[11], p[1]); + word3_add(&w2, &w1, &w0, z[12]); + ws[12] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[12], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[13]); + word3_muladd(&w2, &w1, &w0, ws[1], p[12]); + word3_muladd(&w2, &w1, &w0, ws[2], p[11]); + word3_muladd(&w2, &w1, &w0, ws[3], p[10]); + word3_muladd(&w2, &w1, &w0, ws[4], p[9]); + word3_muladd(&w2, &w1, &w0, ws[5], p[8]); + word3_muladd(&w2, &w1, &w0, ws[6], p[7]); + word3_muladd(&w2, &w1, &w0, ws[7], p[6]); + word3_muladd(&w2, &w1, &w0, ws[8], p[5]); + word3_muladd(&w2, &w1, &w0, ws[9], p[4]); + word3_muladd(&w2, &w1, &w0, ws[10], p[3]); + word3_muladd(&w2, &w1, &w0, ws[11], p[2]); + word3_muladd(&w2, &w1, &w0, ws[12], p[1]); + word3_add(&w2, &w1, &w0, z[13]); + ws[13] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[13], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[14]); + word3_muladd(&w2, &w1, &w0, ws[1], p[13]); + word3_muladd(&w2, &w1, &w0, ws[2], p[12]); + word3_muladd(&w2, &w1, &w0, ws[3], p[11]); + word3_muladd(&w2, &w1, &w0, ws[4], p[10]); + word3_muladd(&w2, &w1, &w0, ws[5], p[9]); + word3_muladd(&w2, &w1, &w0, ws[6], p[8]); + word3_muladd(&w2, &w1, &w0, ws[7], p[7]); + word3_muladd(&w2, &w1, &w0, ws[8], p[6]); + word3_muladd(&w2, &w1, &w0, ws[9], p[5]); + word3_muladd(&w2, &w1, &w0, ws[10], p[4]); + word3_muladd(&w2, &w1, &w0, ws[11], p[3]); + word3_muladd(&w2, &w1, &w0, ws[12], p[2]); + word3_muladd(&w2, &w1, &w0, ws[13], p[1]); + word3_add(&w2, &w1, &w0, z[14]); + ws[14] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[14], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[15]); + word3_muladd(&w2, &w1, &w0, ws[1], p[14]); + word3_muladd(&w2, &w1, &w0, ws[2], p[13]); + word3_muladd(&w2, &w1, &w0, ws[3], p[12]); + word3_muladd(&w2, &w1, &w0, ws[4], p[11]); + word3_muladd(&w2, &w1, &w0, ws[5], p[10]); + word3_muladd(&w2, &w1, &w0, ws[6], p[9]); + word3_muladd(&w2, &w1, &w0, ws[7], p[8]); + word3_muladd(&w2, &w1, &w0, ws[8], p[7]); + word3_muladd(&w2, &w1, &w0, ws[9], p[6]); + word3_muladd(&w2, &w1, &w0, ws[10], p[5]); + word3_muladd(&w2, &w1, &w0, ws[11], p[4]); + word3_muladd(&w2, &w1, &w0, ws[12], p[3]); + word3_muladd(&w2, &w1, &w0, ws[13], p[2]); + word3_muladd(&w2, &w1, &w0, ws[14], p[1]); + word3_add(&w2, &w1, &w0, z[15]); + ws[15] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[15], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[16]); + word3_muladd(&w2, &w1, &w0, ws[1], p[15]); + word3_muladd(&w2, &w1, &w0, ws[2], p[14]); + word3_muladd(&w2, &w1, &w0, ws[3], p[13]); + word3_muladd(&w2, &w1, &w0, ws[4], p[12]); + word3_muladd(&w2, &w1, &w0, ws[5], p[11]); + word3_muladd(&w2, &w1, &w0, ws[6], p[10]); + word3_muladd(&w2, &w1, &w0, ws[7], p[9]); + word3_muladd(&w2, &w1, &w0, ws[8], p[8]); + word3_muladd(&w2, &w1, &w0, ws[9], p[7]); + word3_muladd(&w2, &w1, &w0, ws[10], p[6]); + word3_muladd(&w2, &w1, &w0, ws[11], p[5]); + word3_muladd(&w2, &w1, &w0, ws[12], p[4]); + word3_muladd(&w2, &w1, &w0, ws[13], p[3]); + word3_muladd(&w2, &w1, &w0, ws[14], p[2]); + word3_muladd(&w2, &w1, &w0, ws[15], p[1]); + word3_add(&w2, &w1, &w0, z[16]); + ws[16] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[16], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[17]); + word3_muladd(&w2, &w1, &w0, ws[1], p[16]); + word3_muladd(&w2, &w1, &w0, ws[2], p[15]); + word3_muladd(&w2, &w1, &w0, ws[3], p[14]); + word3_muladd(&w2, &w1, &w0, ws[4], p[13]); + word3_muladd(&w2, &w1, &w0, ws[5], p[12]); + word3_muladd(&w2, &w1, &w0, ws[6], p[11]); + word3_muladd(&w2, &w1, &w0, ws[7], p[10]); + word3_muladd(&w2, &w1, &w0, ws[8], p[9]); + word3_muladd(&w2, &w1, &w0, ws[9], p[8]); + word3_muladd(&w2, &w1, &w0, ws[10], p[7]); + word3_muladd(&w2, &w1, &w0, ws[11], p[6]); + word3_muladd(&w2, &w1, &w0, ws[12], p[5]); + word3_muladd(&w2, &w1, &w0, ws[13], p[4]); + word3_muladd(&w2, &w1, &w0, ws[14], p[3]); + word3_muladd(&w2, &w1, &w0, ws[15], p[2]); + word3_muladd(&w2, &w1, &w0, ws[16], p[1]); + word3_add(&w2, &w1, &w0, z[17]); + ws[17] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[17], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[18]); + word3_muladd(&w2, &w1, &w0, ws[1], p[17]); + word3_muladd(&w2, &w1, &w0, ws[2], p[16]); + word3_muladd(&w2, &w1, &w0, ws[3], p[15]); + word3_muladd(&w2, &w1, &w0, ws[4], p[14]); + word3_muladd(&w2, &w1, &w0, ws[5], p[13]); + word3_muladd(&w2, &w1, &w0, ws[6], p[12]); + word3_muladd(&w2, &w1, &w0, ws[7], p[11]); + word3_muladd(&w2, &w1, &w0, ws[8], p[10]); + word3_muladd(&w2, &w1, &w0, ws[9], p[9]); + word3_muladd(&w2, &w1, &w0, ws[10], p[8]); + word3_muladd(&w2, &w1, &w0, ws[11], p[7]); + word3_muladd(&w2, &w1, &w0, ws[12], p[6]); + word3_muladd(&w2, &w1, &w0, ws[13], p[5]); + word3_muladd(&w2, &w1, &w0, ws[14], p[4]); + word3_muladd(&w2, &w1, &w0, ws[15], p[3]); + word3_muladd(&w2, &w1, &w0, ws[16], p[2]); + word3_muladd(&w2, &w1, &w0, ws[17], p[1]); + word3_add(&w2, &w1, &w0, z[18]); + ws[18] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[18], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[19]); + word3_muladd(&w2, &w1, &w0, ws[1], p[18]); + word3_muladd(&w2, &w1, &w0, ws[2], p[17]); + word3_muladd(&w2, &w1, &w0, ws[3], p[16]); + word3_muladd(&w2, &w1, &w0, ws[4], p[15]); + word3_muladd(&w2, &w1, &w0, ws[5], p[14]); + word3_muladd(&w2, &w1, &w0, ws[6], p[13]); + word3_muladd(&w2, &w1, &w0, ws[7], p[12]); + word3_muladd(&w2, &w1, &w0, ws[8], p[11]); + word3_muladd(&w2, &w1, &w0, ws[9], p[10]); + word3_muladd(&w2, &w1, &w0, ws[10], p[9]); + word3_muladd(&w2, &w1, &w0, ws[11], p[8]); + word3_muladd(&w2, &w1, &w0, ws[12], p[7]); + word3_muladd(&w2, &w1, &w0, ws[13], p[6]); + word3_muladd(&w2, &w1, &w0, ws[14], p[5]); + word3_muladd(&w2, &w1, &w0, ws[15], p[4]); + word3_muladd(&w2, &w1, &w0, ws[16], p[3]); + word3_muladd(&w2, &w1, &w0, ws[17], p[2]); + word3_muladd(&w2, &w1, &w0, ws[18], p[1]); + word3_add(&w2, &w1, &w0, z[19]); + ws[19] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[19], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[20]); + word3_muladd(&w2, &w1, &w0, ws[1], p[19]); + word3_muladd(&w2, &w1, &w0, ws[2], p[18]); + word3_muladd(&w2, &w1, &w0, ws[3], p[17]); + word3_muladd(&w2, &w1, &w0, ws[4], p[16]); + word3_muladd(&w2, &w1, &w0, ws[5], p[15]); + word3_muladd(&w2, &w1, &w0, ws[6], p[14]); + word3_muladd(&w2, &w1, &w0, ws[7], p[13]); + word3_muladd(&w2, &w1, &w0, ws[8], p[12]); + word3_muladd(&w2, &w1, &w0, ws[9], p[11]); + word3_muladd(&w2, &w1, &w0, ws[10], p[10]); + word3_muladd(&w2, &w1, &w0, ws[11], p[9]); + word3_muladd(&w2, &w1, &w0, ws[12], p[8]); + word3_muladd(&w2, &w1, &w0, ws[13], p[7]); + word3_muladd(&w2, &w1, &w0, ws[14], p[6]); + word3_muladd(&w2, &w1, &w0, ws[15], p[5]); + word3_muladd(&w2, &w1, &w0, ws[16], p[4]); + word3_muladd(&w2, &w1, &w0, ws[17], p[3]); + word3_muladd(&w2, &w1, &w0, ws[18], p[2]); + word3_muladd(&w2, &w1, &w0, ws[19], p[1]); + word3_add(&w2, &w1, &w0, z[20]); + ws[20] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[20], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[21]); + word3_muladd(&w2, &w1, &w0, ws[1], p[20]); + word3_muladd(&w2, &w1, &w0, ws[2], p[19]); + word3_muladd(&w2, &w1, &w0, ws[3], p[18]); + word3_muladd(&w2, &w1, &w0, ws[4], p[17]); + word3_muladd(&w2, &w1, &w0, ws[5], p[16]); + word3_muladd(&w2, &w1, &w0, ws[6], p[15]); + word3_muladd(&w2, &w1, &w0, ws[7], p[14]); + word3_muladd(&w2, &w1, &w0, ws[8], p[13]); + word3_muladd(&w2, &w1, &w0, ws[9], p[12]); + word3_muladd(&w2, &w1, &w0, ws[10], p[11]); + word3_muladd(&w2, &w1, &w0, ws[11], p[10]); + word3_muladd(&w2, &w1, &w0, ws[12], p[9]); + word3_muladd(&w2, &w1, &w0, ws[13], p[8]); + word3_muladd(&w2, &w1, &w0, ws[14], p[7]); + word3_muladd(&w2, &w1, &w0, ws[15], p[6]); + word3_muladd(&w2, &w1, &w0, ws[16], p[5]); + word3_muladd(&w2, &w1, &w0, ws[17], p[4]); + word3_muladd(&w2, &w1, &w0, ws[18], p[3]); + word3_muladd(&w2, &w1, &w0, ws[19], p[2]); + word3_muladd(&w2, &w1, &w0, ws[20], p[1]); + word3_add(&w2, &w1, &w0, z[21]); + ws[21] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[21], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[22]); + word3_muladd(&w2, &w1, &w0, ws[1], p[21]); + word3_muladd(&w2, &w1, &w0, ws[2], p[20]); + word3_muladd(&w2, &w1, &w0, ws[3], p[19]); + word3_muladd(&w2, &w1, &w0, ws[4], p[18]); + word3_muladd(&w2, &w1, &w0, ws[5], p[17]); + word3_muladd(&w2, &w1, &w0, ws[6], p[16]); + word3_muladd(&w2, &w1, &w0, ws[7], p[15]); + word3_muladd(&w2, &w1, &w0, ws[8], p[14]); + word3_muladd(&w2, &w1, &w0, ws[9], p[13]); + word3_muladd(&w2, &w1, &w0, ws[10], p[12]); + word3_muladd(&w2, &w1, &w0, ws[11], p[11]); + word3_muladd(&w2, &w1, &w0, ws[12], p[10]); + word3_muladd(&w2, &w1, &w0, ws[13], p[9]); + word3_muladd(&w2, &w1, &w0, ws[14], p[8]); + word3_muladd(&w2, &w1, &w0, ws[15], p[7]); + word3_muladd(&w2, &w1, &w0, ws[16], p[6]); + word3_muladd(&w2, &w1, &w0, ws[17], p[5]); + word3_muladd(&w2, &w1, &w0, ws[18], p[4]); + word3_muladd(&w2, &w1, &w0, ws[19], p[3]); + word3_muladd(&w2, &w1, &w0, ws[20], p[2]); + word3_muladd(&w2, &w1, &w0, ws[21], p[1]); + word3_add(&w2, &w1, &w0, z[22]); + ws[22] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[22], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[23]); + word3_muladd(&w2, &w1, &w0, ws[1], p[22]); + word3_muladd(&w2, &w1, &w0, ws[2], p[21]); + word3_muladd(&w2, &w1, &w0, ws[3], p[20]); + word3_muladd(&w2, &w1, &w0, ws[4], p[19]); + word3_muladd(&w2, &w1, &w0, ws[5], p[18]); + word3_muladd(&w2, &w1, &w0, ws[6], p[17]); + word3_muladd(&w2, &w1, &w0, ws[7], p[16]); + word3_muladd(&w2, &w1, &w0, ws[8], p[15]); + word3_muladd(&w2, &w1, &w0, ws[9], p[14]); + word3_muladd(&w2, &w1, &w0, ws[10], p[13]); + word3_muladd(&w2, &w1, &w0, ws[11], p[12]); + word3_muladd(&w2, &w1, &w0, ws[12], p[11]); + word3_muladd(&w2, &w1, &w0, ws[13], p[10]); + word3_muladd(&w2, &w1, &w0, ws[14], p[9]); + word3_muladd(&w2, &w1, &w0, ws[15], p[8]); + word3_muladd(&w2, &w1, &w0, ws[16], p[7]); + word3_muladd(&w2, &w1, &w0, ws[17], p[6]); + word3_muladd(&w2, &w1, &w0, ws[18], p[5]); + word3_muladd(&w2, &w1, &w0, ws[19], p[4]); + word3_muladd(&w2, &w1, &w0, ws[20], p[3]); + word3_muladd(&w2, &w1, &w0, ws[21], p[2]); + word3_muladd(&w2, &w1, &w0, ws[22], p[1]); + word3_add(&w2, &w1, &w0, z[23]); + ws[23] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[23], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[24]); + word3_muladd(&w2, &w1, &w0, ws[1], p[23]); + word3_muladd(&w2, &w1, &w0, ws[2], p[22]); + word3_muladd(&w2, &w1, &w0, ws[3], p[21]); + word3_muladd(&w2, &w1, &w0, ws[4], p[20]); + word3_muladd(&w2, &w1, &w0, ws[5], p[19]); + word3_muladd(&w2, &w1, &w0, ws[6], p[18]); + word3_muladd(&w2, &w1, &w0, ws[7], p[17]); + word3_muladd(&w2, &w1, &w0, ws[8], p[16]); + word3_muladd(&w2, &w1, &w0, ws[9], p[15]); + word3_muladd(&w2, &w1, &w0, ws[10], p[14]); + word3_muladd(&w2, &w1, &w0, ws[11], p[13]); + word3_muladd(&w2, &w1, &w0, ws[12], p[12]); + word3_muladd(&w2, &w1, &w0, ws[13], p[11]); + word3_muladd(&w2, &w1, &w0, ws[14], p[10]); + word3_muladd(&w2, &w1, &w0, ws[15], p[9]); + word3_muladd(&w2, &w1, &w0, ws[16], p[8]); + word3_muladd(&w2, &w1, &w0, ws[17], p[7]); + word3_muladd(&w2, &w1, &w0, ws[18], p[6]); + word3_muladd(&w2, &w1, &w0, ws[19], p[5]); + word3_muladd(&w2, &w1, &w0, ws[20], p[4]); + word3_muladd(&w2, &w1, &w0, ws[21], p[3]); + word3_muladd(&w2, &w1, &w0, ws[22], p[2]); + word3_muladd(&w2, &w1, &w0, ws[23], p[1]); + word3_add(&w2, &w1, &w0, z[24]); + ws[24] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[24], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[25]); + word3_muladd(&w2, &w1, &w0, ws[1], p[24]); + word3_muladd(&w2, &w1, &w0, ws[2], p[23]); + word3_muladd(&w2, &w1, &w0, ws[3], p[22]); + word3_muladd(&w2, &w1, &w0, ws[4], p[21]); + word3_muladd(&w2, &w1, &w0, ws[5], p[20]); + word3_muladd(&w2, &w1, &w0, ws[6], p[19]); + word3_muladd(&w2, &w1, &w0, ws[7], p[18]); + word3_muladd(&w2, &w1, &w0, ws[8], p[17]); + word3_muladd(&w2, &w1, &w0, ws[9], p[16]); + word3_muladd(&w2, &w1, &w0, ws[10], p[15]); + word3_muladd(&w2, &w1, &w0, ws[11], p[14]); + word3_muladd(&w2, &w1, &w0, ws[12], p[13]); + word3_muladd(&w2, &w1, &w0, ws[13], p[12]); + word3_muladd(&w2, &w1, &w0, ws[14], p[11]); + word3_muladd(&w2, &w1, &w0, ws[15], p[10]); + word3_muladd(&w2, &w1, &w0, ws[16], p[9]); + word3_muladd(&w2, &w1, &w0, ws[17], p[8]); + word3_muladd(&w2, &w1, &w0, ws[18], p[7]); + word3_muladd(&w2, &w1, &w0, ws[19], p[6]); + word3_muladd(&w2, &w1, &w0, ws[20], p[5]); + word3_muladd(&w2, &w1, &w0, ws[21], p[4]); + word3_muladd(&w2, &w1, &w0, ws[22], p[3]); + word3_muladd(&w2, &w1, &w0, ws[23], p[2]); + word3_muladd(&w2, &w1, &w0, ws[24], p[1]); + word3_add(&w2, &w1, &w0, z[25]); + ws[25] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[25], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[26]); + word3_muladd(&w2, &w1, &w0, ws[1], p[25]); + word3_muladd(&w2, &w1, &w0, ws[2], p[24]); + word3_muladd(&w2, &w1, &w0, ws[3], p[23]); + word3_muladd(&w2, &w1, &w0, ws[4], p[22]); + word3_muladd(&w2, &w1, &w0, ws[5], p[21]); + word3_muladd(&w2, &w1, &w0, ws[6], p[20]); + word3_muladd(&w2, &w1, &w0, ws[7], p[19]); + word3_muladd(&w2, &w1, &w0, ws[8], p[18]); + word3_muladd(&w2, &w1, &w0, ws[9], p[17]); + word3_muladd(&w2, &w1, &w0, ws[10], p[16]); + word3_muladd(&w2, &w1, &w0, ws[11], p[15]); + word3_muladd(&w2, &w1, &w0, ws[12], p[14]); + word3_muladd(&w2, &w1, &w0, ws[13], p[13]); + word3_muladd(&w2, &w1, &w0, ws[14], p[12]); + word3_muladd(&w2, &w1, &w0, ws[15], p[11]); + word3_muladd(&w2, &w1, &w0, ws[16], p[10]); + word3_muladd(&w2, &w1, &w0, ws[17], p[9]); + word3_muladd(&w2, &w1, &w0, ws[18], p[8]); + word3_muladd(&w2, &w1, &w0, ws[19], p[7]); + word3_muladd(&w2, &w1, &w0, ws[20], p[6]); + word3_muladd(&w2, &w1, &w0, ws[21], p[5]); + word3_muladd(&w2, &w1, &w0, ws[22], p[4]); + word3_muladd(&w2, &w1, &w0, ws[23], p[3]); + word3_muladd(&w2, &w1, &w0, ws[24], p[2]); + word3_muladd(&w2, &w1, &w0, ws[25], p[1]); + word3_add(&w2, &w1, &w0, z[26]); + ws[26] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[26], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[27]); + word3_muladd(&w2, &w1, &w0, ws[1], p[26]); + word3_muladd(&w2, &w1, &w0, ws[2], p[25]); + word3_muladd(&w2, &w1, &w0, ws[3], p[24]); + word3_muladd(&w2, &w1, &w0, ws[4], p[23]); + word3_muladd(&w2, &w1, &w0, ws[5], p[22]); + word3_muladd(&w2, &w1, &w0, ws[6], p[21]); + word3_muladd(&w2, &w1, &w0, ws[7], p[20]); + word3_muladd(&w2, &w1, &w0, ws[8], p[19]); + word3_muladd(&w2, &w1, &w0, ws[9], p[18]); + word3_muladd(&w2, &w1, &w0, ws[10], p[17]); + word3_muladd(&w2, &w1, &w0, ws[11], p[16]); + word3_muladd(&w2, &w1, &w0, ws[12], p[15]); + word3_muladd(&w2, &w1, &w0, ws[13], p[14]); + word3_muladd(&w2, &w1, &w0, ws[14], p[13]); + word3_muladd(&w2, &w1, &w0, ws[15], p[12]); + word3_muladd(&w2, &w1, &w0, ws[16], p[11]); + word3_muladd(&w2, &w1, &w0, ws[17], p[10]); + word3_muladd(&w2, &w1, &w0, ws[18], p[9]); + word3_muladd(&w2, &w1, &w0, ws[19], p[8]); + word3_muladd(&w2, &w1, &w0, ws[20], p[7]); + word3_muladd(&w2, &w1, &w0, ws[21], p[6]); + word3_muladd(&w2, &w1, &w0, ws[22], p[5]); + word3_muladd(&w2, &w1, &w0, ws[23], p[4]); + word3_muladd(&w2, &w1, &w0, ws[24], p[3]); + word3_muladd(&w2, &w1, &w0, ws[25], p[2]); + word3_muladd(&w2, &w1, &w0, ws[26], p[1]); + word3_add(&w2, &w1, &w0, z[27]); + ws[27] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[27], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[28]); + word3_muladd(&w2, &w1, &w0, ws[1], p[27]); + word3_muladd(&w2, &w1, &w0, ws[2], p[26]); + word3_muladd(&w2, &w1, &w0, ws[3], p[25]); + word3_muladd(&w2, &w1, &w0, ws[4], p[24]); + word3_muladd(&w2, &w1, &w0, ws[5], p[23]); + word3_muladd(&w2, &w1, &w0, ws[6], p[22]); + word3_muladd(&w2, &w1, &w0, ws[7], p[21]); + word3_muladd(&w2, &w1, &w0, ws[8], p[20]); + word3_muladd(&w2, &w1, &w0, ws[9], p[19]); + word3_muladd(&w2, &w1, &w0, ws[10], p[18]); + word3_muladd(&w2, &w1, &w0, ws[11], p[17]); + word3_muladd(&w2, &w1, &w0, ws[12], p[16]); + word3_muladd(&w2, &w1, &w0, ws[13], p[15]); + word3_muladd(&w2, &w1, &w0, ws[14], p[14]); + word3_muladd(&w2, &w1, &w0, ws[15], p[13]); + word3_muladd(&w2, &w1, &w0, ws[16], p[12]); + word3_muladd(&w2, &w1, &w0, ws[17], p[11]); + word3_muladd(&w2, &w1, &w0, ws[18], p[10]); + word3_muladd(&w2, &w1, &w0, ws[19], p[9]); + word3_muladd(&w2, &w1, &w0, ws[20], p[8]); + word3_muladd(&w2, &w1, &w0, ws[21], p[7]); + word3_muladd(&w2, &w1, &w0, ws[22], p[6]); + word3_muladd(&w2, &w1, &w0, ws[23], p[5]); + word3_muladd(&w2, &w1, &w0, ws[24], p[4]); + word3_muladd(&w2, &w1, &w0, ws[25], p[3]); + word3_muladd(&w2, &w1, &w0, ws[26], p[2]); + word3_muladd(&w2, &w1, &w0, ws[27], p[1]); + word3_add(&w2, &w1, &w0, z[28]); + ws[28] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[28], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[29]); + word3_muladd(&w2, &w1, &w0, ws[1], p[28]); + word3_muladd(&w2, &w1, &w0, ws[2], p[27]); + word3_muladd(&w2, &w1, &w0, ws[3], p[26]); + word3_muladd(&w2, &w1, &w0, ws[4], p[25]); + word3_muladd(&w2, &w1, &w0, ws[5], p[24]); + word3_muladd(&w2, &w1, &w0, ws[6], p[23]); + word3_muladd(&w2, &w1, &w0, ws[7], p[22]); + word3_muladd(&w2, &w1, &w0, ws[8], p[21]); + word3_muladd(&w2, &w1, &w0, ws[9], p[20]); + word3_muladd(&w2, &w1, &w0, ws[10], p[19]); + word3_muladd(&w2, &w1, &w0, ws[11], p[18]); + word3_muladd(&w2, &w1, &w0, ws[12], p[17]); + word3_muladd(&w2, &w1, &w0, ws[13], p[16]); + word3_muladd(&w2, &w1, &w0, ws[14], p[15]); + word3_muladd(&w2, &w1, &w0, ws[15], p[14]); + word3_muladd(&w2, &w1, &w0, ws[16], p[13]); + word3_muladd(&w2, &w1, &w0, ws[17], p[12]); + word3_muladd(&w2, &w1, &w0, ws[18], p[11]); + word3_muladd(&w2, &w1, &w0, ws[19], p[10]); + word3_muladd(&w2, &w1, &w0, ws[20], p[9]); + word3_muladd(&w2, &w1, &w0, ws[21], p[8]); + word3_muladd(&w2, &w1, &w0, ws[22], p[7]); + word3_muladd(&w2, &w1, &w0, ws[23], p[6]); + word3_muladd(&w2, &w1, &w0, ws[24], p[5]); + word3_muladd(&w2, &w1, &w0, ws[25], p[4]); + word3_muladd(&w2, &w1, &w0, ws[26], p[3]); + word3_muladd(&w2, &w1, &w0, ws[27], p[2]); + word3_muladd(&w2, &w1, &w0, ws[28], p[1]); + word3_add(&w2, &w1, &w0, z[29]); + ws[29] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[29], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[30]); + word3_muladd(&w2, &w1, &w0, ws[1], p[29]); + word3_muladd(&w2, &w1, &w0, ws[2], p[28]); + word3_muladd(&w2, &w1, &w0, ws[3], p[27]); + word3_muladd(&w2, &w1, &w0, ws[4], p[26]); + word3_muladd(&w2, &w1, &w0, ws[5], p[25]); + word3_muladd(&w2, &w1, &w0, ws[6], p[24]); + word3_muladd(&w2, &w1, &w0, ws[7], p[23]); + word3_muladd(&w2, &w1, &w0, ws[8], p[22]); + word3_muladd(&w2, &w1, &w0, ws[9], p[21]); + word3_muladd(&w2, &w1, &w0, ws[10], p[20]); + word3_muladd(&w2, &w1, &w0, ws[11], p[19]); + word3_muladd(&w2, &w1, &w0, ws[12], p[18]); + word3_muladd(&w2, &w1, &w0, ws[13], p[17]); + word3_muladd(&w2, &w1, &w0, ws[14], p[16]); + word3_muladd(&w2, &w1, &w0, ws[15], p[15]); + word3_muladd(&w2, &w1, &w0, ws[16], p[14]); + word3_muladd(&w2, &w1, &w0, ws[17], p[13]); + word3_muladd(&w2, &w1, &w0, ws[18], p[12]); + word3_muladd(&w2, &w1, &w0, ws[19], p[11]); + word3_muladd(&w2, &w1, &w0, ws[20], p[10]); + word3_muladd(&w2, &w1, &w0, ws[21], p[9]); + word3_muladd(&w2, &w1, &w0, ws[22], p[8]); + word3_muladd(&w2, &w1, &w0, ws[23], p[7]); + word3_muladd(&w2, &w1, &w0, ws[24], p[6]); + word3_muladd(&w2, &w1, &w0, ws[25], p[5]); + word3_muladd(&w2, &w1, &w0, ws[26], p[4]); + word3_muladd(&w2, &w1, &w0, ws[27], p[3]); + word3_muladd(&w2, &w1, &w0, ws[28], p[2]); + word3_muladd(&w2, &w1, &w0, ws[29], p[1]); + word3_add(&w2, &w1, &w0, z[30]); + ws[30] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[30], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[0], p[31]); + word3_muladd(&w2, &w1, &w0, ws[1], p[30]); + word3_muladd(&w2, &w1, &w0, ws[2], p[29]); + word3_muladd(&w2, &w1, &w0, ws[3], p[28]); + word3_muladd(&w2, &w1, &w0, ws[4], p[27]); + word3_muladd(&w2, &w1, &w0, ws[5], p[26]); + word3_muladd(&w2, &w1, &w0, ws[6], p[25]); + word3_muladd(&w2, &w1, &w0, ws[7], p[24]); + word3_muladd(&w2, &w1, &w0, ws[8], p[23]); + word3_muladd(&w2, &w1, &w0, ws[9], p[22]); + word3_muladd(&w2, &w1, &w0, ws[10], p[21]); + word3_muladd(&w2, &w1, &w0, ws[11], p[20]); + word3_muladd(&w2, &w1, &w0, ws[12], p[19]); + word3_muladd(&w2, &w1, &w0, ws[13], p[18]); + word3_muladd(&w2, &w1, &w0, ws[14], p[17]); + word3_muladd(&w2, &w1, &w0, ws[15], p[16]); + word3_muladd(&w2, &w1, &w0, ws[16], p[15]); + word3_muladd(&w2, &w1, &w0, ws[17], p[14]); + word3_muladd(&w2, &w1, &w0, ws[18], p[13]); + word3_muladd(&w2, &w1, &w0, ws[19], p[12]); + word3_muladd(&w2, &w1, &w0, ws[20], p[11]); + word3_muladd(&w2, &w1, &w0, ws[21], p[10]); + word3_muladd(&w2, &w1, &w0, ws[22], p[9]); + word3_muladd(&w2, &w1, &w0, ws[23], p[8]); + word3_muladd(&w2, &w1, &w0, ws[24], p[7]); + word3_muladd(&w2, &w1, &w0, ws[25], p[6]); + word3_muladd(&w2, &w1, &w0, ws[26], p[5]); + word3_muladd(&w2, &w1, &w0, ws[27], p[4]); + word3_muladd(&w2, &w1, &w0, ws[28], p[3]); + word3_muladd(&w2, &w1, &w0, ws[29], p[2]); + word3_muladd(&w2, &w1, &w0, ws[30], p[1]); + word3_add(&w2, &w1, &w0, z[31]); + ws[31] = w0 * p_dash; + word3_muladd(&w2, &w1, &w0, ws[31], p[0]); + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[1], p[31]); + word3_muladd(&w2, &w1, &w0, ws[2], p[30]); + word3_muladd(&w2, &w1, &w0, ws[3], p[29]); + word3_muladd(&w2, &w1, &w0, ws[4], p[28]); + word3_muladd(&w2, &w1, &w0, ws[5], p[27]); + word3_muladd(&w2, &w1, &w0, ws[6], p[26]); + word3_muladd(&w2, &w1, &w0, ws[7], p[25]); + word3_muladd(&w2, &w1, &w0, ws[8], p[24]); + word3_muladd(&w2, &w1, &w0, ws[9], p[23]); + word3_muladd(&w2, &w1, &w0, ws[10], p[22]); + word3_muladd(&w2, &w1, &w0, ws[11], p[21]); + word3_muladd(&w2, &w1, &w0, ws[12], p[20]); + word3_muladd(&w2, &w1, &w0, ws[13], p[19]); + word3_muladd(&w2, &w1, &w0, ws[14], p[18]); + word3_muladd(&w2, &w1, &w0, ws[15], p[17]); + word3_muladd(&w2, &w1, &w0, ws[16], p[16]); + word3_muladd(&w2, &w1, &w0, ws[17], p[15]); + word3_muladd(&w2, &w1, &w0, ws[18], p[14]); + word3_muladd(&w2, &w1, &w0, ws[19], p[13]); + word3_muladd(&w2, &w1, &w0, ws[20], p[12]); + word3_muladd(&w2, &w1, &w0, ws[21], p[11]); + word3_muladd(&w2, &w1, &w0, ws[22], p[10]); + word3_muladd(&w2, &w1, &w0, ws[23], p[9]); + word3_muladd(&w2, &w1, &w0, ws[24], p[8]); + word3_muladd(&w2, &w1, &w0, ws[25], p[7]); + word3_muladd(&w2, &w1, &w0, ws[26], p[6]); + word3_muladd(&w2, &w1, &w0, ws[27], p[5]); + word3_muladd(&w2, &w1, &w0, ws[28], p[4]); + word3_muladd(&w2, &w1, &w0, ws[29], p[3]); + word3_muladd(&w2, &w1, &w0, ws[30], p[2]); + word3_muladd(&w2, &w1, &w0, ws[31], p[1]); + word3_add(&w2, &w1, &w0, z[32]); + ws[0] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[2], p[31]); + word3_muladd(&w2, &w1, &w0, ws[3], p[30]); + word3_muladd(&w2, &w1, &w0, ws[4], p[29]); + word3_muladd(&w2, &w1, &w0, ws[5], p[28]); + word3_muladd(&w2, &w1, &w0, ws[6], p[27]); + word3_muladd(&w2, &w1, &w0, ws[7], p[26]); + word3_muladd(&w2, &w1, &w0, ws[8], p[25]); + word3_muladd(&w2, &w1, &w0, ws[9], p[24]); + word3_muladd(&w2, &w1, &w0, ws[10], p[23]); + word3_muladd(&w2, &w1, &w0, ws[11], p[22]); + word3_muladd(&w2, &w1, &w0, ws[12], p[21]); + word3_muladd(&w2, &w1, &w0, ws[13], p[20]); + word3_muladd(&w2, &w1, &w0, ws[14], p[19]); + word3_muladd(&w2, &w1, &w0, ws[15], p[18]); + word3_muladd(&w2, &w1, &w0, ws[16], p[17]); + word3_muladd(&w2, &w1, &w0, ws[17], p[16]); + word3_muladd(&w2, &w1, &w0, ws[18], p[15]); + word3_muladd(&w2, &w1, &w0, ws[19], p[14]); + word3_muladd(&w2, &w1, &w0, ws[20], p[13]); + word3_muladd(&w2, &w1, &w0, ws[21], p[12]); + word3_muladd(&w2, &w1, &w0, ws[22], p[11]); + word3_muladd(&w2, &w1, &w0, ws[23], p[10]); + word3_muladd(&w2, &w1, &w0, ws[24], p[9]); + word3_muladd(&w2, &w1, &w0, ws[25], p[8]); + word3_muladd(&w2, &w1, &w0, ws[26], p[7]); + word3_muladd(&w2, &w1, &w0, ws[27], p[6]); + word3_muladd(&w2, &w1, &w0, ws[28], p[5]); + word3_muladd(&w2, &w1, &w0, ws[29], p[4]); + word3_muladd(&w2, &w1, &w0, ws[30], p[3]); + word3_muladd(&w2, &w1, &w0, ws[31], p[2]); + word3_add(&w2, &w1, &w0, z[33]); + ws[1] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[3], p[31]); + word3_muladd(&w2, &w1, &w0, ws[4], p[30]); + word3_muladd(&w2, &w1, &w0, ws[5], p[29]); + word3_muladd(&w2, &w1, &w0, ws[6], p[28]); + word3_muladd(&w2, &w1, &w0, ws[7], p[27]); + word3_muladd(&w2, &w1, &w0, ws[8], p[26]); + word3_muladd(&w2, &w1, &w0, ws[9], p[25]); + word3_muladd(&w2, &w1, &w0, ws[10], p[24]); + word3_muladd(&w2, &w1, &w0, ws[11], p[23]); + word3_muladd(&w2, &w1, &w0, ws[12], p[22]); + word3_muladd(&w2, &w1, &w0, ws[13], p[21]); + word3_muladd(&w2, &w1, &w0, ws[14], p[20]); + word3_muladd(&w2, &w1, &w0, ws[15], p[19]); + word3_muladd(&w2, &w1, &w0, ws[16], p[18]); + word3_muladd(&w2, &w1, &w0, ws[17], p[17]); + word3_muladd(&w2, &w1, &w0, ws[18], p[16]); + word3_muladd(&w2, &w1, &w0, ws[19], p[15]); + word3_muladd(&w2, &w1, &w0, ws[20], p[14]); + word3_muladd(&w2, &w1, &w0, ws[21], p[13]); + word3_muladd(&w2, &w1, &w0, ws[22], p[12]); + word3_muladd(&w2, &w1, &w0, ws[23], p[11]); + word3_muladd(&w2, &w1, &w0, ws[24], p[10]); + word3_muladd(&w2, &w1, &w0, ws[25], p[9]); + word3_muladd(&w2, &w1, &w0, ws[26], p[8]); + word3_muladd(&w2, &w1, &w0, ws[27], p[7]); + word3_muladd(&w2, &w1, &w0, ws[28], p[6]); + word3_muladd(&w2, &w1, &w0, ws[29], p[5]); + word3_muladd(&w2, &w1, &w0, ws[30], p[4]); + word3_muladd(&w2, &w1, &w0, ws[31], p[3]); + word3_add(&w2, &w1, &w0, z[34]); + ws[2] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[4], p[31]); + word3_muladd(&w2, &w1, &w0, ws[5], p[30]); + word3_muladd(&w2, &w1, &w0, ws[6], p[29]); + word3_muladd(&w2, &w1, &w0, ws[7], p[28]); + word3_muladd(&w2, &w1, &w0, ws[8], p[27]); + word3_muladd(&w2, &w1, &w0, ws[9], p[26]); + word3_muladd(&w2, &w1, &w0, ws[10], p[25]); + word3_muladd(&w2, &w1, &w0, ws[11], p[24]); + word3_muladd(&w2, &w1, &w0, ws[12], p[23]); + word3_muladd(&w2, &w1, &w0, ws[13], p[22]); + word3_muladd(&w2, &w1, &w0, ws[14], p[21]); + word3_muladd(&w2, &w1, &w0, ws[15], p[20]); + word3_muladd(&w2, &w1, &w0, ws[16], p[19]); + word3_muladd(&w2, &w1, &w0, ws[17], p[18]); + word3_muladd(&w2, &w1, &w0, ws[18], p[17]); + word3_muladd(&w2, &w1, &w0, ws[19], p[16]); + word3_muladd(&w2, &w1, &w0, ws[20], p[15]); + word3_muladd(&w2, &w1, &w0, ws[21], p[14]); + word3_muladd(&w2, &w1, &w0, ws[22], p[13]); + word3_muladd(&w2, &w1, &w0, ws[23], p[12]); + word3_muladd(&w2, &w1, &w0, ws[24], p[11]); + word3_muladd(&w2, &w1, &w0, ws[25], p[10]); + word3_muladd(&w2, &w1, &w0, ws[26], p[9]); + word3_muladd(&w2, &w1, &w0, ws[27], p[8]); + word3_muladd(&w2, &w1, &w0, ws[28], p[7]); + word3_muladd(&w2, &w1, &w0, ws[29], p[6]); + word3_muladd(&w2, &w1, &w0, ws[30], p[5]); + word3_muladd(&w2, &w1, &w0, ws[31], p[4]); + word3_add(&w2, &w1, &w0, z[35]); + ws[3] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[5], p[31]); + word3_muladd(&w2, &w1, &w0, ws[6], p[30]); + word3_muladd(&w2, &w1, &w0, ws[7], p[29]); + word3_muladd(&w2, &w1, &w0, ws[8], p[28]); + word3_muladd(&w2, &w1, &w0, ws[9], p[27]); + word3_muladd(&w2, &w1, &w0, ws[10], p[26]); + word3_muladd(&w2, &w1, &w0, ws[11], p[25]); + word3_muladd(&w2, &w1, &w0, ws[12], p[24]); + word3_muladd(&w2, &w1, &w0, ws[13], p[23]); + word3_muladd(&w2, &w1, &w0, ws[14], p[22]); + word3_muladd(&w2, &w1, &w0, ws[15], p[21]); + word3_muladd(&w2, &w1, &w0, ws[16], p[20]); + word3_muladd(&w2, &w1, &w0, ws[17], p[19]); + word3_muladd(&w2, &w1, &w0, ws[18], p[18]); + word3_muladd(&w2, &w1, &w0, ws[19], p[17]); + word3_muladd(&w2, &w1, &w0, ws[20], p[16]); + word3_muladd(&w2, &w1, &w0, ws[21], p[15]); + word3_muladd(&w2, &w1, &w0, ws[22], p[14]); + word3_muladd(&w2, &w1, &w0, ws[23], p[13]); + word3_muladd(&w2, &w1, &w0, ws[24], p[12]); + word3_muladd(&w2, &w1, &w0, ws[25], p[11]); + word3_muladd(&w2, &w1, &w0, ws[26], p[10]); + word3_muladd(&w2, &w1, &w0, ws[27], p[9]); + word3_muladd(&w2, &w1, &w0, ws[28], p[8]); + word3_muladd(&w2, &w1, &w0, ws[29], p[7]); + word3_muladd(&w2, &w1, &w0, ws[30], p[6]); + word3_muladd(&w2, &w1, &w0, ws[31], p[5]); + word3_add(&w2, &w1, &w0, z[36]); + ws[4] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[6], p[31]); + word3_muladd(&w2, &w1, &w0, ws[7], p[30]); + word3_muladd(&w2, &w1, &w0, ws[8], p[29]); + word3_muladd(&w2, &w1, &w0, ws[9], p[28]); + word3_muladd(&w2, &w1, &w0, ws[10], p[27]); + word3_muladd(&w2, &w1, &w0, ws[11], p[26]); + word3_muladd(&w2, &w1, &w0, ws[12], p[25]); + word3_muladd(&w2, &w1, &w0, ws[13], p[24]); + word3_muladd(&w2, &w1, &w0, ws[14], p[23]); + word3_muladd(&w2, &w1, &w0, ws[15], p[22]); + word3_muladd(&w2, &w1, &w0, ws[16], p[21]); + word3_muladd(&w2, &w1, &w0, ws[17], p[20]); + word3_muladd(&w2, &w1, &w0, ws[18], p[19]); + word3_muladd(&w2, &w1, &w0, ws[19], p[18]); + word3_muladd(&w2, &w1, &w0, ws[20], p[17]); + word3_muladd(&w2, &w1, &w0, ws[21], p[16]); + word3_muladd(&w2, &w1, &w0, ws[22], p[15]); + word3_muladd(&w2, &w1, &w0, ws[23], p[14]); + word3_muladd(&w2, &w1, &w0, ws[24], p[13]); + word3_muladd(&w2, &w1, &w0, ws[25], p[12]); + word3_muladd(&w2, &w1, &w0, ws[26], p[11]); + word3_muladd(&w2, &w1, &w0, ws[27], p[10]); + word3_muladd(&w2, &w1, &w0, ws[28], p[9]); + word3_muladd(&w2, &w1, &w0, ws[29], p[8]); + word3_muladd(&w2, &w1, &w0, ws[30], p[7]); + word3_muladd(&w2, &w1, &w0, ws[31], p[6]); + word3_add(&w2, &w1, &w0, z[37]); + ws[5] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[7], p[31]); + word3_muladd(&w2, &w1, &w0, ws[8], p[30]); + word3_muladd(&w2, &w1, &w0, ws[9], p[29]); + word3_muladd(&w2, &w1, &w0, ws[10], p[28]); + word3_muladd(&w2, &w1, &w0, ws[11], p[27]); + word3_muladd(&w2, &w1, &w0, ws[12], p[26]); + word3_muladd(&w2, &w1, &w0, ws[13], p[25]); + word3_muladd(&w2, &w1, &w0, ws[14], p[24]); + word3_muladd(&w2, &w1, &w0, ws[15], p[23]); + word3_muladd(&w2, &w1, &w0, ws[16], p[22]); + word3_muladd(&w2, &w1, &w0, ws[17], p[21]); + word3_muladd(&w2, &w1, &w0, ws[18], p[20]); + word3_muladd(&w2, &w1, &w0, ws[19], p[19]); + word3_muladd(&w2, &w1, &w0, ws[20], p[18]); + word3_muladd(&w2, &w1, &w0, ws[21], p[17]); + word3_muladd(&w2, &w1, &w0, ws[22], p[16]); + word3_muladd(&w2, &w1, &w0, ws[23], p[15]); + word3_muladd(&w2, &w1, &w0, ws[24], p[14]); + word3_muladd(&w2, &w1, &w0, ws[25], p[13]); + word3_muladd(&w2, &w1, &w0, ws[26], p[12]); + word3_muladd(&w2, &w1, &w0, ws[27], p[11]); + word3_muladd(&w2, &w1, &w0, ws[28], p[10]); + word3_muladd(&w2, &w1, &w0, ws[29], p[9]); + word3_muladd(&w2, &w1, &w0, ws[30], p[8]); + word3_muladd(&w2, &w1, &w0, ws[31], p[7]); + word3_add(&w2, &w1, &w0, z[38]); + ws[6] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[8], p[31]); + word3_muladd(&w2, &w1, &w0, ws[9], p[30]); + word3_muladd(&w2, &w1, &w0, ws[10], p[29]); + word3_muladd(&w2, &w1, &w0, ws[11], p[28]); + word3_muladd(&w2, &w1, &w0, ws[12], p[27]); + word3_muladd(&w2, &w1, &w0, ws[13], p[26]); + word3_muladd(&w2, &w1, &w0, ws[14], p[25]); + word3_muladd(&w2, &w1, &w0, ws[15], p[24]); + word3_muladd(&w2, &w1, &w0, ws[16], p[23]); + word3_muladd(&w2, &w1, &w0, ws[17], p[22]); + word3_muladd(&w2, &w1, &w0, ws[18], p[21]); + word3_muladd(&w2, &w1, &w0, ws[19], p[20]); + word3_muladd(&w2, &w1, &w0, ws[20], p[19]); + word3_muladd(&w2, &w1, &w0, ws[21], p[18]); + word3_muladd(&w2, &w1, &w0, ws[22], p[17]); + word3_muladd(&w2, &w1, &w0, ws[23], p[16]); + word3_muladd(&w2, &w1, &w0, ws[24], p[15]); + word3_muladd(&w2, &w1, &w0, ws[25], p[14]); + word3_muladd(&w2, &w1, &w0, ws[26], p[13]); + word3_muladd(&w2, &w1, &w0, ws[27], p[12]); + word3_muladd(&w2, &w1, &w0, ws[28], p[11]); + word3_muladd(&w2, &w1, &w0, ws[29], p[10]); + word3_muladd(&w2, &w1, &w0, ws[30], p[9]); + word3_muladd(&w2, &w1, &w0, ws[31], p[8]); + word3_add(&w2, &w1, &w0, z[39]); + ws[7] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[9], p[31]); + word3_muladd(&w2, &w1, &w0, ws[10], p[30]); + word3_muladd(&w2, &w1, &w0, ws[11], p[29]); + word3_muladd(&w2, &w1, &w0, ws[12], p[28]); + word3_muladd(&w2, &w1, &w0, ws[13], p[27]); + word3_muladd(&w2, &w1, &w0, ws[14], p[26]); + word3_muladd(&w2, &w1, &w0, ws[15], p[25]); + word3_muladd(&w2, &w1, &w0, ws[16], p[24]); + word3_muladd(&w2, &w1, &w0, ws[17], p[23]); + word3_muladd(&w2, &w1, &w0, ws[18], p[22]); + word3_muladd(&w2, &w1, &w0, ws[19], p[21]); + word3_muladd(&w2, &w1, &w0, ws[20], p[20]); + word3_muladd(&w2, &w1, &w0, ws[21], p[19]); + word3_muladd(&w2, &w1, &w0, ws[22], p[18]); + word3_muladd(&w2, &w1, &w0, ws[23], p[17]); + word3_muladd(&w2, &w1, &w0, ws[24], p[16]); + word3_muladd(&w2, &w1, &w0, ws[25], p[15]); + word3_muladd(&w2, &w1, &w0, ws[26], p[14]); + word3_muladd(&w2, &w1, &w0, ws[27], p[13]); + word3_muladd(&w2, &w1, &w0, ws[28], p[12]); + word3_muladd(&w2, &w1, &w0, ws[29], p[11]); + word3_muladd(&w2, &w1, &w0, ws[30], p[10]); + word3_muladd(&w2, &w1, &w0, ws[31], p[9]); + word3_add(&w2, &w1, &w0, z[40]); + ws[8] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[10], p[31]); + word3_muladd(&w2, &w1, &w0, ws[11], p[30]); + word3_muladd(&w2, &w1, &w0, ws[12], p[29]); + word3_muladd(&w2, &w1, &w0, ws[13], p[28]); + word3_muladd(&w2, &w1, &w0, ws[14], p[27]); + word3_muladd(&w2, &w1, &w0, ws[15], p[26]); + word3_muladd(&w2, &w1, &w0, ws[16], p[25]); + word3_muladd(&w2, &w1, &w0, ws[17], p[24]); + word3_muladd(&w2, &w1, &w0, ws[18], p[23]); + word3_muladd(&w2, &w1, &w0, ws[19], p[22]); + word3_muladd(&w2, &w1, &w0, ws[20], p[21]); + word3_muladd(&w2, &w1, &w0, ws[21], p[20]); + word3_muladd(&w2, &w1, &w0, ws[22], p[19]); + word3_muladd(&w2, &w1, &w0, ws[23], p[18]); + word3_muladd(&w2, &w1, &w0, ws[24], p[17]); + word3_muladd(&w2, &w1, &w0, ws[25], p[16]); + word3_muladd(&w2, &w1, &w0, ws[26], p[15]); + word3_muladd(&w2, &w1, &w0, ws[27], p[14]); + word3_muladd(&w2, &w1, &w0, ws[28], p[13]); + word3_muladd(&w2, &w1, &w0, ws[29], p[12]); + word3_muladd(&w2, &w1, &w0, ws[30], p[11]); + word3_muladd(&w2, &w1, &w0, ws[31], p[10]); + word3_add(&w2, &w1, &w0, z[41]); + ws[9] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[11], p[31]); + word3_muladd(&w2, &w1, &w0, ws[12], p[30]); + word3_muladd(&w2, &w1, &w0, ws[13], p[29]); + word3_muladd(&w2, &w1, &w0, ws[14], p[28]); + word3_muladd(&w2, &w1, &w0, ws[15], p[27]); + word3_muladd(&w2, &w1, &w0, ws[16], p[26]); + word3_muladd(&w2, &w1, &w0, ws[17], p[25]); + word3_muladd(&w2, &w1, &w0, ws[18], p[24]); + word3_muladd(&w2, &w1, &w0, ws[19], p[23]); + word3_muladd(&w2, &w1, &w0, ws[20], p[22]); + word3_muladd(&w2, &w1, &w0, ws[21], p[21]); + word3_muladd(&w2, &w1, &w0, ws[22], p[20]); + word3_muladd(&w2, &w1, &w0, ws[23], p[19]); + word3_muladd(&w2, &w1, &w0, ws[24], p[18]); + word3_muladd(&w2, &w1, &w0, ws[25], p[17]); + word3_muladd(&w2, &w1, &w0, ws[26], p[16]); + word3_muladd(&w2, &w1, &w0, ws[27], p[15]); + word3_muladd(&w2, &w1, &w0, ws[28], p[14]); + word3_muladd(&w2, &w1, &w0, ws[29], p[13]); + word3_muladd(&w2, &w1, &w0, ws[30], p[12]); + word3_muladd(&w2, &w1, &w0, ws[31], p[11]); + word3_add(&w2, &w1, &w0, z[42]); + ws[10] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[12], p[31]); + word3_muladd(&w2, &w1, &w0, ws[13], p[30]); + word3_muladd(&w2, &w1, &w0, ws[14], p[29]); + word3_muladd(&w2, &w1, &w0, ws[15], p[28]); + word3_muladd(&w2, &w1, &w0, ws[16], p[27]); + word3_muladd(&w2, &w1, &w0, ws[17], p[26]); + word3_muladd(&w2, &w1, &w0, ws[18], p[25]); + word3_muladd(&w2, &w1, &w0, ws[19], p[24]); + word3_muladd(&w2, &w1, &w0, ws[20], p[23]); + word3_muladd(&w2, &w1, &w0, ws[21], p[22]); + word3_muladd(&w2, &w1, &w0, ws[22], p[21]); + word3_muladd(&w2, &w1, &w0, ws[23], p[20]); + word3_muladd(&w2, &w1, &w0, ws[24], p[19]); + word3_muladd(&w2, &w1, &w0, ws[25], p[18]); + word3_muladd(&w2, &w1, &w0, ws[26], p[17]); + word3_muladd(&w2, &w1, &w0, ws[27], p[16]); + word3_muladd(&w2, &w1, &w0, ws[28], p[15]); + word3_muladd(&w2, &w1, &w0, ws[29], p[14]); + word3_muladd(&w2, &w1, &w0, ws[30], p[13]); + word3_muladd(&w2, &w1, &w0, ws[31], p[12]); + word3_add(&w2, &w1, &w0, z[43]); + ws[11] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[13], p[31]); + word3_muladd(&w2, &w1, &w0, ws[14], p[30]); + word3_muladd(&w2, &w1, &w0, ws[15], p[29]); + word3_muladd(&w2, &w1, &w0, ws[16], p[28]); + word3_muladd(&w2, &w1, &w0, ws[17], p[27]); + word3_muladd(&w2, &w1, &w0, ws[18], p[26]); + word3_muladd(&w2, &w1, &w0, ws[19], p[25]); + word3_muladd(&w2, &w1, &w0, ws[20], p[24]); + word3_muladd(&w2, &w1, &w0, ws[21], p[23]); + word3_muladd(&w2, &w1, &w0, ws[22], p[22]); + word3_muladd(&w2, &w1, &w0, ws[23], p[21]); + word3_muladd(&w2, &w1, &w0, ws[24], p[20]); + word3_muladd(&w2, &w1, &w0, ws[25], p[19]); + word3_muladd(&w2, &w1, &w0, ws[26], p[18]); + word3_muladd(&w2, &w1, &w0, ws[27], p[17]); + word3_muladd(&w2, &w1, &w0, ws[28], p[16]); + word3_muladd(&w2, &w1, &w0, ws[29], p[15]); + word3_muladd(&w2, &w1, &w0, ws[30], p[14]); + word3_muladd(&w2, &w1, &w0, ws[31], p[13]); + word3_add(&w2, &w1, &w0, z[44]); + ws[12] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[14], p[31]); + word3_muladd(&w2, &w1, &w0, ws[15], p[30]); + word3_muladd(&w2, &w1, &w0, ws[16], p[29]); + word3_muladd(&w2, &w1, &w0, ws[17], p[28]); + word3_muladd(&w2, &w1, &w0, ws[18], p[27]); + word3_muladd(&w2, &w1, &w0, ws[19], p[26]); + word3_muladd(&w2, &w1, &w0, ws[20], p[25]); + word3_muladd(&w2, &w1, &w0, ws[21], p[24]); + word3_muladd(&w2, &w1, &w0, ws[22], p[23]); + word3_muladd(&w2, &w1, &w0, ws[23], p[22]); + word3_muladd(&w2, &w1, &w0, ws[24], p[21]); + word3_muladd(&w2, &w1, &w0, ws[25], p[20]); + word3_muladd(&w2, &w1, &w0, ws[26], p[19]); + word3_muladd(&w2, &w1, &w0, ws[27], p[18]); + word3_muladd(&w2, &w1, &w0, ws[28], p[17]); + word3_muladd(&w2, &w1, &w0, ws[29], p[16]); + word3_muladd(&w2, &w1, &w0, ws[30], p[15]); + word3_muladd(&w2, &w1, &w0, ws[31], p[14]); + word3_add(&w2, &w1, &w0, z[45]); + ws[13] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[15], p[31]); + word3_muladd(&w2, &w1, &w0, ws[16], p[30]); + word3_muladd(&w2, &w1, &w0, ws[17], p[29]); + word3_muladd(&w2, &w1, &w0, ws[18], p[28]); + word3_muladd(&w2, &w1, &w0, ws[19], p[27]); + word3_muladd(&w2, &w1, &w0, ws[20], p[26]); + word3_muladd(&w2, &w1, &w0, ws[21], p[25]); + word3_muladd(&w2, &w1, &w0, ws[22], p[24]); + word3_muladd(&w2, &w1, &w0, ws[23], p[23]); + word3_muladd(&w2, &w1, &w0, ws[24], p[22]); + word3_muladd(&w2, &w1, &w0, ws[25], p[21]); + word3_muladd(&w2, &w1, &w0, ws[26], p[20]); + word3_muladd(&w2, &w1, &w0, ws[27], p[19]); + word3_muladd(&w2, &w1, &w0, ws[28], p[18]); + word3_muladd(&w2, &w1, &w0, ws[29], p[17]); + word3_muladd(&w2, &w1, &w0, ws[30], p[16]); + word3_muladd(&w2, &w1, &w0, ws[31], p[15]); + word3_add(&w2, &w1, &w0, z[46]); + ws[14] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[16], p[31]); + word3_muladd(&w2, &w1, &w0, ws[17], p[30]); + word3_muladd(&w2, &w1, &w0, ws[18], p[29]); + word3_muladd(&w2, &w1, &w0, ws[19], p[28]); + word3_muladd(&w2, &w1, &w0, ws[20], p[27]); + word3_muladd(&w2, &w1, &w0, ws[21], p[26]); + word3_muladd(&w2, &w1, &w0, ws[22], p[25]); + word3_muladd(&w2, &w1, &w0, ws[23], p[24]); + word3_muladd(&w2, &w1, &w0, ws[24], p[23]); + word3_muladd(&w2, &w1, &w0, ws[25], p[22]); + word3_muladd(&w2, &w1, &w0, ws[26], p[21]); + word3_muladd(&w2, &w1, &w0, ws[27], p[20]); + word3_muladd(&w2, &w1, &w0, ws[28], p[19]); + word3_muladd(&w2, &w1, &w0, ws[29], p[18]); + word3_muladd(&w2, &w1, &w0, ws[30], p[17]); + word3_muladd(&w2, &w1, &w0, ws[31], p[16]); + word3_add(&w2, &w1, &w0, z[47]); + ws[15] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[17], p[31]); + word3_muladd(&w2, &w1, &w0, ws[18], p[30]); + word3_muladd(&w2, &w1, &w0, ws[19], p[29]); + word3_muladd(&w2, &w1, &w0, ws[20], p[28]); + word3_muladd(&w2, &w1, &w0, ws[21], p[27]); + word3_muladd(&w2, &w1, &w0, ws[22], p[26]); + word3_muladd(&w2, &w1, &w0, ws[23], p[25]); + word3_muladd(&w2, &w1, &w0, ws[24], p[24]); + word3_muladd(&w2, &w1, &w0, ws[25], p[23]); + word3_muladd(&w2, &w1, &w0, ws[26], p[22]); + word3_muladd(&w2, &w1, &w0, ws[27], p[21]); + word3_muladd(&w2, &w1, &w0, ws[28], p[20]); + word3_muladd(&w2, &w1, &w0, ws[29], p[19]); + word3_muladd(&w2, &w1, &w0, ws[30], p[18]); + word3_muladd(&w2, &w1, &w0, ws[31], p[17]); + word3_add(&w2, &w1, &w0, z[48]); + ws[16] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[18], p[31]); + word3_muladd(&w2, &w1, &w0, ws[19], p[30]); + word3_muladd(&w2, &w1, &w0, ws[20], p[29]); + word3_muladd(&w2, &w1, &w0, ws[21], p[28]); + word3_muladd(&w2, &w1, &w0, ws[22], p[27]); + word3_muladd(&w2, &w1, &w0, ws[23], p[26]); + word3_muladd(&w2, &w1, &w0, ws[24], p[25]); + word3_muladd(&w2, &w1, &w0, ws[25], p[24]); + word3_muladd(&w2, &w1, &w0, ws[26], p[23]); + word3_muladd(&w2, &w1, &w0, ws[27], p[22]); + word3_muladd(&w2, &w1, &w0, ws[28], p[21]); + word3_muladd(&w2, &w1, &w0, ws[29], p[20]); + word3_muladd(&w2, &w1, &w0, ws[30], p[19]); + word3_muladd(&w2, &w1, &w0, ws[31], p[18]); + word3_add(&w2, &w1, &w0, z[49]); + ws[17] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[19], p[31]); + word3_muladd(&w2, &w1, &w0, ws[20], p[30]); + word3_muladd(&w2, &w1, &w0, ws[21], p[29]); + word3_muladd(&w2, &w1, &w0, ws[22], p[28]); + word3_muladd(&w2, &w1, &w0, ws[23], p[27]); + word3_muladd(&w2, &w1, &w0, ws[24], p[26]); + word3_muladd(&w2, &w1, &w0, ws[25], p[25]); + word3_muladd(&w2, &w1, &w0, ws[26], p[24]); + word3_muladd(&w2, &w1, &w0, ws[27], p[23]); + word3_muladd(&w2, &w1, &w0, ws[28], p[22]); + word3_muladd(&w2, &w1, &w0, ws[29], p[21]); + word3_muladd(&w2, &w1, &w0, ws[30], p[20]); + word3_muladd(&w2, &w1, &w0, ws[31], p[19]); + word3_add(&w2, &w1, &w0, z[50]); + ws[18] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[20], p[31]); + word3_muladd(&w2, &w1, &w0, ws[21], p[30]); + word3_muladd(&w2, &w1, &w0, ws[22], p[29]); + word3_muladd(&w2, &w1, &w0, ws[23], p[28]); + word3_muladd(&w2, &w1, &w0, ws[24], p[27]); + word3_muladd(&w2, &w1, &w0, ws[25], p[26]); + word3_muladd(&w2, &w1, &w0, ws[26], p[25]); + word3_muladd(&w2, &w1, &w0, ws[27], p[24]); + word3_muladd(&w2, &w1, &w0, ws[28], p[23]); + word3_muladd(&w2, &w1, &w0, ws[29], p[22]); + word3_muladd(&w2, &w1, &w0, ws[30], p[21]); + word3_muladd(&w2, &w1, &w0, ws[31], p[20]); + word3_add(&w2, &w1, &w0, z[51]); + ws[19] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[21], p[31]); + word3_muladd(&w2, &w1, &w0, ws[22], p[30]); + word3_muladd(&w2, &w1, &w0, ws[23], p[29]); + word3_muladd(&w2, &w1, &w0, ws[24], p[28]); + word3_muladd(&w2, &w1, &w0, ws[25], p[27]); + word3_muladd(&w2, &w1, &w0, ws[26], p[26]); + word3_muladd(&w2, &w1, &w0, ws[27], p[25]); + word3_muladd(&w2, &w1, &w0, ws[28], p[24]); + word3_muladd(&w2, &w1, &w0, ws[29], p[23]); + word3_muladd(&w2, &w1, &w0, ws[30], p[22]); + word3_muladd(&w2, &w1, &w0, ws[31], p[21]); + word3_add(&w2, &w1, &w0, z[52]); + ws[20] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[22], p[31]); + word3_muladd(&w2, &w1, &w0, ws[23], p[30]); + word3_muladd(&w2, &w1, &w0, ws[24], p[29]); + word3_muladd(&w2, &w1, &w0, ws[25], p[28]); + word3_muladd(&w2, &w1, &w0, ws[26], p[27]); + word3_muladd(&w2, &w1, &w0, ws[27], p[26]); + word3_muladd(&w2, &w1, &w0, ws[28], p[25]); + word3_muladd(&w2, &w1, &w0, ws[29], p[24]); + word3_muladd(&w2, &w1, &w0, ws[30], p[23]); + word3_muladd(&w2, &w1, &w0, ws[31], p[22]); + word3_add(&w2, &w1, &w0, z[53]); + ws[21] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[23], p[31]); + word3_muladd(&w2, &w1, &w0, ws[24], p[30]); + word3_muladd(&w2, &w1, &w0, ws[25], p[29]); + word3_muladd(&w2, &w1, &w0, ws[26], p[28]); + word3_muladd(&w2, &w1, &w0, ws[27], p[27]); + word3_muladd(&w2, &w1, &w0, ws[28], p[26]); + word3_muladd(&w2, &w1, &w0, ws[29], p[25]); + word3_muladd(&w2, &w1, &w0, ws[30], p[24]); + word3_muladd(&w2, &w1, &w0, ws[31], p[23]); + word3_add(&w2, &w1, &w0, z[54]); + ws[22] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[24], p[31]); + word3_muladd(&w2, &w1, &w0, ws[25], p[30]); + word3_muladd(&w2, &w1, &w0, ws[26], p[29]); + word3_muladd(&w2, &w1, &w0, ws[27], p[28]); + word3_muladd(&w2, &w1, &w0, ws[28], p[27]); + word3_muladd(&w2, &w1, &w0, ws[29], p[26]); + word3_muladd(&w2, &w1, &w0, ws[30], p[25]); + word3_muladd(&w2, &w1, &w0, ws[31], p[24]); + word3_add(&w2, &w1, &w0, z[55]); + ws[23] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[25], p[31]); + word3_muladd(&w2, &w1, &w0, ws[26], p[30]); + word3_muladd(&w2, &w1, &w0, ws[27], p[29]); + word3_muladd(&w2, &w1, &w0, ws[28], p[28]); + word3_muladd(&w2, &w1, &w0, ws[29], p[27]); + word3_muladd(&w2, &w1, &w0, ws[30], p[26]); + word3_muladd(&w2, &w1, &w0, ws[31], p[25]); + word3_add(&w2, &w1, &w0, z[56]); + ws[24] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[26], p[31]); + word3_muladd(&w2, &w1, &w0, ws[27], p[30]); + word3_muladd(&w2, &w1, &w0, ws[28], p[29]); + word3_muladd(&w2, &w1, &w0, ws[29], p[28]); + word3_muladd(&w2, &w1, &w0, ws[30], p[27]); + word3_muladd(&w2, &w1, &w0, ws[31], p[26]); + word3_add(&w2, &w1, &w0, z[57]); + ws[25] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[27], p[31]); + word3_muladd(&w2, &w1, &w0, ws[28], p[30]); + word3_muladd(&w2, &w1, &w0, ws[29], p[29]); + word3_muladd(&w2, &w1, &w0, ws[30], p[28]); + word3_muladd(&w2, &w1, &w0, ws[31], p[27]); + word3_add(&w2, &w1, &w0, z[58]); + ws[26] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[28], p[31]); + word3_muladd(&w2, &w1, &w0, ws[29], p[30]); + word3_muladd(&w2, &w1, &w0, ws[30], p[29]); + word3_muladd(&w2, &w1, &w0, ws[31], p[28]); + word3_add(&w2, &w1, &w0, z[59]); + ws[27] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[29], p[31]); + word3_muladd(&w2, &w1, &w0, ws[30], p[30]); + word3_muladd(&w2, &w1, &w0, ws[31], p[29]); + word3_add(&w2, &w1, &w0, z[60]); + ws[28] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[30], p[31]); + word3_muladd(&w2, &w1, &w0, ws[31], p[30]); + word3_add(&w2, &w1, &w0, z[61]); + ws[29] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_muladd(&w2, &w1, &w0, ws[31], p[31]); + word3_add(&w2, &w1, &w0, z[62]); + ws[30] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[63]); + ws[31] = w0; + w0 = w1; w1 = w2; w2 = 0; + word3_add(&w2, &w1, &w0, z[65]); + ws[32] = w0; + ws[33] = w1; + word borrow = bigint_sub3(ws + 32 + 1, ws, 32 + 1, p, 32); + CT::conditional_copy_mem(borrow, z, ws, ws + 33, 33); + clear_mem(z + 32, 2*(32+1) - 32); + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/curve_nistp.h b/src/libs/3rdparty/botan/src/lib/math/numbertheory/curve_nistp.h new file mode 100644 index 0000000000..c9936a338b --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/curve_nistp.h @@ -0,0 +1,46 @@ +/* +* Arithmetic operations specialized for NIST ECC primes +* (C) 2014,2015 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_NIST_PRIMES_H_ +#define BOTAN_NIST_PRIMES_H_ + +#include <botan/bigint.h> + +namespace Botan { + +/** +* NIST Prime reduction functions. +* +* Reduces the value in place +* +* ws is a workspace function which is used as a temporary, +* and will be resized as needed. +*/ +BOTAN_PUBLIC_API(2,0) const BigInt& prime_p521(); +BOTAN_PUBLIC_API(2,0) void redc_p521(BigInt& x, secure_vector<word>& ws); + +#if (BOTAN_MP_WORD_BITS == 32) || (BOTAN_MP_WORD_BITS == 64) + +#define BOTAN_HAS_NIST_PRIME_REDUCERS_W32 + +BOTAN_PUBLIC_API(2,0) const BigInt& prime_p384(); +BOTAN_PUBLIC_API(2,0) void redc_p384(BigInt& x, secure_vector<word>& ws); + +BOTAN_PUBLIC_API(2,0) const BigInt& prime_p256(); +BOTAN_PUBLIC_API(2,0) void redc_p256(BigInt& x, secure_vector<word>& ws); + +BOTAN_PUBLIC_API(2,0) const BigInt& prime_p224(); +BOTAN_PUBLIC_API(2,0) void redc_p224(BigInt& x, secure_vector<word>& ws); + +BOTAN_PUBLIC_API(2,0) const BigInt& prime_p192(); +BOTAN_PUBLIC_API(2,0) void redc_p192(BigInt& x, secure_vector<word>& ws); + +#endif + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/def_powm.h b/src/libs/3rdparty/botan/src/lib/math/numbertheory/def_powm.h new file mode 100644 index 0000000000..6b1f33835f --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/def_powm.h @@ -0,0 +1,68 @@ +/* +* Modular Exponentiation +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_DEFAULT_MODEXP_H_ +#define BOTAN_DEFAULT_MODEXP_H_ + +#include <botan/pow_mod.h> +#include <botan/reducer.h> +#include <vector> + +namespace Botan { + +/** +* Fixed Window Exponentiator +*/ +class Fixed_Window_Exponentiator final : public Modular_Exponentiator + { + public: + void set_exponent(const BigInt&) override; + void set_base(const BigInt&) override; + BigInt execute() const override; + + Modular_Exponentiator* copy() const override + { return new Fixed_Window_Exponentiator(*this); } + + Fixed_Window_Exponentiator(const BigInt&, Power_Mod::Usage_Hints); + private: + Modular_Reducer m_reducer; + BigInt m_exp; + size_t m_window_bits; + std::vector<BigInt> m_g; + Power_Mod::Usage_Hints m_hints; + }; + +class Montgomery_Params; +class Montgomery_Exponentation_State; + +/** +* Montgomery Exponentiator +*/ +class Montgomery_Exponentiator final : public Modular_Exponentiator + { + public: + void set_exponent(const BigInt&) override; + void set_base(const BigInt&) override; + BigInt execute() const override; + + Modular_Exponentiator* copy() const override + { return new Montgomery_Exponentiator(*this); } + + Montgomery_Exponentiator(const BigInt&, Power_Mod::Usage_Hints); + private: + BigInt m_p; + Modular_Reducer m_mod_p; + std::shared_ptr<const Montgomery_Params> m_monty_params; + std::shared_ptr<const Montgomery_Exponentation_State> m_monty; + + BigInt m_e; + Power_Mod::Usage_Hints m_hints; + }; + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/dsa_gen.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/dsa_gen.cpp new file mode 100644 index 0000000000..a5efbc2662 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/dsa_gen.cpp @@ -0,0 +1,136 @@ +/* +* DSA Parameter Generation +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/numthry.h> +#include <botan/hash.h> +#include <botan/reducer.h> +#include <botan/rng.h> + +namespace Botan { + +namespace { + +/* +* Check if this size is allowed by FIPS 186-3 +*/ +bool fips186_3_valid_size(size_t pbits, size_t qbits) + { + if(qbits == 160) + return (pbits == 1024); + + if(qbits == 224) + return (pbits == 2048); + + if(qbits == 256) + return (pbits == 2048 || pbits == 3072); + + return false; + } + +} + +/* +* Attempt DSA prime generation with given seed +*/ +bool generate_dsa_primes(RandomNumberGenerator& rng, + BigInt& p, BigInt& q, + size_t pbits, size_t qbits, + const std::vector<uint8_t>& seed_c, + size_t offset) + { + if(!fips186_3_valid_size(pbits, qbits)) + throw Invalid_Argument( + "FIPS 186-3 does not allow DSA domain parameters of " + + std::to_string(pbits) + "/" + std::to_string(qbits) + " bits long"); + + if(seed_c.size() * 8 < qbits) + throw Invalid_Argument( + "Generating a DSA parameter set with a " + std::to_string(qbits) + + " bit long q requires a seed at least as many bits long"); + + const std::string hash_name = "SHA-" + std::to_string(qbits); + std::unique_ptr<HashFunction> hash(HashFunction::create_or_throw(hash_name)); + + const size_t HASH_SIZE = hash->output_length(); + + class Seed final + { + public: + explicit Seed(const std::vector<uint8_t>& s) : m_seed(s) {} + + const std::vector<uint8_t>& value() const { return m_seed; } + + Seed& operator++() + { + for(size_t j = m_seed.size(); j > 0; --j) + if(++m_seed[j-1]) + break; + return (*this); + } + private: + std::vector<uint8_t> m_seed; + }; + + Seed seed(seed_c); + + q.binary_decode(hash->process(seed.value())); + q.set_bit(qbits-1); + q.set_bit(0); + + if(!is_prime(q, rng, 128, true)) + return false; + + const size_t n = (pbits-1) / (HASH_SIZE * 8), + b = (pbits-1) % (HASH_SIZE * 8); + + BigInt X; + std::vector<uint8_t> V(HASH_SIZE * (n+1)); + + Modular_Reducer mod_2q(2*q); + + for(size_t j = 0; j != 4*pbits; ++j) + { + for(size_t k = 0; k <= n; ++k) + { + ++seed; + hash->update(seed.value()); + hash->final(&V[HASH_SIZE * (n-k)]); + } + + if(j >= offset) + { + X.binary_decode(&V[HASH_SIZE - 1 - b/8], + V.size() - (HASH_SIZE - 1 - b/8)); + X.set_bit(pbits-1); + + p = X - (mod_2q.reduce(X) - 1); + + if(p.bits() == pbits && is_prime(p, rng, 128, true)) + return true; + } + } + return false; + } + +/* +* Generate DSA Primes +*/ +std::vector<uint8_t> generate_dsa_primes(RandomNumberGenerator& rng, + BigInt& p, BigInt& q, + size_t pbits, size_t qbits) + { + while(true) + { + std::vector<uint8_t> seed(qbits / 8); + rng.randomize(seed.data(), seed.size()); + + if(generate_dsa_primes(rng, p, q, pbits, qbits, seed)) + return seed; + } + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/info.txt b/src/libs/3rdparty/botan/src/lib/math/numbertheory/info.txt new file mode 100644 index 0000000000..8da52f9f43 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/info.txt @@ -0,0 +1,24 @@ +<defines> +NUMBERTHEORY -> 20131128 +</defines> + +load_on auto + +<header:public> +curve_nistp.h +numthry.h +pow_mod.h +reducer.h +monty.h +</header:public> + +<header:internal> +def_powm.h +monty_exp.h +</header:internal> + +<requires> +bigint +hash +rng +</requires> diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/jacobi.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/jacobi.cpp new file mode 100644 index 0000000000..d3e8d75572 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/jacobi.cpp @@ -0,0 +1,53 @@ +/* +* Jacobi Function +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/numthry.h> + +namespace Botan { + +/* +* Calculate the Jacobi symbol +*/ +int32_t jacobi(const BigInt& a, const BigInt& n) + { + if(a.is_negative()) + throw Invalid_Argument("jacobi: first argument must be non-negative"); + if(n.is_even() || n < 2) + throw Invalid_Argument("jacobi: second argument must be odd and > 1"); + + BigInt x = a, y = n; + int32_t J = 1; + + while(y > 1) + { + x %= y; + if(x > y / 2) + { + x = y - x; + if(y % 4 == 3) + J = -J; + } + if(x.is_zero()) + return 0; + + size_t shifts = low_zero_bits(x); + x >>= shifts; + if(shifts % 2) + { + word y_mod_8 = y % 8; + if(y_mod_8 == 3 || y_mod_8 == 5) + J = -J; + } + + if(x % 4 == 3 && y % 4 == 3) + J = -J; + std::swap(x, y); + } + return J; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/make_prm.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/make_prm.cpp new file mode 100644 index 0000000000..1979fa5502 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/make_prm.cpp @@ -0,0 +1,285 @@ +/* +* Prime Generation +* (C) 1999-2007,2018 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/numthry.h> +#include <botan/rng.h> +#include <botan/internal/bit_ops.h> +#include <algorithm> + +namespace Botan { + +namespace { + +class Prime_Sieve + { + public: + Prime_Sieve(const BigInt& init_value) : m_sieve(PRIME_TABLE_SIZE) + { + for(size_t i = 0; i != m_sieve.size(); ++i) + m_sieve[i] = static_cast<uint16_t>(init_value % PRIMES[i]); + } + + void step(word increment) + { + for(size_t i = 0; i != m_sieve.size(); ++i) + { + m_sieve[i] = (m_sieve[i] + increment) % PRIMES[i]; + } + } + + bool passes(bool check_2p1 = false) const + { + for(size_t i = 0; i != m_sieve.size(); ++i) + { + /* + In this case, p is a multiple of PRIMES[i] + */ + if(m_sieve[i] == 0) + return false; + + if(check_2p1) + { + /* + In this case, 2*p+1 will be a multiple of PRIMES[i] + + So if potentially generating a safe prime, we want to + avoid this value because 2*p+1 will certainly not be prime. + + See "Safe Prime Generation with a Combined Sieve" M. Wiener + https://eprint.iacr.org/2003/186.pdf + */ + if(m_sieve[i] == (PRIMES[i] - 1) / 2) + return false; + } + } + + return true; + } + + private: + std::vector<uint16_t> m_sieve; + }; + +} + + +/* +* Generate a random prime +*/ +BigInt random_prime(RandomNumberGenerator& rng, + size_t bits, const BigInt& coprime, + size_t equiv, size_t modulo, + size_t prob) + { + if(coprime.is_negative()) + { + throw Invalid_Argument("random_prime: coprime must be >= 0"); + } + if(modulo == 0) + { + throw Invalid_Argument("random_prime: Invalid modulo value"); + } + + equiv %= modulo; + + if(equiv == 0) + throw Invalid_Argument("random_prime Invalid value for equiv/modulo"); + + // Handle small values: + if(bits <= 1) + { + throw Invalid_Argument("random_prime: Can't make a prime of " + + std::to_string(bits) + " bits"); + } + else if(bits == 2) + { + return ((rng.next_byte() % 2) ? 2 : 3); + } + else if(bits == 3) + { + return ((rng.next_byte() % 2) ? 5 : 7); + } + else if(bits == 4) + { + return ((rng.next_byte() % 2) ? 11 : 13); + } + else if(bits <= 16) + { + for(;;) + { + size_t idx = make_uint16(rng.next_byte(), rng.next_byte()) % PRIME_TABLE_SIZE; + uint16_t small_prime = PRIMES[idx]; + + if(high_bit(small_prime) == bits) + return small_prime; + } + } + + const size_t MAX_ATTEMPTS = 32*1024; + + while(true) + { + BigInt p(rng, bits); + + // Force lowest and two top bits on + p.set_bit(bits - 1); + p.set_bit(bits - 2); + p.set_bit(0); + + // Force p to be equal to equiv mod modulo + p += (modulo - (p % modulo)) + equiv; + + Prime_Sieve sieve(p); + + size_t counter = 0; + while(true) + { + ++counter; + + if(counter > MAX_ATTEMPTS) + { + break; // don't try forever, choose a new starting point + } + + p += modulo; + + sieve.step(modulo); + + if(sieve.passes(true) == false) + continue; + + if(coprime > 1) + { + /* + * Check if gcd(p - 1, coprime) != 1 by computing the inverse. The + * gcd algorithm is not constant time, but modular inverse is (for + * odd modulus anyway). This avoids a side channel attack against RSA + * key generation, though RSA keygen should be using generate_rsa_prime. + */ + if(inverse_mod(p - 1, coprime).is_zero()) + continue; + } + + if(p.bits() > bits) + break; + + if(is_prime(p, rng, prob, true)) + return p; + } + } + } + +BigInt generate_rsa_prime(RandomNumberGenerator& keygen_rng, + RandomNumberGenerator& prime_test_rng, + size_t bits, + const BigInt& coprime, + size_t prob) + { + if(bits < 512) + throw Invalid_Argument("generate_rsa_prime bits too small"); + + /* + * The restriction on coprime <= 64 bits is arbitrary but generally speaking + * very large RSA public exponents are a bad idea both for performance and due + * to attacks on small d. + */ + if(coprime <= 1 || coprime.is_even() || coprime.bits() > 64) + throw Invalid_Argument("generate_rsa_prime coprime must be small odd positive integer"); + + const size_t MAX_ATTEMPTS = 32*1024; + + while(true) + { + BigInt p(keygen_rng, bits); + + // Force lowest and two top bits on + p.set_bit(bits - 1); + p.set_bit(bits - 2); + p.set_bit(0); + + Prime_Sieve sieve(p); + + const word step = 2; + + size_t counter = 0; + while(true) + { + ++counter; + + if(counter > MAX_ATTEMPTS) + { + break; // don't try forever, choose a new starting point + } + + p += step; + + sieve.step(step); + + if(sieve.passes() == false) + continue; + + /* + * Check if p - 1 and coprime are relatively prime by computing the inverse. + * + * We avoid gcd here because that algorithm is not constant time. + * Modular inverse is (for odd modulus anyway). + * + * We earlier verified that coprime argument is odd. Thus the factors of 2 + * in (p - 1) cannot possibly be factors in coprime, so remove them from p - 1. + * Using an odd modulus allows the const time algorithm to be used. + * + * This assumes coprime < p - 1 which is always true for RSA. + */ + BigInt p1 = p - 1; + p1 >>= low_zero_bits(p1); + if(inverse_mod(coprime, p1).is_zero()) + { + BOTAN_DEBUG_ASSERT(gcd(p1, coprime) > 1); + continue; + } + + BOTAN_DEBUG_ASSERT(gcd(p1, coprime) == 1); + + if(p.bits() > bits) + break; + + if(is_prime(p, prime_test_rng, prob, true)) + return p; + } + } + } + +/* +* Generate a random safe prime +*/ +BigInt random_safe_prime(RandomNumberGenerator& rng, size_t bits) + { + if(bits <= 64) + throw Invalid_Argument("random_safe_prime: Can't make a prime of " + + std::to_string(bits) + " bits"); + + BigInt q, p; + for(;;) + { + /* + Generate q == 2 (mod 3) + + Otherwise [q == 1 (mod 3) case], 2*q+1 == 3 (mod 3) and not prime. + */ + q = random_prime(rng, bits - 1, 0, 2, 3, 8); + p = (q << 1) + 1; + + if(is_prime(p, rng, 128, true)) + { + // We did only a weak check before, go back and verify q before returning + if(is_prime(q, rng, 128, true)) + return p; + } + } + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty.cpp new file mode 100644 index 0000000000..b91560fd58 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty.cpp @@ -0,0 +1,449 @@ +/* +* (C) 2018 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/monty.h> +#include <botan/reducer.h> +#include <botan/internal/mp_core.h> + +namespace Botan { + +Montgomery_Params::Montgomery_Params(const BigInt& p, + const Modular_Reducer& mod_p) + { + if(p.is_negative() || p.is_even()) + throw Invalid_Argument("Montgomery_Params invalid modulus"); + + m_p = p; + m_p_words = m_p.sig_words(); + m_p_dash = monty_inverse(m_p.word_at(0)); + + const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS); + + m_r1 = mod_p.reduce(r); + m_r2 = mod_p.square(m_r1); + m_r3 = mod_p.multiply(m_r1, m_r2); + } + +Montgomery_Params::Montgomery_Params(const BigInt& p) + { + + if(p.is_negative() || p.is_even()) + throw Invalid_Argument("Montgomery_Params invalid modulus"); + + m_p = p; + m_p_words = m_p.sig_words(); + m_p_dash = monty_inverse(m_p.word_at(0)); + + const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS); + + Modular_Reducer mod_p(p); + + m_r1 = mod_p.reduce(r); + m_r2 = mod_p.square(m_r1); + m_r3 = mod_p.multiply(m_r1, m_r2); + } + +BigInt Montgomery_Params::inv_mod_p(const BigInt& x) const + { + return ct_inverse_mod_odd_modulus(x, p()); + } + +BigInt Montgomery_Params::redc(const BigInt& x, secure_vector<word>& ws) const + { + const size_t output_size = 2*m_p_words + 2; + + if(ws.size() < output_size) + ws.resize(output_size); + + BigInt z = x; + z.grow_to(output_size); + + bigint_monty_redc(z.mutable_data(), + m_p.data(), m_p_words, m_p_dash, + ws.data(), ws.size()); + + return z; + } + +BigInt Montgomery_Params::mul(const BigInt& x, const BigInt& y, + secure_vector<word>& ws) const + { + const size_t output_size = 2*m_p_words + 2; + + if(ws.size() < output_size) + ws.resize(output_size); + + BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words); + BOTAN_DEBUG_ASSERT(y.sig_words() <= m_p_words); + + BigInt z(BigInt::Positive, output_size); + bigint_mul(z.mutable_data(), z.size(), + x.data(), x.size(), std::min(m_p_words, x.size()), + y.data(), y.size(), std::min(m_p_words, y.size()), + ws.data(), ws.size()); + + bigint_monty_redc(z.mutable_data(), + m_p.data(), m_p_words, m_p_dash, + ws.data(), ws.size()); + + return z; + } + +BigInt Montgomery_Params::mul(const BigInt& x, + const secure_vector<word>& y, + secure_vector<word>& ws) const + { + const size_t output_size = 2*m_p_words + 2; + if(ws.size() < output_size) + ws.resize(output_size); + BigInt z(BigInt::Positive, output_size); + + BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words); + + bigint_mul(z.mutable_data(), z.size(), + x.data(), x.size(), std::min(m_p_words, x.size()), + y.data(), y.size(), std::min(m_p_words, y.size()), + ws.data(), ws.size()); + + bigint_monty_redc(z.mutable_data(), + m_p.data(), m_p_words, m_p_dash, + ws.data(), ws.size()); + + return z; + } + +void Montgomery_Params::mul_by(BigInt& x, + const secure_vector<word>& y, + secure_vector<word>& ws) const + { + const size_t output_size = 2*m_p_words + 2; + + if(ws.size() < 2*output_size) + ws.resize(2*output_size); + + word* z_data = &ws[0]; + word* ws_data = &ws[output_size]; + + BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words); + + bigint_mul(z_data, output_size, + x.data(), x.size(), std::min(m_p_words, x.size()), + y.data(), y.size(), std::min(m_p_words, y.size()), + ws_data, output_size); + + bigint_monty_redc(z_data, + m_p.data(), m_p_words, m_p_dash, + ws_data, output_size); + + if(x.size() < output_size) + x.grow_to(output_size); + copy_mem(x.mutable_data(), z_data, output_size); + } + +void Montgomery_Params::mul_by(BigInt& x, + const BigInt& y, + secure_vector<word>& ws) const + { + const size_t output_size = 2*m_p_words + 2; + + if(ws.size() < 2*output_size) + ws.resize(2*output_size); + + word* z_data = &ws[0]; + word* ws_data = &ws[output_size]; + + BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words); + + bigint_mul(z_data, output_size, + x.data(), x.size(), std::min(m_p_words, x.size()), + y.data(), y.size(), std::min(m_p_words, y.size()), + ws_data, output_size); + + bigint_monty_redc(z_data, + m_p.data(), m_p_words, m_p_dash, + ws_data, output_size); + + if(x.size() < output_size) + x.grow_to(output_size); + copy_mem(x.mutable_data(), z_data, output_size); + } + +BigInt Montgomery_Params::sqr(const BigInt& x, secure_vector<word>& ws) const + { + const size_t output_size = 2*m_p_words + 2; + + if(ws.size() < output_size) + ws.resize(output_size); + + BigInt z(BigInt::Positive, output_size); + + BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words); + + bigint_sqr(z.mutable_data(), z.size(), + x.data(), x.size(), std::min(m_p_words, x.size()), + ws.data(), ws.size()); + + bigint_monty_redc(z.mutable_data(), + m_p.data(), m_p_words, m_p_dash, + ws.data(), ws.size()); + + return z; + } + +void Montgomery_Params::square_this(BigInt& x, + secure_vector<word>& ws) const + { + const size_t output_size = 2*m_p_words + 2; + + if(ws.size() < 2*output_size) + ws.resize(2*output_size); + + word* z_data = &ws[0]; + word* ws_data = &ws[output_size]; + + BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words); + + bigint_sqr(z_data, output_size, + x.data(), x.size(), std::min(m_p_words, x.size()), + ws_data, output_size); + + bigint_monty_redc(z_data, + m_p.data(), m_p_words, m_p_dash, + ws_data, output_size); + + if(x.size() < output_size) + x.grow_to(output_size); + copy_mem(x.mutable_data(), z_data, output_size); + } + +Montgomery_Int::Montgomery_Int(const std::shared_ptr<const Montgomery_Params> params, + const BigInt& v, + bool redc_needed) : + m_params(params) + { + if(redc_needed == false) + { + m_v = v; + } + else + { + secure_vector<word> ws; + m_v = m_params->mul(v % m_params->p(), m_params->R2(), ws); + } + } + +Montgomery_Int::Montgomery_Int(std::shared_ptr<const Montgomery_Params> params, + const uint8_t bits[], size_t len, + bool redc_needed) : + m_params(params), + m_v(bits, len) + { + if(redc_needed) + { + secure_vector<word> ws; + m_v = m_params->mul(m_v % m_params->p(), m_params->R2(), ws); + } + } + +Montgomery_Int::Montgomery_Int(std::shared_ptr<const Montgomery_Params> params, + const word words[], size_t len, + bool redc_needed) : + m_params(params), + m_v(words, len) + { + if(redc_needed) + { + secure_vector<word> ws; + m_v = m_params->mul(m_v % m_params->p(), m_params->R2(), ws); + } + } + +void Montgomery_Int::fix_size() + { + const size_t p_words = m_params->p_words(); + + if(m_v.sig_words() > p_words) + throw Internal_Error("Montgomery_Int::fix_size v too large"); + + secure_vector<word>& w = m_v.get_word_vector(); + + if(w.size() != p_words) + { + w.resize(p_words); + w.shrink_to_fit(); + } + } + +bool Montgomery_Int::operator==(const Montgomery_Int& other) const + { + return m_v == other.m_v && m_params->p() == other.m_params->p(); + } + +std::vector<uint8_t> Montgomery_Int::serialize() const + { + std::vector<uint8_t> v(size()); + BigInt::encode_1363(v.data(), v.size(), value()); + return v; + } + +size_t Montgomery_Int::size() const + { + return m_params->p().bytes(); + } + +bool Montgomery_Int::is_one() const + { + return m_v == m_params->R1(); + } + +bool Montgomery_Int::is_zero() const + { + return m_v.is_zero(); + } + +BigInt Montgomery_Int::value() const + { + secure_vector<word> ws; + return m_params->redc(m_v, ws); + } + +Montgomery_Int Montgomery_Int::operator+(const Montgomery_Int& other) const + { + BigInt z = m_v + other.m_v; + secure_vector<word> ws; + z.reduce_below(m_params->p(), ws); + return Montgomery_Int(m_params, z, false); + } + +Montgomery_Int Montgomery_Int::operator-(const Montgomery_Int& other) const + { + BigInt z = m_v - other.m_v; + if(z.is_negative()) + z += m_params->p(); + return Montgomery_Int(m_params, z, false); + } + +Montgomery_Int& Montgomery_Int::operator+=(const Montgomery_Int& other) + { + secure_vector<word> ws; + return this->add(other, ws); + } + +Montgomery_Int& Montgomery_Int::add(const Montgomery_Int& other, secure_vector<word>& ws) + { + m_v.mod_add(other.m_v, m_params->p(), ws); + return (*this); + } + +Montgomery_Int& Montgomery_Int::operator-=(const Montgomery_Int& other) + { + secure_vector<word> ws; + return this->sub(other, ws); + } + +Montgomery_Int& Montgomery_Int::sub(const Montgomery_Int& other, secure_vector<word>& ws) + { + m_v.mod_sub(other.m_v, m_params->p(), ws); + return (*this); + } + +Montgomery_Int Montgomery_Int::operator*(const Montgomery_Int& other) const + { + secure_vector<word> ws; + return Montgomery_Int(m_params, m_params->mul(m_v, other.m_v, ws), false); + } + +Montgomery_Int Montgomery_Int::mul(const Montgomery_Int& other, + secure_vector<word>& ws) const + { + return Montgomery_Int(m_params, m_params->mul(m_v, other.m_v, ws), false); + } + +Montgomery_Int& Montgomery_Int::mul_by(const Montgomery_Int& other, + secure_vector<word>& ws) + { + m_params->mul_by(m_v, other.m_v, ws); + return (*this); + } + +Montgomery_Int& Montgomery_Int::mul_by(const secure_vector<word>& other, + secure_vector<word>& ws) + { + m_params->mul_by(m_v, other, ws); + return (*this); + } + +Montgomery_Int& Montgomery_Int::operator*=(const Montgomery_Int& other) + { + secure_vector<word> ws; + return mul_by(other, ws); + } + +Montgomery_Int& Montgomery_Int::operator*=(const secure_vector<word>& other) + { + secure_vector<word> ws; + return mul_by(other, ws); + } + +Montgomery_Int& Montgomery_Int::square_this_n_times(secure_vector<word>& ws, size_t n) + { + for(size_t i = 0; i != n; ++i) + m_params->square_this(m_v, ws); + return (*this); + } + +Montgomery_Int& Montgomery_Int::square_this(secure_vector<word>& ws) + { + m_params->square_this(m_v, ws); + return (*this); + } + +Montgomery_Int Montgomery_Int::square(secure_vector<word>& ws) const + { + return Montgomery_Int(m_params, m_params->sqr(m_v, ws), false); + } + +Montgomery_Int Montgomery_Int::multiplicative_inverse() const + { + secure_vector<word> ws; + const BigInt iv = m_params->mul(m_params->inv_mod_p(m_v), m_params->R3(), ws); + return Montgomery_Int(m_params, iv, false); + } + +Montgomery_Int Montgomery_Int::additive_inverse() const + { + return Montgomery_Int(m_params, m_params->p()) - (*this); + } + +Montgomery_Int& Montgomery_Int::mul_by_2(secure_vector<word>& ws) + { + m_v <<= 1; + m_v.reduce_below(m_params->p(), ws); + return (*this); + } + +Montgomery_Int& Montgomery_Int::mul_by_3(secure_vector<word>& ws) + { + m_v *= 3; + m_v.reduce_below(m_params->p(), ws); + return (*this); + } + +Montgomery_Int& Montgomery_Int::mul_by_4(secure_vector<word>& ws) + { + m_v <<= 2; + m_v.reduce_below(m_params->p(), ws); + return (*this); + } + +Montgomery_Int& Montgomery_Int::mul_by_8(secure_vector<word>& ws) + { + m_v <<= 3; + m_v.reduce_below(m_params->p(), ws); + return (*this); + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty.h b/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty.h new file mode 100644 index 0000000000..e5ab2f9ada --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty.h @@ -0,0 +1,190 @@ +/* +* (C) 2018 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_MONTY_INT_H_ +#define BOTAN_MONTY_INT_H_ + +#include <botan/bigint.h> + +namespace Botan { + +class Modular_Reducer; + +class Montgomery_Params; + +/** +* The Montgomery representation of an integer +*/ +class BOTAN_UNSTABLE_API Montgomery_Int final + { + public: + /** + * Create a zero-initialized Montgomery_Int + */ + Montgomery_Int(std::shared_ptr<const Montgomery_Params> params) : m_params(params) {} + + /** + * Create a Montgomery_Int + */ + Montgomery_Int(std::shared_ptr<const Montgomery_Params> params, + const BigInt& v, + bool redc_needed = true); + + /** + * Create a Montgomery_Int + */ + Montgomery_Int(std::shared_ptr<const Montgomery_Params> params, + const uint8_t bits[], size_t len, + bool redc_needed = true); + + /** + * Create a Montgomery_Int + */ + Montgomery_Int(std::shared_ptr<const Montgomery_Params> params, + const word words[], size_t len, + bool redc_needed = true); + + bool operator==(const Montgomery_Int& other) const; + bool operator!=(const Montgomery_Int& other) const { return (m_v != other.m_v); } + + std::vector<uint8_t> serialize() const; + + size_t size() const; + bool is_one() const; + bool is_zero() const; + + void fix_size(); + + /** + * Return the value to normal mod-p space + */ + BigInt value() const; + + /** + * Return the Montgomery representation + */ + const BigInt& repr() const { return m_v; } + + Montgomery_Int operator+(const Montgomery_Int& other) const; + + Montgomery_Int operator-(const Montgomery_Int& other) const; + + Montgomery_Int& operator+=(const Montgomery_Int& other); + + Montgomery_Int& operator-=(const Montgomery_Int& other); + + Montgomery_Int operator*(const Montgomery_Int& other) const; + + Montgomery_Int& operator*=(const Montgomery_Int& other); + + Montgomery_Int& operator*=(const secure_vector<word>& other); + + Montgomery_Int& add(const Montgomery_Int& other, + secure_vector<word>& ws); + + Montgomery_Int& sub(const Montgomery_Int& other, + secure_vector<word>& ws); + + Montgomery_Int mul(const Montgomery_Int& other, + secure_vector<word>& ws) const; + + Montgomery_Int& mul_by(const Montgomery_Int& other, + secure_vector<word>& ws); + + Montgomery_Int& mul_by(const secure_vector<word>& other, + secure_vector<word>& ws); + + Montgomery_Int square(secure_vector<word>& ws) const; + + Montgomery_Int& square_this(secure_vector<word>& ws); + + Montgomery_Int& square_this_n_times(secure_vector<word>& ws, size_t n); + + Montgomery_Int multiplicative_inverse() const; + + Montgomery_Int additive_inverse() const; + + Montgomery_Int& mul_by_2(secure_vector<word>& ws); + + Montgomery_Int& mul_by_3(secure_vector<word>& ws); + + Montgomery_Int& mul_by_4(secure_vector<word>& ws); + + Montgomery_Int& mul_by_8(secure_vector<word>& ws); + + void const_time_poison() const { m_v.const_time_poison(); } + void const_time_unpoison() const { return m_v.const_time_unpoison(); } + + private: + std::shared_ptr<const Montgomery_Params> m_params; + BigInt m_v; + }; + +/** +* Parameters for Montgomery Reduction +*/ +class BOTAN_UNSTABLE_API Montgomery_Params final + { + public: + /** + * Initialize a set of Montgomery reduction parameters. These values + * can be shared by all values in a specific Montgomery domain. + */ + Montgomery_Params(const BigInt& p, const Modular_Reducer& mod_p); + + /** + * Initialize a set of Montgomery reduction parameters. These values + * can be shared by all values in a specific Montgomery domain. + */ + Montgomery_Params(const BigInt& p); + + const BigInt& p() const { return m_p; } + const BigInt& R1() const { return m_r1; } + const BigInt& R2() const { return m_r2; } + const BigInt& R3() const { return m_r3; } + + word p_dash() const { return m_p_dash; } + + size_t p_words() const { return m_p_words; } + + BigInt redc(const BigInt& x, + secure_vector<word>& ws) const; + + BigInt mul(const BigInt& x, + const BigInt& y, + secure_vector<word>& ws) const; + + BigInt mul(const BigInt& x, + const secure_vector<word>& y, + secure_vector<word>& ws) const; + + void mul_by(BigInt& x, + const secure_vector<word>& y, + secure_vector<word>& ws) const; + + void mul_by(BigInt& x, const BigInt& y, + secure_vector<word>& ws) const; + + BigInt sqr(const BigInt& x, + secure_vector<word>& ws) const; + + void square_this(BigInt& x, + secure_vector<word>& ws) const; + + BigInt inv_mod_p(const BigInt& x) const; + + private: + BigInt m_p; + BigInt m_r1; + BigInt m_r2; + BigInt m_r3; + word m_p_dash; + size_t m_p_words; + }; + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty_exp.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty_exp.cpp new file mode 100644 index 0000000000..5674920915 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty_exp.cpp @@ -0,0 +1,248 @@ +/* +* Montgomery Exponentiation +* (C) 1999-2010,2012,2018 Jack Lloyd +* 2016 Matthias Gierlings +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/monty_exp.h> +#include <botan/internal/ct_utils.h> +#include <botan/internal/rounding.h> +#include <botan/numthry.h> +#include <botan/reducer.h> +#include <botan/monty.h> + +namespace Botan { + +class Montgomery_Exponentation_State + { + public: + Montgomery_Exponentation_State(std::shared_ptr<const Montgomery_Params> params, + const BigInt& g, + size_t window_bits, + bool const_time); + + BigInt exponentiation(const BigInt& k, size_t max_k_bits) const; + + BigInt exponentiation_vartime(const BigInt& k) const; + private: + std::shared_ptr<const Montgomery_Params> m_params; + std::vector<Montgomery_Int> m_g; + size_t m_window_bits; + bool m_const_time; + }; + +Montgomery_Exponentation_State::Montgomery_Exponentation_State(std::shared_ptr<const Montgomery_Params> params, + const BigInt& g, + size_t window_bits, + bool const_time) : + m_params(params), + m_window_bits(window_bits == 0 ? 4 : window_bits), + m_const_time(const_time) + { + if(m_window_bits < 1 || m_window_bits > 12) // really even 8 is too large ... + throw Invalid_Argument("Invalid window bits for Montgomery exponentiation"); + + const size_t window_size = (1U << m_window_bits); + + m_g.reserve(window_size); + + m_g.push_back(Montgomery_Int(m_params, m_params->R1(), false)); + + m_g.push_back(Montgomery_Int(m_params, g)); + + const Montgomery_Int& monty_g = m_g[1]; + + for(size_t i = 2; i != window_size; ++i) + { + m_g.push_back(monty_g * m_g[i - 1]); + } + + // Resize each element to exactly p words + for(size_t i = 0; i != window_size; ++i) + { + m_g[i].fix_size(); + if(const_time) + m_g[i].const_time_poison(); + } + } + +namespace { + +void const_time_lookup(secure_vector<word>& output, + const std::vector<Montgomery_Int>& g, + size_t nibble) + { + const size_t words = output.size(); + + clear_mem(output.data(), output.size()); + + for(size_t i = 0; i != g.size(); ++i) + { + const secure_vector<word>& vec = g[i].repr().get_word_vector(); + + BOTAN_ASSERT(vec.size() >= words, + "Word size as expected in const_time_lookup"); + + const word mask = CT::is_equal<word>(i, nibble); + + for(size_t w = 0; w != words; ++w) + output[w] |= (mask & vec[w]); + } + } + +} + +BigInt Montgomery_Exponentation_State::exponentiation(const BigInt& scalar, size_t max_k_bits) const + { + BOTAN_DEBUG_ASSERT(scalar.bits() <= max_k_bits); + // TODO add a const-time implementation of above assert and use it in release builds + + const size_t exp_nibbles = (max_k_bits + m_window_bits - 1) / m_window_bits; + + if(exp_nibbles == 0) + return 1; + + secure_vector<word> e_bits(m_params->p_words()); + secure_vector<word> ws; + + const_time_lookup(e_bits, m_g, scalar.get_substring(m_window_bits*(exp_nibbles-1), m_window_bits)); + Montgomery_Int x(m_params, e_bits.data(), e_bits.size(), false); + + for(size_t i = exp_nibbles - 1; i > 0; --i) + { + x.square_this_n_times(ws, m_window_bits); + const_time_lookup(e_bits, m_g, scalar.get_substring(m_window_bits*(i-1), m_window_bits)); + x.mul_by(e_bits, ws); + } + + x.const_time_unpoison(); + return x.value(); + } + +BigInt Montgomery_Exponentation_State::exponentiation_vartime(const BigInt& scalar) const + { + BOTAN_ASSERT_NOMSG(m_const_time == false); + + const size_t exp_nibbles = (scalar.bits() + m_window_bits - 1) / m_window_bits; + + secure_vector<word> ws; + + if(exp_nibbles == 0) + return 1; + + Montgomery_Int x = m_g[scalar.get_substring(m_window_bits*(exp_nibbles-1), m_window_bits)]; + + for(size_t i = exp_nibbles - 1; i > 0; --i) + { + x.square_this_n_times(ws, m_window_bits); + + const uint32_t nibble = scalar.get_substring(m_window_bits*(i-1), m_window_bits); + if(nibble > 0) + x.mul_by(m_g[nibble], ws); + } + + x.const_time_unpoison(); + return x.value(); + } + +std::shared_ptr<const Montgomery_Exponentation_State> +monty_precompute(std::shared_ptr<const Montgomery_Params> params, + const BigInt& g, + size_t window_bits, + bool const_time) + { + return std::make_shared<const Montgomery_Exponentation_State>(params, g, window_bits, const_time); + } + +BigInt monty_execute(const Montgomery_Exponentation_State& precomputed_state, + const BigInt& k, size_t max_k_bits) + { + return precomputed_state.exponentiation(k, max_k_bits); + } + +BigInt monty_execute_vartime(const Montgomery_Exponentation_State& precomputed_state, + const BigInt& k) + { + return precomputed_state.exponentiation_vartime(k); + } + +BigInt monty_multi_exp(std::shared_ptr<const Montgomery_Params> params_p, + const BigInt& x_bn, + const BigInt& z1, + const BigInt& y_bn, + const BigInt& z2) + { + if(z1.is_negative() || z2.is_negative()) + throw Invalid_Argument("multi_exponentiate exponents must be positive"); + + const size_t z_bits = round_up(std::max(z1.bits(), z2.bits()), 2); + + secure_vector<word> ws; + + const Montgomery_Int one(params_p, params_p->R1(), false); + //const Montgomery_Int one(params_p, 1); + + const Montgomery_Int x1(params_p, x_bn); + const Montgomery_Int x2 = x1.square(ws); + const Montgomery_Int x3 = x2.mul(x1, ws); + + const Montgomery_Int y1(params_p, y_bn); + const Montgomery_Int y2 = y1.square(ws); + const Montgomery_Int y3 = y2.mul(y1, ws); + + const Montgomery_Int y1x1 = y1.mul(x1, ws); + const Montgomery_Int y1x2 = y1.mul(x2, ws); + const Montgomery_Int y1x3 = y1.mul(x3, ws); + + const Montgomery_Int y2x1 = y2.mul(x1, ws); + const Montgomery_Int y2x2 = y2.mul(x2, ws); + const Montgomery_Int y2x3 = y2.mul(x3, ws); + + const Montgomery_Int y3x1 = y3.mul(x1, ws); + const Montgomery_Int y3x2 = y3.mul(x2, ws); + const Montgomery_Int y3x3 = y3.mul(x3, ws); + + const Montgomery_Int* M[16] = { + &one, + &x1, // 0001 + &x2, // 0010 + &x3, // 0011 + &y1, // 0100 + &y1x1, + &y1x2, + &y1x3, + &y2, // 1000 + &y2x1, + &y2x2, + &y2x3, + &y3, // 1100 + &y3x1, + &y3x2, + &y3x3 + }; + + Montgomery_Int H = one; + + for(size_t i = 0; i != z_bits; i += 2) + { + if(i > 0) + { + H.square_this(ws); + H.square_this(ws); + } + + const uint8_t z1_b = z1.get_substring(z_bits - i - 2, 2); + const uint8_t z2_b = z2.get_substring(z_bits - i - 2, 2); + + const uint8_t z12 = (4*z2_b) + z1_b; + + H.mul_by(*M[z12], ws); + } + + return H.value(); + } + +} + diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty_exp.h b/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty_exp.h new file mode 100644 index 0000000000..632d7f7d6e --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/monty_exp.h @@ -0,0 +1,54 @@ +/* +* (C) 2018 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_MONTY_EXP_H_ +#define BOTAN_MONTY_EXP_H_ + +#include <memory> + +namespace Botan { + +class BigInt; +class Modular_Reducer; + +class Montgomery_Params; + +class Montgomery_Exponentation_State; + +/* +* Precompute for calculating values g^x mod p +*/ +std::shared_ptr<const Montgomery_Exponentation_State> +monty_precompute(std::shared_ptr<const Montgomery_Params> params_p, + const BigInt& g, + size_t window_bits, + bool const_time = true); + +/* +* Return g^k mod p +*/ +BigInt monty_execute(const Montgomery_Exponentation_State& precomputed_state, + const BigInt& k, size_t max_k_bits); + +/* +* Return g^k mod p taking variable time depending on k +* @warning only use this if k is public +*/ +BigInt monty_execute_vartime(const Montgomery_Exponentation_State& precomputed_state, + const BigInt& k); + +/** +* Return (x^z1 * y^z2) % p +*/ +BigInt monty_multi_exp(std::shared_ptr<const Montgomery_Params> params_p, + const BigInt& x, + const BigInt& z1, + const BigInt& y, + const BigInt& z2); + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/mp_numth.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/mp_numth.cpp new file mode 100644 index 0000000000..eef6419965 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/mp_numth.cpp @@ -0,0 +1,84 @@ +/* +* Fused and Important MP Algorithms +* (C) 1999-2007 Jack Lloyd +* 2016 Matthias Gierlings +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/numthry.h> +#include <botan/internal/mp_core.h> +#include <botan/internal/rounding.h> +#include <algorithm> + +namespace Botan { + +/* +* Square a BigInt +*/ +BigInt square(const BigInt& x) + { + BigInt z = x; + secure_vector<word> ws; + z.square(ws); + return z; + } + +/* +* Multiply-Add Operation +*/ +BigInt mul_add(const BigInt& a, const BigInt& b, const BigInt& c) + { + if(c.is_negative()) + throw Invalid_Argument("mul_add: Third argument must be > 0"); + + BigInt::Sign sign = BigInt::Positive; + if(a.sign() != b.sign()) + sign = BigInt::Negative; + + const size_t a_sw = a.sig_words(); + const size_t b_sw = b.sig_words(); + const size_t c_sw = c.sig_words(); + + BigInt r(sign, std::max(a_sw + b_sw, c_sw) + 1); + secure_vector<word> workspace(r.size()); + + bigint_mul(r.mutable_data(), r.size(), + a.data(), a.size(), a_sw, + b.data(), b.size(), b_sw, + workspace.data(), workspace.size()); + + const size_t r_size = std::max(r.sig_words(), c_sw); + bigint_add2(r.mutable_data(), r_size, c.data(), c_sw); + return r; + } + +/* +* Subtract-Multiply Operation +*/ +BigInt sub_mul(const BigInt& a, const BigInt& b, const BigInt& c) + { + if(a.is_negative() || b.is_negative()) + throw Invalid_Argument("sub_mul: First two arguments must be >= 0"); + + BigInt r = a; + r -= b; + r *= c; + return r; + } + +/* +* Multiply-Subtract Operation +*/ +BigInt mul_sub(const BigInt& a, const BigInt& b, const BigInt& c) + { + if(c.is_negative() || c.is_zero()) + throw Invalid_Argument("mul_sub: Third argument must be > 0"); + + BigInt r = a; + r *= b; + r -= c; + return r; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/nistp_redc.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/nistp_redc.cpp new file mode 100644 index 0000000000..b74a2f9c6b --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/nistp_redc.cpp @@ -0,0 +1,623 @@ +/* +* NIST prime reductions +* (C) 2014,2015,2018 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/curve_nistp.h> +#include <botan/internal/mp_core.h> +#include <botan/internal/mp_asmi.h> + +namespace Botan { + +const BigInt& prime_p521() + { + static const BigInt p521("0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" + "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + + return p521; + } + +void redc_p521(BigInt& x, secure_vector<word>& ws) + { + const size_t p_full_words = 521 / BOTAN_MP_WORD_BITS; + const size_t p_top_bits = 521 % BOTAN_MP_WORD_BITS; + const size_t p_words = p_full_words + 1; + + const size_t x_sw = x.sig_words(); + + if(x_sw < p_words) + return; // already smaller + + if(ws.size() < p_words + 1) + ws.resize(p_words + 1); + + clear_mem(ws.data(), ws.size()); + bigint_shr2(ws.data(), x.data(), x_sw, p_full_words, p_top_bits); + + x.mask_bits(521); + + // Word-level carry will be zero + word carry = bigint_add3_nc(x.mutable_data(), x.data(), p_words, ws.data(), p_words); + BOTAN_ASSERT_EQUAL(carry, 0, "Final carry in P-521 reduction"); + + // Now find the actual carry in bit 522 + const uint8_t bit_522_set = x.word_at(p_full_words) >> (p_top_bits); + +#if (BOTAN_MP_WORD_BITS == 64) + static const word p521_words[9] = { + 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, + 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, + 0x1FF }; +#endif + + /* + * If bit 522 is set then we overflowed and must reduce. Otherwise, if the + * top bit is set, it is possible we have x == 2**521 - 1 so check for that. + */ + if(bit_522_set) + { +#if (BOTAN_MP_WORD_BITS == 64) + bigint_sub2(x.mutable_data(), x.size(), p521_words, 9); +#else + x -= prime_p521(); +#endif + } + else if(x.word_at(p_full_words) >> (p_top_bits - 1)) + { + /* + * Otherwise we must reduce if p is exactly 2^512-1 + */ + + word possibly_521 = MP_WORD_MAX; + for(size_t i = 0; i != p_full_words; ++i) + possibly_521 &= x.word_at(i); + + if(possibly_521 == MP_WORD_MAX) + x.reduce_below(prime_p521(), ws); + } + } + +#if defined(BOTAN_HAS_NIST_PRIME_REDUCERS_W32) + +namespace { + +/** +* Treating this MPI as a sequence of 32-bit words in big-endian +* order, return word i (or 0 if out of range) +*/ +inline uint32_t get_uint32_t(const BigInt& x, size_t i) + { +#if (BOTAN_MP_WORD_BITS == 32) + return x.word_at(i); +#elif (BOTAN_MP_WORD_BITS == 64) + return static_cast<uint32_t>(x.word_at(i/2) >> ((i % 2)*32)); +#else + #error "Not implemented" +#endif + } + +inline void set_words(BigInt& x, size_t i, uint32_t R0, uint32_t R1) + { +#if (BOTAN_MP_WORD_BITS == 32) + x.set_word_at(i, R0); + x.set_word_at(i+1, R1); +#elif (BOTAN_MP_WORD_BITS == 64) + x.set_word_at(i/2, (static_cast<uint64_t>(R1) << 32) | R0); +#else + #error "Not implemented" +#endif + } + +} + +const BigInt& prime_p192() + { + static const BigInt p192("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"); + return p192; + } + +void redc_p192(BigInt& x, secure_vector<word>& ws) + { + BOTAN_UNUSED(ws); + + static const size_t p192_limbs = 192 / BOTAN_MP_WORD_BITS; + + const uint64_t X00 = get_uint32_t(x, 0); + const uint64_t X01 = get_uint32_t(x, 1); + const uint64_t X02 = get_uint32_t(x, 2); + const uint64_t X03 = get_uint32_t(x, 3); + const uint64_t X04 = get_uint32_t(x, 4); + const uint64_t X05 = get_uint32_t(x, 5); + const uint64_t X06 = get_uint32_t(x, 6); + const uint64_t X07 = get_uint32_t(x, 7); + const uint64_t X08 = get_uint32_t(x, 8); + const uint64_t X09 = get_uint32_t(x, 9); + const uint64_t X10 = get_uint32_t(x, 10); + const uint64_t X11 = get_uint32_t(x, 11); + + const uint64_t S0 = X00 + X06 + X10; + const uint64_t S1 = X01 + X07 + X11; + const uint64_t S2 = X02 + X06 + X08 + X10; + const uint64_t S3 = X03 + X07 + X09 + X11; + const uint64_t S4 = X04 + X08 + X10; + const uint64_t S5 = X05 + X09 + X11; + + x.mask_bits(192); + + uint64_t S = 0; + uint32_t R0 = 0, R1 = 0; + + S += S0; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S1; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 0, R0, R1); + + S += S2; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S3; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 2, R0, R1); + + S += S4; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S5; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 4, R0, R1); + + // No underflow possible + + BOTAN_ASSERT(S <= 2, "Expected overflow in P-192 reduce"); + + /* + This is a table of (i*P-192) % 2**192 for i in 1...3 + */ + static const word p192_mults[3][p192_limbs] = { +#if (BOTAN_MP_WORD_BITS == 64) + {0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF}, + {0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFD, 0xFFFFFFFFFFFFFFFF}, + {0xFFFFFFFFFFFFFFFD, 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF}, +#else + {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, + {0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, + {0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, +#endif + }; + + if(S == 0 && x.word_at(p192_limbs-1) < p192_mults[0][p192_limbs-1]) + { + return; + } + + word borrow = bigint_sub2(x.mutable_data(), x.size(), p192_mults[S], p192_limbs); + + BOTAN_ASSERT(borrow == 0 || borrow == 1, "Expected borrow during P-192 reduction"); + + if(borrow) + { + bigint_add2(x.mutable_data(), x.size() - 1, p192_mults[0], p192_limbs); + } + } + +const BigInt& prime_p224() + { + static const BigInt p224("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"); + return p224; + } + +void redc_p224(BigInt& x, secure_vector<word>& ws) + { + static const size_t p224_limbs = (BOTAN_MP_WORD_BITS == 32) ? 7 : 4; + + BOTAN_UNUSED(ws); + + const int64_t X00 = get_uint32_t(x, 0); + const int64_t X01 = get_uint32_t(x, 1); + const int64_t X02 = get_uint32_t(x, 2); + const int64_t X03 = get_uint32_t(x, 3); + const int64_t X04 = get_uint32_t(x, 4); + const int64_t X05 = get_uint32_t(x, 5); + const int64_t X06 = get_uint32_t(x, 6); + const int64_t X07 = get_uint32_t(x, 7); + const int64_t X08 = get_uint32_t(x, 8); + const int64_t X09 = get_uint32_t(x, 9); + const int64_t X10 = get_uint32_t(x, 10); + const int64_t X11 = get_uint32_t(x, 11); + const int64_t X12 = get_uint32_t(x, 12); + const int64_t X13 = get_uint32_t(x, 13); + + // One full copy of P224 is added, so the result is always positive + + const int64_t S0 = 0x00000001 + X00 - X07 - X11; + const int64_t S1 = 0x00000000 + X01 - X08 - X12; + const int64_t S2 = 0x00000000 + X02 - X09 - X13; + const int64_t S3 = 0xFFFFFFFF + X03 + X07 + X11 - X10; + const int64_t S4 = 0xFFFFFFFF + X04 + X08 + X12 - X11; + const int64_t S5 = 0xFFFFFFFF + X05 + X09 + X13 - X12; + const int64_t S6 = 0xFFFFFFFF + X06 + X10 - X13; + + x.mask_bits(224); + x.shrink_to_fit(p224_limbs + 1); + + int64_t S = 0; + uint32_t R0 = 0, R1 = 0; + + S += S0; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S1; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 0, R0, R1); + + S += S2; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S3; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 2, R0, R1); + + S += S4; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S5; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 4, R0, R1); + + S += S6; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 6, R0, 0); + + BOTAN_ASSERT(S >= 0 && S <= 2, "Expected overflow in P-224 reduce"); + + static const word p224_mults[3][p224_limbs] = { +#if (BOTAN_MP_WORD_BITS == 64) + {0x0000000000000001, 0xFFFFFFFF00000000, 0xFFFFFFFFFFFFFFFF, 0x00000000FFFFFFFF}, + {0x0000000000000002, 0xFFFFFFFE00000000, 0xFFFFFFFFFFFFFFFF, 0x00000000FFFFFFFF}, + {0x0000000000000003, 0xFFFFFFFD00000000, 0xFFFFFFFFFFFFFFFF, 0x00000000FFFFFFFF}, +#else + {0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, + {0x00000002, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, + {0x00000003, 0x00000000, 0x00000000, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} +#endif + + }; + + if(S == 0 && x.word_at(p224_limbs-1) < p224_mults[0][p224_limbs-1]) + { + return; + } + + word borrow = bigint_sub2(x.mutable_data(), x.size(), p224_mults[S], p224_limbs); + + BOTAN_ASSERT(borrow == 0 || borrow == 1, "Expected borrow during P-224 reduction"); + + if(borrow) + { + bigint_add2(x.mutable_data(), x.size() - 1, p224_mults[0], p224_limbs); + } + } + +const BigInt& prime_p256() + { + static const BigInt p256("0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"); + return p256; + } + +void redc_p256(BigInt& x, secure_vector<word>& ws) + { + static const size_t p256_limbs = (BOTAN_MP_WORD_BITS == 32) ? 8 : 4; + + BOTAN_UNUSED(ws); + + const int64_t X00 = get_uint32_t(x, 0); + const int64_t X01 = get_uint32_t(x, 1); + const int64_t X02 = get_uint32_t(x, 2); + const int64_t X03 = get_uint32_t(x, 3); + const int64_t X04 = get_uint32_t(x, 4); + const int64_t X05 = get_uint32_t(x, 5); + const int64_t X06 = get_uint32_t(x, 6); + const int64_t X07 = get_uint32_t(x, 7); + const int64_t X08 = get_uint32_t(x, 8); + const int64_t X09 = get_uint32_t(x, 9); + const int64_t X10 = get_uint32_t(x, 10); + const int64_t X11 = get_uint32_t(x, 11); + const int64_t X12 = get_uint32_t(x, 12); + const int64_t X13 = get_uint32_t(x, 13); + const int64_t X14 = get_uint32_t(x, 14); + const int64_t X15 = get_uint32_t(x, 15); + + // Adds 6 * P-256 to prevent underflow + const int64_t S0 = 0xFFFFFFFA + X00 + X08 + X09 - X11 - X12 - X13 - X14; + const int64_t S1 = 0xFFFFFFFF + X01 + X09 + X10 - X12 - X13 - X14 - X15; + const int64_t S2 = 0xFFFFFFFF + X02 + X10 + X11 - X13 - X14 - X15; + const int64_t S3 = 0x00000005 + X03 + (X11 + X12)*2 + X13 - X15 - X08 - X09; + const int64_t S4 = 0x00000000 + X04 + (X12 + X13)*2 + X14 - X09 - X10; + const int64_t S5 = 0x00000000 + X05 + (X13 + X14)*2 + X15 - X10 - X11; + const int64_t S6 = 0x00000006 + X06 + X13 + X14*3 + X15*2 - X08 - X09; + const int64_t S7 = 0xFFFFFFFA + X07 + X15*3 + X08 - X10 - X11 - X12 - X13; + + x.mask_bits(256); + x.shrink_to_fit(p256_limbs + 1); + + int64_t S = 0; + + uint32_t R0 = 0, R1 = 0; + + S += S0; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S1; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 0, R0, R1); + + S += S2; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S3; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 2, R0, R1); + + S += S4; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S5; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 4, R0, R1); + + S += S6; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S7; + R1 = static_cast<uint32_t>(S); + S >>= 32; + set_words(x, 6, R0, R1); + + S += 5; // the top digits of 6*P-256 + + BOTAN_ASSERT(S >= 0 && S <= 10, "Expected overflow"); + + /* + This is a table of (i*P-256) % 2**256 for i in 1...10 + */ + static const word p256_mults[11][p256_limbs] = { +#if (BOTAN_MP_WORD_BITS == 64) + {0xFFFFFFFFFFFFFFFF, 0x00000000FFFFFFFF, 0x0000000000000000, 0xFFFFFFFF00000001}, + {0xFFFFFFFFFFFFFFFE, 0x00000001FFFFFFFF, 0x0000000000000000, 0xFFFFFFFE00000002}, + {0xFFFFFFFFFFFFFFFD, 0x00000002FFFFFFFF, 0x0000000000000000, 0xFFFFFFFD00000003}, + {0xFFFFFFFFFFFFFFFC, 0x00000003FFFFFFFF, 0x0000000000000000, 0xFFFFFFFC00000004}, + {0xFFFFFFFFFFFFFFFB, 0x00000004FFFFFFFF, 0x0000000000000000, 0xFFFFFFFB00000005}, + {0xFFFFFFFFFFFFFFFA, 0x00000005FFFFFFFF, 0x0000000000000000, 0xFFFFFFFA00000006}, + {0xFFFFFFFFFFFFFFF9, 0x00000006FFFFFFFF, 0x0000000000000000, 0xFFFFFFF900000007}, + {0xFFFFFFFFFFFFFFF8, 0x00000007FFFFFFFF, 0x0000000000000000, 0xFFFFFFF800000008}, + {0xFFFFFFFFFFFFFFF7, 0x00000008FFFFFFFF, 0x0000000000000000, 0xFFFFFFF700000009}, + {0xFFFFFFFFFFFFFFF6, 0x00000009FFFFFFFF, 0x0000000000000000, 0xFFFFFFF60000000A}, + {0xFFFFFFFFFFFFFFF5, 0x0000000AFFFFFFFF, 0x0000000000000000, 0xFFFFFFF50000000B}, +#else + {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF}, + {0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000001, 0x00000000, 0x00000000, 0x00000002, 0xFFFFFFFE}, + {0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000002, 0x00000000, 0x00000000, 0x00000003, 0xFFFFFFFD}, + {0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000003, 0x00000000, 0x00000000, 0x00000004, 0xFFFFFFFC}, + {0xFFFFFFFB, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000004, 0x00000000, 0x00000000, 0x00000005, 0xFFFFFFFB}, + {0xFFFFFFFA, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000005, 0x00000000, 0x00000000, 0x00000006, 0xFFFFFFFA}, + {0xFFFFFFF9, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000006, 0x00000000, 0x00000000, 0x00000007, 0xFFFFFFF9}, + {0xFFFFFFF8, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000007, 0x00000000, 0x00000000, 0x00000008, 0xFFFFFFF8}, + {0xFFFFFFF7, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000008, 0x00000000, 0x00000000, 0x00000009, 0xFFFFFFF7}, + {0xFFFFFFF6, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000009, 0x00000000, 0x00000000, 0x0000000A, 0xFFFFFFF6}, + {0xFFFFFFF5, 0xFFFFFFFF, 0xFFFFFFFF, 0x0000000A, 0x00000000, 0x00000000, 0x0000000B, 0xFFFFFFF5}, +#endif + }; + + if(S == 0 && x.word_at(p256_limbs-1) < p256_mults[0][p256_limbs-1]) + { + return; + } + + word borrow = bigint_sub2(x.mutable_data(), x.size(), p256_mults[S], p256_limbs); + + BOTAN_ASSERT(borrow == 0 || borrow == 1, "Expected borrow during P-256 reduction"); + + if(borrow) + { + bigint_add2(x.mutable_data(), x.size() - 1, p256_mults[0], p256_limbs); + } + } + +const BigInt& prime_p384() + { + static const BigInt p384("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"); + return p384; + } + +void redc_p384(BigInt& x, secure_vector<word>& ws) + { + BOTAN_UNUSED(ws); + + static const size_t p384_limbs = (BOTAN_MP_WORD_BITS == 32) ? 12 : 6; + + const int64_t X00 = get_uint32_t(x, 0); + const int64_t X01 = get_uint32_t(x, 1); + const int64_t X02 = get_uint32_t(x, 2); + const int64_t X03 = get_uint32_t(x, 3); + const int64_t X04 = get_uint32_t(x, 4); + const int64_t X05 = get_uint32_t(x, 5); + const int64_t X06 = get_uint32_t(x, 6); + const int64_t X07 = get_uint32_t(x, 7); + const int64_t X08 = get_uint32_t(x, 8); + const int64_t X09 = get_uint32_t(x, 9); + const int64_t X10 = get_uint32_t(x, 10); + const int64_t X11 = get_uint32_t(x, 11); + const int64_t X12 = get_uint32_t(x, 12); + const int64_t X13 = get_uint32_t(x, 13); + const int64_t X14 = get_uint32_t(x, 14); + const int64_t X15 = get_uint32_t(x, 15); + const int64_t X16 = get_uint32_t(x, 16); + const int64_t X17 = get_uint32_t(x, 17); + const int64_t X18 = get_uint32_t(x, 18); + const int64_t X19 = get_uint32_t(x, 19); + const int64_t X20 = get_uint32_t(x, 20); + const int64_t X21 = get_uint32_t(x, 21); + const int64_t X22 = get_uint32_t(x, 22); + const int64_t X23 = get_uint32_t(x, 23); + + // One copy of P-384 is added to prevent underflow + const int64_t S0 = 0xFFFFFFFF + X00 + X12 + X20 + X21 - X23; + const int64_t S1 = 0x00000000 + X01 + X13 + X22 + X23 - X12 - X20; + const int64_t S2 = 0x00000000 + X02 + X14 + X23 - X13 - X21; + const int64_t S3 = 0xFFFFFFFF + X03 + X12 + X15 + X20 + X21 - X14 - X22 - X23; + const int64_t S4 = 0xFFFFFFFE + X04 + X12 + X13 + X16 + X20 + X21*2 + X22 - X15 - X23*2; + const int64_t S5 = 0xFFFFFFFF + X05 + X13 + X14 + X17 + X21 + X22*2 + X23 - X16; + const int64_t S6 = 0xFFFFFFFF + X06 + X14 + X15 + X18 + X22 + X23*2 - X17; + const int64_t S7 = 0xFFFFFFFF + X07 + X15 + X16 + X19 + X23 - X18; + const int64_t S8 = 0xFFFFFFFF + X08 + X16 + X17 + X20 - X19; + const int64_t S9 = 0xFFFFFFFF + X09 + X17 + X18 + X21 - X20; + const int64_t SA = 0xFFFFFFFF + X10 + X18 + X19 + X22 - X21; + const int64_t SB = 0xFFFFFFFF + X11 + X19 + X20 + X23 - X22; + + x.mask_bits(384); + x.shrink_to_fit(p384_limbs + 1); + + int64_t S = 0; + + uint32_t R0 = 0, R1 = 0; + + S += S0; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S1; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 0, R0, R1); + + S += S2; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S3; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 2, R0, R1); + + S += S4; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S5; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 4, R0, R1); + + S += S6; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S7; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 6, R0, R1); + + S += S8; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += S9; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 8, R0, R1); + + S += SA; + R0 = static_cast<uint32_t>(S); + S >>= 32; + + S += SB; + R1 = static_cast<uint32_t>(S); + S >>= 32; + + set_words(x, 10, R0, R1); + + BOTAN_ASSERT(S >= 0 && S <= 4, "Expected overflow in P-384 reduction"); + + /* + This is a table of (i*P-384) % 2**384 for i in 1...4 + */ + static const word p384_mults[5][p384_limbs] = { +#if (BOTAN_MP_WORD_BITS == 64) + {0x00000000FFFFFFFF, 0xFFFFFFFF00000000, 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, + {0x00000001FFFFFFFE, 0xFFFFFFFE00000000, 0xFFFFFFFFFFFFFFFD, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, + {0x00000002FFFFFFFD, 0xFFFFFFFD00000000, 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, + {0x00000003FFFFFFFC, 0xFFFFFFFC00000000, 0xFFFFFFFFFFFFFFFB, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, + {0x00000004FFFFFFFB, 0xFFFFFFFB00000000, 0xFFFFFFFFFFFFFFFA, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, + +#else + {0xFFFFFFFF, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, + 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, + {0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF, + 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, + {0xFFFFFFFD, 0x00000002, 0x00000000, 0xFFFFFFFD, 0xFFFFFFFC, 0xFFFFFFFF, + 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, + {0xFFFFFFFC, 0x00000003, 0x00000000, 0xFFFFFFFC, 0xFFFFFFFB, 0xFFFFFFFF, + 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, + {0xFFFFFFFB, 0x00000004, 0x00000000, 0xFFFFFFFB, 0xFFFFFFFA, 0xFFFFFFFF, + 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, +#endif + }; + + if(S == 0 && x.word_at(p384_limbs-1) < p384_mults[0][p384_limbs-1]) + { + return; + } + + word borrow = bigint_sub2(x.mutable_data(), x.size(), p384_mults[S], p384_limbs); + + BOTAN_ASSERT(borrow == 0 || borrow == 1, "Expected borrow during P-384 reduction"); + + if(borrow) + { + bigint_add2(x.mutable_data(), x.size() - 1, p384_mults[0], p384_limbs); + } + } + +#endif + + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/numthry.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/numthry.cpp new file mode 100644 index 0000000000..a312ba3a1c --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/numthry.cpp @@ -0,0 +1,566 @@ +/* +* Number Theory Functions +* (C) 1999-2011,2016,2018 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/numthry.h> +#include <botan/pow_mod.h> +#include <botan/reducer.h> +#include <botan/monty.h> +#include <botan/rng.h> +#include <botan/internal/bit_ops.h> +#include <botan/internal/mp_core.h> +#include <botan/internal/ct_utils.h> +#include <botan/internal/monty_exp.h> +#include <algorithm> + +namespace Botan { + +/* +* Return the number of 0 bits at the end of n +*/ +size_t low_zero_bits(const BigInt& n) + { + size_t low_zero = 0; + + if(n.is_positive() && n.is_nonzero()) + { + for(size_t i = 0; i != n.size(); ++i) + { + const word x = n.word_at(i); + + if(x) + { + low_zero += ctz(x); + break; + } + else + low_zero += BOTAN_MP_WORD_BITS; + } + } + + return low_zero; + } + +/* +* Calculate the GCD +*/ +BigInt gcd(const BigInt& a, const BigInt& b) + { + if(a.is_zero() || b.is_zero()) + return 0; + if(a == 1 || b == 1) + return 1; + + BigInt X[2] = { a, b }; + X[0].set_sign(BigInt::Positive); + X[1].set_sign(BigInt::Positive); + + const size_t shift = std::min(low_zero_bits(X[0]), low_zero_bits(X[1])); + + X[0] >>= shift; + X[1] >>= shift; + + while(X[0].is_nonzero()) + { + X[0] >>= low_zero_bits(X[0]); + X[1] >>= low_zero_bits(X[1]); + + const uint8_t sel = static_cast<uint8_t>(X[0] >= X[1]); + + X[sel^1] -= X[sel]; + X[sel^1] >>= 1; + } + + return (X[1] << shift); + } + +/* +* Calculate the LCM +*/ +BigInt lcm(const BigInt& a, const BigInt& b) + { + return ((a * b) / gcd(a, b)); + } + +/* +Sets result to a^-1 * 2^k mod a +with n <= k <= 2n +Returns k + +"The Montgomery Modular Inverse - Revisited" Çetin Koç, E. Savas +https://citeseerx.ist.psu.edu/viewdoc/citations?doi=10.1.1.75.8377 + +A const time implementation of this algorithm is described in +"Constant Time Modular Inversion" Joppe W. Bos +http://www.joppebos.com/files/CTInversion.pdf +*/ +size_t almost_montgomery_inverse(BigInt& result, + const BigInt& a, + const BigInt& p) + { + size_t k = 0; + + BigInt u = p, v = a, r = 0, s = 1; + + while(v > 0) + { + if(u.is_even()) + { + u >>= 1; + s <<= 1; + } + else if(v.is_even()) + { + v >>= 1; + r <<= 1; + } + else if(u > v) + { + u -= v; + u >>= 1; + r += s; + s <<= 1; + } + else + { + v -= u; + v >>= 1; + s += r; + r <<= 1; + } + + ++k; + } + + if(r >= p) + { + r -= p; + } + + result = p - r; + + return k; + } + +BigInt normalized_montgomery_inverse(const BigInt& a, const BigInt& p) + { + BigInt r; + size_t k = almost_montgomery_inverse(r, a, p); + + for(size_t i = 0; i != k; ++i) + { + if(r.is_odd()) + r += p; + r >>= 1; + } + + return r; + } + +BigInt ct_inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod) + { + if(n.is_negative() || mod.is_negative()) + throw Invalid_Argument("ct_inverse_mod_odd_modulus: arguments must be non-negative"); + if(mod < 3 || mod.is_even()) + throw Invalid_Argument("Bad modulus to ct_inverse_mod_odd_modulus"); + if(n >= mod) + throw Invalid_Argument("ct_inverse_mod_odd_modulus n >= mod not supported"); + + /* + This uses a modular inversion algorithm designed by Niels Möller + and implemented in Nettle. The same algorithm was later also + adapted to GMP in mpn_sec_invert. + + It can be easily implemented in a way that does not depend on + secret branches or memory lookups, providing resistance against + some forms of side channel attack. + + There is also a description of the algorithm in Appendix 5 of "Fast + Software Polynomial Multiplication on ARM Processors using the NEON Engine" + by Danilo Câmara, Conrado P. L. Gouvêa, Julio López, and Ricardo + Dahab in LNCS 8182 + https://conradoplg.cryptoland.net/files/2010/12/mocrysen13.pdf + + Thanks to Niels for creating the algorithm, explaining some things + about it, and the reference to the paper. + */ + + // todo allow this to be pre-calculated and passed in as arg + BigInt mp1o2 = (mod + 1) >> 1; + + const size_t mod_words = mod.sig_words(); + BOTAN_ASSERT(mod_words > 0, "Not empty"); + + BigInt a = n; + BigInt b = mod; + BigInt u = 1, v = 0; + + a.grow_to(mod_words); + u.grow_to(mod_words); + v.grow_to(mod_words); + mp1o2.grow_to(mod_words); + + secure_vector<word>& a_w = a.get_word_vector(); + secure_vector<word>& b_w = b.get_word_vector(); + secure_vector<word>& u_w = u.get_word_vector(); + secure_vector<word>& v_w = v.get_word_vector(); + + CT::poison(a_w.data(), a_w.size()); + CT::poison(b_w.data(), b_w.size()); + CT::poison(u_w.data(), u_w.size()); + CT::poison(v_w.data(), v_w.size()); + + // Only n.bits() + mod.bits() iterations are required, but avoid leaking the size of n + size_t bits = 2 * mod.bits(); + + while(bits--) + { + /* + const word odd = a.is_odd(); + a -= odd * b; + const word underflow = a.is_negative(); + b += a * underflow; + a.set_sign(BigInt::Positive); + + a >>= 1; + + if(underflow) + { + std::swap(u, v); + } + + u -= odd * v; + u += u.is_negative() * mod; + + const word odd_u = u.is_odd(); + + u >>= 1; + u += mp1o2 * odd_u; + */ + + const word odd_a = a_w[0] & 1; + + //if(odd_a) a -= b + word underflow = bigint_cnd_sub(odd_a, a_w.data(), b_w.data(), mod_words); + + //if(underflow) { b -= a; a = abs(a); swap(u, v); } + bigint_cnd_add(underflow, b_w.data(), a_w.data(), mod_words); + bigint_cnd_abs(underflow, a_w.data(), mod_words); + bigint_cnd_swap(underflow, u_w.data(), v_w.data(), mod_words); + + // a >>= 1 + bigint_shr1(a_w.data(), mod_words, 0, 1); + + //if(odd_a) u -= v; + word borrow = bigint_cnd_sub(odd_a, u_w.data(), v_w.data(), mod_words); + + // if(borrow) u += p + bigint_cnd_add(borrow, u_w.data(), mod.data(), mod_words); + + const word odd_u = u_w[0] & 1; + + // u >>= 1 + bigint_shr1(u_w.data(), mod_words, 0, 1); + + //if(odd_u) u += mp1o2; + bigint_cnd_add(odd_u, u_w.data(), mp1o2.data(), mod_words); + } + + CT::unpoison(a_w.data(), a_w.size()); + CT::unpoison(b_w.data(), b_w.size()); + CT::unpoison(u_w.data(), u_w.size()); + CT::unpoison(v_w.data(), v_w.size()); + + BOTAN_ASSERT(a.is_zero(), "A is zero"); + + if(b != 1) + return 0; + + return v; + } + +/* +* Find the Modular Inverse +*/ +BigInt inverse_mod(const BigInt& n, const BigInt& mod) + { + if(mod.is_zero()) + throw BigInt::DivideByZero(); + if(mod.is_negative() || n.is_negative()) + throw Invalid_Argument("inverse_mod: arguments must be non-negative"); + + if(n.is_zero() || (n.is_even() && mod.is_even())) + return 0; // fast fail checks + + if(mod.is_odd() && n < mod) + return ct_inverse_mod_odd_modulus(n, mod); + + return inverse_euclid(n, mod); + } + +BigInt inverse_euclid(const BigInt& n, const BigInt& mod) + { + if(mod.is_zero()) + throw BigInt::DivideByZero(); + if(mod.is_negative() || n.is_negative()) + throw Invalid_Argument("inverse_mod: arguments must be non-negative"); + + if(n.is_zero() || (n.is_even() && mod.is_even())) + return 0; // fast fail checks + + BigInt u = mod, v = n; + BigInt A = 1, B = 0, C = 0, D = 1; + + while(u.is_nonzero()) + { + const size_t u_zero_bits = low_zero_bits(u); + u >>= u_zero_bits; + for(size_t i = 0; i != u_zero_bits; ++i) + { + if(A.is_odd() || B.is_odd()) + { A += n; B -= mod; } + A >>= 1; B >>= 1; + } + + const size_t v_zero_bits = low_zero_bits(v); + v >>= v_zero_bits; + for(size_t i = 0; i != v_zero_bits; ++i) + { + if(C.is_odd() || D.is_odd()) + { C += n; D -= mod; } + C >>= 1; D >>= 1; + } + + if(u >= v) { u -= v; A -= C; B -= D; } + else { v -= u; C -= A; D -= B; } + } + + if(v != 1) + return 0; // no modular inverse + + while(D.is_negative()) D += mod; + while(D >= mod) D -= mod; + + return D; + } + +word monty_inverse(word input) + { + if(input == 0) + throw Exception("monty_inverse: divide by zero"); + + word b = input; + word x2 = 1, x1 = 0, y2 = 0, y1 = 1; + + // First iteration, a = n+1 + word q = bigint_divop(1, 0, b); + word r = (MP_WORD_MAX - q*b) + 1; + word x = x2 - q*x1; + word y = y2 - q*y1; + + word a = b; + b = r; + x2 = x1; + x1 = x; + y2 = y1; + y1 = y; + + while(b > 0) + { + q = a / b; + r = a - q*b; + x = x2 - q*x1; + y = y2 - q*y1; + + a = b; + b = r; + x2 = x1; + x1 = x; + y2 = y1; + y1 = y; + } + + const word check = y2 * input; + BOTAN_ASSERT_EQUAL(check, 1, "monty_inverse result is inverse of input"); + + // Now invert in addition space + y2 = (MP_WORD_MAX - y2) + 1; + + return y2; + } + +/* +* Modular Exponentiation +*/ +BigInt power_mod(const BigInt& base, const BigInt& exp, const BigInt& mod) + { + if(mod.is_negative() || mod == 1) + { + return 0; + } + + if(base.is_zero() || mod.is_zero()) + { + if(exp.is_zero()) + return 1; + return 0; + } + + Power_Mod pow_mod(mod); + + /* + * Calling set_base before set_exponent means we end up using a + * minimal window. This makes sense given that here we know that any + * precomputation is wasted. + */ + + if(base.is_negative()) + { + pow_mod.set_base(-base); + pow_mod.set_exponent(exp); + if(exp.is_even()) + return pow_mod.execute(); + else + return (mod - pow_mod.execute()); + } + else + { + pow_mod.set_base(base); + pow_mod.set_exponent(exp); + return pow_mod.execute(); + } + } + +namespace { + +bool mr_witness(BigInt&& y, + const Modular_Reducer& reducer_n, + const BigInt& n_minus_1, size_t s) + { + if(y == 1 || y == n_minus_1) + return false; + + for(size_t i = 1; i != s; ++i) + { + y = reducer_n.square(y); + + if(y == 1) // found a non-trivial square root + return true; + + /* + -1 is the trivial square root of unity, so ``a`` is not a + witness for this number - give up + */ + if(y == n_minus_1) + return false; + } + + return true; // is a witness + } + +size_t mr_test_iterations(size_t n_bits, size_t prob, bool random) + { + const size_t base = (prob + 2) / 2; // worst case 4^-t error rate + + /* + * If the candidate prime was maliciously constructed, we can't rely + * on arguments based on p being random. + */ + if(random == false) + return base; + + /* + * For randomly chosen numbers we can use the estimates from + * http://www.math.dartmouth.edu/~carlp/PDF/paper88.pdf + * + * These values are derived from the inequality for p(k,t) given on + * the second page. + */ + if(prob <= 128) + { + if(n_bits >= 1536) + return 4; // < 2^-133 + if(n_bits >= 1024) + return 6; // < 2^-133 + if(n_bits >= 512) + return 12; // < 2^-129 + if(n_bits >= 256) + return 29; // < 2^-128 + } + + /* + If the user desires a smaller error probability than we have + precomputed error estimates for, just fall back to using the worst + case error rate. + */ + return base; + } + +} + +/* +* Test for primality using Miller-Rabin +*/ +bool is_prime(const BigInt& n, RandomNumberGenerator& rng, + size_t prob, bool is_random) + { + if(n == 2) + return true; + if(n <= 1 || n.is_even()) + return false; + + // Fast path testing for small numbers (<= 65521) + if(n <= PRIMES[PRIME_TABLE_SIZE-1]) + { + const uint16_t num = static_cast<uint16_t>(n.word_at(0)); + + return std::binary_search(PRIMES, PRIMES + PRIME_TABLE_SIZE, num); + } + + const size_t test_iterations = + mr_test_iterations(n.bits(), prob, is_random && rng.is_seeded()); + + const BigInt n_minus_1 = n - 1; + const size_t s = low_zero_bits(n_minus_1); + const BigInt nm1_s = n_minus_1 >> s; + const size_t n_bits = n.bits(); + + const Modular_Reducer mod_n(n); + auto monty_n = std::make_shared<Montgomery_Params>(n, mod_n); + + const size_t powm_window = 4; + + for(size_t i = 0; i != test_iterations; ++i) + { + BigInt a; + + if(rng.is_seeded()) + { + a = BigInt::random_integer(rng, 2, n_minus_1); + } + else + { + /* + * If passed a null RNG just use 2,3,5, ... as bases + * + * This is not ideal but in certain circumstances we need to + * test for primality but have no RNG available. + */ + a = PRIMES[i]; + } + + auto powm_a_n = monty_precompute(monty_n, a, powm_window); + + BigInt y = monty_execute(*powm_a_n, nm1_s, n_bits); + + if(mr_witness(std::move(y), mod_n, n_minus_1, s)) + return false; + } + + return true; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/numthry.h b/src/libs/3rdparty/botan/src/lib/math/numbertheory/numthry.h new file mode 100644 index 0000000000..7097979bd7 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/numthry.h @@ -0,0 +1,278 @@ +/* +* Number Theory Functions +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_NUMBER_THEORY_H_ +#define BOTAN_NUMBER_THEORY_H_ + +#include <botan/bigint.h> + +namespace Botan { + +class RandomNumberGenerator; + +/** +* Fused multiply-add +* @param a an integer +* @param b an integer +* @param c an integer +* @return (a*b)+c +*/ +BigInt BOTAN_PUBLIC_API(2,0) mul_add(const BigInt& a, + const BigInt& b, + const BigInt& c); + +/** +* Fused subtract-multiply +* @param a an integer +* @param b an integer +* @param c an integer +* @return (a-b)*c +*/ +BigInt BOTAN_PUBLIC_API(2,0) sub_mul(const BigInt& a, + const BigInt& b, + const BigInt& c); + +/** +* Fused multiply-subtract +* @param a an integer +* @param b an integer +* @param c an integer +* @return (a*b)-c +*/ +BigInt BOTAN_PUBLIC_API(2,0) mul_sub(const BigInt& a, + const BigInt& b, + const BigInt& c); + +/** +* Return the absolute value +* @param n an integer +* @return absolute value of n +*/ +inline BigInt abs(const BigInt& n) { return n.abs(); } + +/** +* Compute the greatest common divisor +* @param x a positive integer +* @param y a positive integer +* @return gcd(x,y) +*/ +BigInt BOTAN_PUBLIC_API(2,0) gcd(const BigInt& x, const BigInt& y); + +/** +* Least common multiple +* @param x a positive integer +* @param y a positive integer +* @return z, smallest integer such that z % x == 0 and z % y == 0 +*/ +BigInt BOTAN_PUBLIC_API(2,0) lcm(const BigInt& x, const BigInt& y); + +/** +* @param x an integer +* @return (x*x) +*/ +BigInt BOTAN_PUBLIC_API(2,0) square(const BigInt& x); + +/** +* Modular inversion +* @param x a positive integer +* @param modulus a positive integer +* @return y st (x*y) % modulus == 1 or 0 if no such value +* Not const time +*/ +BigInt BOTAN_PUBLIC_API(2,0) inverse_mod(const BigInt& x, + const BigInt& modulus); + +/** +* Modular inversion using extended binary Euclidian algorithm +* @param x a positive integer +* @param modulus a positive integer +* @return y st (x*y) % modulus == 1 or 0 if no such value +* Not const time +*/ +BigInt BOTAN_PUBLIC_API(2,5) inverse_euclid(const BigInt& x, + const BigInt& modulus); + +/** +* Const time modular inversion +* Requires the modulus be odd +*/ +BigInt BOTAN_PUBLIC_API(2,0) ct_inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod); + +/** +* Return a^-1 * 2^k mod b +* Returns k, between n and 2n +* Not const time +*/ +size_t BOTAN_PUBLIC_API(2,0) almost_montgomery_inverse(BigInt& result, + const BigInt& a, + const BigInt& b); + +/** +* Call almost_montgomery_inverse and correct the result to a^-1 mod b +*/ +BigInt BOTAN_PUBLIC_API(2,0) normalized_montgomery_inverse(const BigInt& a, const BigInt& b); + + +/** +* Compute the Jacobi symbol. If n is prime, this is equivalent +* to the Legendre symbol. +* @see http://mathworld.wolfram.com/JacobiSymbol.html +* +* @param a is a non-negative integer +* @param n is an odd integer > 1 +* @return (n / m) +*/ +int32_t BOTAN_PUBLIC_API(2,0) jacobi(const BigInt& a, + const BigInt& n); + +/** +* Modular exponentation +* @param b an integer base +* @param x a positive exponent +* @param m a positive modulus +* @return (b^x) % m +*/ +BigInt BOTAN_PUBLIC_API(2,0) power_mod(const BigInt& b, + const BigInt& x, + const BigInt& m); + +/** +* Compute the square root of x modulo a prime using the +* Shanks-Tonnelli algorithm +* +* @param x the input +* @param p the prime +* @return y such that (y*y)%p == x, or -1 if no such integer +*/ +BigInt BOTAN_PUBLIC_API(2,0) ressol(const BigInt& x, const BigInt& p); + +/* +* Compute -input^-1 mod 2^MP_WORD_BITS. Returns zero if input +* is even. If input is odd, input and 2^n are relatively prime +* and an inverse exists. +*/ +word BOTAN_PUBLIC_API(2,0) monty_inverse(word input); + +/** +* @param x a positive integer +* @return count of the zero bits in x, or, equivalently, the largest +* value of n such that 2^n divides x evenly. Returns zero if +* n is less than or equal to zero. +*/ +size_t BOTAN_PUBLIC_API(2,0) low_zero_bits(const BigInt& x); + +/** +* Check for primality +* @param n a positive integer to test for primality +* @param rng a random number generator +* @param prob chance of false positive is bounded by 1/2**prob +* @param is_random true if n was randomly chosen by us +* @return true if all primality tests passed, otherwise false +*/ +bool BOTAN_PUBLIC_API(2,0) is_prime(const BigInt& n, + RandomNumberGenerator& rng, + size_t prob = 56, + bool is_random = false); + +inline bool quick_check_prime(const BigInt& n, RandomNumberGenerator& rng) + { return is_prime(n, rng, 32); } + +inline bool check_prime(const BigInt& n, RandomNumberGenerator& rng) + { return is_prime(n, rng, 56); } + +inline bool verify_prime(const BigInt& n, RandomNumberGenerator& rng) + { return is_prime(n, rng, 80); } + + +/** +* Randomly generate a prime suitable for discrete logarithm parameters +* @param rng a random number generator +* @param bits how large the resulting prime should be in bits +* @param coprime a positive integer that (prime - 1) should be coprime to +* @param equiv a non-negative number that the result should be + equivalent to modulo equiv_mod +* @param equiv_mod the modulus equiv should be checked against +* @param prob use test so false positive is bounded by 1/2**prob +* @return random prime with the specified criteria +*/ +BigInt BOTAN_PUBLIC_API(2,0) random_prime(RandomNumberGenerator& rng, + size_t bits, + const BigInt& coprime = 0, + size_t equiv = 1, + size_t equiv_mod = 2, + size_t prob = 128); + +/** +* Generate a prime suitable for RSA p/q +* @param keygen_rng a random number generator +* @param prime_test_rng a random number generator +* @param bits how large the resulting prime should be in bits (must be >= 512) +* @param coprime a positive integer that (prime - 1) should be coprime to +* @param prob use test so false positive is bounded by 1/2**prob +* @return random prime with the specified criteria +*/ +BigInt BOTAN_PUBLIC_API(2,7) generate_rsa_prime(RandomNumberGenerator& keygen_rng, + RandomNumberGenerator& prime_test_rng, + size_t bits, + const BigInt& coprime, + size_t prob = 128); + +/** +* Return a 'safe' prime, of the form p=2*q+1 with q prime +* @param rng a random number generator +* @param bits is how long the resulting prime should be +* @return prime randomly chosen from safe primes of length bits +*/ +BigInt BOTAN_PUBLIC_API(2,0) random_safe_prime(RandomNumberGenerator& rng, + size_t bits); + +/** +* Generate DSA parameters using the FIPS 186 kosherizer +* @param rng a random number generator +* @param p_out where the prime p will be stored +* @param q_out where the prime q will be stored +* @param pbits how long p will be in bits +* @param qbits how long q will be in bits +* @return random seed used to generate this parameter set +*/ +std::vector<uint8_t> BOTAN_PUBLIC_API(2,0) +generate_dsa_primes(RandomNumberGenerator& rng, + BigInt& p_out, BigInt& q_out, + size_t pbits, size_t qbits); + +/** +* Generate DSA parameters using the FIPS 186 kosherizer +* @param rng a random number generator +* @param p_out where the prime p will be stored +* @param q_out where the prime q will be stored +* @param pbits how long p will be in bits +* @param qbits how long q will be in bits +* @param seed the seed used to generate the parameters +* @param offset optional offset from seed to start searching at +* @return true if seed generated a valid DSA parameter set, otherwise + false. p_out and q_out are only valid if true was returned. +*/ +bool BOTAN_PUBLIC_API(2,0) +generate_dsa_primes(RandomNumberGenerator& rng, + BigInt& p_out, BigInt& q_out, + size_t pbits, size_t qbits, + const std::vector<uint8_t>& seed, + size_t offset = 0); + +/** +* The size of the PRIMES[] array +*/ +const size_t PRIME_TABLE_SIZE = 6541; + +/** +* A const array of all primes less than 65535 +*/ +extern const uint16_t BOTAN_PUBLIC_API(2,0) PRIMES[]; + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/pow_mod.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/pow_mod.cpp new file mode 100644 index 0000000000..00917a5f91 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/pow_mod.cpp @@ -0,0 +1,196 @@ +/* +* Modular Exponentiation Proxy +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/pow_mod.h> +#include <botan/internal/def_powm.h> + +namespace Botan { + +/* +* Power_Mod Constructor +*/ +Power_Mod::Power_Mod(const BigInt& n, Usage_Hints hints, bool disable_monty) + { + set_modulus(n, hints, disable_monty); + } + +/* +* Power_Mod Copy Constructor +*/ +Power_Mod::Power_Mod(const Power_Mod& other) + { + if(other.m_core.get()) + m_core.reset(other.m_core->copy()); + } + +/* +* Power_Mod Assignment Operator +*/ +Power_Mod& Power_Mod::operator=(const Power_Mod& other) + { + if(this != &other) + { + if(other.m_core) + m_core.reset(other.m_core->copy()); + else + m_core.reset(); + } + return (*this); + } + +/* +* Set the modulus +*/ +void Power_Mod::set_modulus(const BigInt& n, Usage_Hints hints, bool disable_monty) const + { + // Allow set_modulus(0) to mean "drop old state" + + m_core.reset(); + + if(n != 0) + { + if(n.is_odd() && disable_monty == false) + m_core.reset(new Montgomery_Exponentiator(n, hints)); + else + m_core.reset(new Fixed_Window_Exponentiator(n, hints)); + } + } + +/* +* Set the base +*/ +void Power_Mod::set_base(const BigInt& b) const + { + if(b.is_zero() || b.is_negative()) + throw Invalid_Argument("Power_Mod::set_base: arg must be > 0"); + + if(!m_core) + throw Internal_Error("Power_Mod::set_base: m_core was NULL"); + m_core->set_base(b); + } + +/* +* Set the exponent +*/ +void Power_Mod::set_exponent(const BigInt& e) const + { + if(e.is_negative()) + throw Invalid_Argument("Power_Mod::set_exponent: arg must be > 0"); + + if(!m_core) + throw Internal_Error("Power_Mod::set_exponent: m_core was NULL"); + m_core->set_exponent(e); + } + +/* +* Compute the result +*/ +BigInt Power_Mod::execute() const + { + if(!m_core) + throw Internal_Error("Power_Mod::execute: m_core was NULL"); + return m_core->execute(); + } + +/* +* Try to choose a good window size +*/ +size_t Power_Mod::window_bits(size_t exp_bits, size_t, + Power_Mod::Usage_Hints hints) + { + static const size_t wsize[][2] = { + { 1434, 7 }, + { 539, 6 }, + { 197, 4 }, + { 70, 3 }, + { 17, 2 }, + { 0, 0 } + }; + + size_t window_bits = 1; + + if(exp_bits) + { + for(size_t j = 0; wsize[j][0]; ++j) + { + if(exp_bits >= wsize[j][0]) + { + window_bits += wsize[j][1]; + break; + } + } + } + + if(hints & Power_Mod::BASE_IS_FIXED) + window_bits += 2; + if(hints & Power_Mod::EXP_IS_LARGE) + ++window_bits; + + return window_bits; + } + +namespace { + +/* +* Choose potentially useful hints +*/ +Power_Mod::Usage_Hints choose_base_hints(const BigInt& b, const BigInt& n) + { + if(b == 2) + return Power_Mod::Usage_Hints(Power_Mod::BASE_IS_2 | + Power_Mod::BASE_IS_SMALL); + + const size_t b_bits = b.bits(); + const size_t n_bits = n.bits(); + + if(b_bits < n_bits / 32) + return Power_Mod::BASE_IS_SMALL; + if(b_bits > n_bits / 4) + return Power_Mod::BASE_IS_LARGE; + + return Power_Mod::NO_HINTS; + } + +/* +* Choose potentially useful hints +*/ +Power_Mod::Usage_Hints choose_exp_hints(const BigInt& e, const BigInt& n) + { + const size_t e_bits = e.bits(); + const size_t n_bits = n.bits(); + + if(e_bits < n_bits / 32) + return Power_Mod::BASE_IS_SMALL; + if(e_bits > n_bits / 4) + return Power_Mod::BASE_IS_LARGE; + return Power_Mod::NO_HINTS; + } + +} + +/* +* Fixed_Exponent_Power_Mod Constructor +*/ +Fixed_Exponent_Power_Mod::Fixed_Exponent_Power_Mod(const BigInt& e, + const BigInt& n, + Usage_Hints hints) : + Power_Mod(n, Usage_Hints(hints | EXP_IS_FIXED | choose_exp_hints(e, n))) + { + set_exponent(e); + } + +/* +* Fixed_Base_Power_Mod Constructor +*/ +Fixed_Base_Power_Mod::Fixed_Base_Power_Mod(const BigInt& b, const BigInt& n, + Usage_Hints hints) : + Power_Mod(n, Usage_Hints(hints | BASE_IS_FIXED | choose_base_hints(b, n))) + { + set_base(b); + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/pow_mod.h b/src/libs/3rdparty/botan/src/lib/math/numbertheory/pow_mod.h new file mode 100644 index 0000000000..077f4ccf72 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/pow_mod.h @@ -0,0 +1,135 @@ +/* +* Modular Exponentiator +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_POWER_MOD_H_ +#define BOTAN_POWER_MOD_H_ + +#include <botan/bigint.h> + +namespace Botan { + +/** +* Modular Exponentiator Interface +*/ +class BOTAN_PUBLIC_API(2,0) Modular_Exponentiator + { + public: + virtual void set_base(const BigInt&) = 0; + virtual void set_exponent(const BigInt&) = 0; + virtual BigInt execute() const = 0; + virtual Modular_Exponentiator* copy() const = 0; + + Modular_Exponentiator() = default; + Modular_Exponentiator(const Modular_Exponentiator&) = default; + Modular_Exponentiator & operator=(const Modular_Exponentiator&) = default; + virtual ~Modular_Exponentiator() = default; + }; + +/** +* Modular Exponentiator Proxy +*/ +class BOTAN_PUBLIC_API(2,0) Power_Mod + { + public: + + enum Usage_Hints { + NO_HINTS = 0x0000, + + BASE_IS_FIXED = 0x0001, + BASE_IS_SMALL = 0x0002, + BASE_IS_LARGE = 0x0004, + BASE_IS_2 = 0x0008, + + EXP_IS_FIXED = 0x0100, + EXP_IS_SMALL = 0x0200, + EXP_IS_LARGE = 0x0400 + }; + + /* + * Try to choose a good window size + */ + static size_t window_bits(size_t exp_bits, size_t base_bits, + Power_Mod::Usage_Hints hints); + + /** + * @param modulus the modulus + * @param hints Passed to set_modulus if modulus > 0 + * @param disable_montgomery_arith Disables use of Montgomery + * representation. Likely only useful for testing. + */ + void set_modulus(const BigInt& modulus, + Usage_Hints hints = NO_HINTS, + bool disable_montgomery_arith = false) const; + + /** + * Set the base + */ + void set_base(const BigInt& base) const; + + /** + * Set the exponent + */ + void set_exponent(const BigInt& exponent) const; + + /** + * All three of the above functions must have already been called. + * @return result of g^x%p + */ + BigInt execute() const; + + Power_Mod& operator=(const Power_Mod&); + + /** + * @param modulus Optionally call set_modulus + * @param hints Passed to set_modulus if modulus > 0 + * @param disable_montgomery_arith Disables use of Montgomery + * representation. Likely only useful for testing. + */ + Power_Mod(const BigInt& modulus = 0, + Usage_Hints hints = NO_HINTS, + bool disable_montgomery_arith = false); + Power_Mod(const Power_Mod&); + virtual ~Power_Mod() = default; + private: + mutable std::unique_ptr<Modular_Exponentiator> m_core; + }; + +/** +* Fixed Exponent Modular Exponentiator Proxy +*/ +class BOTAN_PUBLIC_API(2,0) Fixed_Exponent_Power_Mod final : public Power_Mod + { + public: + BigInt operator()(const BigInt& b) const + { set_base(b); return execute(); } + + Fixed_Exponent_Power_Mod() = default; + + Fixed_Exponent_Power_Mod(const BigInt& exponent, + const BigInt& modulus, + Usage_Hints hints = NO_HINTS); + }; + +/** +* Fixed Base Modular Exponentiator Proxy +*/ +class BOTAN_PUBLIC_API(2,0) Fixed_Base_Power_Mod final : public Power_Mod + { + public: + BigInt operator()(const BigInt& e) const + { set_exponent(e); return execute(); } + + Fixed_Base_Power_Mod() = default; + + Fixed_Base_Power_Mod(const BigInt& base, + const BigInt& modulus, + Usage_Hints hints = NO_HINTS); + }; + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/powm_fw.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/powm_fw.cpp new file mode 100644 index 0000000000..85a0364b5a --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/powm_fw.cpp @@ -0,0 +1,65 @@ +/* +* Fixed Window Exponentiation +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/def_powm.h> +#include <vector> + +namespace Botan { + +/* +* Set the exponent +*/ +void Fixed_Window_Exponentiator::set_exponent(const BigInt& e) + { + m_exp = e; + } + +/* +* Set the base +*/ +void Fixed_Window_Exponentiator::set_base(const BigInt& base) + { + m_window_bits = Power_Mod::window_bits(m_exp.bits(), base.bits(), m_hints); + + m_g.resize(1U << m_window_bits); + m_g[0] = 1; + m_g[1] = base; + + for(size_t i = 2; i != m_g.size(); ++i) + m_g[i] = m_reducer.multiply(m_g[i-1], m_g[1]); + } + +/* +* Compute the result +*/ +BigInt Fixed_Window_Exponentiator::execute() const + { + const size_t exp_nibbles = (m_exp.bits() + m_window_bits - 1) / m_window_bits; + + BigInt x = 1; + + for(size_t i = exp_nibbles; i > 0; --i) + { + for(size_t j = 0; j != m_window_bits; ++j) + x = m_reducer.square(x); + + const uint32_t nibble = m_exp.get_substring(m_window_bits*(i-1), m_window_bits); + + x = m_reducer.multiply(x, m_g[nibble]); + } + return x; + } + +/* +* Fixed_Window_Exponentiator Constructor +*/ +Fixed_Window_Exponentiator::Fixed_Window_Exponentiator(const BigInt& n, + Power_Mod::Usage_Hints hints) + : m_reducer{Modular_Reducer(n)}, m_exp{}, m_window_bits{}, m_g{}, m_hints{hints} + {} + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/powm_mnt.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/powm_mnt.cpp new file mode 100644 index 0000000000..8cb3f6a08e --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/powm_mnt.cpp @@ -0,0 +1,46 @@ +/* +* Montgomery Exponentiation +* (C) 1999-2010,2012,2018 Jack Lloyd +* 2016 Matthias Gierlings +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/def_powm.h> +#include <botan/numthry.h> +#include <botan/monty.h> +#include <botan/internal/monty_exp.h> +#include <botan/internal/rounding.h> + +namespace Botan { + +void Montgomery_Exponentiator::set_exponent(const BigInt& exp) + { + m_e = exp; + } + +void Montgomery_Exponentiator::set_base(const BigInt& base) + { + size_t window_bits = Power_Mod::window_bits(m_e.bits(), base.bits(), m_hints); + m_monty = monty_precompute(m_monty_params, base, window_bits); + } + +BigInt Montgomery_Exponentiator::execute() const + { + /* + This leaks size of e via loop iterations, not possible to fix without + breaking this API. Round up to avoid leaking fine details. + */ + return monty_execute(*m_monty, m_e, round_up(m_e.bits(), 8)); + } + +Montgomery_Exponentiator::Montgomery_Exponentiator(const BigInt& mod, + Power_Mod::Usage_Hints hints) : + m_p(mod), + m_mod_p(mod), + m_monty_params(std::make_shared<Montgomery_Params>(m_p, m_mod_p)), + m_hints(hints) + { + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/primes.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/primes.cpp new file mode 100644 index 0000000000..4a3eb46f2c --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/primes.cpp @@ -0,0 +1,609 @@ +/* +* Small Primes Table +* (C) 1999-2007 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/numthry.h> + +namespace Botan { + +const uint16_t PRIMES[PRIME_TABLE_SIZE+1] = { + 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, + 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, + 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, + 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, + 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, + 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, + 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, + 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, + 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, + 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, + 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, + 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, + 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, + 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, + 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, + 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, + 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, + 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, + 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, + 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, + 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, + 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, + 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, + 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, + 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, + 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, + 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, + 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, + 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, + 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, + 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, + 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, + 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, + 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, + 2579, 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a/src/libs/3rdparty/botan/src/lib/math/numbertheory/reducer.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/reducer.cpp new file mode 100644 index 0000000000..98cf698ed7 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/reducer.cpp @@ -0,0 +1,90 @@ +/* +* Modular Reducer +* (C) 1999-2011,2018 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/reducer.h> +#include <botan/internal/ct_utils.h> + +namespace Botan { + +/* +* Modular_Reducer Constructor +*/ +Modular_Reducer::Modular_Reducer(const BigInt& mod) + { + if(mod < 0) + throw Invalid_Argument("Modular_Reducer: modulus must be positive"); + + // Left uninitialized if mod == 0 + m_mod_words = 0; + + if(mod > 0) + { + m_modulus = mod; + m_mod_words = m_modulus.sig_words(); + + m_modulus_2 = Botan::square(m_modulus); + + m_mu = BigInt::power_of_2(2 * BOTAN_MP_WORD_BITS * m_mod_words) / m_modulus; + } + } + +/* +* Barrett Reduction +*/ +BigInt Modular_Reducer::reduce(const BigInt& x) const + { + if(m_mod_words == 0) + throw Invalid_State("Modular_Reducer: Never initalized"); + + const size_t x_sw = x.sig_words(); + + if(x_sw >= (2*m_mod_words - 1) && x.cmp(m_modulus_2, false) >= 0) + { + // too big, fall back to normal division + return (x % m_modulus); + } + + secure_vector<word> ws; + + BigInt t1 = x; + t1.set_sign(BigInt::Positive); + t1 >>= (BOTAN_MP_WORD_BITS * (m_mod_words - 1)); + + t1.mul(m_mu, ws); + t1 >>= (BOTAN_MP_WORD_BITS * (m_mod_words + 1)); + + // TODO add masked mul to avoid computing high bits + t1.mul(m_modulus, ws); + t1.mask_bits(BOTAN_MP_WORD_BITS * (m_mod_words + 1)); + + t1.rev_sub(x.data(), std::min(x_sw, m_mod_words + 1), ws); + + /* + * If t1 < 0 then we must add b^(k+1) where b = 2^w. To avoid a + * side channel perform the addition unconditionally, with ws set + * to either b^(k+1) or else 0. + */ + const word t1_neg = t1.is_negative(); + + if(ws.size() < m_mod_words + 2) + ws.resize(m_mod_words + 2); + clear_mem(ws.data(), ws.size()); + ws[m_mod_words + 1] = t1_neg; + + t1.add(ws.data(), m_mod_words + 2, BigInt::Positive); + + t1.reduce_below(m_modulus, ws); + + if(x.is_negative() && t1.is_nonzero()) + { + t1.rev_sub(m_modulus.data(), m_modulus.size(), ws); + } + + return t1; + } + +} diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/reducer.h b/src/libs/3rdparty/botan/src/lib/math/numbertheory/reducer.h new file mode 100644 index 0000000000..c66c220342 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/reducer.h @@ -0,0 +1,61 @@ +/* +* Modular Reducer +* (C) 1999-2010 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#ifndef BOTAN_MODULAR_REDUCER_H_ +#define BOTAN_MODULAR_REDUCER_H_ + +#include <botan/numthry.h> + +namespace Botan { + +/** +* Modular Reducer (using Barrett's technique) +*/ +class BOTAN_PUBLIC_API(2,0) Modular_Reducer + { + public: + const BigInt& get_modulus() const { return m_modulus; } + + BigInt reduce(const BigInt& x) const; + + /** + * Multiply mod p + * @param x the first operand + * @param y the second operand + * @return (x * y) % p + */ + BigInt multiply(const BigInt& x, const BigInt& y) const + { return reduce(x * y); } + + /** + * Square mod p + * @param x the value to square + * @return (x * x) % p + */ + BigInt square(const BigInt& x) const + { return reduce(Botan::square(x)); } + + /** + * Cube mod p + * @param x the value to cube + * @return (x * x * x) % p + */ + BigInt cube(const BigInt& x) const + { return multiply(x, this->square(x)); } + + bool initialized() const { return (m_mod_words != 0); } + + Modular_Reducer() { m_mod_words = 0; } + explicit Modular_Reducer(const BigInt& mod); + private: + BigInt m_modulus, m_modulus_2, m_mu; + size_t m_mod_words; + }; + +} + +#endif diff --git a/src/libs/3rdparty/botan/src/lib/math/numbertheory/ressol.cpp b/src/libs/3rdparty/botan/src/lib/math/numbertheory/ressol.cpp new file mode 100644 index 0000000000..9d11ebbc42 --- /dev/null +++ b/src/libs/3rdparty/botan/src/lib/math/numbertheory/ressol.cpp @@ -0,0 +1,87 @@ +/* +* Shanks-Tonnelli (RESSOL) +* (C) 2007-2008 Falko Strenzke, FlexSecure GmbH +* (C) 2008 Jack Lloyd +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/numthry.h> +#include <botan/reducer.h> + +namespace Botan { + +/* +* Shanks-Tonnelli algorithm +*/ +BigInt ressol(const BigInt& a, const BigInt& p) + { + if(a == 0) + return 0; + else if(a < 0) + throw Invalid_Argument("ressol: value to solve for must be positive"); + else if(a >= p) + throw Invalid_Argument("ressol: value to solve for must be less than p"); + + if(p == 2) + return a; + else if(p <= 1) + throw Invalid_Argument("ressol: prime must be > 1 a"); + else if(p.is_even()) + throw Invalid_Argument("ressol: invalid prime"); + + if(jacobi(a, p) != 1) // not a quadratic residue + return -BigInt(1); + + if(p % 4 == 3) + return power_mod(a, ((p+1) >> 2), p); + + size_t s = low_zero_bits(p - 1); + BigInt q = p >> s; + + q -= 1; + q >>= 1; + + Modular_Reducer mod_p(p); + + BigInt r = power_mod(a, q, p); + BigInt n = mod_p.multiply(a, mod_p.square(r)); + r = mod_p.multiply(r, a); + + if(n == 1) + return r; + + // find random non quadratic residue z + BigInt z = 2; + while(jacobi(z, p) == 1) // while z quadratic residue + ++z; + + BigInt c = power_mod(z, (q << 1) + 1, p); + + while(n > 1) + { + q = n; + + size_t i = 0; + while(q != 1) + { + q = mod_p.square(q); + ++i; + + if(i >= s) + { + return -BigInt(1); + } + } + + c = power_mod(c, BigInt::power_of_2(s-i-1), p); + r = mod_p.multiply(r, c); + c = mod_p.square(c); + n = mod_p.multiply(n, c); + s = i; + } + + return r; + } + +} |