diff options
Diffstat (limited to 'old/botan/src/math')
67 files changed, 11493 insertions, 0 deletions
diff --git a/old/botan/src/math/bigint/big_code.cpp b/old/botan/src/math/bigint/big_code.cpp new file mode 100644 index 0000000..74701e5 --- /dev/null +++ b/old/botan/src/math/bigint/big_code.cpp @@ -0,0 +1,154 @@ +/* +* BigInt Encoding/Decoding +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/bigint.h> +#include <botan/divide.h> +#include <botan/charset.h> +#include <botan/hex.h> + +namespace Botan { + +/* +* Encode a BigInt +*/ +void BigInt::encode(byte output[], const BigInt& n, Base base) + { + if(base == Binary) + n.binary_encode(output); + else if(base == Hexadecimal) + { + SecureVector<byte> binary(n.encoded_size(Binary)); + n.binary_encode(binary); + for(u32bit j = 0; j != binary.size(); ++j) + Hex_Encoder::encode(binary[j], output + 2*j); + } + else if(base == Octal) + { + BigInt copy = n; + const u32bit output_size = n.encoded_size(Octal); + for(u32bit j = 0; j != output_size; ++j) + { + output[output_size - 1 - j] = Charset::digit2char(copy % 8); + copy /= 8; + } + } + else if(base == Decimal) + { + BigInt copy = n; + BigInt remainder; + copy.set_sign(Positive); + const u32bit output_size = n.encoded_size(Decimal); + for(u32bit j = 0; j != output_size; ++j) + { + divide(copy, 10, copy, remainder); + output[output_size - 1 - j] = + Charset::digit2char(remainder.word_at(0)); + if(copy.is_zero()) + break; + } + } + else + throw Invalid_Argument("Unknown BigInt encoding method"); + } + +/* +* Encode a BigInt +*/ +SecureVector<byte> BigInt::encode(const BigInt& n, Base base) + { + SecureVector<byte> output(n.encoded_size(base)); + encode(output, n, base); + if(base != Binary) + for(u32bit j = 0; j != output.size(); ++j) + if(output[j] == 0) + output[j] = '0'; + return output; + } + +/* +* Encode a BigInt, with leading 0s if needed +*/ +SecureVector<byte> BigInt::encode_1363(const BigInt& n, u32bit bytes) + { + const u32bit n_bytes = n.bytes(); + if(n_bytes > bytes) + throw Encoding_Error("encode_1363: n is too large to encode properly"); + + const u32bit leading_0s = bytes - n_bytes; + + SecureVector<byte> output(bytes); + encode(output + leading_0s, n, Binary); + return output; + } + +/* +* Decode a BigInt +*/ +BigInt BigInt::decode(const MemoryRegion<byte>& buf, Base base) + { + return BigInt::decode(buf, buf.size(), base); + } + +/* +* Decode a BigInt +*/ +BigInt BigInt::decode(const byte buf[], u32bit length, Base base) + { + BigInt r; + if(base == Binary) + r.binary_decode(buf, length); + else if(base == Hexadecimal) + { + SecureVector<byte> hex; + for(u32bit j = 0; j != length; ++j) + if(Hex_Decoder::is_valid(buf[j])) + hex.append(buf[j]); + + u32bit offset = (hex.size() % 2); + SecureVector<byte> binary(hex.size() / 2 + offset); + + if(offset) + { + byte temp[2] = { '0', hex[0] }; + binary[0] = Hex_Decoder::decode(temp); + } + + for(u32bit j = offset; j != binary.size(); ++j) + binary[j] = Hex_Decoder::decode(hex+2*j-offset); + r.binary_decode(binary, binary.size()); + } + else if(base == Decimal || base == Octal) + { + const u32bit RADIX = ((base == Decimal) ? 10 : 8); + for(u32bit j = 0; j != length; ++j) + { + if(Charset::is_space(buf[j])) + continue; + + if(!Charset::is_digit(buf[j])) + throw Invalid_Argument("BigInt::decode: " + "Invalid character in decimal input"); + + byte x = Charset::char2digit(buf[j]); + if(x >= RADIX) + { + if(RADIX == 10) + throw Invalid_Argument("BigInt: Invalid decimal string"); + else + throw Invalid_Argument("BigInt: Invalid octal string"); + } + + r *= RADIX; + r += x; + } + } + else + throw Invalid_Argument("Unknown BigInt decoding method"); + return r; + } + +} diff --git a/old/botan/src/math/bigint/big_io.cpp b/old/botan/src/math/bigint/big_io.cpp new file mode 100644 index 0000000..b50fcce --- /dev/null +++ b/old/botan/src/math/bigint/big_io.cpp @@ -0,0 +1,55 @@ +/* +* BigInt Input/Output +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/bigint.h> +#include <iostream> + +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) + base = BigInt::Octal; + + if(n == 0) + stream.write("0", 1); + else + { + if(n < 0) + stream.write("-", 1); + SecureVector<byte> buffer = BigInt::encode(n, base); + u32bit skip = 0; + while(buffer[skip] == '0' && skip < buffer.size()) + ++skip; + stream.write(reinterpret_cast<const char*>(buffer.begin()) + 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/old/botan/src/math/bigint/big_ops2.cpp b/old/botan/src/math/bigint/big_ops2.cpp new file mode 100644 index 0000000..488eca9 --- /dev/null +++ b/old/botan/src/math/bigint/big_ops2.cpp @@ -0,0 +1,224 @@ +/* +* BigInt Assignment Operators +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/bigint.h> +#include <botan/mp_core.h> +#include <botan/bit_ops.h> +#include <algorithm> + +namespace Botan { + +/* +* Addition Operator +*/ +BigInt& BigInt::operator+=(const BigInt& y) + { + const u32bit x_sw = sig_words(), y_sw = y.sig_words(); + + const u32bit reg_size = std::max(x_sw, y_sw) + 1; + grow_to(reg_size); + + if(sign() == y.sign()) + bigint_add2(get_reg(), reg_size - 1, y.data(), y_sw); + else + { + s32bit relative_size = bigint_cmp(data(), x_sw, y.data(), y_sw); + + if(relative_size < 0) + { + SecureVector<word> z(reg_size - 1); + bigint_sub3(z, y.data(), reg_size - 1, data(), x_sw); + copy_mem(get_reg().begin(), z.begin(), z.size()); + set_sign(y.sign()); + } + else if(relative_size == 0) + { + get_reg().clear(); + set_sign(Positive); + } + else if(relative_size > 0) + bigint_sub2(get_reg(), x_sw, y.data(), y_sw); + } + + return (*this); + } + +/* +* Subtraction Operator +*/ +BigInt& BigInt::operator-=(const BigInt& y) + { + const u32bit x_sw = sig_words(), y_sw = y.sig_words(); + + s32bit relative_size = bigint_cmp(data(), x_sw, y.data(), y_sw); + + const u32bit reg_size = std::max(x_sw, y_sw) + 1; + grow_to(reg_size); + + if(relative_size < 0) + { + if(sign() == y.sign()) + { + SecureVector<word> z(reg_size - 1); + bigint_sub3(z, y.data(), reg_size - 1, data(), x_sw); + copy_mem(get_reg().begin(), z.begin(), z.size()); + } + else + bigint_add2(get_reg(), reg_size - 1, y.data(), y_sw); + + set_sign(y.reverse_sign()); + } + else if(relative_size == 0) + { + if(sign() == y.sign()) + { + get_reg().clear(); + set_sign(Positive); + } + else + bigint_shl1(get_reg(), x_sw, 0, 1); + } + else if(relative_size > 0) + { + if(sign() == y.sign()) + bigint_sub2(get_reg(), x_sw, y.data(), y_sw); + else + bigint_add2(get_reg(), reg_size - 1, y.data(), y_sw); + } + + return (*this); + } + +/* +* Multiplication Operator +*/ +BigInt& BigInt::operator*=(const BigInt& y) + { + const u32bit x_sw = sig_words(), y_sw = y.sig_words(); + set_sign((sign() == y.sign()) ? Positive : Negative); + + if(x_sw == 0 || y_sw == 0) + { + get_reg().clear(); + set_sign(Positive); + } + else if(x_sw == 1 && y_sw) + { + grow_to(y_sw + 2); + bigint_linmul3(get_reg(), y.data(), y_sw, word_at(0)); + } + else if(y_sw == 1 && x_sw) + { + grow_to(x_sw + 2); + bigint_linmul2(get_reg(), x_sw, y.word_at(0)); + } + else + { + grow_to(size() + y.size()); + + SecureVector<word> z(data(), x_sw); + SecureVector<word> workspace(size()); + + bigint_mul(get_reg(), size(), workspace, + z, z.size(), x_sw, + y.data(), y.size(), y_sw); + } + + return (*this); + } + +/* +* Division Operator +*/ +BigInt& BigInt::operator/=(const BigInt& y) + { + if(y.sig_words() == 1 && 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(power_of_2(mod)) + { + word result = (word_at(0) & (mod - 1)); + clear(); + grow_to(2); + get_reg()[0] = result; + return result; + } + + word remainder = 0; + + for(u32bit j = sig_words(); j > 0; --j) + remainder = bigint_modop(remainder, word_at(j-1), mod); + clear(); + grow_to(2); + + if(remainder && sign() == BigInt::Negative) + get_reg()[0] = mod - remainder; + else + get_reg()[0] = remainder; + + set_sign(BigInt::Positive); + + return word_at(0); + } + +/* +* Left Shift Operator +*/ +BigInt& BigInt::operator<<=(u32bit shift) + { + if(shift) + { + const u32bit shift_words = shift / MP_WORD_BITS, + shift_bits = shift % MP_WORD_BITS, + words = sig_words(); + + grow_to(words + shift_words + (shift_bits ? 1 : 0)); + bigint_shl1(get_reg(), words, shift_words, shift_bits); + } + + return (*this); + } + +/* +* Right Shift Operator +*/ +BigInt& BigInt::operator>>=(u32bit shift) + { + if(shift) + { + const u32bit shift_words = shift / MP_WORD_BITS, + shift_bits = shift % MP_WORD_BITS; + + bigint_shr1(get_reg(), sig_words(), shift_words, shift_bits); + + if(is_zero()) + set_sign(Positive); + } + + return (*this); + } + +} diff --git a/old/botan/src/math/bigint/big_ops3.cpp b/old/botan/src/math/bigint/big_ops3.cpp new file mode 100644 index 0000000..ad8b7bb --- /dev/null +++ b/old/botan/src/math/bigint/big_ops3.cpp @@ -0,0 +1,190 @@ +/* +* BigInt Binary Operators +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/bigint.h> +#include <botan/divide.h> +#include <botan/mp_core.h> +#include <botan/bit_ops.h> +#include <algorithm> + +namespace Botan { + +/* +* Addition Operator +*/ +BigInt operator+(const BigInt& x, const BigInt& y) + { + const u32bit x_sw = x.sig_words(), y_sw = y.sig_words(); + + BigInt z(x.sign(), std::max(x_sw, y_sw) + 1); + + if((x.sign() == y.sign())) + bigint_add3(z.get_reg(), x.data(), x_sw, y.data(), y_sw); + else + { + s32bit relative_size = bigint_cmp(x.data(), x_sw, y.data(), y_sw); + + if(relative_size < 0) + { + bigint_sub3(z.get_reg(), y.data(), 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.get_reg(), x.data(), x_sw, y.data(), y_sw); + } + + return z; + } + +/* +* Subtraction Operator +*/ +BigInt operator-(const BigInt& x, const BigInt& y) + { + const u32bit x_sw = x.sig_words(), y_sw = y.sig_words(); + + s32bit relative_size = bigint_cmp(x.data(), x_sw, y.data(), 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.get_reg(), y.data(), y_sw, x.data(), x_sw); + else + bigint_add3(z.get_reg(), x.data(), x_sw, y.data(), y_sw); + z.set_sign(y.reverse_sign()); + } + else if(relative_size == 0) + { + if(x.sign() != y.sign()) + bigint_shl2(z.get_reg(), x.data(), x_sw, 0, 1); + } + else if(relative_size > 0) + { + if(x.sign() == y.sign()) + bigint_sub3(z.get_reg(), x.data(), x_sw, y.data(), y_sw); + else + bigint_add3(z.get_reg(), x.data(), x_sw, y.data(), y_sw); + z.set_sign(x.sign()); + } + return z; + } + +/* +* Multiplication Operator +*/ +BigInt operator*(const BigInt& x, const BigInt& y) + { + const u32bit 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.get_reg(), y.data(), y_sw, x.word_at(0)); + else if(y_sw == 1 && x_sw) + bigint_linmul3(z.get_reg(), x.data(), x_sw, y.word_at(0)); + else if(x_sw && y_sw) + { + SecureVector<word> workspace(z.size()); + bigint_mul(z.get_reg(), z.size(), workspace, + x.data(), x.size(), x_sw, + y.data(), y.size(), y_sw); + } + + if(x_sw && y_sw && x.sign() != y.sign()) + z.flip_sign(); + return z; + } + +/* +* Division Operator +*/ +BigInt operator/(const BigInt& x, const BigInt& y) + { + 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(power_of_2(mod)) + return (n.word_at(0) & (mod - 1)); + + word remainder = 0; + + for(u32bit 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, u32bit shift) + { + if(shift == 0) + return x; + + const u32bit shift_words = shift / MP_WORD_BITS, + shift_bits = shift % MP_WORD_BITS; + + const u32bit x_sw = x.sig_words(); + + BigInt y(x.sign(), x_sw + shift_words + (shift_bits ? 1 : 0)); + bigint_shl2(y.get_reg(), x.data(), x_sw, shift_words, shift_bits); + return y; + } + +/* +* Right Shift Operator +*/ +BigInt operator>>(const BigInt& x, u32bit shift) + { + if(shift == 0) + return x; + if(x.bits() <= shift) + return 0; + + const u32bit shift_words = shift / MP_WORD_BITS, + shift_bits = shift % MP_WORD_BITS, + x_sw = x.sig_words(); + + BigInt y(x.sign(), x_sw - shift_words); + bigint_shr2(y.get_reg(), x.data(), x_sw, shift_words, shift_bits); + return y; + } + +} diff --git a/old/botan/src/math/bigint/big_rand.cpp b/old/botan/src/math/bigint/big_rand.cpp new file mode 100644 index 0000000..b641bae --- /dev/null +++ b/old/botan/src/math/bigint/big_rand.cpp @@ -0,0 +1,61 @@ +/* +* BigInt Random Generation +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/bigint.h> +#include <botan/parsing.h> + +namespace Botan { + +/* +* Construct a BigInt of a specific form +*/ +BigInt::BigInt(NumberType type, u32bit bits) + { + set_sign(Positive); + + if(type == Power2) + set_bit(bits); + else + throw Invalid_Argument("BigInt(NumberType): Unknown type"); + } + +/* +* Randomize this number +*/ +void BigInt::randomize(RandomNumberGenerator& rng, + u32bit bitsize) + { + set_sign(Positive); + + if(bitsize == 0) + clear(); + else + { + SecureVector<byte> array((bitsize + 7) / 8); + rng.randomize(array, array.size()); + if(bitsize % 8) + array[0] &= 0xFF >> (8 - (bitsize % 8)); + array[0] |= 0x80 >> ((bitsize % 8) ? (8 - bitsize % 8) : 0); + binary_decode(array, array.size()); + } + } + +/* +* Generate a random integer within given range +*/ +BigInt BigInt::random_integer(RandomNumberGenerator& rng, + const BigInt& min, const BigInt& max) + { + BigInt range = max - min; + + if(range <= 0) + throw Invalid_Argument("random_integer: invalid min/max values"); + + return (min + (BigInt(rng, range.bits() + 2) % range)); + } + +} diff --git a/old/botan/src/math/bigint/bigint.cpp b/old/botan/src/math/bigint/bigint.cpp new file mode 100644 index 0000000..926bedc --- /dev/null +++ b/old/botan/src/math/bigint/bigint.cpp @@ -0,0 +1,369 @@ +/* +* BigInt Base +* (C) 1999-2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/bigint.h> +#include <botan/mp_core.h> +#include <botan/loadstor.h> +#include <botan/parsing.h> +#include <botan/util.h> + +namespace Botan { + +/* +* Construct a BigInt from a regular number +*/ +BigInt::BigInt(u64bit n) + { + set_sign(Positive); + + if(n == 0) + return; + + const u32bit limbs_needed = sizeof(u64bit) / sizeof(word); + + reg.create(4*limbs_needed); + for(u32bit j = 0; j != limbs_needed; ++j) + reg[j] = ((n >> (j*MP_WORD_BITS)) & MP_WORD_MASK); + } + +/* +* Construct a BigInt of the specified size +*/ +BigInt::BigInt(Sign s, u32bit size) + { + reg.create(round_up(size, 8)); + signedness = s; + } + +/* +* Construct a BigInt from a "raw" BigInt +*/ +BigInt::BigInt(const BigInt& b) + { + const u32bit b_words = b.sig_words(); + + if(b_words) + { + reg.create(round_up(b_words, 8)); + reg.copy(b.data(), b_words); + set_sign(b.sign()); + } + else + { + reg.create(2); + set_sign(Positive); + } + } + +/* +* Construct a BigInt from a string +*/ +BigInt::BigInt(const std::string& str) + { + Base base = Decimal; + u32bit 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; } + else if(str.length() > markers + 1 && str[markers] == '0') + { markers += 1; base = Octal; } + + *this = decode(reinterpret_cast<const byte*>(str.data()) + markers, + str.length() - markers, base); + + if(negative) set_sign(Negative); + else set_sign(Positive); + } + +/* +* Construct a BigInt from an encoded BigInt +*/ +BigInt::BigInt(const byte input[], u32bit length, Base base) + { + set_sign(Positive); + *this = decode(input, length, base); + } + +/* +* Construct a BigInt from an encoded BigInt +*/ +BigInt::BigInt(RandomNumberGenerator& rng, u32bit bits) + { + set_sign(Positive); + randomize(rng, bits); + } + +/* +* Swap this BigInt with another +*/ +void BigInt::swap(BigInt& other) + { + reg.swap(other.reg); + std::swap(signedness, other.signedness); + } + +/* +* Grow the internal storage +*/ +void BigInt::grow_reg(u32bit n) + { + reg.grow_to(round_up(size() + n, 8)); + } + +/* +* Grow the internal storage +*/ +void BigInt::grow_to(u32bit n) + { + if(n > size()) + reg.grow_to(round_up(n, 8)); + } + +/* +* Comparison Function +*/ +s32bit BigInt::cmp(const BigInt& n, bool check_signs) const + { + if(check_signs) + { + if(n.is_positive() && this->is_negative()) return -1; + if(n.is_negative() && this->is_positive()) return 1; + if(n.is_negative() && this->is_negative()) + return (-bigint_cmp(data(), sig_words(), n.data(), n.sig_words())); + } + return bigint_cmp(data(), sig_words(), n.data(), n.sig_words()); + } + +/* +* Convert this number to a u32bit, if possible +*/ +u32bit 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"); + + u32bit out = 0; + for(u32bit j = 0; j != 4; ++j) + out = (out << 8) | byte_at(3-j); + return out; + } + +/* +* Return byte n of this number +*/ +byte BigInt::byte_at(u32bit n) const + { + const u32bit WORD_BYTES = sizeof(word); + u32bit word_num = n / WORD_BYTES, byte_num = n % WORD_BYTES; + if(word_num >= size()) + return 0; + else + return get_byte(WORD_BYTES - byte_num - 1, reg[word_num]); + } + +/* +* Return bit n of this number +*/ +bool BigInt::get_bit(u32bit n) const + { + return ((word_at(n / MP_WORD_BITS) >> (n % MP_WORD_BITS)) & 1); + } + +/* +* Return bits {offset...offset+length} +*/ +u32bit BigInt::get_substring(u32bit offset, u32bit length) const + { + if(length > 32) + throw Invalid_Argument("BigInt::get_substring: Substring size too big"); + + u64bit piece = 0; + for(u32bit j = 0; j != 8; ++j) + piece = (piece << 8) | byte_at((offset / 8) + (7-j)); + + u64bit mask = (1 << length) - 1; + u32bit shift = (offset % 8); + + return static_cast<u32bit>((piece >> shift) & mask); + } + +/* +* Set bit number n +*/ +void BigInt::set_bit(u32bit n) + { + const u32bit which = n / MP_WORD_BITS; + const word mask = static_cast<word>(1) << (n % MP_WORD_BITS); + if(which >= size()) grow_to(which + 1); + reg[which] |= mask; + } + +/* +* Clear bit number n +*/ +void BigInt::clear_bit(u32bit n) + { + const u32bit which = n / MP_WORD_BITS; + const word mask = static_cast<word>(1) << (n % MP_WORD_BITS); + if(which < size()) + reg[which] &= ~mask; + } + +/* +* Clear all but the lowest n bits +*/ +void BigInt::mask_bits(u32bit n) + { + if(n == 0) { clear(); return; } + if(n >= bits()) return; + + const u32bit top_word = n / MP_WORD_BITS; + const word mask = (static_cast<word>(1) << (n % MP_WORD_BITS)) - 1; + + if(top_word < size()) + for(u32bit j = top_word + 1; j != size(); ++j) + reg[j] = 0; + + reg[top_word] &= mask; + } + +/* +* Count how many bytes are being used +*/ +u32bit BigInt::bytes() const + { + return (bits() + 7) / 8; + } + +/* +* Count how many bits are being used +*/ +u32bit BigInt::bits() const + { + if(sig_words() == 0) + return 0; + + u32bit full_words = sig_words() - 1, top_bits = MP_WORD_BITS; + word top_word = word_at(full_words), mask = MP_WORD_TOP_BIT; + + while(top_bits && ((top_word & mask) == 0)) + { mask >>= 1; top_bits--; } + + return (full_words * MP_WORD_BITS + top_bits); + } + +/* +* Calcluate the size in a certain base +*/ +u32bit 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 == Octal) + return ((bits() + 2) / 3); + else if(base == Decimal) + return static_cast<u32bit>((bits() * LOG_2_BASE_10) + 1); + else + throw Invalid_Argument("Unknown base for BigInt encoding"); + } + +/* +* Set the sign +*/ +void BigInt::set_sign(Sign s) + { + if(is_zero()) + signedness = Positive; + else + signedness = s; + } + +/* +* Reverse the value of the sign flag +*/ +void BigInt::flip_sign() + { + set_sign(reverse_sign()); + } + +/* +* Return the opposite value of the current sign +*/ +BigInt::Sign BigInt::reverse_sign() const + { + if(sign() == Positive) + return Negative; + return Positive; + } + +/* +* Return the negation of this number +*/ +BigInt BigInt::operator-() const + { + BigInt x = (*this); + x.flip_sign(); + return x; + } + +/* +* Return the absolute value of this number +*/ +BigInt BigInt::abs() const + { + BigInt x = (*this); + x.set_sign(Positive); + return x; + } + +/* +* Encode this number into bytes +*/ +void BigInt::binary_encode(byte output[]) const + { + const u32bit sig_bytes = bytes(); + for(u32bit j = 0; j != sig_bytes; ++j) + output[sig_bytes-j-1] = byte_at(j); + } + +/* +* Set this number to the value in buf +*/ +void BigInt::binary_decode(const byte buf[], u32bit length) + { + const u32bit WORD_BYTES = sizeof(word); + + reg.create(round_up((length / WORD_BYTES) + 1, 8)); + + for(u32bit j = 0; j != length / WORD_BYTES; ++j) + { + u32bit top = length - WORD_BYTES*j; + for(u32bit k = WORD_BYTES; k > 0; --k) + reg[j] = (reg[j] << 8) | buf[top - k]; + } + for(u32bit j = 0; j != length % WORD_BYTES; ++j) + reg[length / WORD_BYTES] = (reg[length / WORD_BYTES] << 8) | buf[j]; + } + +/* +* Set this number to the value in buf +*/ +void BigInt::binary_decode(const MemoryRegion<byte>& buf) + { + binary_decode(buf, buf.size()); + } + +} diff --git a/old/botan/src/math/bigint/bigint.h b/old/botan/src/math/bigint/bigint.h new file mode 100644 index 0000000..16a1bba --- /dev/null +++ b/old/botan/src/math/bigint/bigint.h @@ -0,0 +1,534 @@ +/* +* BigInt +* (C) 1999-2008 Jack Lloyd +* 2007 FlexSecure +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_BIGINT_H__ +#define BOTAN_BIGINT_H__ + +#include <botan/rng.h> +#include <botan/secmem.h> +#include <botan/mp_types.h> +#include <iosfwd> + +namespace Botan { + +/** + * Big Integer representation. This class defines an integer type, + * that can be very big. Additionally some helper functions are + * defined to work more comfortably. + + */ +class BOTAN_DLL BigInt + { + public: + /** + * Base-Enumerator (currently 8,10,16 and 256 are defined) + */ + enum Base { Octal = 8, Decimal = 10, Hexadecimal = 16, Binary = 256 }; + + /** + * Sign symbol definitions for positive and negative numbers + */ + enum Sign { Negative = 0, Positive = 1 }; + + /** + * Number types (Powers of 2) + */ + enum NumberType { Power2 }; + + /** + * DivideByZero Exception + */ + struct DivideByZero : public Exception + { DivideByZero() : Exception("BigInt divide by zero") {} }; + + /************* + * operators + *************/ + + /** + * += Operator + * @param y the BigInt to add to the local value + */ + BigInt& operator+=(const BigInt& y); + + /** + * -= Operator + * @param y the BigInt to subtract from the local value + */ + BigInt& operator-=(const BigInt& y); + + /** + * *= Operator + * @param y the BigInt to multiply with the local value + */ + BigInt& operator*=(const BigInt& y); + + /** + * /= Operator + * @param y the BigInt to divide the local value by + */ + BigInt& operator/=(const BigInt& y); + + /** + * %= Operator, modulo operator. + * @param y the modulus to reduce the local value by + */ + BigInt& operator%=(const BigInt& y); + + /** + * %= Operator + * @param y the modulus (word) to reduce the local value by + */ + word operator%=(word y); + + /** + * <<= Operator + * @param y the amount of bits to shift the local value left + */ + BigInt& operator<<=(u32bit y); + + /** + * >>= Operator + * @param y the amount of bits to shift the local value right + */ + BigInt& operator>>=(u32bit y); + + /** + * ++ Operator + */ + BigInt& operator++() { return (*this += 1); } + + /** + * -- Operator + */ + BigInt& operator--() { return (*this -= 1); } + + /** + * ++ Operator (postfix) + */ + BigInt operator++(int) { BigInt x = (*this); ++(*this); return x; } + + /** + * -- Operator (postfix) + */ + BigInt operator--(int) { BigInt x = (*this); --(*this); return x; } + + /** + * - Operator + */ + BigInt operator-() const; + + /** + * ! Operator + */ + bool operator !() const { return (!is_nonzero()); } + + /** + * [] Operator (array access) + */ + word& operator[](u32bit i) { return reg[i]; } + + /** + * [] Operator (array access) + */ + word operator[](u32bit i) const { return reg[i]; } + + /** + * Zeroize the BigInt + */ + void clear() { get_reg().clear(); } + + /************* + * functions + ************/ + + /** + * Compare *this to another BigInt. + * @param n the BigInt value to compare to the local value. + * @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. + */ + s32bit cmp(const BigInt& n, bool check_signs = true) const; + + /** + * Test if the integer has an even value + * @result true, if the integer an even value, false otherwise + */ + bool is_even() const { return (get_bit(0) == 0); } + + /** + * Test if the integer has an odd value + * @result true, if the integer an odd value, false otherwise + */ + bool is_odd() const { return (get_bit(0) == 1); } + + /** + * Test if the integer is not zero. + * @result true, if the integer has a non-zero value, false otherwise + */ + bool is_nonzero() const { return (!is_zero()); } + + /** + * Test if the integer is zero. + * @result true, if the integer has the value zero, false otherwise + */ + bool is_zero() const + { + const u32bit sw = sig_words(); + + for(u32bit i = 0; i != sw; ++i) + if(reg[i]) + return false; + return true; + } + + /** + * Set bit at specified position + * @param n bit position to set + */ + void set_bit(u32bit n); + + /** + * Clear bit at specified position + * @param n bit position to clear + */ + void clear_bit(u32bit n); + + /** + * Clear all but the lowest n bits + * @param n amount of bits to keep + */ + void mask_bits(u32bit n); + + /** + * 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(u32bit n) const; + + /** + * 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 + */ + u32bit get_substring(u32bit offset, u32bit length) const; + + byte byte_at(u32bit) const; + + /** + * Return the word at a specified position of the internal register + * @param n position in the register + * @return the value at position n + */ + word word_at(u32bit n) const + { return ((n < size()) ? reg[n] : 0); } + + /** + * Return the integer as an unsigned 32bit-integer-value. If the + * value is negative OR to big to be stored in 32bits, this + * function will throw an exception. + * @result a 32bit-integer + */ + u32bit to_u32bit() const; + + /** + * Tests if the sign of the integer is negative. + * @result true, if the integer has a negative sign, + */ + bool is_negative() const { return (sign() == Negative); } + + /** + * Tests if the sign of the integer is positive. + * @result true, if 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 (signedness); } + + /** + * Return the opposite sign of the represented integer value + * @result the opposite sign of the represented integer value + */ + Sign reverse_sign() const; + + /** + * Flip (change!) the sign of the integer to its opposite value + */ + void flip_sign(); + + /** + * Set sign of the integer + * @param sign new Sign to set + */ + void set_sign(Sign sign); + + /** + * Give absolute (positive) value of the integer + * @result absolute (positive) value of the integer + */ + BigInt abs() const; + + /** + * Give size of internal register + * @result size of internal register in words + */ + u32bit size() const { return get_reg().size(); } + + /** + * Give significant words of the represented integer value + * @result significant words of the represented integer value + */ + u32bit sig_words() const + { + const word* x = reg.begin(); + u32bit sig = 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 + */ + u32bit bytes() const; + + /** + * Get the bit-length of the integer. + * @result bit-length of the represented integer value + */ + u32bit bits() const; + + /** + * Return a pointer to the big integer word register. + * @result a pointer to the start of the internal register of + * the integer value + */ + const word* data() const { return reg.begin(); } + + /** + * return a reference to the internal register containing the value + * @result a reference to the word-array (SecureVector<word>) + * with the internal register value (containing the integer + * value) + */ + SecureVector<word>& get_reg() { return reg; } + + /** + * return a const reference to the internal register containing the value + * @result a const reference to the word-array (SecureVector<word>) + * with the internal register value (containing the integer + * value) + */ + const SecureVector<word>& get_reg() const { return reg; } + + /** + * Increase internal register buffer by n words + * @param n increase by n words + */ + void grow_reg(u32bit n); + + void grow_to(u32bit n); + + /** + * Fill BigInt with a random number with size of bitsize + * @param rng the random number generator to use + * @param bitsize number of bits the created random value should have + */ + void randomize(RandomNumberGenerator& rng, u32bit bitsize = 0); + + /** + * Store BigInt-value in a given byte array + * @param buf destination byte array for the integer value + */ + void binary_encode(byte 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 byte buf[], u32bit length); + + /** + * Read integer value from a byte array (MemoryRegion<byte>) + * @param buf the BigInt value to compare to the local value. + */ + void binary_decode(const MemoryRegion<byte>& buf); + + u32bit encoded_size(Base = Binary) const; + + /** + @param rng a random number generator + @result a random integer between min and max + */ + static BigInt random_integer(RandomNumberGenerator& rng, + const BigInt& min, const BigInt& max); + + /** + * Encode the integer value from a BigInt to a SecureVector of bytes + * @param n the BigInt to use as integer source + * @param base number-base of resulting byte array representation + * @result SecureVector of bytes containing the integer with given base + */ + static SecureVector<byte> encode(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(byte buf[], const BigInt& n, Base base = Binary); + + /** + * Create a BigInt from an integer in a byte array + * @param buf the BigInt value to compare to the local value. + * @param length size of buf + * @param base number-base of the integer in buf + * @result BigInt-representing the given integer read from the byte array + */ + static BigInt decode(const byte buf[], u32bit length, + Base base = Binary); + + static BigInt decode(const MemoryRegion<byte>&, Base = Binary); + + /** + * Encode a Big Integer to a byte array according to IEEE1363. + * @param n the Big Integer to encode + * @param bytes the length of the resulting SecureVector<byte> + * @result a SecureVector<byte> containing the encoded Big Integer + */ + static SecureVector<byte> encode_1363(const BigInt& n, u32bit bytes); + + /** + * Swap BigInt-value with given BigInt. + * @param bigint the BigInt to swap values with + */ + void swap(BigInt& bigint); + + /** + * constructors + */ + + /** + * Create empty BigInt + */ + BigInt() { signedness = Positive; } + + /** + * Create BigInt from 64bit-Integer value + * @param n 64bit-integer + */ + BigInt(u64bit n); + + /** + * Copy-Constructor: clone given BigInt + * @param bigint the BigInt to clone + */ + BigInt(const BigInt& bigint); + + /** + * Create BigInt from a string. + * If the string starts with 0x the rest of the string will be + * interpreted as hexadecimal digits. + * If the string starts with 0 and the second character is NOT + * an 'x' the string will be interpreted as octal digits. + * If the string starts with non-zero digit, it will be + * interpreted as a decimal number. + * @param str the string to parse for an integer value + */ + BigInt(const std::string& str); + + /** + * Create a BigInt from an integer in a byte array + * @param buf the BigInt value to compare to the local value. + * @param length size of buf + * @param base number-base of the integer in buf + */ + BigInt(const byte buf[], u32bit length, Base base = Binary); + + /** + * Create a random BigInt of the specified size + * @param rng random number generator + * @param bits size in bits + */ + BigInt(RandomNumberGenerator& rng, u32bit bits); + + /** + * Create BigInt from unsigned 32 bit integer value and an + * also specify the sign of the value + * @param n integer value + */ + BigInt(Sign, u32bit n); + + /** + * Create a number of the specified type and size + * @param type the type of number to create + * @param n the size + */ + BigInt(NumberType type, u32bit n); + + private: + SecureVector<word> reg; + Sign signedness; + }; + +/* +* Arithmetic Operators +*/ +BigInt BOTAN_DLL operator+(const BigInt&, const BigInt&); +BigInt BOTAN_DLL operator-(const BigInt&, const BigInt&); +BigInt BOTAN_DLL operator*(const BigInt&, const BigInt&); +BigInt BOTAN_DLL operator/(const BigInt&, const BigInt&); +BigInt BOTAN_DLL operator%(const BigInt&, const BigInt&); +word BOTAN_DLL operator%(const BigInt&, word); +BigInt BOTAN_DLL operator<<(const BigInt&, u32bit); +BigInt BOTAN_DLL operator>>(const BigInt&, u32bit); + +/* +* 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); } + +/* +* I/O Operators +*/ +BOTAN_DLL std::ostream& operator<<(std::ostream&, const BigInt&); +BOTAN_DLL std::istream& operator>>(std::istream&, BigInt&); + +} + +namespace std { + +inline void swap(Botan::BigInt& a, Botan::BigInt& b) { a.swap(b); } + +} + +#endif diff --git a/old/botan/src/math/bigint/divide.cpp b/old/botan/src/math/bigint/divide.cpp new file mode 100644 index 0000000..6afaa0f --- /dev/null +++ b/old/botan/src/math/bigint/divide.cpp @@ -0,0 +1,106 @@ +/* +* Division Algorithm +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/divide.h> +#include <botan/mp_core.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(); + } + +} + +/* +* 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 u32bit y_words = y.sig_words(); + r = x; + + r.set_sign(BigInt::Positive); + y.set_sign(BigInt::Positive); + + s32bit compare = r.cmp(y); + + if(compare < 0) + q = 0; + else if(compare == 0) + { + q = 1; + r = 0; + } + else + { + u32bit shifts = 0; + word y_top = y[y.sig_words()-1]; + while(y_top < MP_WORD_TOP_BIT) { y_top <<= 1; ++shifts; } + y <<= shifts; + r <<= shifts; + + const u32bit n = r.sig_words() - 1, t = y_words - 1; + + q.get_reg().create(n - t + 1); + if(n <= t) + { + while(r > y) { r -= y; ++q; } + r >>= shifts; + sign_fixup(x, y_arg, q, r); + return; + } + + BigInt temp = y << (MP_WORD_BITS * (n-t)); + + while(r >= temp) { r -= temp; ++q[n-t]; } + + for(u32bit 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[j-t-1] = MP_WORD_MAX; + else + q[j-t-1] = bigint_divop(x_j0, x_j1, y_t); + + while(bigint_divcore(q[j-t-1], y_t, y.word_at(t-1), + x_j0, x_j1, r.word_at(j-2))) + --q[j-t-1]; + + r -= (q[j-t-1] * y) << (MP_WORD_BITS * (j-t-1)); + if(r.is_negative()) + { + r += y << (MP_WORD_BITS * (j-t-1)); + --q[j-t-1]; + } + } + r >>= shifts; + } + + sign_fixup(x, y_arg, q, r); + } + +} diff --git a/old/botan/src/math/bigint/divide.h b/old/botan/src/math/bigint/divide.h new file mode 100644 index 0000000..9445b13 --- /dev/null +++ b/old/botan/src/math/bigint/divide.h @@ -0,0 +1,19 @@ +/* +* Division +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_DIVISON_ALGORITHM_H__ +#define BOTAN_DIVISON_ALGORITHM_H__ + +#include <botan/bigint.h> + +namespace Botan { + +void BOTAN_DLL divide(const BigInt&, const BigInt&, BigInt&, BigInt&); + +} + +#endif diff --git a/old/botan/src/math/bigint/info.txt b/old/botan/src/math/bigint/info.txt new file mode 100644 index 0000000..513703d --- /dev/null +++ b/old/botan/src/math/bigint/info.txt @@ -0,0 +1,33 @@ +realname "BigInt" + +load_on auto + +define BIGINT + +<add> +bigint.h +divide.h +mp_core.h +mp_types.h +big_code.cpp +big_io.cpp +big_ops2.cpp +big_ops3.cpp +big_rand.cpp +bigint.cpp +divide.cpp +mp_asm.cpp +mp_comba.cpp +mp_karat.cpp +mp_misc.cpp +mp_shift.cpp +</add> + +<requires> +alloc +hex +mp_amd64|mp_asm64|mp_ia32|mp_ia32_msvc|mp_generic +monty_generic +mulop_generic +rng +</requires> diff --git a/old/botan/src/math/bigint/monty_amd64/info.txt b/old/botan/src/math/bigint/monty_amd64/info.txt new file mode 100644 index 0000000..a897045 --- /dev/null +++ b/old/botan/src/math/bigint/monty_amd64/info.txt @@ -0,0 +1,32 @@ +realname "Montgomery Reduction (x86-64)" + +mp_bits 64 + +load_on never + +<add> +mp_monty.S +</add> + +<arch> +amd64 +</arch> + +<cc> +gcc +icc +</cc> + +# ELF systems +<os> +linux +freebsd +dragonfly +netbsd +openbsd +solaris +</os> + +<requires> +asm_amd64 +</requires> diff --git a/old/botan/src/math/bigint/monty_amd64/mp_monty.S b/old/botan/src/math/bigint/monty_amd64/mp_monty.S new file mode 100644 index 0000000..22045c3 --- /dev/null +++ b/old/botan/src/math/bigint/monty_amd64/mp_monty.S @@ -0,0 +1,399 @@ +/* +* Montgomery Reduction Source File +* (C) 2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/asm_macr.h> + +START_LISTING(mp_monty.S) + +START_FUNCTION(bigint_monty_redc) + pushq %r15 # + pushq %r14 # + pushq %r13 # + pushq %r12 # + pushq %rbp # + pushq %rbx # + + movq %rdi, %r14 # z + movq %rdx, %r12 # x + movl %esi, %ebp # z_size + + xorl %esi, %esi # j.76 + movq %r8, -16(%rsp) # u, u + movl %ecx, %ebx # x_size, x_size + movl %ecx, %r8d # x_size, blocks_of_8 + andl $-8, %r8d #, blocks_of_8 + testl %ecx, %ecx # x_size + je .L3 #, + mov %ecx, %eax # x_size, pretmp.71 + leal 1(%rbx), %r15d #, k.73 + salq $3, %rax #, + xorl %r13d, %r13d # j + movq %rax, -8(%rsp) #, pretmp.21 + .p2align 4,,10 + .p2align 3 +.L11: + mov %r13d, %eax # j, j + movq -16(%rsp), %rdi # u, y + leaq (%r14,%rax,8), %r11 #, z_j + xorl %r9d, %r9d # i + imulq (%r11), %rdi #* z_j, y + xorl %r10d, %r10d # carry + testl %r8d, %r8d # blocks_of_8 + je .L7 #, + .p2align 4,,10 + .p2align 3 +.LOOP_MUL_ADD: + mov %r9d, %ecx # i, i + addl $8, %r9d #, i + salq $3, %rcx #, D.2315 + leaq (%r11,%rcx), %rsi #, tmp130 + leaq (%r12,%rcx), %rcx #, tmp131 + + movq 8*0(%rcx), %rax + mulq %rdi # y + addq %r10, %rax # carry + adcq $0,%rdx + addq 8*0(%rsi), %rax + adcq $0,%rdx + movq %rdx,%r10 # carry + movq %rax, 8*0 (%rsi) + + movq 8*1(%rcx), %rax + mulq %rdi # y + addq %r10, %rax # carry + adcq $0,%rdx + addq 8*1(%rsi), %rax + adcq $0,%rdx + movq %rdx,%r10 # carry + movq %rax, 8*1 (%rsi) + + movq 8*2(%rcx), %rax + mulq %rdi # y + addq %r10, %rax # carry + adcq $0,%rdx + addq 8*2(%rsi), %rax + adcq $0,%rdx + movq %rdx,%r10 # carry + movq %rax, 8*2 (%rsi) + + movq 8*3(%rcx), %rax + mulq %rdi # y + addq %r10, %rax # carry + adcq $0,%rdx + addq 8*3(%rsi), %rax + adcq $0,%rdx + movq %rdx,%r10 # carry + movq %rax, 8*3 (%rsi) + + movq 8*4(%rcx), %rax + mulq %rdi # y + addq %r10, %rax # carry + adcq $0,%rdx + addq 8*4(%rsi), %rax + adcq $0,%rdx + movq %rdx,%r10 # carry + movq %rax, 8*4 (%rsi) + + movq 8*5(%rcx), %rax + mulq %rdi # y + addq %r10, %rax # carry + adcq $0,%rdx + addq 8*5(%rsi), %rax + adcq $0,%rdx + movq %rdx,%r10 # carry + movq %rax, 8*5 (%rsi) + + movq 8*6(%rcx), %rax + mulq %rdi # y + addq %r10, %rax # carry + adcq $0,%rdx + addq 8*6(%rsi), %rax + adcq $0,%rdx + movq %rdx,%r10 # carry + movq %rax, 8*6 (%rsi) + + movq 8*7(%rcx), %rax + mulq %rdi # y + addq %r10, %rax # carry + adcq $0,%rdx + addq 8*7(%rsi), %rax + adcq $0,%rdx + movq %rdx,%r10 # carry + movq %rax, 8*7 (%rsi) + + cmpl %r9d, %r8d # i, blocks_of_8 + jne .LOOP_MUL_ADD #, + cmpl %r8d, %ebx # blocks_of_8, x_size + je .L8 #, +.L7: + movl %r8d, %esi # blocks_of_8, i + .p2align 4,,10 + .p2align 3 +.L5: + mov %esi, %eax # i, i + movq %rdi, %rcx # y, b + leaq (%r11, %rax,8), %r9 #, D.2325 + incl %esi # i + movq (%r12, %rax,8), %rax #* x, tmp133 + + mulq %rcx # b + addq (%r9), %rax #* D.2325, a + adcq $0,%rdx # + addq %r10, %rax # carry, a + adcq $0,%rdx # + + cmpl %esi, %ebx # i, x_size + movq %rdx, %r10 #, carry + movq %rax, (%r9) # a,* D.2325 + jne .L5 #, +.L8: + movq -8(%rsp), %rdx # pretmp.21, + leaq (%r11,%rdx), %rax #, D.2332 + movq (%rax), %rcx #* D.2332, D.2333 + leaq (%r10,%rcx), %rdx #, z_sum + movq %rdx, (%rax) # z_sum,* D.2332 + cmpq %rdx, %rcx # z_sum, D.2333 + jbe .L9 #, + cmpl %ebp, %r15d # z_size, k.73 + je .L9 #, + movl %r15d, %ecx # k.73, k + jmp .L10 # + .p2align 4,,10 + .p2align 3 +.L31: + incl %ecx # k + cmpl %ecx, %ebp # k, z_size + .p2align 4,,4 + .p2align 3 + je .L9 #, +.L10: + mov %ecx, %edx # k, k + leaq (%r11,%rdx,8), %rdx #, D.2342 + movq (%rdx), %rax #* D.2342, tmp136 + incq %rax # D.2344 + movq %rax, (%rdx) # D.2344,* D.2342 + testq %rax, %rax # D.2344 + je .L31 #, +.L9: + incl %r13d # j + decl %ebp # z_size + cmpl %r13d, %ebx # j, x_size + jne .L11 #, + movl %ebx, %esi # x_size, j.76 +.L3: + leal (%rbx,%rbx), %eax #, tmp137 + mov %eax, %eax + leaq (%r14, %rax,8), %rdi #, D.2349 + cmpq $0, (%rdi) #,* D.2349 + jne .L12 #, + testl %ebx, %ebx # x_size + je .L12 #, + leal -1(%rbx), %ecx #, j + leal (%rsi,%rcx), %edx #, tmp141 + mov %ecx, %eax # j, j + movq (%r14,%rdx,8), %rbp #* z, + cmpq %rbp, (%r12, %rax,8) #,* x + jb .L12 #, + ja .L_EXIT #, + leal -2(%rsi,%rbx), %edx #, ivtmp.45 + jmp .L14 # + .p2align 4,,10 + .p2align 3 +.L15: + mov %edx, %eax # ivtmp.45, ivtmp.45 + decl %ecx # j + movq (%r14, %rax,8), %rsi #* z, D.2360 + mov %ecx, %eax # j, j + movq (%r12, %rax,8), %rax #* x, temp.68 + cmpq %rax, %rsi + ja .L12 #, + decl %edx # ivtmp.45 + cmpq %rax, %rsi + jb .L_EXIT #, +.L14: + testl %ecx, %ecx # j + jne .L15 #, +.L12: + xorl %ecx, %ecx # j + xorl %r10d, %r10d # carry + mov %ebx, %esi # x_size, pretmp.19 + testl %r8d, %r8d # blocks_of_8 + je .L17 #, + .p2align 4,,10 + .p2align 3 +.L22: + mov %ecx, %edx # j, D.2375 + addl $8, %ecx #, j + leaq (%rdx,%rsi), %rax #, tmp146 + leaq (%r12,%rdx,8), %rdx #, tmp150 + leaq (%r14, %rax,8), %rax #, tmp148 + + rorq %r10 # carry + + movq 8*0(%rdx), %r10 + sbbq %r10, 8*0(%rax) + + movq 8*1(%rdx), %r10 + sbbq %r10, 8*1(%rax) + + movq 8*2(%rdx), %r10 + sbbq %r10, 8*2(%rax) + + movq 8*3(%rdx), %r10 + sbbq %r10, 8*3(%rax) + + movq 8*4(%rdx), %r10 + sbbq %r10, 8*4(%rax) + + movq 8*5(%rdx), %r10 + sbbq %r10, 8*5(%rax) + + movq 8*6(%rdx), %r10 + sbbq %r10, 8*6(%rax) + + movq 8*7(%rdx), %r10 + sbbq %r10, 8*7(%rax) + + sbbq %r10,%r10 # carry + negq %r10 # carry + + cmpl %ecx, %r8d # j, blocks_of_8 + jne .L22 #, +.L17: + cmpl %r8d, %ebx # blocks_of_8, x_size + je .L19 #, + leal (%r8,%rbx), %r9d #, ivtmp.33 + movl %r8d, %esi # blocks_of_8, j + .p2align 4,,10 + .p2align 3 +.L20: + mov %r9d, %eax # ivtmp.33, ivtmp.33 + mov %esi, %ecx # j, j + leaq (%r14, %rax,8), %rax #, D.2387 + incl %esi # j + movq (%rax), %rdx #* D.2387, tmp153 + incl %r9d # ivtmp.33 + + rorq %r10 # carry + sbbq (%r12,%rcx,8),%rdx #* x, x + sbbq %r10,%r10 # carry + negq %r10 # carry + + cmpl %esi, %ebx # j, x_size + movq %rdx, (%rax) # x,* D.2387 + jne .L20 #, +.L19: + testq %r10, %r10 # carry + je .L_EXIT #, + decq (%rdi) #* D.2349 +.L_EXIT: + popq %rbx # + popq %rbp # + popq %r12 # + popq %r13 # + popq %r14 # + popq %r15 # +END_FUNCTION(bigint_monty_redc) + + +#if 0 + #define Z_ARR ARG_1 // rdi +#define Z_SIZE ARG_2_32 // esi +// X_ARR is ARG_3 == rdx, moved b/c needed for multiply +#define X_SIZE ARG_4_32 // ecx +#define U ARG_5 // r8 + +/* + We need all arguments for a while (we can reuse U eventually) + So only temp registers are + TEMP_1 %r10 + TEMP_2 %r11 + TEMP_3 = ARG_6 = %r9 + void return, so also + R0 %rax (aka TEMP_9) + is free (but needed for multiply) + + Can push: + %rbx (base pointer, callee saved) + %rpb (frame pointer, callee saved) + %r12-%r15 (callee saved) + + Can push base/frame pointers since this is a leaf function + and does not reference any data. +*/ + + push %r12 + push %r13 + push %r14 + push %r15 + +#define LOOP_CTR_I %r12 +#define LOOP_CTR_J %r13 + +#define CARRY TEMP_1 +#define Z_WORD TEMP_2 +#define X_ARR TEMP_3 +#define MUL_LO %rax +#define MUL_HI %rdx + + ASSIGN(X_ARR, ARG_3) + + /* + ZEROIZE(CARRY) + + ASSIGN(LOOP_CTR, X_SIZE) + + JUMP_IF_ZERO(LOOP_CTR, .L_MULADD_DONE) + JUMP_IF_LT(LOOP_CTR, 8, .LOOP_MULADD1) + +#define MULADD_OP(N) \ + ASSIGN(MUL_LO, ARRAY8(X_ARR, N)) ; \ + ASSIGN(Z_WORD, ARRAY8(Z_ARR, N)) ; \ + MUL(Y) ; \ + ADD(Z_WORD, CARRY) ; \ + ASSIGN(CARRY, MUL_HI) ; \ + ADD_LAST_CARRY(CARRY) ; \ + ADD(Z_WORD, MUL_LO) ; \ + ADD_LAST_CARRY(CARRY) ; \ + ASSIGN(ARRAY8(Z_ARR, N), Z_WORD) + +ALIGN +.LOOP_MULADD8: + MULADD_OP(0) + MULADD_OP(1) + MULADD_OP(2) + MULADD_OP(3) + MULADD_OP(4) + MULADD_OP(5) + MULADD_OP(6) + MULADD_OP(7) + + SUB_IMM(LOOP_CTR, 8) + ADD_IMM(Z_ARR, 64) + ADD_IMM(X_ARR, 64) + cmp IMM(8), LOOP_CTR + jge .LOOP_MULADD8 + + JUMP_IF_ZERO(LOOP_CTR, .L_MULADD_DONE) + +ALIGN +.LOOP_MULADD1: + MULADD_OP(0) + + SUB_IMM(LOOP_CTR, 1) + ADD_IMM(Z_ARR, 8) + ADD_IMM(X_ARR, 8) + + cmp IMM(0), LOOP_CTR + jne .LOOP_MULADD1 +*/ + + pop %r15 + pop %r14 + pop %r13 + pop %r12 +#endif diff --git a/old/botan/src/math/bigint/monty_generic/info.txt b/old/botan/src/math/bigint/monty_generic/info.txt new file mode 100644 index 0000000..6f5f0e7 --- /dev/null +++ b/old/botan/src/math/bigint/monty_generic/info.txt @@ -0,0 +1,7 @@ +realname "Montgomery Reduction" + +load_on dep + +<add> +mp_monty.cpp +</add> diff --git a/old/botan/src/math/bigint/monty_generic/mp_monty.cpp b/old/botan/src/math/bigint/monty_generic/mp_monty.cpp new file mode 100644 index 0000000..5409e25 --- /dev/null +++ b/old/botan/src/math/bigint/monty_generic/mp_monty.cpp @@ -0,0 +1,78 @@ +/* +* Montgomery Reduction +* (C) 1999-2008 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/mp_core.h> +#include <botan/mp_asm.h> +#include <botan/mp_asmi.h> + +namespace Botan { + +extern "C" { + +/* +* Montgomery Reduction Algorithm +*/ +void bigint_monty_redc(word z[], u32bit z_size, + const word x[], u32bit x_size, word u) + { + const u32bit blocks_of_8 = x_size - (x_size % 8); + + for(u32bit i = 0; i != x_size; ++i) + { + word* z_i = z + i; + + const word y = z_i[0] * u; + + word carry = 0; + + for(u32bit j = 0; j != blocks_of_8; j += 8) + carry = word8_madd3(z_i + j, x + j, y, carry); + + for(u32bit j = blocks_of_8; j != x_size; ++j) + z_i[j] = word_madd3(x[j], y, z_i[j], &carry); + + word z_sum = z_i[x_size] + carry; + carry = (z_sum < z_i[x_size]); + z_i[x_size] = z_sum; + + for(u32bit j = x_size + 1; carry && j != z_size - i; ++j) + { + ++z_i[j]; + carry = !z_i[j]; + } + } + + // Check if z[x_size...x_size+1] >= x[0...x_size] using bigint_cmp (inlined) + if(!z[x_size + x_size]) + { + for(u32bit i = x_size; i > 0; --i) + { + if(z[x_size + i - 1] > x[i-1]) + break; + + if(z[x_size + i - 1] < x[i-1]) + return; + } + } + + // If the compare above is true, subtract using bigint_sub2 (inlined) + word carry = 0; + + for(u32bit i = 0; i != blocks_of_8; i += 8) + carry = word8_sub2(z + x_size + i, x + i, carry); + + for(u32bit i = blocks_of_8; i != x_size; ++i) + z[x_size + i] = word_sub(z[x_size + i], x[i], &carry); + + if(carry) + --z[x_size+x_size]; + } + +} + +} diff --git a/old/botan/src/math/bigint/mp_amd64/info.txt b/old/botan/src/math/bigint/mp_amd64/info.txt new file mode 100644 index 0000000..84a5bcf --- /dev/null +++ b/old/botan/src/math/bigint/mp_amd64/info.txt @@ -0,0 +1,19 @@ +realname "MPI Core (x86-64)" + +mp_bits 64 + +load_on dep + +<add> +mp_asm.h +mp_asmi.h +</add> + +<arch> +amd64 +</arch> + +<cc> +gcc +icc +</cc> diff --git a/old/botan/src/math/bigint/mp_amd64/mp_asm.h b/old/botan/src/math/bigint/mp_amd64/mp_asm.h new file mode 100644 index 0000000..fa66d04 --- /dev/null +++ b/old/botan/src/math/bigint/mp_amd64/mp_asm.h @@ -0,0 +1,69 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2008 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_ASM_H__ +#define BOTAN_MP_ASM_H__ + +#include <botan/mp_types.h> + +#if (BOTAN_MP_WORD_BITS != 64) + #error The mp_amd64 module requires that BOTAN_MP_WORD_BITS == 64 +#endif + +namespace Botan { + +extern "C" { + +/* +* Helper Macros for amd64 Assembly +*/ +#define ASM(x) x "\n\t" + +/* +* Word Multiply +*/ +inline word word_madd2(word a, word b, word* c) + { + 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; + } + +/* +* Word Multiply/Add +*/ +inline word word_madd3(word a, word b, word c, word* d) + { + 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; + } + +#undef ASM + +} + +} + +#endif diff --git a/old/botan/src/math/bigint/mp_amd64/mp_asmi.h b/old/botan/src/math/bigint/mp_amd64/mp_asmi.h new file mode 100644 index 0000000..8bccbaa --- /dev/null +++ b/old/botan/src/math/bigint/mp_amd64/mp_asmi.h @@ -0,0 +1,243 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2007 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_ASM_INTERNAL_H__ +#define BOTAN_MP_ASM_INTERNAL_H__ + +#include <botan/mp_asm.h> + +namespace Botan { + +extern "C" { + +/* +* Helper Macros for amd64 Assembly +*/ +#ifndef ASM + #define ASM(x) x "\n\t" +#endif + +#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 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) + +#define ADD_OR_SUBTRACT(CORE_CODE) \ + ASM("rorq %[carry]") \ + CORE_CODE \ + ASM("sbbq %[carry],%[carry]") \ + ASM("negq %[carry]") + +/* +* Word Addition +*/ +inline word word_add(word x, word y, word* carry) + { +#if 0 + 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) + { + 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; + } + +/* +* Eight Word Block Addition, Three Argument +*/ +inline word word8_add3(word z[8], const word x[8], const word y[8], word carry) + { + 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; + } + +/* +* Word Subtraction +*/ +inline word word_sub(word x, word y, word* carry) + { + asm( + ADD_OR_SUBTRACT(ASM("sbbq %[y],%[x]")) + : [x]"=r"(x), [carry]"=r"(*carry) + : "0"(x), [y]"rm"(y), "1"(*carry) + : "cc"); + return x; + } + +/* +* Eight Word Block Subtraction, Two Argument +*/ +inline word word8_sub2(word x[8], const word y[8], word carry) + { + 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; + } + +/* +* Eight Word Block Subtraction, Three Argument +*/ +inline word word8_sub3(word z[8], const word x[8], const word y[8], word carry) + { + 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; + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul2(word x[8], word y, word carry) + { + asm( + DO_8_TIMES(LINMUL_OP, "x") + : [carry]"=r"(carry) + : [x]"r"(x), [y]"rm"(y), "0"(carry) + : "cc", "%rax", "%rdx"); + return carry; + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul3(word z[8], const word x[8], word y, word carry) + { + 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; + } + +/* +* Eight Word Block Multiply/Add +*/ +inline word word8_madd3(word z[8], const word x[8], word y, word carry) + { + 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; + } + +/* +* Multiply-Add Accumulator +*/ +inline void word3_muladd(word* w2, word* w1, word* w0, word x, word y) + { + asm( + ASM("mulq %[y]") + + ASM("addq %[x],%[w0]") + ASM("adcq %[y],%[w1]") + ASM("adcq $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [x]"a"(x), [y]"d"(y), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + } + +/* +* Multiply-Add Accumulator +*/ +inline void word3_muladd_2(word* w2, word* w1, word* w0, word x, word y) + { + asm( + ASM("mulq %[y]") + + ASM("addq %[x],%[w0]") + ASM("adcq %[y],%[w1]") + ASM("adcq $0,%[w2]") + + ASM("addq %[x],%[w0]") + ASM("adcq %[y],%[w1]") + ASM("adcq $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [x]"a"(x), [y]"d"(y), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + } + + +#undef ASM +#undef DO_8_TIMES +#undef ADD_OR_SUBTRACT +#undef ADDSUB2_OP +#undef ADDSUB3_OP +#undef LINMUL_OP +#undef MULADD_OP + +} + +} +#endif diff --git a/old/botan/src/math/bigint/mp_asm.cpp b/old/botan/src/math/bigint/mp_asm.cpp new file mode 100644 index 0000000..ea9738d --- /dev/null +++ b/old/botan/src/math/bigint/mp_asm.cpp @@ -0,0 +1,179 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2008 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/mp_asm.h> +#include <botan/mp_asmi.h> +#include <botan/mp_core.h> +#include <botan/mem_ops.h> + +namespace Botan { + +extern "C" { + +/* +* Two Operand Addition, No Carry +*/ +word bigint_add2_nc(word x[], u32bit x_size, const word y[], u32bit y_size) + { + word carry = 0; + + const u32bit blocks = y_size - (y_size % 8); + + for(u32bit j = 0; j != blocks; j += 8) + carry = word8_add2(x + j, y + j, carry); + + for(u32bit j = blocks; j != y_size; ++j) + x[j] = word_add(x[j], y[j], &carry); + + if(!carry) + return 0; + + for(u32bit j = y_size; j != x_size; ++j) + if(++x[j]) + return 0; + + return 1; + } + +/* +* Three Operand Addition, No Carry +*/ +word bigint_add3_nc(word z[], const word x[], u32bit x_size, + const word y[], u32bit y_size) + { + if(x_size < y_size) + { return bigint_add3_nc(z, y, y_size, x, x_size); } + + word carry = 0; + + const u32bit blocks = y_size - (y_size % 8); + + for(u32bit j = 0; j != blocks; j += 8) + carry = word8_add3(z + j, x + j, y + j, carry); + + for(u32bit j = blocks; j != y_size; ++j) + z[j] = word_add(x[j], y[j], &carry); + + for(u32bit j = y_size; j != x_size; ++j) + { + word x_j = x[j] + carry; + if(carry && x_j) + carry = 0; + z[j] = x_j; + } + + return carry; + } + +/* +* Two Operand Addition +*/ +void bigint_add2(word x[], u32bit x_size, const word y[], u32bit y_size) + { + if(bigint_add2_nc(x, x_size, y, y_size)) + ++x[x_size]; + } + +/* +* Three Operand Addition +*/ +void bigint_add3(word z[], const word x[], u32bit x_size, + const word y[], u32bit y_size) + { + if(bigint_add3_nc(z, x, x_size, y, y_size)) + ++z[(x_size > y_size ? x_size : y_size)]; + } + +/* +* Two Operand Subtraction +*/ +void bigint_sub2(word x[], u32bit x_size, const word y[], u32bit y_size) + { + word carry = 0; + + const u32bit blocks = y_size - (y_size % 8); + + for(u32bit j = 0; j != blocks; j += 8) + carry = word8_sub2(x + j, y + j, carry); + + for(u32bit j = blocks; j != y_size; ++j) + x[j] = word_sub(x[j], y[j], &carry); + + if(!carry) return; + + for(u32bit j = y_size; j != x_size; ++j) + { + --x[j]; + if(x[j] != MP_WORD_MAX) return; + } + } + +/* +* Three Operand Subtraction +*/ +void bigint_sub3(word z[], const word x[], u32bit x_size, + const word y[], u32bit y_size) + { + word carry = 0; + + const u32bit blocks = y_size - (y_size % 8); + + for(u32bit j = 0; j != blocks; j += 8) + carry = word8_sub3(z + j, x + j, y + j, carry); + + for(u32bit j = blocks; j != y_size; ++j) + z[j] = word_sub(x[j], y[j], &carry); + + for(u32bit j = y_size; j != x_size; ++j) + { + word x_j = x[j] - carry; + if(carry && x_j != MP_WORD_MAX) + carry = 0; + z[j] = x_j; + } + } + +/* +* Two Operand Linear Multiply +*/ +void bigint_linmul2(word x[], u32bit x_size, word y) + { + const u32bit blocks = x_size - (x_size % 8); + + word carry = 0; + + for(u32bit j = 0; j != blocks; j += 8) + carry = word8_linmul2(x + j, y, carry); + + for(u32bit j = blocks; j != x_size; ++j) + x[j] = word_madd2(x[j], y, &carry); + + x[x_size] = carry; + } + +/* +* Three Operand Linear Multiply +*/ +void bigint_linmul3(word z[], const word x[], u32bit x_size, word y) + { + const u32bit blocks = x_size - (x_size % 8); + + word carry = 0; + + for(u32bit j = 0; j != blocks; j += 8) + carry = word8_linmul3(z + j, x + j, y, carry); + + for(u32bit j = blocks; j != x_size; ++j) + z[j] = word_madd2(x[j], y, &carry); + + z[x_size] = carry; + } + +} + +} diff --git a/old/botan/src/math/bigint/mp_asm64/info.txt b/old/botan/src/math/bigint/mp_asm64/info.txt new file mode 100644 index 0000000..5c112c4 --- /dev/null +++ b/old/botan/src/math/bigint/mp_asm64/info.txt @@ -0,0 +1,27 @@ +realname "MPI Core (Alpha/IA-64/MIPS64/PowerPC-64/SPARC64)" + +mp_bits 64 + +load_on dep + +<add> +mp_asm.h +mp_generic:mp_asmi.h +</add> + +<arch> +#amd64 +alpha +ia64 +mips64 +ppc64 +sparc64 +</arch> + +# The inline asm only works with gcc, but it looks like (at least on +# UltraSPARC), using 64-bit words and the sythensized multiply is a 5 to 25% +# win, so it's probably worth using elsewhere. +<cc> +gcc +sunwspro +</cc> diff --git a/old/botan/src/math/bigint/mp_asm64/mp_asm.h b/old/botan/src/math/bigint/mp_asm64/mp_asm.h new file mode 100644 index 0000000..c9159ea --- /dev/null +++ b/old/botan/src/math/bigint/mp_asm64/mp_asm.h @@ -0,0 +1,119 @@ +/* +* MPI Multiply-Add Core +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_MADD_H__ +#define BOTAN_MP_MADD_H__ + +#include <botan/mp_types.h> + +namespace Botan { + +#if (BOTAN_MP_WORD_BITS != 64) + #error The mp_asm64 module requires that BOTAN_MP_WORD_BITS == 64 +#endif + +#if defined(BOTAN_TARGET_ARCH_IS_ALPHA) + +#define BOTAN_WORD_MUL(a,b,z1,z0) do { \ + asm("umulh %1,%2,%0" : "=r" (z0) : "r" (a), "r" (b)); \ + z1 = a * b; \ +} while(0); + +#elif defined(BOTAN_TARGET_ARCH_IS_AMD64) + +#define BOTAN_WORD_MUL(a,b,z1,z0) do { \ + asm("mulq %3" : "=d" (z0), "=a" (z1) : \ + "a" (a), "rm" (b) : "cc"); \ +} while(0); + +#elif defined(BOTAN_TARGET_ARCH_IS_IA64) + +#define BOTAN_WORD_MUL(a,b,z1,z0) do { \ + asm("xmpy.hu %0=%1,%2" : "=f" (z0) : "f" (a), "f" (b)); \ + z1 = a * b; \ +} while(0); + +#elif defined(BOTAN_TARGET_ARCH_IS_PPC64) + +#define BOTAN_WORD_MUL(a,b,z1,z0) do { \ + asm("mulhdu %0,%1,%2" : "=r" (z0) : "r" (a), "r" (b) : "cc"); \ + z1 = a * b; \ +} while(0); + +#elif defined(BOTAN_TARGET_ARCH_IS_MIPS64) + +#define BOTAN_WORD_MUL(a,b,z1,z0) do { \ + asm("dmultu %2,%3" : "=h" (z0), "=l" (z1) : "r" (a), "r" (b)); \ +} while(0); + +#else + +// Do a 64x64->128 multiply using four 64x64->64 multiplies +// plus some adds and shifts. Last resort for CPUs like UltraSPARC, +// with 64-bit registers/ALU, but no 64x64->128 multiply. +inline void bigint_2word_mul(word a, word b, word* z1, word* z0) + { + const u32bit MP_HWORD_BITS = BOTAN_MP_WORD_BITS / 2; + const word MP_HWORD_MASK = ((word)1 << MP_HWORD_BITS) - 1; + + const word a_hi = (a >> MP_HWORD_BITS); + const word a_lo = (a & MP_HWORD_MASK); + const word b_hi = (b >> MP_HWORD_BITS); + const word b_lo = (b & MP_HWORD_MASK); + + word x0 = a_hi * b_hi; + word x1 = a_lo * b_hi; + word x2 = a_hi * b_lo; + word x3 = a_lo * b_lo; + + x2 += x3 >> (MP_HWORD_BITS); + x2 += x1; + if(x2 < x1) + x0 += ((word)1 << MP_HWORD_BITS); + + *z0 = x0 + (x2 >> MP_HWORD_BITS); + *z1 = ((x2 & MP_HWORD_MASK) << MP_HWORD_BITS) + (x3 & MP_HWORD_MASK); + } + +#define BOTAN_WORD_MUL(a,b,z1,z0) bigint_2word_mul(a, b, &z1, &z0) + +#endif + +/* +* Word Multiply/Add +*/ +inline word word_madd2(word a, word b, word* c) + { + word z0 = 0, z1 = 0; + + BOTAN_WORD_MUL(a, b, z1, z0); + + z1 += *c; if(z1 < *c) z0++; + + *c = z0; + return z1; + } + +/* +* Word Multiply/Add +*/ +inline word word_madd3(word a, word b, word c, word* d) + { + word z0 = 0, z1 = 0; + + BOTAN_WORD_MUL(a, b, z1, z0); + + z1 += c; if(z1 < c) z0++; + z1 += *d; if(z1 < *d) z0++; + + *d = z0; + return z1; + } + +} + +#endif diff --git a/old/botan/src/math/bigint/mp_comba.cpp b/old/botan/src/math/bigint/mp_comba.cpp new file mode 100644 index 0000000..218038d --- /dev/null +++ b/old/botan/src/math/bigint/mp_comba.cpp @@ -0,0 +1,920 @@ +/* +* Comba Multiplication and Squaring +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/mp_core.h> +#include <botan/mp_asmi.h> + +namespace Botan { + +extern "C" { + +/* +* 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[1]); + z[1] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[2]); + word3_muladd(&w2, &w1, &w0, x[1], x[1]); + z[2] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[1], x[3]); + word3_muladd(&w2, &w1, &w0, x[2], x[2]); + z[4] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[2], x[3]); + z[5] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[1]); + word3_muladd(&w2, &w1, &w0, x[1], y[0]); + z[1] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[2]); + word3_muladd(&w2, &w1, &w0, x[1], y[1]); + word3_muladd(&w2, &w1, &w0, x[2], y[0]); + z[2] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[1], y[3]); + word3_muladd(&w2, &w1, &w0, x[2], y[2]); + word3_muladd(&w2, &w1, &w0, x[3], y[1]); + z[4] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[2], y[3]); + word3_muladd(&w2, &w1, &w0, x[3], y[2]); + z[5] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[1]); + z[1] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[2]); + word3_muladd(&w2, &w1, &w0, x[1], x[1]); + z[2] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[4]); + word3_muladd_2(&w2, &w1, &w0, x[1], x[3]); + word3_muladd(&w2, &w1, &w0, x[2], x[2]); + z[4] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[5]); + word3_muladd_2(&w2, &w1, &w0, x[1], x[4]); + word3_muladd_2(&w2, &w1, &w0, x[2], x[3]); + z[5] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[2], x[5]); + word3_muladd_2(&w2, &w1, &w0, x[3], x[4]); + z[7] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[3], x[5]); + word3_muladd(&w2, &w1, &w0, x[4], x[4]); + z[8] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[4], x[5]); + z[9] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[5], x[5]); + z[10] = w0; + z[11] = w1; + } + +/* +* 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[1]); + word3_muladd(&w2, &w1, &w0, x[1], y[0]); + z[1] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[2]); + word3_muladd(&w2, &w1, &w0, x[1], y[1]); + word3_muladd(&w2, &w1, &w0, x[2], y[0]); + z[2] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[4]); + word3_muladd(&w2, &w1, &w0, x[1], y[3]); + word3_muladd(&w2, &w1, &w0, x[2], y[2]); + word3_muladd(&w2, &w1, &w0, x[3], y[1]); + word3_muladd(&w2, &w1, &w0, x[4], y[0]); + z[4] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[5]); + word3_muladd(&w2, &w1, &w0, x[1], y[4]); + word3_muladd(&w2, &w1, &w0, x[2], y[3]); + word3_muladd(&w2, &w1, &w0, x[3], y[2]); + word3_muladd(&w2, &w1, &w0, x[4], y[1]); + word3_muladd(&w2, &w1, &w0, x[5], y[0]); + z[5] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[2], y[5]); + word3_muladd(&w2, &w1, &w0, x[3], y[4]); + word3_muladd(&w2, &w1, &w0, x[4], y[3]); + word3_muladd(&w2, &w1, &w0, x[5], y[2]); + z[7] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[3], y[5]); + word3_muladd(&w2, &w1, &w0, x[4], y[4]); + word3_muladd(&w2, &w1, &w0, x[5], y[3]); + z[8] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[5], y[5]); + z[10] = w0; + z[11] = w1; + } + +/* +* 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[1]); + z[1] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[2]); + word3_muladd(&w2, &w1, &w0, x[1], x[1]); + z[2] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[4]); + word3_muladd_2(&w2, &w1, &w0, x[1], x[3]); + word3_muladd(&w2, &w1, &w0, x[2], x[2]); + z[4] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[5]); + word3_muladd_2(&w2, &w1, &w0, x[1], x[4]); + word3_muladd_2(&w2, &w1, &w0, x[2], x[3]); + z[5] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[0], x[7]); + word3_muladd_2(&w2, &w1, &w0, x[1], x[6]); + word3_muladd_2(&w2, &w1, &w0, x[2], x[5]); + word3_muladd_2(&w2, &w1, &w0, x[3], x[4]); + z[7] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[1], x[7]); + word3_muladd_2(&w2, &w1, &w0, x[2], x[6]); + word3_muladd_2(&w2, &w1, &w0, x[3], x[5]); + word3_muladd(&w2, &w1, &w0, x[4], x[4]); + z[8] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[3], x[7]); + word3_muladd_2(&w2, &w1, &w0, x[4], x[6]); + word3_muladd(&w2, &w1, &w0, x[5], x[5]); + z[10] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[4], x[7]); + word3_muladd_2(&w2, &w1, &w0, x[5], x[6]); + z[11] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[6], x[7]); + z[13] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[7], x[7]); + z[14] = w0; + z[15] = w1; + } + +/* +* 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[1]); + word3_muladd(&w2, &w1, &w0, x[1], y[0]); + z[1] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[2]); + word3_muladd(&w2, &w1, &w0, x[1], y[1]); + word3_muladd(&w2, &w1, &w0, x[2], y[0]); + z[2] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[4]); + word3_muladd(&w2, &w1, &w0, x[1], y[3]); + word3_muladd(&w2, &w1, &w0, x[2], y[2]); + word3_muladd(&w2, &w1, &w0, x[3], y[1]); + word3_muladd(&w2, &w1, &w0, x[4], y[0]); + z[4] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[5]); + word3_muladd(&w2, &w1, &w0, x[1], y[4]); + word3_muladd(&w2, &w1, &w0, x[2], y[3]); + word3_muladd(&w2, &w1, &w0, x[3], y[2]); + word3_muladd(&w2, &w1, &w0, x[4], y[1]); + word3_muladd(&w2, &w1, &w0, x[5], y[0]); + z[5] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[0], y[7]); + word3_muladd(&w2, &w1, &w0, x[1], y[6]); + word3_muladd(&w2, &w1, &w0, x[2], y[5]); + word3_muladd(&w2, &w1, &w0, x[3], y[4]); + word3_muladd(&w2, &w1, &w0, x[4], y[3]); + word3_muladd(&w2, &w1, &w0, x[5], y[2]); + word3_muladd(&w2, &w1, &w0, x[6], y[1]); + word3_muladd(&w2, &w1, &w0, x[7], y[0]); + z[7] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[1], y[7]); + word3_muladd(&w2, &w1, &w0, x[2], y[6]); + word3_muladd(&w2, &w1, &w0, x[3], y[5]); + word3_muladd(&w2, &w1, &w0, x[4], y[4]); + word3_muladd(&w2, &w1, &w0, x[5], y[3]); + word3_muladd(&w2, &w1, &w0, x[6], y[2]); + word3_muladd(&w2, &w1, &w0, x[7], y[1]); + z[8] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[3], y[7]); + word3_muladd(&w2, &w1, &w0, x[4], y[6]); + word3_muladd(&w2, &w1, &w0, x[5], y[5]); + word3_muladd(&w2, &w1, &w0, x[6], y[4]); + word3_muladd(&w2, &w1, &w0, x[7], y[3]); + z[10] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[4], y[7]); + word3_muladd(&w2, &w1, &w0, x[5], y[6]); + word3_muladd(&w2, &w1, &w0, x[6], y[5]); + word3_muladd(&w2, &w1, &w0, x[7], y[4]); + z[11] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[6], y[7]); + word3_muladd(&w2, &w1, &w0, x[7], y[6]); + z[13] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[7], y[7]); + z[14] = w0; + z[15] = w1; + } + +/* +* 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 1]); + z[ 1] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 1], x[ 1]); + z[ 2] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 4]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 2], x[ 2]); + z[ 4] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 5]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 4]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 3]); + z[ 5] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 7]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 5]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 4]); + z[ 7] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 7]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 6]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 4], x[ 4]); + z[ 8] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 7]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 5], x[ 5]); + z[10] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 7]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 6]); + z[11] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 8]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[ 7]); + z[13] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 0], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 9]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 7], x[ 7]); + z[14] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 1], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 8], x[ 8]); + z[16] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 2], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 3], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[10]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[ 9]); + z[17] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 4], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[11]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[10]); + z[19] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 5], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 6], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[12]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[11]); + word3_muladd(&w2, &w1, &w0, x[10], x[10]); + z[20] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 7], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[10], x[12]); + word3_muladd(&w2, &w1, &w0, x[11], x[11]); + z[22] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[ 8], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[ 9], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[10], x[13]); + word3_muladd_2(&w2, &w1, &w0, x[11], x[12]); + z[23] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[10], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[11], x[14]); + word3_muladd_2(&w2, &w1, &w0, x[12], x[13]); + z[25] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[11], x[15]); + word3_muladd_2(&w2, &w1, &w0, x[12], x[14]); + word3_muladd(&w2, &w1, &w0, x[13], x[13]); + z[26] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[13], x[15]); + word3_muladd(&w2, &w1, &w0, x[14], x[14]); + z[28] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd_2(&w2, &w1, &w0, x[14], x[15]); + z[29] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 0]); + z[1] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 0]); + z[2] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 0]); + z[4] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 0]); + z[5] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 0]); + z[7] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 0]); + z[8] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 0]); + z[10] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 0]); + z[11] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 0]); + z[13] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 0], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 1], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 1]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 0]); + z[14] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 1], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 2], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 2]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 1]); + z[16] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 2], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 3], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 4], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[10]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 4]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 3]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 2]); + z[17] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 4], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 5], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[11]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[10]); + word3_muladd(&w2, &w1, &w0, x[10], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 5]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 4]); + z[19] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 5], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 6], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 7], y[13]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[12]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[11]); + word3_muladd(&w2, &w1, &w0, x[10], y[10]); + word3_muladd(&w2, &w1, &w0, x[11], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[12], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 7]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 6]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 5]); + z[20] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 7], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 8], y[14]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[13]); + word3_muladd(&w2, &w1, &w0, x[10], y[12]); + word3_muladd(&w2, &w1, &w0, x[11], y[11]); + word3_muladd(&w2, &w1, &w0, x[12], y[10]); + word3_muladd(&w2, &w1, &w0, x[13], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 8]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 7]); + z[22] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[ 8], y[15]); + word3_muladd(&w2, &w1, &w0, x[ 9], y[14]); + word3_muladd(&w2, &w1, &w0, x[10], y[13]); + word3_muladd(&w2, &w1, &w0, x[11], y[12]); + word3_muladd(&w2, &w1, &w0, x[12], y[11]); + word3_muladd(&w2, &w1, &w0, x[13], y[10]); + word3_muladd(&w2, &w1, &w0, x[14], y[ 9]); + word3_muladd(&w2, &w1, &w0, x[15], y[ 8]); + z[23] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[10], y[15]); + word3_muladd(&w2, &w1, &w0, x[11], y[14]); + word3_muladd(&w2, &w1, &w0, x[12], y[13]); + word3_muladd(&w2, &w1, &w0, x[13], y[12]); + word3_muladd(&w2, &w1, &w0, x[14], y[11]); + word3_muladd(&w2, &w1, &w0, x[15], y[10]); + z[25] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[11], y[15]); + word3_muladd(&w2, &w1, &w0, x[12], y[14]); + word3_muladd(&w2, &w1, &w0, x[13], y[13]); + word3_muladd(&w2, &w1, &w0, x[14], y[12]); + word3_muladd(&w2, &w1, &w0, x[15], y[11]); + z[26] = w0; w0 = w1; w1 = 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 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[13], y[15]); + word3_muladd(&w2, &w1, &w0, x[14], y[14]); + word3_muladd(&w2, &w1, &w0, x[15], y[13]); + z[28] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[14], y[15]); + word3_muladd(&w2, &w1, &w0, x[15], y[14]); + z[29] = w0; w0 = w1; w1 = w2; w2 = 0; + + word3_muladd(&w2, &w1, &w0, x[15], y[15]); + z[30] = w0; + z[31] = w1; + } + +} + +} diff --git a/old/botan/src/math/bigint/mp_core.h b/old/botan/src/math/bigint/mp_core.h new file mode 100644 index 0000000..ea27a77 --- /dev/null +++ b/old/botan/src/math/bigint/mp_core.h @@ -0,0 +1,98 @@ +/* +* MPI Algorithms +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_CORE_H__ +#define BOTAN_MP_CORE_H__ + +#include <botan/mp_types.h> + +namespace Botan { + +/* +* The size of the word type, in bits +*/ +const u32bit MP_WORD_BITS = BOTAN_MP_WORD_BITS; + +extern "C" { + +/* +* Addition/Subtraction Operations +*/ +void bigint_add2(word[], u32bit, const word[], u32bit); +void bigint_add3(word[], const word[], u32bit, const word[], u32bit); + +word bigint_add2_nc(word[], u32bit, const word[], u32bit); +word bigint_add3_nc(word[], const word[], u32bit, const word[], u32bit); + +void bigint_sub2(word[], u32bit, const word[], u32bit); +void bigint_sub3(word[], const word[], u32bit, const word[], u32bit); + +/* +* Shift Operations +*/ +void bigint_shl1(word[], u32bit, u32bit, u32bit); +void bigint_shl2(word[], const word[], u32bit, u32bit, u32bit); +void bigint_shr1(word[], u32bit, u32bit, u32bit); +void bigint_shr2(word[], const word[], u32bit, u32bit, u32bit); + +/* +* Simple O(N^2) Multiplication and Squaring +*/ +void bigint_simple_mul(word z[], const word x[], u32bit x_size, + const word y[], u32bit y_size); +void bigint_simple_sqr(word z[], const word x[], u32bit x_size); + +/* +* Linear Multiply +*/ +void bigint_linmul2(word[], u32bit, word); +void bigint_linmul3(word[], const word[], u32bit, word); +void bigint_linmul_add(word[], u32bit, const word[], u32bit, word); + +/* +* Montgomery Reduction +*/ +void bigint_monty_redc(word[], u32bit, const word[], u32bit, word); + +/* +* Misc Utility Operations +*/ +u32bit bigint_divcore(word, word, word, word, word, word); +s32bit bigint_cmp(const word[], u32bit, const word[], u32bit); +word bigint_divop(word, word, word); +word bigint_modop(word, word, word); +void bigint_wordmul(word, word, word*, word*); + +/* +* Comba Multiplication / Squaring +*/ +void bigint_comba_mul4(word[8], const word[4], const word[4]); +void bigint_comba_mul6(word[12], const word[6], const word[6]); +void bigint_comba_mul8(word[16], const word[8], const word[8]); +void bigint_comba_mul16(word[32], const word[16], const word[16]); + +void bigint_comba_sqr4(word[8], const word[4]); +void bigint_comba_sqr6(word[12], const word[6]); +void bigint_comba_sqr8(word[16], const word[8]); +void bigint_comba_sqr8(word[32], const word[16]); +void bigint_comba_sqr16(word[64], const word[32]); + +} + +/* +* High Level Multiplication/Squaring Interfaces +*/ +void bigint_mul(word[], u32bit, word[], + const word[], u32bit, u32bit, + const word[], u32bit, u32bit); + +void bigint_sqr(word[], u32bit, word[], + const word[], u32bit, u32bit); + +} + +#endif diff --git a/old/botan/src/math/bigint/mp_generic/info.txt b/old/botan/src/math/bigint/mp_generic/info.txt new file mode 100644 index 0000000..8bf75fe --- /dev/null +++ b/old/botan/src/math/bigint/mp_generic/info.txt @@ -0,0 +1,8 @@ +realname "MPI Core (C++)" + +load_on dep + +<add> +mp_asm.h +mp_asmi.h +</add> diff --git a/old/botan/src/math/bigint/mp_generic/mp_asm.h b/old/botan/src/math/bigint/mp_generic/mp_asm.h new file mode 100644 index 0000000..7c18343 --- /dev/null +++ b/old/botan/src/math/bigint/mp_generic/mp_asm.h @@ -0,0 +1,54 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2008 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_ASM_H__ +#define BOTAN_MP_ASM_H__ + +#include <botan/mp_types.h> + +#if (BOTAN_MP_WORD_BITS == 8) + typedef Botan::u16bit dword; +#elif (BOTAN_MP_WORD_BITS == 16) + typedef Botan::u32bit dword; +#elif (BOTAN_MP_WORD_BITS == 32) + typedef Botan::u64bit dword; +#elif (BOTAN_MP_WORD_BITS == 64) + #error BOTAN_MP_WORD_BITS can be 64 only with assembly support +#else + #error BOTAN_MP_WORD_BITS must be 8, 16, 32, or 64 +#endif + +namespace Botan { + +extern "C" { + +/* +* Word Multiply/Add +*/ +inline word word_madd2(word a, word b, word* c) + { + dword z = (dword)a * b + *c; + *c = (word)(z >> BOTAN_MP_WORD_BITS); + return (word)z; + } + +/* +* Word Multiply/Add +*/ +inline word word_madd3(word a, word b, word c, word* d) + { + dword z = (dword)a * b + c + *d; + *d = (word)(z >> BOTAN_MP_WORD_BITS); + return (word)z; + } + +} + +} + +#endif diff --git a/old/botan/src/math/bigint/mp_generic/mp_asmi.h b/old/botan/src/math/bigint/mp_generic/mp_asmi.h new file mode 100644 index 0000000..21c4db2 --- /dev/null +++ b/old/botan/src/math/bigint/mp_generic/mp_asmi.h @@ -0,0 +1,191 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2008 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_ASM_INTERNAL_H__ +#define BOTAN_MP_ASM_INTERNAL_H__ + +#include <botan/mp_asm.h> + +namespace Botan { + +extern "C" { + +/* +* Word Addition +*/ +inline word word_add(word x, word y, word* carry) + { + word z = x + y; + word c1 = (z < x); + z += *carry; + *carry = c1 | (z < *carry); + return z; + } + +/* +* Eight Word Block Addition, Two Argument +*/ +inline word word8_add2(word x[8], const word y[8], word carry) + { + 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; + } + +/* +* Eight Word Block Addition, Three Argument +*/ +inline word word8_add3(word z[8], const word x[8], + const word y[8], word carry) + { + 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; + } + +/* +* Word Subtraction +*/ +inline word word_sub(word x, word y, word* carry) + { + word t0 = x - y; + word c1 = (t0 > x); + word z = t0 - *carry; + *carry = c1 | (z > t0); + return z; + } + +/* +* Eight Word Block Subtraction, Two Argument +*/ +inline word word8_sub2(word x[4], const word y[4], word carry) + { + 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; + } + +/* +* Eight Word Block Subtraction, Three Argument +*/ +inline word word8_sub3(word z[8], const word x[8], + const word y[8], word carry) + { + 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; + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul2(word x[4], word y, word carry) + { + 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; + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul3(word z[8], const word x[8], word y, word carry) + { + 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; + } + +/* +* Eight Word Block Multiply/Add +*/ +inline word word8_madd3(word z[8], const word x[8], word y, word carry) + { + 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; + } + +/* +* Multiply-Add Accumulator +*/ +inline void word3_muladd(word* w2, word* w1, word* w0, word a, word b) + { + word carry = *w0; + *w0 = word_madd2(a, b, &carry); + *w1 += carry; + *w2 += (*w1 < carry) ? 1 : 0; + } + +/* +* Multiply-Add Accumulator +*/ +inline void word3_muladd_2(word* w2, word* w1, word* w0, word a, word b) + { + word carry = 0; + a = word_madd2(a, b, &carry); + b = carry; + + word top = (b >> (BOTAN_MP_WORD_BITS-1)); + b <<= 1; + b |= (a >> (BOTAN_MP_WORD_BITS-1)); + a <<= 1; + + carry = 0; + *w0 = word_add(*w0, a, &carry); + *w1 = word_add(*w1, b, &carry); + *w2 = word_add(*w2, top, &carry); + } + +} + +} + +#endif diff --git a/old/botan/src/math/bigint/mp_ia32/info.txt b/old/botan/src/math/bigint/mp_ia32/info.txt new file mode 100644 index 0000000..51f98fd --- /dev/null +++ b/old/botan/src/math/bigint/mp_ia32/info.txt @@ -0,0 +1,19 @@ +realname "MPI Core (IA-32)" + +mp_bits 32 + +load_on asm_ok + +<add> +mp_asm.h +mp_asmi.h +</add> + +<arch> +ia32 +</arch> + +<cc> +gcc +icc +</cc> diff --git a/old/botan/src/math/bigint/mp_ia32/mp_asm.h b/old/botan/src/math/bigint/mp_ia32/mp_asm.h new file mode 100644 index 0000000..4d3afc9 --- /dev/null +++ b/old/botan/src/math/bigint/mp_ia32/mp_asm.h @@ -0,0 +1,67 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2008 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_ASM_H__ +#define BOTAN_MP_ASM_H__ + +#include <botan/mp_types.h> + +#if (BOTAN_MP_WORD_BITS != 32) + #error The mp_ia32 module requires that BOTAN_MP_WORD_BITS == 32 +#endif + +namespace Botan { + +extern "C" { + +/* +* Helper Macros for x86 Assembly +*/ +#define ASM(x) x "\n\t" + +/* +* Word Multiply +*/ +inline word word_madd2(word a, word b, word* c) + { + 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; + } + +/* +* Word Multiply/Add +*/ +inline word word_madd3(word a, word b, word c, word* d) + { + 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; + } + +} + +} + +#endif diff --git a/old/botan/src/math/bigint/mp_ia32/mp_asmi.h b/old/botan/src/math/bigint/mp_ia32/mp_asmi.h new file mode 100644 index 0000000..28b99ab --- /dev/null +++ b/old/botan/src/math/bigint/mp_ia32/mp_asmi.h @@ -0,0 +1,235 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2007 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_ASM_INTERNAL_H__ +#define BOTAN_MP_ASM_INTERNAL_H__ + +#include <botan/mp_asm.h> + +namespace Botan { + +extern "C" { + +/* +* Helper Macros for x86 Assembly +*/ +#ifndef ASM + #define ASM(x) x "\n\t" +#endif + +#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 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) + +#define ADD_OR_SUBTRACT(CORE_CODE) \ + ASM("rorl %[carry]") \ + CORE_CODE \ + ASM("sbbl %[carry],%[carry]") \ + ASM("negl %[carry]") + +/* +* Word Addition +*/ +inline word word_add(word x, word y, word* carry) + { +#if 0 + asm( + ADD_OR_SUBTRACT(ASM("adcl %[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) + { + 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; + } + +/* +* Eight Word Block Addition, Three Argument +*/ +inline word word8_add3(word z[8], const word x[8], const word y[8], word carry) + { + 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; + } + +/* +* Word Subtraction +*/ +inline word word_sub(word x, word y, word* carry) + { + asm( + ADD_OR_SUBTRACT(ASM("sbbl %[y],%[x]")) + : [x]"=r"(x), [carry]"=r"(*carry) + : "0"(x), [y]"rm"(y), "1"(*carry) + : "cc"); + return x; + } + +/* +* Eight Word Block Subtraction, Two Argument +*/ +inline word word8_sub2(word x[8], const word y[8], word carry) + { + 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; + } + +/* +* Eight Word Block Subtraction, Three Argument +*/ +inline word word8_sub3(word z[8], const word x[8], const word y[8], word carry) + { + 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; + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul2(word x[8], word y, word carry) + { + asm( + DO_8_TIMES(LINMUL_OP, "x") + : [carry]"=r"(carry) + : [x]"r"(x), [y]"rm"(y), "0"(carry) + : "cc", "%eax", "%edx"); + return carry; + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul3(word z[8], const word x[8], word y, word carry) + { + 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; + } + +/* +* Eight Word Block Multiply/Add +*/ +inline word word8_madd3(word z[8], const word x[8], word y, word carry) + { + 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; + } + +/* +* Multiply-Add Accumulator +*/ +inline void word3_muladd(word* w2, word* w1, word* w0, word x, word y) + { + asm( + ASM("mull %[y]") + + ASM("addl %[x],%[w0]") + ASM("adcl %[y],%[w1]") + ASM("adcl $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [x]"a"(x), [y]"d"(y), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + } + +/* +* Multiply-Add Accumulator +*/ +inline void word3_muladd_2(word* w2, word* w1, word* w0, word x, word y) + { + asm( + ASM("mull %[y]") + + ASM("addl %[x],%[w0]") + ASM("adcl %[y],%[w1]") + ASM("adcl $0,%[w2]") + + ASM("addl %[x],%[w0]") + ASM("adcl %[y],%[w1]") + ASM("adcl $0,%[w2]") + + : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) + : [x]"a"(x), [y]"d"(y), "0"(*w0), "1"(*w1), "2"(*w2) + : "cc"); + } + +} + +} + +#endif diff --git a/old/botan/src/math/bigint/mp_ia32_msvc/info.txt b/old/botan/src/math/bigint/mp_ia32_msvc/info.txt new file mode 100644 index 0000000..9c7ac9b --- /dev/null +++ b/old/botan/src/math/bigint/mp_ia32_msvc/info.txt @@ -0,0 +1,18 @@ +realname "x86 MPI Assembler Core (MSVC)" + +mp_bits 32 + +load_on dep + +<add> +mp_generic:mp_asm.h +mp_asmi.h +</add> + +<arch> +ia32 +</arch> + +<cc> +msvc +</cc> diff --git a/old/botan/src/math/bigint/mp_ia32_msvc/mp_asmi.h b/old/botan/src/math/bigint/mp_ia32_msvc/mp_asmi.h new file mode 100644 index 0000000..33ce6eb --- /dev/null +++ b/old/botan/src/math/bigint/mp_ia32_msvc/mp_asmi.h @@ -0,0 +1,528 @@ +/* +* Lowest Level MPI Algorithms +* (C) 1999-2006 Jack Lloyd +* 2006 Luca Piccarreta +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MP_ASM_INTERNAL_H__ +#define BOTAN_MP_ASM_INTERNAL_H__ + +#include <botan/mp_asm.h> + +namespace Botan { + +extern "C" { + +/* +* Word Addition +*/ +inline word word_add(word x, word y, word* carry) + { + word z = x + y; + word c1 = (z < x); + z += *carry; + *carry = c1 | (z < *carry); + return z; + } + +/* +* Eight Word Block Addition, Two Argument +*/ +inline word word8_add2(word x[8], const word y[8], word carry) + { + __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 + } + } + +/* +* Eight Word Block Addition, Three Argument +*/ +inline word word8_add3(word z[8], const word x[8], const word y[8], word carry) + { + __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 + } + } + +/* +* Word Subtraction +*/ +inline word word_sub(word x, word y, word* carry) + { + word t0 = x - y; + word c1 = (t0 > x); + word z = t0 - *carry; + *carry = c1 | (z > t0); + return z; + } + +/* +* Eight Word Block Subtraction, Two Argument +*/ +inline word word8_sub2(word x[8], const word y[8], word carry) + { + _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 + } + } + +/* +* Eight Word Block Subtraction, Three Argument +*/ +inline word word8_sub3(word z[8], const word x[8], + const word y[8], word carry) + { + __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 + } + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_linmul2(word x[8], word y, word carry) + { + __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 + } + } + +/* +* Eight Word Block Linear Multiplication +*/ +inline word word8_muladd(word z[8], const word x[8], + word y, word carry) + { + __asm + { + mov esi,[x] + mov ebx,[y] + mov edi,[z] + mov eax,[esi] //load a + mul ebx //edx(hi):eax(lo)=a*b + add eax,[carry] //sum lo carry + adc edx,0 //sum hi carry + add eax,[edi] //sum lo z + adc edx,0 //sum hi z + mov ecx,edx //carry for next block = hi z + mov [edi],eax //save lo z + + mov eax,[esi+4] + mul ebx + add eax,ecx + adc edx,0 + add eax,[edi+4] + adc edx,0 + mov ecx,edx + mov [edi+4],eax + + mov eax,[esi+8] + mul ebx + add eax,ecx + adc edx,0 + add eax,[edi+8] + adc edx,0 + mov ecx,edx + mov [edi+8],eax + + mov eax,[esi+12] + mul ebx + add eax,ecx + adc edx,0 + add eax,[edi+12] + adc edx,0 + mov ecx,edx + mov [edi+12],eax + + mov eax,[esi+16] + mul ebx + add eax,ecx + adc edx,0 + add eax,[edi+16] + adc edx,0 + mov ecx,edx + mov [edi+16],eax + + mov eax,[esi+20] + mul ebx + add eax,ecx + adc edx,0 + add eax,[edi+20] + adc edx,0 + mov ecx,edx + mov [edi+20],eax + + mov eax,[esi+24] + mul ebx + add eax,ecx + adc edx,0 + add eax,[edi+24] + adc edx,0 + mov ecx,edx + mov [edi+24],eax + + mov eax,[esi+28] + mul ebx + add eax,ecx + adc edx,0 + add eax,[edi+28] + adc edx,0 + mov [edi+28],eax + mov eax,edx + } + } + +inline word word8_linmul3(word z[4], const word x[4], word y, word carry) + { + __asm + { +#if 0 + //it's slower!!! + mov edx,[z] + mov eax,[x] + movd mm7,[y] + + movd mm0,[eax] + movd mm1,[eax+4] + movd mm2,[eax+8] + pmuludq mm0,mm7 + pmuludq mm1,mm7 + pmuludq mm2,mm7 + + movd mm6,[carry] + paddq mm0,mm6 + movd [edx],mm0 + + psrlq mm0,32 + paddq mm1,mm0 + movd [edx+4],mm1 + + movd mm3,[eax+12] + psrlq mm1,32 + paddq mm2,mm1 + movd [edx+8],mm2 + + pmuludq mm3,mm7 + movd mm4,[eax+16] + psrlq mm2,32 + paddq mm3,mm2 + movd [edx+12],mm3 + + pmuludq mm4,mm7 + movd mm5,[eax+20] + psrlq mm3,32 + paddq mm4,mm3 + movd [edx+16],mm4 + + pmuludq mm5,mm7 + movd mm0,[eax+24] + psrlq mm4,32 + paddq mm5,mm4 + movd [edx+20],mm5 + + pmuludq mm0,mm7 + movd mm1,[eax+28] + psrlq mm5,32 + paddq mm0,mm5 + movd [edx+24],mm0 + + pmuludq mm1,mm7 + psrlq mm0,32 + paddq mm1,mm0 + movd [edx+28],mm1 + + psrlq mm1,32 + movd eax,mm1 + emms +#else + 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 +#endif + } + } + +/* +* Eight Word Block Multiply/Add +*/ +inline word word8_madd3(word z[8], const word x[8], word y, word carry) + { + 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; + } + +/* +* Multiply-Add Accumulator +*/ +inline void word3_muladd(word* w2, word* w1, word* w0, word a, word b) + { + word carry = *w0; + *w0 = word_madd2(a, b, &carry); + *w1 += carry; + *w2 += (*w1 < carry) ? 1 : 0; + } + +/* +* Multiply-Add Accumulator +*/ +inline void word3_muladd_2(word* w2, word* w1, word* w0, word a, word b) + { + word carry = 0; + a = word_madd2(a, b, &carry); + b = carry; + + word top = (b >> (BOTAN_MP_WORD_BITS-1)); + b <<= 1; + b |= (a >> (BOTAN_MP_WORD_BITS-1)); + a <<= 1; + + carry = 0; + *w0 = word_add(*w0, a, &carry); + *w1 = word_add(*w1, b, &carry); + *w2 = word_add(*w2, top, &carry); + } + +} + +} + +#endif diff --git a/old/botan/src/math/bigint/mp_karat.cpp b/old/botan/src/math/bigint/mp_karat.cpp new file mode 100644 index 0000000..f30d418 --- /dev/null +++ b/old/botan/src/math/bigint/mp_karat.cpp @@ -0,0 +1,336 @@ +/* +* Karatsuba Multiplication/Squaring +* (C) 1999-2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/mp_core.h> +#include <botan/mem_ops.h> +#include <botan/mp_asmi.h> + +namespace Botan { + +namespace { + +/* +* Karatsuba Multiplication Operation +*/ +void karatsuba_mul(word z[], const word x[], const word y[], u32bit N, + word workspace[]) + { + if(N == 6) + bigint_comba_mul6(z, x, y); + else if(N == 8) + bigint_comba_mul8(z, x, y); + else if(N == 16) + bigint_comba_mul16(z, x, y); + else if(N < BOTAN_KARAT_MUL_THRESHOLD || N % 2) + bigint_simple_mul(z, x, N, y, N); + else + { + const u32bit 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; + + const s32bit cmp0 = bigint_cmp(x0, N2, x1, N2); + const s32bit cmp1 = bigint_cmp(y1, N2, y0, N2); + + clear_mem(workspace, 2*N); + + if(cmp0 && cmp1) + { + if(cmp0 > 0) + bigint_sub3(z0, x0, N2, x1, N2); + else + bigint_sub3(z0, x1, N2, x0, N2); + + if(cmp1 > 0) + bigint_sub3(z1, y1, N2, y0, N2); + else + bigint_sub3(z1, y0, N2, y1, N2); + + karatsuba_mul(workspace, z0, z1, N2, workspace+N); + } + + karatsuba_mul(z0, x0, y0, N2, workspace+N); + karatsuba_mul(z1, x1, y1, N2, workspace+N); + + const u32bit blocks_of_8 = N - (N % 8); + + word carry = 0; + + for(u32bit j = 0; j != blocks_of_8; j += 8) + carry = word8_add3(workspace + N + j, z0 + j, z1 + j, carry); + + for(u32bit j = blocks_of_8; j != N; ++j) + workspace[N + j] = word_add(z0[j], z1[j], &carry); + + word carry2 = 0; + + for(u32bit j = 0; j != blocks_of_8; j += 8) + carry2 = word8_add2(z + N2 + j, workspace + N + j, carry2); + + for(u32bit j = blocks_of_8; j != N; ++j) + z[N2 + j] = word_add(z[N2 + j], workspace[N + j], &carry2); + + z[N + N2] = word_add(z[N + N2], carry2, &carry); + + if(carry) + for(u32bit j = 1; j != N2; ++j) + if(++z[N + N2 + j]) + break; + + if((cmp0 == cmp1) || (cmp0 == 0) || (cmp1 == 0)) + bigint_add2(z + N2, 2*N-N2, workspace, N); + else + bigint_sub2(z + N2, 2*N-N2, workspace, N); + } + } + +/* +* Karatsuba Squaring Operation +*/ +void karatsuba_sqr(word z[], const word x[], u32bit N, word workspace[]) + { + if(N == 6) + bigint_comba_sqr6(z, x); + else if(N == 8) + bigint_comba_sqr8(z, x); + else if(N == 16) + bigint_comba_sqr16(z, x); + else if(N < BOTAN_KARAT_SQR_THRESHOLD || N % 2) + bigint_simple_sqr(z, x, N); + else + { + const u32bit N2 = N / 2; + + const word* x0 = x; + const word* x1 = x + N2; + word* z0 = z; + word* z1 = z + N; + + const s32bit cmp = bigint_cmp(x0, N2, x1, N2); + + clear_mem(workspace, 2*N); + + if(cmp) + { + if(cmp > 0) + bigint_sub3(z0, x0, N2, x1, N2); + else + bigint_sub3(z0, x1, N2, x0, N2); + + karatsuba_sqr(workspace, z0, N2, workspace+N); + } + + karatsuba_sqr(z0, x0, N2, workspace+N); + karatsuba_sqr(z1, x1, N2, workspace+N); + + const u32bit blocks_of_8 = N - (N % 8); + + word carry = 0; + + for(u32bit j = 0; j != blocks_of_8; j += 8) + carry = word8_add3(workspace + N + j, z0 + j, z1 + j, carry); + + for(u32bit j = blocks_of_8; j != N; ++j) + workspace[N + j] = word_add(z0[j], z1[j], &carry); + + word carry2 = 0; + + for(u32bit j = 0; j != blocks_of_8; j += 8) + carry2 = word8_add2(z + N2 + j, workspace + N + j, carry2); + + for(u32bit j = blocks_of_8; j != N; ++j) + z[N2 + j] = word_add(z[N2 + j], workspace[N + j], &carry2); + + z[N + N2] = word_add(z[N + N2], carry2, &carry); + + if(carry) + for(u32bit j = 1; j != N2; ++j) + if(++z[N + N2 + j]) + break; + + if(cmp == 0) + bigint_add2(z + N2, 2*N-N2, workspace, N); + else + bigint_sub2(z + N2, 2*N-N2, workspace, N); + } + } + +/* +* Pick a good size for the Karatsuba multiply +*/ +u32bit karatsuba_size(u32bit z_size, + u32bit x_size, u32bit x_sw, + u32bit y_size, u32bit 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 u32bit start = (x_sw > y_sw) ? x_sw : y_sw; + const u32bit end = (x_size < y_size) ? x_size : y_size; + + if(start == end) + { + if(start % 2) + return 0; + return start; + } + + for(u32bit 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 +*/ +u32bit karatsuba_size(u32bit z_size, u32bit x_size, u32bit x_sw) + { + if(x_sw == x_size) + { + if(x_sw % 2) + return 0; + return x_sw; + } + + for(u32bit 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; + } + +} + +/* +* Multiplication Algorithm Dispatcher +*/ +void bigint_mul(word z[], u32bit z_size, word workspace[], + const word x[], u32bit x_size, u32bit x_sw, + const word y[], u32bit y_size, u32bit y_sw) + { + 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(x_sw <= 4 && x_size >= 4 && + y_sw <= 4 && y_size >= 4 && z_size >= 8) + { + bigint_comba_mul4(z, x, y); + } + else if(x_sw <= 6 && x_size >= 6 && + y_sw <= 6 && y_size >= 6 && z_size >= 12) + { + bigint_comba_mul6(z, x, y); + } + else if(x_sw <= 8 && x_size >= 8 && + y_sw <= 8 && y_size >= 8 && z_size >= 16) + { + bigint_comba_mul8(z, x, y); + } + else if(x_sw <= 16 && x_size >= 16 && + y_sw <= 16 && y_size >= 16 && z_size >= 32) + { + bigint_comba_mul16(z, x, y); + } + else if(x_sw < BOTAN_KARAT_MUL_THRESHOLD || y_sw < BOTAN_KARAT_MUL_THRESHOLD) + bigint_simple_mul(z, x, x_sw, y, y_sw); + else + { + const u32bit N = karatsuba_size(z_size, x_size, x_sw, y_size, y_sw); + + if(N) + { + clear_mem(workspace, 2*N); + karatsuba_mul(z, x, y, N, workspace); + } + else + bigint_simple_mul(z, x, x_sw, y, y_sw); + } + } + +/* +* Squaring Algorithm Dispatcher +*/ +void bigint_sqr(word z[], u32bit z_size, word workspace[], + const word x[], u32bit x_size, u32bit x_sw) + { + if(x_sw == 1) + { + bigint_linmul3(z, x, x_sw, x[0]); + } + else if(x_sw <= 4 && x_size >= 4 && z_size >= 8) + { + bigint_comba_sqr4(z, x); + } + else if(x_sw <= 6 && x_size >= 6 && z_size >= 12) + { + bigint_comba_sqr6(z, x); + } + else if(x_sw <= 8 && x_size >= 8 && z_size >= 16) + { + bigint_comba_sqr8(z, x); + } + else if(x_sw <= 16 && x_size >= 16 && z_size >= 32) + { + bigint_comba_sqr16(z, x); + } + else if(x_size < BOTAN_KARAT_SQR_THRESHOLD) + { + bigint_simple_sqr(z, x, x_sw); + } + else + { + const u32bit N = karatsuba_size(z_size, x_size, x_sw); + + if(N) + { + clear_mem(workspace, 2*N); + karatsuba_sqr(z, x, N, workspace); + } + else + bigint_simple_sqr(z, x, x_sw); + } + } + +} diff --git a/old/botan/src/math/bigint/mp_misc.cpp b/old/botan/src/math/bigint/mp_misc.cpp new file mode 100644 index 0000000..6b7fc65 --- /dev/null +++ b/old/botan/src/math/bigint/mp_misc.cpp @@ -0,0 +1,94 @@ +/* +* MP Misc Functions +* (C) 1999-2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/mp_core.h> +#include <botan/mp_asm.h> + +namespace Botan { + +extern "C" { + +/* +* Core Division Operation +*/ +u32bit bigint_divcore(word q, word y1, word y2, + word x1, word x2, word x3) + { + word y0 = 0; + y2 = word_madd2(q, y2, &y0); + y1 = word_madd2(q, y1, &y0); + + if(y0 > x1) return 1; + if(y0 < x1) return 0; + if(y1 > x2) return 1; + if(y1 < x2) return 0; + if(y2 > x3) return 1; + if(y2 < x3) return 0; + return 0; + } + +/* +* Compare two MP integers +*/ +s32bit bigint_cmp(const word x[], u32bit x_size, + const word y[], u32bit 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(u32bit j = x_size; j > 0; --j) + { + if(x[j-1] > y[j-1]) return 1; + if(x[j-1] < y[j-1]) return -1; + } + return 0; + } + +/* +* Do a 2-word/1-word Division +*/ +word bigint_divop(word n1, word n0, word d) + { + word high = n1 % d, quotient = 0; + + for(u32bit j = 0; j != MP_WORD_BITS; ++j) + { + word high_top_bit = (high & MP_WORD_TOP_BIT); + + high <<= 1; + high |= (n0 >> (MP_WORD_BITS-1-j)) & 1; + quotient <<= 1; + + if(high_top_bit || high >= d) + { + high -= d; + quotient |= 1; + } + } + + return quotient; + } + +/* +* Do a 2-word/1-word Modulo +*/ +word bigint_modop(word n1, word n0, word d) + { + word z = bigint_divop(n1, n0, d); + word dummy = 0; + z = word_madd2(z, d, &dummy); + return (n0-z); + } + +} + +} diff --git a/old/botan/src/math/bigint/mp_shift.cpp b/old/botan/src/math/bigint/mp_shift.cpp new file mode 100644 index 0000000..a7de79c --- /dev/null +++ b/old/botan/src/math/bigint/mp_shift.cpp @@ -0,0 +1,138 @@ +/* +* MP Shift Algorithms +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/mp_core.h> +#include <botan/mem_ops.h> + +namespace Botan { + +extern "C" { + +/* +* Single Operand Left Shift +*/ +void bigint_shl1(word x[], u32bit x_size, u32bit word_shift, u32bit bit_shift) + { + if(word_shift) + { + for(u32bit j = 1; j != x_size + 1; ++j) + x[(x_size - j) + word_shift] = x[x_size - j]; + clear_mem(x, word_shift); + } + + if(bit_shift) + { + word carry = 0; + for(u32bit j = word_shift; j != x_size + word_shift + 1; ++j) + { + word temp = x[j]; + x[j] = (temp << bit_shift) | carry; + carry = (temp >> (MP_WORD_BITS - bit_shift)); + } + } + } + +/* +* Single Operand Right Shift +*/ +void bigint_shr1(word x[], u32bit x_size, u32bit word_shift, u32bit 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; + + u32bit top = x_size - word_shift; + + while(top >= 4) + { + word w = x[top-1]; + x[top-1] = (w >> bit_shift) | carry; + carry = (w << (MP_WORD_BITS - bit_shift)); + + w = x[top-2]; + x[top-2] = (w >> bit_shift) | carry; + carry = (w << (MP_WORD_BITS - bit_shift)); + + w = x[top-3]; + x[top-3] = (w >> bit_shift) | carry; + carry = (w << (MP_WORD_BITS - bit_shift)); + + w = x[top-4]; + x[top-4] = (w >> bit_shift) | carry; + carry = (w << (MP_WORD_BITS - bit_shift)); + + top -= 4; + } + + while(top) + { + word w = x[top-1]; + x[top-1] = (w >> bit_shift) | carry; + carry = (w << (MP_WORD_BITS - bit_shift)); + + top--; + } + } + } + +/* +* Two Operand Left Shift +*/ +void bigint_shl2(word y[], const word x[], u32bit x_size, + u32bit word_shift, u32bit bit_shift) + { + for(u32bit j = 0; j != x_size; ++j) + y[j + word_shift] = x[j]; + if(bit_shift) + { + word carry = 0; + for(u32bit j = word_shift; j != x_size + word_shift + 1; ++j) + { + word w = y[j]; + y[j] = (w << bit_shift) | carry; + carry = (w >> (MP_WORD_BITS - bit_shift)); + } + } + } + +/* +* Two Operand Right Shift +*/ +void bigint_shr2(word y[], const word x[], u32bit x_size, + u32bit word_shift, u32bit bit_shift) + { + if(x_size < word_shift) return; + + for(u32bit j = 0; j != x_size - word_shift; ++j) + y[j] = x[j + word_shift]; + if(bit_shift) + { + word carry = 0; + for(u32bit j = x_size - word_shift; j > 0; --j) + { + word w = y[j-1]; + y[j-1] = (w >> bit_shift) | carry; + carry = (w << (MP_WORD_BITS - bit_shift)); + } + } + } + +} + +} diff --git a/old/botan/src/math/bigint/mp_types.h b/old/botan/src/math/bigint/mp_types.h new file mode 100644 index 0000000..1648713 --- /dev/null +++ b/old/botan/src/math/bigint/mp_types.h @@ -0,0 +1,33 @@ +/* +* Low Level MPI Types +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MPI_TYPES_H__ +#define BOTAN_MPI_TYPES_H__ + +#include <botan/types.h> + +namespace Botan { + +#if (BOTAN_MP_WORD_BITS == 8) + typedef byte word; +#elif (BOTAN_MP_WORD_BITS == 16) + typedef u16bit word; +#elif (BOTAN_MP_WORD_BITS == 32) + typedef u32bit word; +#elif (BOTAN_MP_WORD_BITS == 64) + typedef u64bit word; +#else + #error BOTAN_MP_WORD_BITS must be 8, 16, 32, or 64 +#endif + +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; + +} + +#endif diff --git a/old/botan/src/math/bigint/mulop_amd64/info.txt b/old/botan/src/math/bigint/mulop_amd64/info.txt new file mode 100644 index 0000000..77990df --- /dev/null +++ b/old/botan/src/math/bigint/mulop_amd64/info.txt @@ -0,0 +1,32 @@ +realname "BigInt Multiply-Add (x86-64)" + +mp_bits 64 + +load_on never + +<add> +mp_mulop_amd64.S +</add> + +<arch> +amd64 +</arch> + +<cc> +gcc +icc +</cc> + +# ELF systems +<os> +linux +freebsd +dragonfly +netbsd +openbsd +solaris +</os> + +<requires> +asm_amd64 +</requires> diff --git a/old/botan/src/math/bigint/mulop_amd64/mp_mulop.cpp b/old/botan/src/math/bigint/mulop_amd64/mp_mulop.cpp new file mode 100644 index 0000000..cbd723e --- /dev/null +++ b/old/botan/src/math/bigint/mulop_amd64/mp_mulop.cpp @@ -0,0 +1,96 @@ +/* +* Simple O(N^2) Multiplication and Squaring +* (C) 1999-2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/mp_asm.h> +#include <botan/mp_asmi.h> +#include <botan/mp_core.h> +#include <botan/mem_ops.h> + +namespace Botan { + +extern "C" { + +/* +* Simple O(N^2) Multiplication +*/ +void bigint_simple_mul(word z[], const word x[], u32bit x_size, + const word y[], u32bit y_size) + { + const u32bit blocks = x_size - (x_size % 8); + + clear_mem(z, x_size + y_size); + + for(u32bit i = 0; i != y_size; ++i) + { + word carry = 0; + + for(u32bit j = 0; j != blocks; j += 8) + carry = word8_madd3(z + i + j, x + j, y[i], carry); + + for(u32bit j = blocks; j != x_size; ++j) + z[i+j] = word_madd3(x[j], y[i], z[i+j], &carry); + + z[x_size+i] = carry; + } + } + +inline word word_sqr(word x, + +/* +* Simple O(N^2) Squaring + +This is exactly the same algorithm as bigint_simple_mul, +however because C/C++ compilers suck at alias analysis it +is good to have the version where the compiler knows +that x == y +*/ +void bigint_simple_sqr(word z[], const word x[], u32bit x_size) + { + clear_mem(z, 2*x_size); + + for(u32bit i = 0; i != x_size; ++i) + { + const word x_i = x[i]; + + word carry = z[2*i]; + z[2*i] = word_madd2(x_i, x_i, z[2*i], &carry); + + for(u32bit j = i; j != x_size; ++j) + { + // z[i+j] = z[i+j] + 2 * x[j] * x_i + carry; + + /* + load z[i+j] into register + load x[j] into %hi + mulq %[x_i] -> x[i] * x[j] -> %lo:%hi + shlq %lo, $1 + + // put carry bit (cf) from %lo into %temp + xorl %temp + adcq $0, %temp + + // high bit of lo now in cf + shl %hi, $1 + // add in lowest bid from %lo + orl %temp, %hi + + addq %[c], %[lo] + adcq $0, %[hi] + addq %[z_ij], %[lo] + adcq $0, %[hi] + + */ + + } + + z[x_size+i] = carry; + } + } + +} + +} diff --git a/old/botan/src/math/bigint/mulop_amd64/mp_mulop_amd64.S b/old/botan/src/math/bigint/mulop_amd64/mp_mulop_amd64.S new file mode 100644 index 0000000..63ac55e --- /dev/null +++ b/old/botan/src/math/bigint/mulop_amd64/mp_mulop_amd64.S @@ -0,0 +1,130 @@ +/* +* Simple O(N^2) Multiplication and Squaring +* (C) 1999-2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/asm_macr.h> + +START_LISTING(mp_mulop.S) + +#if 0 +void bigint_simple_sqr(word z[], const word x[], u32bit x_size) + { + const u32bit blocks = x_size - (x_size % 8); + + clear_mem(z, 2*x_size); + + for(u32bit i = 0; i != x_size; ++i) + { + word carry = 0; + + /* + for(u32bit j = 0; j != blocks; j += 8) + carry = word8_madd3(z + i + j, x + j, x[i], carry); + + for(u32bit j = blocks; j != x_size; ++j) + z[i+j] = word_madd3(x[j], x[i], z[i+j], &carry); + */ + + + for(u32bit j = 0; j != x_size; ++j) + z[i+j] = word_madd3(x[j], x[i], z[i+j], &carry); + + for(u32bit j = 0; j != x_size; ++j) + { + dword z = (dword)a * b + c + *d; + *d = (word)(z >> BOTAN_MP_WORD_BITS); + return (word)z; + } + + + + z[i+j] = word_madd3(x[j], x[i], z[i+j], &carry); + + } + + + + z[x_size+i] = carry; + } + } + +#endif + +START_FUNCTION(bigint_simple_sqr) + +#define Z_ARR ARG_1 +#define X_ARR ARG_2 +//#define X_SIZE ARG_3_32 + +#define CARRY TEMP_1 +#define Z_WORD TEMP_2 +#define LOOP_I TEMP_3 +#define LOOP_J TEMP_4 +#define X_SIZE TEMP_5 +#define MUL_LO %rax +// arg 3, xsize +#define MUL_HI %rdx + +// need arg3 == rdx for multiply + ASSIGN(X_SIZE, ARG3_32) + + ZEROIZE(CARRY) + + ZEROIZE(LOOP_I) + +.LOOP_ZEROIZE_Z: + + cmp LOOP_I, X_SIZE + + + + + JUMP_IF_ZERO(LOOP_CTR, .L_MULADD_DONE) + JUMP_IF_LT(LOOP_CTR, 8, .LOOP_MULADD1) + +#define MULADD_OP(N) \ + ASSIGN(MUL_LO, ARRAY8(X_ARR, N)) ; \ + ASSIGN(Z_WORD, ARRAY8(Z_ARR, N)) ; \ + MUL(Y) ; \ + ADD(Z_WORD, CARRY) ; \ + ASSIGN(CARRY, MUL_HI) ; \ + ADD_LAST_CARRY(CARRY) ; \ + ADD(Z_WORD, MUL_LO) ; \ + ADD_LAST_CARRY(CARRY) ; \ + ASSIGN(ARRAY8(Z_ARR, N), Z_WORD) + +.LOOP_MULADD8: + MULADD_OP(0) + MULADD_OP(1) + MULADD_OP(2) + MULADD_OP(3) + MULADD_OP(4) + MULADD_OP(5) + MULADD_OP(6) + MULADD_OP(7) + + SUB_IMM(LOOP_CTR, 8) + ADD_IMM(Z_ARR, 64) + ADD_IMM(X_ARR, 64) + cmp IMM(8), LOOP_CTR + jge .LOOP_MULADD8 + + JUMP_IF_ZERO(LOOP_CTR, .L_MULADD_DONE) + +ALIGN +.LOOP_MULADD1: + MULADD_OP(0) + + SUB_IMM(LOOP_CTR, 1) + ADD_IMM(Z_ARR, 8) + ADD_IMM(X_ARR, 8) + + cmp IMM(0), LOOP_CTR + jne .LOOP_MULADD1 + +.L_MULADD_DONE: + RETURN_VALUE_IS(CARRY) +END_FUNCTION(bigint_simple_square) diff --git a/old/botan/src/math/bigint/mulop_generic/info.txt b/old/botan/src/math/bigint/mulop_generic/info.txt new file mode 100644 index 0000000..28ebe41 --- /dev/null +++ b/old/botan/src/math/bigint/mulop_generic/info.txt @@ -0,0 +1,7 @@ +realname "BigInt Multiply-Add" + +load_on dep + +<add> +mp_mulop.cpp +</add> diff --git a/old/botan/src/math/bigint/mulop_generic/mp_mulop.cpp b/old/botan/src/math/bigint/mulop_generic/mp_mulop.cpp new file mode 100644 index 0000000..4647d00 --- /dev/null +++ b/old/botan/src/math/bigint/mulop_generic/mp_mulop.cpp @@ -0,0 +1,77 @@ +/* +* Simple O(N^2) Multiplication and Squaring +* (C) 1999-2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/mp_asm.h> +#include <botan/mp_asmi.h> +#include <botan/mp_core.h> +#include <botan/mem_ops.h> + +namespace Botan { + +extern "C" { + +/* +* Simple O(N^2) Multiplication +*/ +void bigint_simple_mul(word z[], const word x[], u32bit x_size, + const word y[], u32bit y_size) + { + const u32bit x_size_8 = x_size - (x_size % 8); + + clear_mem(z, x_size + y_size); + + for(u32bit i = 0; i != y_size; ++i) + { + const word y_i = y[i]; + + word carry = 0; + + for(u32bit j = 0; j != x_size_8; j += 8) + carry = word8_madd3(z + i + j, x + j, y_i, carry); + + for(u32bit 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; + } + } + +/* +* Simple O(N^2) Squaring + +This is exactly the same algorithm as bigint_simple_mul, +however because C/C++ compilers suck at alias analysis it +is good to have the version where the compiler knows +that x == y + +There is an O(n^1.5) squaring algorithm specified in Handbook of +Applied Cryptography, chapter 14 +*/ +void bigint_simple_sqr(word z[], const word x[], u32bit x_size) + { + const u32bit x_size_8 = x_size - (x_size % 8); + + clear_mem(z, 2*x_size); + + for(u32bit i = 0; i != x_size; ++i) + { + const word x_i = x[i]; + word carry = 0; + + for(u32bit j = 0; j != x_size_8; j += 8) + carry = word8_madd3(z + i + j, x + j, x_i, carry); + + for(u32bit 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; + } + } + +} + +} diff --git a/old/botan/src/math/bigint/mulop_ia32/info.txt b/old/botan/src/math/bigint/mulop_ia32/info.txt new file mode 100644 index 0000000..b995dd8 --- /dev/null +++ b/old/botan/src/math/bigint/mulop_ia32/info.txt @@ -0,0 +1,34 @@ +realname "BigInt Multiply-Add (IA-32)" + +mp_bits 32 + +# Out of date, still implements bigint_mul_add_words + +load_on request + +<add> +mp_mulop.S +</add> + +<arch> +ia32 +</arch> + +<cc> +gcc +icc +</cc> + +# ELF systems +<os> +linux +freebsd +dragonfly +netbsd +openbsd +solaris +</os> + +<requires> +asm_ia32 +</requires> diff --git a/old/botan/src/math/bigint/mulop_ia32/mp_mulop.S b/old/botan/src/math/bigint/mulop_ia32/mp_mulop.S new file mode 100644 index 0000000..716166f --- /dev/null +++ b/old/botan/src/math/bigint/mulop_ia32/mp_mulop.S @@ -0,0 +1,64 @@ +/* +* Multiply/Add Algorithm Source File +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/asm_macr.h> + +START_LISTING(mp_muladd.S) + +START_FUNCTION(bigint_mul_add_words) + SPILL_REGS() +#define PUSHED 4 + +#define LOOP_CTR ESI + ASSIGN(LOOP_CTR, ARG(3)) /* x_size */ + ZEROIZE(EDI) + + ASSIGN(ECX, ARG(1)) /* z[] */ + ASSIGN(EBX, ARG(2)) /* x[] */ + ASSIGN(EBP, ARG(4)) /* y */ + +#define MULADD_OP(N) \ + ASSIGN(EAX, ARRAY4(EBX, N)) ; \ + MUL(EBP) ; \ + ADD_W_CARRY(EAX, EDX, EDI) ; \ + ASSIGN(EDI, EDX) ; \ + ADD_W_CARRY(ARRAY4(ECX, N), EDI, EAX) ; + + JUMP_IF_ZERO(LOOP_CTR, .MUL_ADD_DONE) + JUMP_IF_LT(LOOP_CTR, 8, .MULADD1_LOOP) + +START_LOOP(.MULADD8) + MULADD_OP(0) + MULADD_OP(1) + MULADD_OP(2) + MULADD_OP(3) + MULADD_OP(4) + MULADD_OP(5) + MULADD_OP(6) + MULADD_OP(7) + + SUB_IMM(LOOP_CTR, 8) + ADD_IMM(EBX, 32) + ADD_IMM(ECX, 32) +LOOP_UNTIL_LT(LOOP_CTR, 8, .MULADD8) + + JUMP_IF_ZERO(LOOP_CTR, .MUL_ADD_DONE) + +START_LOOP(.MULADD1) + MULADD_OP(0) + + SUB_IMM(LOOP_CTR, 1) + ADD_IMM(EBX, 4) + ADD_IMM(ECX, 4) +LOOP_UNTIL_EQ(LOOP_CTR, 0, .MULADD1) + +.MUL_ADD_DONE: + + ASSIGN(EAX, EDI) +#undef PUSHED + RESTORE_REGS() +END_FUNCTION(bigint_mul_add_words) diff --git a/old/botan/src/math/gfpmath/curve_gfp.cpp b/old/botan/src/math/gfpmath/curve_gfp.cpp new file mode 100644 index 0000000..e12ade0 --- /dev/null +++ b/old/botan/src/math/gfpmath/curve_gfp.cpp @@ -0,0 +1,165 @@ +/****** +* Elliptic curves over GF(p) +* +* (C) 2007 Martin Doering +* Christoph Ludwig +* Falko Strenzke +* 2008 Jack Lloyd +******/ + +#include <botan/curve_gfp.h> +#include <botan/bigint.h> +#include <assert.h> +#include <ostream> + +namespace Botan { + +void CurveGFp::set_shrd_mod(const std::tr1::shared_ptr<GFpModulus> mod) + { + mp_mod = mod; + mA.turn_off_sp_red_mul();// m.m. is not needed, must be trf. back + mB.turn_off_sp_red_mul();// m.m. is not needed, must be trf. back + //ok, above we destroy any evantually computated montg. mult. values, + // but that won't influence performance in usual applications + mA.set_shrd_mod(mod); + mB.set_shrd_mod(mod); + } + +CurveGFp::CurveGFp(const GFpElement& a, const GFpElement& b, + const BigInt& p) + : mA(a), + mB(b) + { + if(!((p == mA.get_p()) && (p == mB.get_p()))) + { + throw Invalid_Argument("could not construct curve: moduli of arguments differ"); + } + std::tr1::shared_ptr<GFpModulus> p_mod = std::tr1::shared_ptr<GFpModulus>(new GFpModulus(p)); + // the above is the creation of the GFpModuls object which will be shared point-wide + // (in the context of a point of course) + set_shrd_mod(p_mod); + } +// copy constructor +CurveGFp::CurveGFp(const CurveGFp& other) + : mA(other.get_a()), + mB(other.get_b()) + { + mp_mod = std::tr1::shared_ptr<GFpModulus>(new GFpModulus(*other.mp_mod)); + assert(mp_mod->p_equal_to(mA.get_p())); + assert(mp_mod->p_equal_to(mB.get_p())); + set_shrd_mod(mp_mod); + if(other.mp_mres_a.get()) + { + mp_mres_a = std::tr1::shared_ptr<GFpElement>(new GFpElement(*other.mp_mres_a)); + } + if(other.mp_mres_b.get()) + { + mp_mres_b = std::tr1::shared_ptr<GFpElement>(new GFpElement(*other.mp_mres_b)); + } + if(other.mp_mres_one.get()) + { + mp_mres_one = std::tr1::shared_ptr<GFpElement>(new GFpElement(*other.mp_mres_one)); + } + + } + +// assignment operator +const CurveGFp& CurveGFp::operator=(const CurveGFp& other) + { + // for exception safety... + GFpElement a_tmp = other.mA; + GFpElement b_tmp = other.mB; + mA.swap(a_tmp); + mB.swap(b_tmp); + + std::tr1::shared_ptr<GFpModulus> p_mod = std::tr1::shared_ptr<GFpModulus>(new GFpModulus(*other.mp_mod)); + set_shrd_mod(p_mod); + + // exception safety note: no problem if we have a throw from here on... + if(other.mp_mres_a.get()) + { + mp_mres_a = std::tr1::shared_ptr<GFpElement>(new GFpElement(*other.mp_mres_a)); + } + if(other.mp_mres_b.get()) + { + mp_mres_b = std::tr1::shared_ptr<GFpElement>(new GFpElement(*other.mp_mres_b)); + } + if(other.mp_mres_one.get()) + { + mp_mres_one = std::tr1::shared_ptr<GFpElement>(new GFpElement(*other.mp_mres_one)); + } + return *this; + } + +// getters +const GFpElement& CurveGFp::get_a() const + { + return mA; + } + +const GFpElement& CurveGFp::get_b() const + { + return mB; + } + +const BigInt CurveGFp::get_p() const + { + assert(mp_mod.get() != 0); + return mp_mod->get_p(); + } + +// swaps the states of *this and other, does not throw +void CurveGFp::swap(CurveGFp& other) + { + mA.swap(other.mA); + mB.swap(other.mB); + mp_mod.swap(other.mp_mod); + std::swap(mp_mres_a, other.mp_mres_a); + std::swap(mp_mres_b, other.mp_mres_b); + std::swap(mp_mres_one, other.mp_mres_one); + } + +GFpElement const CurveGFp::get_mres_a() const + { + if(mp_mres_a.get() == 0) + { + mp_mres_a = std::tr1::shared_ptr<GFpElement>(new GFpElement(mA)); + mp_mres_a->turn_on_sp_red_mul(); + mp_mres_a->get_mres(); + } + return GFpElement(*mp_mres_a); + } + +GFpElement const CurveGFp::get_mres_b() const + { + if(mp_mres_b.get() == 0) + { + mp_mres_b = std::tr1::shared_ptr<GFpElement>(new GFpElement(mB)); + mp_mres_b->turn_on_sp_red_mul(); + mp_mres_b->get_mres(); + } + return GFpElement(*mp_mres_b); + } + +std::tr1::shared_ptr<GFpElement const> const CurveGFp::get_mres_one() const + { + if(mp_mres_one.get() == 0) + { + mp_mres_one = std::tr1::shared_ptr<GFpElement>(new GFpElement(mp_mod->get_p(), 1)); + mp_mres_one->turn_on_sp_red_mul(); + mp_mres_one->get_mres(); + } + return mp_mres_one; + } + +bool operator==(const CurveGFp& lhs, const CurveGFp& rhs) + { + return (lhs.get_p() == rhs.get_p() && lhs.get_a() == rhs.get_a() && lhs.get_b() == rhs.get_b()); + } + +std::ostream& operator<<(std::ostream& output, const CurveGFp& elem) + { + return output << "y^2f = x^3 + (" << elem.get_a() << ")x + (" << elem.get_b() << ")"; + } + +} diff --git a/old/botan/src/math/gfpmath/curve_gfp.h b/old/botan/src/math/gfpmath/curve_gfp.h new file mode 100644 index 0000000..81cf6ce --- /dev/null +++ b/old/botan/src/math/gfpmath/curve_gfp.h @@ -0,0 +1,177 @@ +/****** + * Elliptic curves over GF(p) (header file) + * + * (C) 2007 Martin Doering + * doering@cdc.informatik.tu-darmstadt.de + * Christoph Ludwig + * ludwig@fh-worms.de + * Falko Strenzke + * strenzke@flexsecure.de + ******/ + +#ifndef BOTAN_GFP_CURVE_H__ +#define BOTAN_GFP_CURVE_H__ + +#include <botan/bigint.h> +#include <botan/gfp_element.h> +#include <iosfwd> + +namespace Botan { + +/** +* This class represents an elliptic curve over GF(p) +* +* Distributed under the terms of the Botan license +*/ +class BOTAN_DLL CurveGFp + { + public: + + /** + * Construct the elliptic curve E: y^2 = x^3 + ax + b over GF(p) + * @param a first coefficient + * @param b second coefficient + * @param p prime number of the field + */ + CurveGFp(const GFpElement& a, const GFpElement& b, + const BigInt& p); + + /** + * Copy constructor + * @param other The curve to clone + */ + CurveGFp(const CurveGFp& other); + + /** + * Assignment operator + * @param other The curve to use as source for the assignment + */ + const CurveGFp& operator=(const CurveGFp& other); + + /** + * Set the shared GFpModulus object. + * Warning: do not use this function unless you know in detail how + * the sharing of values + * in the various EC related objects works. + * Do NOT spread pointers to a GFpModulus over different threads! + * @param mod a shared pointer to a GFpModulus object suitable for + * *this. + */ + void set_shrd_mod(const std::tr1::shared_ptr<GFpModulus> mod); + + // getters + + /** + * Get coefficient a + * @result coefficient a + */ + const GFpElement& get_a() const; + + /** + * Get coefficient b + * @result coefficient b + */ + const GFpElement& get_b() const; + + /** + * Get the GFpElement coefficient a transformed + * to its m-residue. This can be used for efficency reasons: the curve + * stores the transformed version after the first invocation of this + * function. + * @result the coefficient a, transformed to its m-residue + */ + GFpElement const get_mres_a() const; + + /** + * Get the GFpElement coefficient b transformed + * to its m-residue. This can be used for efficency reasons: the curve + * stores the transformed version after the first invocation of this + * function. + * @result the coefficient b, transformed to its m-residue + */ + GFpElement const get_mres_b() const; + + + /** + * Get the GFpElement 1 transformed + * to its m-residue. This can be used for efficency reasons: the curve + * stores the transformed version after the first invocation of this + * function. + * @result the GFpElement 1, transformed to its m-residue + */ + std::tr1::shared_ptr<GFpElement const> const get_mres_one() const; + + /** + * Get prime modulus of the field of the curve + * @result prime modulus of the field of the curve + */ + BigInt const get_p() const; + /*inline std::tr1::shared_ptr<BigInt> const get_ptr_p() const + { + return mp_p; + }*/ + + /** + * Retrieve a shared pointer to the curves GFpModulus object for efficient storage + * and computation of montgomery multiplication related data members and functions. + * Warning: do not use this function unless you know in detail how the sharing of values + * in the various EC related objects works. + * Do NOT spread pointers to a GFpModulus over different threads! + * @result a shared pointer to a GFpModulus object + */ + inline std::tr1::shared_ptr<GFpModulus> const get_ptr_mod() const + { + return mp_mod; + } + + /** + * swaps the states of *this and other, does not throw + * @param other The curve to swap values with + */ + void swap(CurveGFp& other); + + private: + std::tr1::shared_ptr<GFpModulus> mp_mod; + GFpElement mA; + GFpElement mB; + mutable std::tr1::shared_ptr<GFpElement> mp_mres_a; + mutable std::tr1::shared_ptr<GFpElement> mp_mres_b; + mutable std::tr1::shared_ptr<GFpElement> mp_mres_one; + }; + +// relational operators +bool operator==(const CurveGFp& lhs, const CurveGFp& rhs); + +inline bool operator!=(const CurveGFp& lhs, const CurveGFp& rhs) + { + return !(lhs == rhs); + } + +// io operators +std::ostream& operator<<(std::ostream& output, const CurveGFp& elem); + +// swaps the states of curve1 and curve2, does not throw! +// cf. Meyers, Item 25 +inline +void swap(CurveGFp& curve1, CurveGFp& curve2) + { + curve1.swap(curve2); + } + +} // namespace Botan + + +namespace std { + +// swaps the states of curve1 and curve2, does not throw! +// cf. Meyers, Item 25 +template<> inline +void swap<Botan::CurveGFp>(Botan::CurveGFp& curve1, + Botan::CurveGFp& curve2) + { + curve1.swap(curve2); + } + +} // namespace std + +#endif diff --git a/old/botan/src/math/gfpmath/gfp_element.cpp b/old/botan/src/math/gfpmath/gfp_element.cpp new file mode 100644 index 0000000..b718093 --- /dev/null +++ b/old/botan/src/math/gfpmath/gfp_element.cpp @@ -0,0 +1,699 @@ +/****** + * Arithmetic for prime fields GF(p) (source file) + * + * (C) 2007 Martin Doering + * doering@cdc.informatik.tu-darmstadt.de + * Christoph Ludwig + * ludwig@fh-worms.de + * Falko Strenzke + * strenzke@flexsecure.de + ******/ + +#include <botan/gfp_element.h> +#include <botan/numthry.h> +#include <botan/def_powm.h> +#include <botan/mp_types.h> +#include <botan/mp_asm.h> +#include <botan/mp_asmi.h> +#include <assert.h> +#include <ostream> + +namespace Botan { + +namespace { + +void inner_montg_mult_sos(word result[], const word* a_bar, const word* b_bar, const word* n, const word* n_dash, u32bit s) + { + SecureVector<word> t; + t.grow_to(2*s+1); + + // t = a_bar * b_bar + for (u32bit i=0; i<s; i++) + { + word C = 0; + word S = 0; + for (u32bit j=0; j<s; j++) + { + // we use: + // word word_madd3(word a, word b, word c, word d, word* carry) + // returns a * b + c + d and resets the carry (not using it as input) + + S = word_madd3(a_bar[j], b_bar[i], t[i+j], &C); + t[i+j] = S; + } + t[i+s] = C; + } + + // ??? + for (u32bit i=0; i<s; i++) + { + // word word_madd2(word a, word b, word c, word* carry) + // returns a * b + c, resets the carry + + word C = 0; + word zero = 0; + word m = word_madd2(t[i], n_dash[0], &zero); + + for (u32bit j=0; j<s; j++) + { + word S = word_madd3(m, n[j], t[i+j], &C); + t[i+j] = S; + } + + //// mp_mulop.cpp: + ////word bigint_mul_add_words(word z[], const word x[], u32bit x_size, word y) + u32bit cnt = 0; + while (C > 0) + { + // we need not worry here about C > 1, because the other operand is zero + word tmp = word_add(t[i+s+cnt], 0, &C); + t[i+s+cnt] = tmp; + cnt++; + } + } + + // u = t + SecureVector<word> u; + u.grow_to(s+1); + for (u32bit j=0; j<s+1; j++) + { + u[j] = t[j+s]; + } + + // t = u - n + word B = 0; + word D = 0; + for (u32bit i=0; i<s; i++) + { + D = word_sub(u[i], n[i], &B); + t[i] = D; + } + D = word_sub(u[s], 0, &B); + t[s] = D; + + // if t >= 0 (B == 0 -> no borrow), return t + if(B == 0) + { + for (u32bit i=0; i<s; i++) + { + result[i] = t[i]; + } + } + else // else return u + { + for (u32bit i=0; i<s; i++) + { + result[i] = u[i]; + } + } + } + +void montg_mult(BigInt& result, BigInt& a_bar, BigInt& b_bar, const BigInt& m, const BigInt& m_dash, const BigInt) + { + if(m.is_zero() || m_dash.is_zero()) + throw Invalid_Argument("montg_mult(): neither modulus nor m_dash may be zero (and one of them was)"); + + if(a_bar.is_zero() || b_bar.is_zero()) + result = 0; + + u32bit s = m.sig_words(); + a_bar.grow_to(s); + b_bar.grow_to(s); + result.grow_to(s); + + inner_montg_mult_sos(result.get_reg(), a_bar.data(), b_bar.data(), + m.data(), m_dash.data(), s); + } + +/** +*calculates R=b^n (here b=2) with R>m (and R beeing as small as possible) for an odd modulus m. +* no check for oddity is performed! +* +* Distributed under the terms of the Botan license +*/ +BigInt montgm_calc_r_oddmod(const BigInt& prime) + { + u32bit n = prime.sig_words(); + BigInt result(1); + result <<= n*BOTAN_MP_WORD_BITS; + return result; + } + +/** +*calculates m' with r*r^-1 - m*m' = 1 +* where r^-1 is the multiplicative inverse of r to the modulus m +*/ +BigInt montgm_calc_m_dash(const BigInt& r, const BigInt& m, const BigInt& r_inv) + { + BigInt result = ((r * r_inv) - BigInt(1))/m; + return result; + } + +BigInt montg_trf_to_mres(const BigInt& ord_res, const BigInt& r, const BigInt& m) + { + BigInt result(ord_res); + result *= r; + result %= m; + return result; + } + +BigInt montg_trf_to_ordres(const BigInt& m_res, const BigInt& m, const BigInt& r_inv) + { + BigInt result(m_res); + result *= r_inv; + result %= m; + return result; + } + +} + +GFpElement::GFpElement(const BigInt& p, const BigInt& value, bool use_montgm) + : mp_mod(), + m_value(value %p), + m_use_montgm(use_montgm), + m_is_trf(false) + { + assert(mp_mod.get() == 0); + mp_mod = std::tr1::shared_ptr<GFpModulus>(new GFpModulus(p)); + assert(mp_mod->m_p_dash == 0); + if(m_use_montgm) + ensure_montgm_precomp(); + } + +GFpElement::GFpElement(std::tr1::shared_ptr<GFpModulus> const mod, const BigInt& value, bool use_montgm) + : mp_mod(), + m_value(value % mod->m_p), + m_use_montgm(use_montgm), + m_is_trf(false) + { + assert(mp_mod.get() == 0); + mp_mod = mod; + } + +GFpElement::GFpElement(const GFpElement& other) + : m_value(other.m_value), + m_use_montgm(other.m_use_montgm), + m_is_trf(other.m_is_trf) + + { + //creates an independent copy + assert((other.m_is_trf && other.m_use_montgm) || !other.m_is_trf); + mp_mod.reset(new GFpModulus(*other.mp_mod)); // copy-ctor of GFpModulus + } + +void GFpElement::turn_on_sp_red_mul() const + { + ensure_montgm_precomp(); + m_use_montgm = true; + } + +void GFpElement::turn_off_sp_red_mul() const + { + if(m_is_trf) + { + trf_to_ordres(); + // will happen soon anyway, so we can do it here already + // (this is not lazy but way more secure concerning our internal logic here) + } + m_use_montgm = false; + } + +void GFpElement::ensure_montgm_precomp() const + { + if((!mp_mod->m_r.is_zero()) && (!mp_mod->m_r_inv.is_zero()) && (!mp_mod->m_p_dash.is_zero())) + { + // values are already set, nothing more to do + } + else + { + BigInt tmp_r(montgm_calc_r_oddmod(mp_mod->m_p)); + + BigInt tmp_r_inv(inverse_mod(tmp_r, mp_mod->m_p)); + + BigInt tmp_p_dash(montgm_calc_m_dash(tmp_r, mp_mod->m_p, tmp_r_inv)); + + mp_mod->m_r.grow_reg(tmp_r.size()); + mp_mod->m_r_inv.grow_reg(tmp_r_inv.size()); + mp_mod->m_p_dash.grow_reg(tmp_p_dash.size()); + + mp_mod->m_r = tmp_r; + mp_mod->m_r_inv = tmp_r_inv; + mp_mod->m_p_dash = tmp_p_dash; + + assert(!mp_mod->m_r.is_zero()); + assert(!mp_mod->m_r_inv.is_zero()); + assert(!mp_mod->m_p_dash.is_zero()); + } + + } + +void GFpElement::set_shrd_mod(std::tr1::shared_ptr<GFpModulus> const p_mod) + { + mp_mod = p_mod; + } + +void GFpElement::trf_to_mres() const + { + if(!m_use_montgm) + { + throw Illegal_Transformation("GFpElement is not allowed to be transformed to m-residue"); + } + assert(m_is_trf == false); + assert(!mp_mod->m_r_inv.is_zero()); + assert(!mp_mod->m_p_dash.is_zero()); + m_value = montg_trf_to_mres(m_value, mp_mod->m_r, mp_mod->m_p); + m_is_trf = true; + } + +void GFpElement::trf_to_ordres() const + { + assert(m_is_trf == true); + m_value = montg_trf_to_ordres(m_value, mp_mod->m_p, mp_mod->m_r_inv); + m_is_trf = false; + } + +bool GFpElement::align_operands_res(const GFpElement& lhs, const GFpElement& rhs) //static + { + assert(lhs.mp_mod->m_p == rhs.mp_mod->m_p); + if(lhs.m_use_montgm && rhs.m_use_montgm) + { + assert(rhs.mp_mod->m_p_dash == lhs.mp_mod->m_p_dash); + assert(rhs.mp_mod->m_r == lhs.mp_mod->m_r); + assert(rhs.mp_mod->m_r_inv == lhs.mp_mod->m_r_inv); + if(!lhs.m_is_trf && !rhs.m_is_trf) + { + return false; + } + else if(lhs.m_is_trf && rhs.m_is_trf) + { + return true; + } + else // one is transf., the other not + { + if(!lhs.m_is_trf) + { + lhs.trf_to_mres(); + assert(rhs.m_is_trf==true); + return true; + } + assert(rhs.m_is_trf==false); + assert(lhs.m_is_trf==true); + rhs.trf_to_mres(); // the only possibility left... + return true; + } + } + else // at least one of them does not use mm + // (so it is impossible that both use it) + { + if(lhs.m_is_trf) + { + lhs.trf_to_ordres(); + assert(rhs.m_is_trf == false); + return false; + } + if(rhs.m_is_trf) + { + rhs.trf_to_ordres(); + assert(lhs.m_is_trf == false); + return false; + } + return false; + } + assert(false); + } + +bool GFpElement::is_trf_to_mres() const + { + return m_is_trf; + } + +const BigInt& GFpElement::get_p() const + { + return (mp_mod->m_p); + } + +const BigInt& GFpElement::get_value() const + { + if(m_is_trf) + { + assert(m_use_montgm); + trf_to_ordres(); + } + return m_value; + } + +const BigInt& GFpElement::get_mres() const + { + if(!m_use_montgm) + { + // does the following exception really make sense? + // wouldn´t it be better to simply turn on montg.mult. when + // this explicit request is made? + throw Illegal_Transformation("GFpElement is not allowed to be transformed to m-residue"); + } + if(!m_is_trf) + { + trf_to_mres(); + } + + return m_value; + } + +const GFpElement& GFpElement::operator=(const GFpElement& other) + { + m_value.grow_reg(other.m_value.size()); // grow first for exception safety + + //m_value = other.m_value; + + // m_use_montgm = other.m_use_montgm; + // m_is_trf = other.m_is_trf; + // we want to keep the member pointers, which might be part of a "sharing group" + // but we may not simply overwrite the BigInt values with those of the argument!! + // if ours already contains precomputations, it would be hazardous to + // set them back to zero. + // thus we first check for equality of the moduli, + // then whether either of the two objects already contains + // precomputed values. + + // we also deal with the case were the pointers themsevles are equal: + if(mp_mod.get() == other.mp_mod.get()) + { + // everything ok, we are in the same sharing group anyway, nothing to do + m_value = other.m_value; // cannot throw + m_use_montgm = other.m_use_montgm; + m_is_trf = other.m_is_trf; + return *this; + } + if(mp_mod->m_p != other.mp_mod->m_p) + { + // the moduli are different, this is a special case + // which will not occur in usual applications, + // so we don´t hesitate to simply create new objects + // (we do want to create an independent copy) + mp_mod.reset(new GFpModulus(*other.mp_mod)); // this could throw, + // and because of this + // we haven't modified + // anything so far + m_value = other.m_value; // can't throw + m_use_montgm = other.m_use_montgm; + m_is_trf = other.m_is_trf; + return *this; + } + // exception safety note: from now on we are on the safe + // side with respect to the modulus, + // so we can assign the value now: + m_value = other.m_value; + m_use_montgm = other.m_use_montgm; + m_is_trf = other.m_is_trf; + // the moduli are equal, but we deal with different sharing groups. + // we will NOT fuse the sharing goups + // and we will NOT reset already precomputed values + if(mp_mod->has_precomputations()) + { + // our own sharing group already has precomputed values, + // so nothing to do. + return *this; + } + else + { + // let´s see whether the argument has something for us... + if(other.mp_mod->has_precomputations()) + { + // fetch them for our sharing group + // exc. safety note: grow first + mp_mod->m_p_dash.grow_reg(other.mp_mod->m_p_dash.size()); + mp_mod->m_r.grow_reg(other.mp_mod->m_r.size()); + mp_mod->m_r_inv.grow_reg(other.mp_mod->m_r_inv.size()); + + mp_mod->m_p_dash = other.mp_mod->m_p_dash; + mp_mod->m_r = other.mp_mod->m_r; + mp_mod->m_r_inv = other.mp_mod->m_r_inv; + return *this; + } + } + // our precomputations aren´t set, the arguments neither, + // so we let them alone + return *this; + } + +void GFpElement::share_assign(const GFpElement& other) + { + assert((other.m_is_trf && other.m_use_montgm) || !other.m_is_trf); + + // use grow_to to make it exc safe + m_value.grow_reg(other.m_value.size()); + m_value = other.m_value; + + m_use_montgm = other.m_use_montgm; + m_is_trf = other.m_is_trf; + mp_mod = other.mp_mod; // cannot throw + } + +GFpElement& GFpElement::operator+=(const GFpElement& rhs) + { + GFpElement::align_operands_res(*this, rhs); + + workspace = m_value; + workspace += rhs.m_value; + if(workspace >= mp_mod->m_p) + workspace -= mp_mod->m_p; + + m_value = workspace; + assert(m_value < mp_mod->m_p); + assert(m_value >= 0); + + return *this; + } + +GFpElement& GFpElement::operator-=(const GFpElement& rhs) + { + GFpElement::align_operands_res(*this, rhs); + + workspace = m_value; + + workspace -= rhs.m_value; + + if(workspace.is_negative()) + workspace += mp_mod->m_p; + + m_value = workspace; + assert(m_value < mp_mod->m_p); + assert(m_value >= 0); + return *this; + } + +GFpElement& GFpElement::operator*= (u32bit rhs) + { + workspace = m_value; + workspace *= rhs; + workspace %= mp_mod->m_p; + m_value = workspace; + return *this; + } + +GFpElement& GFpElement::operator*=(const GFpElement& rhs) + { + assert(rhs.mp_mod->m_p == mp_mod->m_p); + // here, we do not use align_operands_res() for one simple reason: + // we want to enforce the transformation to an m-residue, otherwise it would + // never happen + if(m_use_montgm && rhs.m_use_montgm) + { + assert(rhs.mp_mod->m_p == mp_mod->m_p); // is montgm. mult is on, then precomps must be there + assert(rhs.mp_mod->m_p_dash == mp_mod->m_p_dash); + assert(rhs.mp_mod->m_r == mp_mod->m_r); + if(!m_is_trf) + { + trf_to_mres(); + } + if(!rhs.m_is_trf) + { + rhs.trf_to_mres(); + } + workspace = m_value; + montg_mult(m_value, workspace, rhs.m_value, mp_mod->m_p, mp_mod->m_p_dash, mp_mod->m_r); + } + else // ordinary multiplication + { + if(m_is_trf) + { + assert(m_use_montgm); + trf_to_ordres(); + } + if(rhs.m_is_trf) + { + assert(rhs.m_use_montgm); + rhs.trf_to_ordres(); + } + + workspace = m_value; + workspace *= rhs.m_value; + workspace %= mp_mod->m_p; + m_value = workspace; + } + return *this; + } + +GFpElement& GFpElement::operator/=(const GFpElement& rhs) + { + bool use_mres = GFpElement::align_operands_res(*this, rhs); + assert((this->m_is_trf && rhs.m_is_trf) || !(this->m_is_trf && rhs.m_is_trf)); + // (internal note: see C86) + if(use_mres) + { + assert(m_use_montgm && rhs.m_use_montgm); + GFpElement rhs_ordres(rhs); + rhs_ordres.trf_to_ordres(); + rhs_ordres.inverse_in_place(); + workspace = m_value; + workspace *= rhs_ordres.get_value(); + workspace %= mp_mod->m_p; + m_value = workspace; + + } + else + { + GFpElement inv_rhs(rhs); + inv_rhs.inverse_in_place(); + *this *= inv_rhs; + } + return *this; + } + +bool GFpElement::is_zero() + { + return (m_value.is_zero()); + // this is correct because x_bar = x * r = x = 0 for x = 0 + } + +GFpElement& GFpElement::inverse_in_place() + { + m_value = inverse_mod(m_value, mp_mod->m_p); + if(m_is_trf) + { + assert(m_use_montgm); + + m_value *= mp_mod->m_r; + m_value *= mp_mod->m_r; + m_value %= mp_mod->m_p; + } + assert(m_value <= mp_mod->m_p); + return *this; + } + +GFpElement& GFpElement::negate() + { + m_value = mp_mod->m_p - m_value; + assert(m_value <= mp_mod->m_p); + return *this; + } + +void GFpElement::swap(GFpElement& other) + { + m_value.swap(other.m_value); + mp_mod.swap(other.mp_mod); + std::swap<bool>(m_use_montgm,other.m_use_montgm); + std::swap<bool>(m_is_trf,other.m_is_trf); + } + +std::ostream& operator<<(std::ostream& output, const GFpElement& elem) + { + return output << '(' << elem.get_value() << "," << elem.get_p() << ')'; + } + +bool operator==(const GFpElement& lhs, const GFpElement& rhs) + { + // for effeciency reasons we firstly check whether + //the modulus pointers are different in the first place: + if(lhs.get_ptr_mod() != rhs.get_ptr_mod()) + { + if(lhs.get_p() != rhs.get_p()) + { + return false; + } + } + // so the modulus is equal, now check the values + bool use_mres = GFpElement::align_operands_res(lhs, rhs); + + if(use_mres) + { + return (lhs.get_mres() == rhs.get_mres()); + } + else + { + return(lhs.get_value() == rhs.get_value()); + } + } + +GFpElement operator+(const GFpElement& lhs, const GFpElement& rhs) + { + // consider the case that lhs and rhs both use montgm: + // then += returns an element which uses montgm. + // thus the return value of op+ here will be an element + // using montgm in this case + // NOTE: the rhs might be transformed when using op+, the lhs never + GFpElement result(lhs); + result += rhs; + return result; + } + +GFpElement operator-(const GFpElement& lhs, const GFpElement& rhs) + { + GFpElement result(lhs); + result -= rhs; + return result; + // NOTE: the rhs might be transformed when using op-, the lhs never + } + +GFpElement operator-(const GFpElement& lhs) + { + return(GFpElement(lhs)).negate(); + } + +GFpElement operator*(const GFpElement& lhs, const GFpElement& rhs) + { + // consider the case that lhs and rhs both use montgm: + // then *= returns an element which uses montgm. + // thus the return value of op* here will be an element + // using montgm in this case + GFpElement result(lhs); + result *= rhs; + return result; + } + +GFpElement operator*(const GFpElement& lhs, u32bit rhs) + { + GFpElement result(lhs); + result *= rhs; + return result; + } + +GFpElement operator*(u32bit lhs, const GFpElement& rhs) + { + return rhs*lhs; + } + +GFpElement operator/(const GFpElement& lhs, const GFpElement& rhs) + { + GFpElement result (lhs); + result /= rhs; + return result; + } + +SecureVector<byte> FE2OSP(const GFpElement& elem) + { + return BigInt::encode_1363(elem.get_value(), elem.get_p().bytes()); + } + +GFpElement OS2FEP(MemoryRegion<byte> const& os, BigInt p) + { + return GFpElement(p, BigInt::decode(os.begin(), os.size())); + } + +GFpElement inverse(const GFpElement& elem) + { + return GFpElement(elem).inverse_in_place(); + } + +} + diff --git a/old/botan/src/math/gfpmath/gfp_element.h b/old/botan/src/math/gfpmath/gfp_element.h new file mode 100644 index 0000000..4e0ee98 --- /dev/null +++ b/old/botan/src/math/gfpmath/gfp_element.h @@ -0,0 +1,311 @@ +/****** + * Arithmetic for prime fields GF(p) (header file) + * + * (C) 2007 Martin Doering + * doering@cdc.informatik.tu-darmstadt.de + * Christoph Ludwig + * ludwig@fh-worms.de + * Falko Strenzke + * strenzke@flexsecure.de + ******/ + +#ifndef BOTAN_GFP_ELEMENT_H__ +#define BOTAN_GFP_ELEMENT_H__ + +#include <botan/bigint.h> +#include <botan/gfp_modulus.h> +#include <iosfwd> + +#if defined(BOTAN_USE_STD_TR1) + #include <tr1/memory> +#elif defined(BOTAN_USE_BOOST_TR1) + #include <boost/tr1/memory.hpp> +#else + #error "Please choose a TR1 implementation in build.h" +#endif + +namespace Botan { + +struct Illegal_Transformation : public Exception + { + Illegal_Transformation(const std::string& err = + "Requested transformation is not possible") + : Exception(err) {} + }; + +/** + * This class represents one element in GF(p). Enables the convenient, + * transparent use of the montgomery multiplication. + */ +class BOTAN_DLL GFpElement + { + private: + std::tr1::shared_ptr<GFpModulus> mp_mod; + mutable BigInt m_value; // ordinary residue or m-residue respectively + mutable BigInt workspace; + + // ***************************************** + // data members for montgomery multiplication + mutable bool m_use_montgm; + //mutable BigInt m_mres; + // this bool tells use whether the m_mres carries + // the actual value (in this case mValue doesn´t) + mutable bool m_is_trf; + + void ensure_montgm_precomp() const; + void trf_to_mres() const; + void trf_to_ordres() const; + + public: + + /** construct an element of GF(p) with the given value. + * use_montg defaults to false and determines wether Montgomery + * multiplications will be use when applying operators *, *= + * @param p the prime number of the field + * @param value the element value + * @param use_montgm whether this object will use Montgomery multiplication + */ + explicit GFpElement (const BigInt& p, const BigInt& value, bool use_montgm = false); + + + /** construct an element of GF(p) with the given value (defaults + * to 0). use_montg defaults to false and determines wether + * montgomery multiplications will be use when applying operators + * '*' , '*='. Use this constructor for efficient use of + * Montgomery multiplication in a context with a fixed a modulus. + * Warning: do not use this function unless you know in detail + * about the implications of using the shared GFpModulus objects! + * @param mod shared pointer to the GFpModulus to be shared + * @param value the element value + * @param use_montgm whether this object will use Montgomery multiplication + */ + explicit GFpElement(std::tr1::shared_ptr<GFpModulus> const mod, + const BigInt& value, bool use_mongm = false); + + /** + * Copy constructor + * @param other The element to clone + */ + GFpElement(const GFpElement& other); + + /** + * Assignment operator. + * makes *this a totally independent object + * (gives *this independent modulus specific values). + + * @param other The element to assign to our object + */ + const GFpElement& operator=(const GFpElement& other); + + /** + * Works like the assignment operator, but lets + * *this share the modulus dependend value with other. + * Warning: do not use this function unless you know in detail about + * the implications of using + * the shared GFpModulus objects! + * @param other The element to assign to our object + */ + void share_assign(const GFpElement& other); + + /** + * Switch Montgomery multiplcation optimizations ON + */ + void turn_on_sp_red_mul() const; + + /** + * Switch Montgomery multiplcation optimizations OFF + */ + void turn_off_sp_red_mul() const; + + /** + * += Operator + * @param rhs the GFpElement to add to the local value + * @result *this + */ + GFpElement& operator+=(const GFpElement& rhs); + + /** + * -= Operator + * @param rhs the GFpElement to subtract from the local value + * @result *this + */ + GFpElement& operator-=(const GFpElement& rhs); + + /** + * *= Operator + * @param rhs the GFpElement to multiply with the local value + * @result *this + */ + GFpElement& operator*=(const GFpElement& rhs); + /** + * /= Operator + * @param rhs the GFpElement to divide the local value by + * @result *this + */ + GFpElement& operator/=(const GFpElement& rhs); + + /** + * *= Operator + * @param rhs the value to multiply with the local value + * @result *this + */ + GFpElement& operator*= (u32bit rhs); + + /** + * Negate internal value(*this *= -1 ) + * @return *this + */ + GFpElement& negate(); + + /** + * Assigns the inverse of *this to *this, i.e. + * *this = (*this)^(-1) + * @result *this + */ + GFpElement& inverse_in_place(); + + /** + * checks whether the value is zero (without provoking + * a backtransformation to the ordinary-residue) + * @result true, if the value is zero, false otherwise. + */ + bool is_zero(); + + /** + * return prime number of GF(p) + * @result a prime number + */ + const BigInt& get_p() const; + + /** + * Return the represented value in GF(p) + * @result The value in GF(p) + */ + const BigInt& get_value() const; + + /** + * Returns the shared pointer to the GFpModulus of *this. + * Warning: do not use this function unless you know in detail about + * the implications of using + * the shared GFpModulus objects! + * @result the shared pointer to the GFpModulus of *this + */ + inline std::tr1::shared_ptr<GFpModulus> const get_ptr_mod() const + { + return mp_mod; + } + + + /** + * Sets the shared pointer to the GFpModulus of *this. + * Warning: do not use this function unless you know in detail about + * the implications of using + * the shared GFpModulus objects! + * @param mod a shared pointer to a GFpModulus that will be held in *this + */ + void set_shrd_mod(std::tr1::shared_ptr<GFpModulus> const mod); + + /** + * Tells whether this GFpElement is currently transformed to it´ m-residue, + * i.e. in the form x_bar = x * r mod m. + * @result true if it is currently transformed to it´s m-residue. + */ + bool is_trf_to_mres() const; + + /** + * Transforms this to x_bar = x * r mod m + * @result return the value x_bar. + */ + const BigInt& get_mres() const; + + /** + * Check, if montgomery multiplication is used. + * @result true, if montgomery multiplication is used, false otherwise + */ + bool is_use_montgm() const + { + return m_use_montgm; + } + + /** + * Transforms the arguments in such way that either both + * are in m-residue representation (returns true) or both are + * in ordinary residue representation (returns false). + * m-residue is prefered in case of ambiguity. + * does not toggle m_use_montgm of the arguments. + * Don´t be confused about the constness of the arguments: + * the transformation between normal residue and m-residue is + * considered as leaving the object const. + * @param lhs the first operand to be aligned + * @param rhs the second operand to be aligned + * @result true if both are transformed to their m-residue, + * false it both are transformed to their normal residue. + */ + static bool align_operands_res(const GFpElement& lhs, const GFpElement& rhs); + + //friend declarations for non-member functions + + /** + * write a GFpElement to an output stream. + * @param output the output stream to write to + * @param elem the object to write + * @result the output stream + */ + friend std::ostream& operator<<(std::ostream& output, const GFpElement& elem); + + friend class Point_Coords_GFp; + + /** + * swaps the states of *this and other, does not throw! + * @param other The value to swap with + */ + void swap(GFpElement& other); + + }; + +// relational operators +bool operator==(const GFpElement& lhs, const GFpElement& rhs); +inline bool operator!=(const GFpElement& lhs, const GFpElement& rhs ) + { + return !operator==(lhs, rhs); + } + +// arithmetic operators +GFpElement operator+(const GFpElement& lhs, const GFpElement& rhs); +GFpElement operator-(const GFpElement& lhs, const GFpElement& rhs); +GFpElement operator-(const GFpElement& lhs); + +GFpElement operator*(const GFpElement& lhs, const GFpElement& rhs); +GFpElement operator/(const GFpElement& lhs, const GFpElement& rhs); +GFpElement operator* (const GFpElement& lhs, u32bit rhs); +GFpElement operator* (u32bit rhs, const GFpElement& lhs); + +// io operators +std::ostream& operator<<(std::ostream& output, const GFpElement& elem); + +// return (*this)^(-1) +GFpElement inverse(const GFpElement& elem); + +// encoding and decoding +SecureVector<byte> FE2OSP(const GFpElement& elem); +GFpElement OS2FEP(MemoryRegion<byte> const& os, BigInt p); + +inline void swap(GFpElement& x, GFpElement& y) + { + x.swap(y); + } + +} + +namespace std { + +template<> inline +void swap<Botan::GFpElement>(Botan::GFpElement& x, + Botan::GFpElement& y) + { + x.swap(y); + } + +} + +#endif diff --git a/old/botan/src/math/gfpmath/gfp_modulus.h b/old/botan/src/math/gfpmath/gfp_modulus.h new file mode 100644 index 0000000..b5c0857 --- /dev/null +++ b/old/botan/src/math/gfpmath/gfp_modulus.h @@ -0,0 +1,127 @@ +/****** + * Modulus and related data for a specific + * implementation of GF(p) (header file) + * + * (C) 2008 Martin Döring + * doering@cdc.informatik.tu-darmstadt.de + * Christoph Ludwig + * ludwig@fh-worms.de + * Falko Strenzke + * strenzke@flexsecure.de + ******/ + +#ifndef BOTAN_GFP_MODULUS_H__ +#define BOTAN_GFP_MODULUS_H__ + +#include <botan/bigint.h> + +namespace Botan +{ + +class BOTAN_DLL GFpElement; +/** +* This class represents a GFpElement modulus including the modulus related +* values necessary for the montgomery multiplication. +* +* Distributed under the terms of the Botan license +*/ +class BOTAN_DLL GFpModulus + { + friend class GFpElement; + private: + BigInt m_p; // the modulus itself + mutable BigInt m_p_dash; + mutable BigInt m_r; + mutable BigInt m_r_inv; + public: + + /** + * Construct a GF(P)-Modulus from a BigInt + */ + GFpModulus(BigInt p) + : m_p(p), + m_p_dash(), + m_r(), + m_r_inv() + {} + + /** + * Tells whether the precomputations necessary for the use of the + * montgomery multiplication have yet been established. + * @result true if the precomputated value are already available. + */ + inline bool has_precomputations() const + { + return(!m_p_dash.is_zero() && !m_r.is_zero() && !m_r_inv.is_zero()); + } + + /** + * Swaps this with another GFpModulus, does not throw. + * @param other the GFpModulus to swap *this with. + */ + inline void swap(GFpModulus& other) + { + m_p.swap(other.m_p); + m_p_dash.swap(other.m_p_dash); + m_r.swap(other.m_r); + m_r_inv.swap(other.m_r_inv); + } + + /** + * Tells whether the modulus of *this is equal to the argument. + * @param mod the modulus to compare this with + * @result true if the modulus of *this and the argument are equal. + */ + inline bool p_equal_to(const BigInt& mod) const + { + return (m_p == mod); + } + + /** + * Return the modulus of this GFpModulus. + * @result the modulus of *this. + */ + inline const BigInt& get_p() const + { + return m_p; + } + + /** + * returns the montgomery multiplication related value r. + * Warning: will be zero if precomputations have not yet been + * performed! + * @result r + */ + inline const BigInt& get_r() const + { + return m_r; + } + + /** + * returns the montgomery multiplication related value r^{-1}. + * Warning: will be zero if precomputations have not yet been + * performed! + * @result r^{-1} + */ + inline const BigInt& get_r_inv() const + { + return m_r_inv; + } + + /** + * returns the montgomery multiplication related value p'. + * Warning: will be zero if precomputations have not yet been + * performed! + * @result p' + */ + inline const BigInt& get_p_dash() const + { + return m_p_dash; + } + // default cp-ctor, op= are fine + }; + +} + +#endif + diff --git a/old/botan/src/math/gfpmath/info.txt b/old/botan/src/math/gfpmath/info.txt new file mode 100644 index 0000000..1a52144 --- /dev/null +++ b/old/botan/src/math/gfpmath/info.txt @@ -0,0 +1,22 @@ +realname "GF(p) Math" + +uses_tr1 yes + +load_on auto + +define BIGINT_GFP + +<add> +curve_gfp.cpp +curve_gfp.h +gfp_element.cpp +gfp_element.h +gfp_modulus.h +point_gfp.cpp +point_gfp.h +</add> + +<requires> +bigint +numbertheory +</requires> diff --git a/old/botan/src/math/gfpmath/point_gfp.cpp b/old/botan/src/math/gfpmath/point_gfp.cpp new file mode 100644 index 0000000..9139c3e --- /dev/null +++ b/old/botan/src/math/gfpmath/point_gfp.cpp @@ -0,0 +1,1154 @@ +/****** +* Arithmetic for point groups of elliptic curves +* over GF(p) (source file) +* +* (C) 2007 Martin Doering +* Christoph Ludwig +* Falko Strenzke +* 2008 Jack Lloyd +******/ + +#include <botan/point_gfp.h> +#include <botan/numthry.h> + +namespace Botan { + +// construct the point at infinity or a random point +PointGFp::PointGFp(const CurveGFp& curve) + : mC(curve), + mX(curve.get_p(), 0), + mY(curve.get_p(), 1), + mZ(curve.get_p(), 0), + mZpow2(curve.get_p(),0), + mZpow3(curve.get_p(),0), + mAZpow4(curve.get_p(),0), + mZpow2_set(false), + mZpow3_set(false), + mAZpow4_set(false) + { + // first set the point wide pointer + + set_shrd_mod(mC.get_ptr_mod()); + + } + +// construct a point given its jacobian projective coordinates +PointGFp::PointGFp(const CurveGFp& curve, const GFpElement& x, + const GFpElement& y, const GFpElement& z) + : mC(curve), + mX(x), + mY(y), + mZ(z), + mZpow2(curve.get_p(),0), + mZpow3(curve.get_p(),0), + mAZpow4(curve.get_p(),0), + mZpow2_set(false), + mZpow3_set(false), + mAZpow4_set(false) + { + set_shrd_mod(mC.get_ptr_mod()); + } +PointGFp::PointGFp ( const CurveGFp& curve, const GFpElement& x, + const GFpElement& y ) + :mC(curve), + mX(x), + mY(y), + mZ(curve.get_p(),1), + mZpow2(curve.get_p(),0), + mZpow3(curve.get_p(),0), + mAZpow4(curve.get_p(),0), + mZpow2_set(false), + mZpow3_set(false), + mAZpow4_set(false) + { + set_shrd_mod(mC.get_ptr_mod()); + } + +// copy constructor +PointGFp::PointGFp(const PointGFp& other) + : mC(other.mC), + mX(other.mX), + mY(other.mY), + mZ(other.mZ), + mZpow2(other.mZpow2), + mZpow3(other.mZpow3), + mAZpow4(other.mAZpow4), + mZpow2_set(other.mZpow2_set), + mZpow3_set(other.mZpow3_set), + mAZpow4_set(other.mAZpow4_set) + { + set_shrd_mod(mC.get_ptr_mod()); + } + +// assignment operator +const PointGFp& PointGFp::operator=(PointGFp const& other) + { + mC = other.get_curve(); + mX = other.get_jac_proj_x(); + mY = other.get_jac_proj_y(); + mZ = other.get_jac_proj_z(); + mZpow2 = GFpElement(other.mZpow2); + mZpow3 = GFpElement(other.mZpow3); + mAZpow4 = GFpElement(other.mAZpow4); + mZpow2_set = other.mZpow2_set; + mZpow3_set = other.mZpow3_set; + mAZpow4_set = other.mAZpow4_set; + set_shrd_mod(mC.get_ptr_mod()); + return *this; + } + +const PointGFp& PointGFp::assign_within_same_curve(PointGFp const& other) + { + mX = other.get_jac_proj_x(); + mY = other.get_jac_proj_y(); + mZ = other.get_jac_proj_z(); + mZpow2_set = false; + mZpow3_set = false; + mAZpow4_set = false; + // the rest stays! + return *this; + } + +void PointGFp::set_shrd_mod(std::tr1::shared_ptr<GFpModulus> p_mod) + { + mX.set_shrd_mod(p_mod); + mY.set_shrd_mod(p_mod); + mZ.set_shrd_mod(p_mod); + mZpow2.set_shrd_mod(p_mod); + mZpow3.set_shrd_mod(p_mod); + mAZpow4.set_shrd_mod(p_mod); + } + +void PointGFp::ensure_worksp() const + { + if (mp_worksp_gfp_el.get() != 0) + { + if ((*mp_worksp_gfp_el).size() == GFPEL_WKSP_SIZE) + { + return; + } + else + { + throw Invalid_State("encountered incorrect size for PointGFp´s GFpElement workspace"); + } + } + + mp_worksp_gfp_el = std::tr1::shared_ptr<std::vector<GFpElement> >(new std::vector<GFpElement>); + mp_worksp_gfp_el->reserve(9); + for (u32bit i=0; i<GFPEL_WKSP_SIZE; i++) + { + mp_worksp_gfp_el->push_back(GFpElement(1,0)); + + } + } + +// arithmetic operators +PointGFp& PointGFp::operator+=(const PointGFp& rhs) + { + if (is_zero()) + { + *this = rhs; + return *this; + } + if (rhs.is_zero()) + { + return *this; + } + ensure_worksp(); + + if (rhs.mZ == *(mC.get_mres_one())) + { + //U1 = mX; + (*mp_worksp_gfp_el)[0].share_assign(mX); + + //S1 = mY; + (*mp_worksp_gfp_el)[2].share_assign(mY); + } + else + { + if ((!rhs.mZpow2_set) || (!rhs.mZpow3_set)) + { + rhs.mZpow2 = rhs.mZ; + rhs.mZpow2 *= rhs.mZ; + rhs.mZpow3 = rhs.mZpow2; + rhs.mZpow3 *= rhs.mZ; + + rhs.mZpow2_set = true; + rhs.mZpow3_set = true; + } + //U1 = mX * rhs.mZpow2; + (*mp_worksp_gfp_el)[0].share_assign(mX); + (*mp_worksp_gfp_el)[0] *= rhs.mZpow2; + + //S1 = mY * rhs.mZpow3; + (*mp_worksp_gfp_el)[2].share_assign(mY); + (*mp_worksp_gfp_el)[2] *= rhs.mZpow3; + + } + if (mZ == *(mC.get_mres_one())) + { + //U2 = rhs.mX; + (*mp_worksp_gfp_el)[1].share_assign(rhs.mX); + + //S2 = rhs.mY; + (*mp_worksp_gfp_el)[3].share_assign(rhs.mY); + } + else + { + if ((!mZpow2_set) || (!mZpow3_set)) + { + // precomputation can´t be used, because *this changes anyway + mZpow2 = mZ; + mZpow2 *= mZ; + + mZpow3 = mZpow2; + mZpow3 *= mZ; + } + //U2 = rhs.mX * mZpow2; + (*mp_worksp_gfp_el)[1].share_assign(rhs.mX); + (*mp_worksp_gfp_el)[1] *= mZpow2; + + //S2 = rhs.mY * mZpow3; + (*mp_worksp_gfp_el)[3].share_assign(rhs.mY); + (*mp_worksp_gfp_el)[3] *= mZpow3; + + } + //GFpElement H(U2 - U1); + + (*mp_worksp_gfp_el)[4].share_assign((*mp_worksp_gfp_el)[1]); + (*mp_worksp_gfp_el)[4] -= (*mp_worksp_gfp_el)[0]; + + //GFpElement r(S2 - S1); + (*mp_worksp_gfp_el)[5].share_assign((*mp_worksp_gfp_el)[3]); + (*mp_worksp_gfp_el)[5] -= (*mp_worksp_gfp_el)[2]; + + //if(H.is_zero()) + if ((*mp_worksp_gfp_el)[4].is_zero()) + + { + if ((*mp_worksp_gfp_el)[5].is_zero()) + + { + mult2_in_place(); + return *this; + } + *this = PointGFp(mC); // setting myself to zero + return *this; + } + + //U2 = H * H; + (*mp_worksp_gfp_el)[1].share_assign((*mp_worksp_gfp_el)[4]); + (*mp_worksp_gfp_el)[1] *= (*mp_worksp_gfp_el)[4]; + + //S2 = U2 * H; + (*mp_worksp_gfp_el)[3].share_assign((*mp_worksp_gfp_el)[1]); + (*mp_worksp_gfp_el)[3] *= (*mp_worksp_gfp_el)[4]; + + //U2 *= U1; + (*mp_worksp_gfp_el)[1] *= (*mp_worksp_gfp_el)[0]; + + //GFpElement x(r*r - S2 - (U2+U2)); + (*mp_worksp_gfp_el)[6].share_assign((*mp_worksp_gfp_el)[5]); + (*mp_worksp_gfp_el)[6] *= (*mp_worksp_gfp_el)[5]; + (*mp_worksp_gfp_el)[6] -= (*mp_worksp_gfp_el)[3]; + (*mp_worksp_gfp_el)[6] -= (*mp_worksp_gfp_el)[1]; + (*mp_worksp_gfp_el)[6] -= (*mp_worksp_gfp_el)[1]; + + //GFpElement z(S1 * S2); + (*mp_worksp_gfp_el)[8].share_assign((*mp_worksp_gfp_el)[2]); + (*mp_worksp_gfp_el)[8] *= (*mp_worksp_gfp_el)[3]; + + //GFpElement y(r * (U2-x) - z); + (*mp_worksp_gfp_el)[7].share_assign((*mp_worksp_gfp_el)[1]); + (*mp_worksp_gfp_el)[7] -= (*mp_worksp_gfp_el)[6]; + (*mp_worksp_gfp_el)[7] *= (*mp_worksp_gfp_el)[5]; + (*mp_worksp_gfp_el)[7] -= (*mp_worksp_gfp_el)[8]; + + if (mZ == *(mC.get_mres_one())) + { + if (rhs.mZ != *(mC.get_mres_one())) + { + //z = rhs.mZ * H; + (*mp_worksp_gfp_el)[8].share_assign(rhs.mZ); + (*mp_worksp_gfp_el)[8] *= (*mp_worksp_gfp_el)[4]; + } + else + { + //z = H; + (*mp_worksp_gfp_el)[8].share_assign((*mp_worksp_gfp_el)[4]); + } + } + else if (rhs.mZ != *(mC.get_mres_one())) + { + //U1 = mZ * rhs.mZ; + (*mp_worksp_gfp_el)[0].share_assign(mZ); + (*mp_worksp_gfp_el)[0] *= rhs.mZ; + + //z = U1 * H; + (*mp_worksp_gfp_el)[8].share_assign((*mp_worksp_gfp_el)[0]); + (*mp_worksp_gfp_el)[8] *= (*mp_worksp_gfp_el)[4]; + + } + else + { + //z = mZ * H; + (*mp_worksp_gfp_el)[8].share_assign(mZ); + (*mp_worksp_gfp_el)[8] *= (*mp_worksp_gfp_el)[4]; + + } + mZpow2_set = false; + mZpow3_set = false; + mAZpow4_set = false; + + mX = (*mp_worksp_gfp_el)[6]; + mY = (*mp_worksp_gfp_el)[7]; + mZ = (*mp_worksp_gfp_el)[8]; + + return *this; + + } +PointGFp& PointGFp::operator-=(const PointGFp& rhs) + { + PointGFp minus_rhs = PointGFp(rhs).negate(); + + if (is_zero()) + { + *this = minus_rhs; + } + else + { + *this += minus_rhs; + } + return *this; + } + +PointGFp& PointGFp::mult_this_secure(const BigInt& scalar, + const BigInt& /*point_order*/, + const BigInt& /*max_secr*/) + { + // NOTE: FS: so far this is code duplication of op*=. + // we have to see how we deal with this. + // fact is that we will probably modify this function + // while evaluating the countermeasures + // whereas we probably will not start modifying the + // function operator*=. + // however, in the end both should be merged. + + // use montgomery mult. in this operation + this->turn_on_sp_red_mul(); + + std::tr1::shared_ptr<PointGFp> H(new PointGFp(this->mC)); + std::tr1::shared_ptr<PointGFp> tmp; // used for AADA + + PointGFp P(*this); + BigInt m(scalar); + + if (m < BigInt(0)) + { + m = -m; + P.negate(); + } + if (P.is_zero() || (m == BigInt(0))) + { + *this = *H; + return *this; + } + if (m == BigInt(1)) + { + return *this; + } + // +#ifdef CM_AADA +#ifndef CM_RAND_EXP + int max_secr_bits = max_secr.bits(); +#endif +#endif + + int mul_bits = m.bits(); // this is used for a determined number of loop runs in + // the mult_loop where leading zero´s are padded if necessary. + // Here we assign the value that will be used when no countermeasures are specified +#ifdef CM_RAND_EXP + u32bit rand_r_bit_len = 20; // Coron(99) proposes 20 bit for r + +#ifdef CM_AADA + + BigInt r_max(1); + +#endif // CM_AADA + + // use randomized exponent +#ifdef TA_COLL_T + static BigInt r_randexp; + if (new_rand) + { + r_randexp = random_integer(rand_r_bit_len); + } + //assert(!r_randexp.is_zero()); +#else + BigInt r_randexp(random_integer(rand_r_bit_len)); +#endif + + m += r_randexp * point_order; + // determine mul_bits... +#ifdef CM_AADA + // AADA with rand. Exp. + //assert(rand_r_bit_len > 0); + r_max <<= rand_r_bit_len; + r_max -= 1; + //assert(r_max.bits() == rand_r_bit_len); + mul_bits = (max_secr + point_order * r_max).bits(); +#else + // rand. Exp. without AADA + mul_bits = m.bits(); +#endif // CM_AADA + + +#endif // CM_RAND_EXP + + // determine mul_bits... +#if (CM_AADA == 1 && CM_RAND_EXP != 1) + + mul_bits = max_secr_bits; +#endif // CM_AADA without CM_RAND_EXP + + //assert(mul_bits != 0); + + + H = mult_loop(mul_bits-1, m, H, tmp, P); + + if (!H->is_zero()) // cannot convert if H == O + { + *this = H->get_z_to_one(); + }else + { + *this = *H; + } + mX.turn_off_sp_red_mul(); + mY.turn_off_sp_red_mul(); + mZ.turn_off_sp_red_mul(); + return *this; + } + +PointGFp& PointGFp::operator*=(const BigInt& scalar) + { + // use montgomery mult. in this operation + + this->turn_on_sp_red_mul(); + + PointGFp H(this->mC); // create as zero + H.turn_on_sp_red_mul(); + PointGFp P(*this); + P.turn_on_sp_red_mul(); + BigInt m(scalar); + if (m < BigInt(0)) + { + m = -m; + P.negate(); + } + if (P.is_zero() || (m == BigInt(0))) + { + *this = H; + return *this; + } + if (m == BigInt(1)) + { + //*this == P already + return *this; + } + + const int l = m.bits() - 1; + for (int i=l; i >=0; i--) + { + + H.mult2_in_place(); + if (m.get_bit(i)) + { + H += P; + } + } + + if (!H.is_zero()) // cannot convert if H == O + { + *this = H.get_z_to_one(); + }else + { + *this = H; + } + return *this; + } + +inline std::tr1::shared_ptr<PointGFp> PointGFp::mult_loop(int l, + const BigInt& m, + std::tr1::shared_ptr<PointGFp> H, + std::tr1::shared_ptr<PointGFp> tmp, + const PointGFp& P) + { + //assert(l >= (int)m.bits()- 1); + tmp = H; + std::tr1::shared_ptr<PointGFp> to_add(new PointGFp(P)); // we just need some point + // so that we can use op= + // inside the loop + for (int i=l; i >=0; i--) + { + H->mult2_in_place(); + +#ifndef CM_AADA + + if (m.get_bit(i)) + { + *H += P; + } +#else // (CM_AADA is in) + + if (H.get() == to_add.get()) + { + to_add = tmp; // otherwise all pointers might point to the same object + // and we always need two objects to be able to switch around + } + to_add->assign_within_same_curve(*H); + tmp = H; + *tmp += P; // tmp already points to H + + if (m.get_bit(i)) + { + H = tmp; // NOTE: assign the pointer, not the value! + // (so that the operation is fast and thus as difficult + // to detect as possible) + } + else + { + H = to_add; // NOTE: this is necessary, because the assignment + // "*tmp = ..." already changed what H pointed to + + + } +#endif // CM_AADA + + } + return H; + } + +PointGFp& PointGFp::negate() + { + if (!is_zero()) + { + mY.negate(); + } + return *this; + } + +// *this *= 2 +PointGFp& PointGFp::mult2_in_place() + { + if (is_zero()) + { + return *this; + } + if (mY.is_zero()) + { + + *this = PointGFp(mC); // setting myself to zero + return *this; + } + ensure_worksp(); + + (*mp_worksp_gfp_el)[0].share_assign(mY); + (*mp_worksp_gfp_el)[0] *= mY; + + //GFpElement S(mX * z); + (*mp_worksp_gfp_el)[1].share_assign(mX); + (*mp_worksp_gfp_el)[1] *= (*mp_worksp_gfp_el)[0]; + + //GFpElement x(S + S); + (*mp_worksp_gfp_el)[2].share_assign((*mp_worksp_gfp_el)[1]); + (*mp_worksp_gfp_el)[2] += (*mp_worksp_gfp_el)[1]; + + //S = x + x; + (*mp_worksp_gfp_el)[1].share_assign((*mp_worksp_gfp_el)[2]); + (*mp_worksp_gfp_el)[1] += (*mp_worksp_gfp_el)[2]; + + if (!mAZpow4_set) + { + if (mZ == *(mC.get_mres_one())) + { + mAZpow4 = mC.get_mres_a(); + mAZpow4_set = true; + } + else + { + if (!mZpow2_set) + { + mZpow2 = mZ; + mZpow2 *= mZ; + + mZpow2_set = true; + } + //x = mZpow2 * mZpow2; + (*mp_worksp_gfp_el)[2].share_assign(mZpow2); + (*mp_worksp_gfp_el)[2] *= mZpow2; + + //mAZpow4 = mC.get_mres_a() * x; + mAZpow4 = mC.get_mres_a(); + mAZpow4 *= (*mp_worksp_gfp_el)[2]; + + } + + } + + //GFpElement y(mX * mX); + (*mp_worksp_gfp_el)[3].share_assign(mX); + (*mp_worksp_gfp_el)[3] *= mX; + + //GFpElement M(y + y + y + mAZpow4); + (*mp_worksp_gfp_el)[4].share_assign((*mp_worksp_gfp_el)[3]); + (*mp_worksp_gfp_el)[4] += (*mp_worksp_gfp_el)[3]; + (*mp_worksp_gfp_el)[4] += (*mp_worksp_gfp_el)[3]; + (*mp_worksp_gfp_el)[4] += mAZpow4; + + //x = M * M - (S+S); + (*mp_worksp_gfp_el)[2].share_assign((*mp_worksp_gfp_el)[4]); + (*mp_worksp_gfp_el)[2] *= (*mp_worksp_gfp_el)[4]; + (*mp_worksp_gfp_el)[2] -= (*mp_worksp_gfp_el)[1]; + (*mp_worksp_gfp_el)[2] -= (*mp_worksp_gfp_el)[1]; + + //y = z * z; + (*mp_worksp_gfp_el)[3].share_assign((*mp_worksp_gfp_el)[0]); + (*mp_worksp_gfp_el)[3] *= (*mp_worksp_gfp_el)[0]; + + //GFpElement U(y + y); + (*mp_worksp_gfp_el)[5].share_assign((*mp_worksp_gfp_el)[3]); + (*mp_worksp_gfp_el)[5] += (*mp_worksp_gfp_el)[3]; + + //z = U + U; + (*mp_worksp_gfp_el)[0].share_assign((*mp_worksp_gfp_el)[5]); + (*mp_worksp_gfp_el)[0] += (*mp_worksp_gfp_el)[5]; + + //U = z + z; + (*mp_worksp_gfp_el)[5].share_assign((*mp_worksp_gfp_el)[0]); + (*mp_worksp_gfp_el)[5] += (*mp_worksp_gfp_el)[0]; + + //y = M * (S - x) - U; + (*mp_worksp_gfp_el)[3].share_assign((*mp_worksp_gfp_el)[1]); + (*mp_worksp_gfp_el)[3] -= (*mp_worksp_gfp_el)[2]; + (*mp_worksp_gfp_el)[3] *= (*mp_worksp_gfp_el)[4]; + (*mp_worksp_gfp_el)[3] -= (*mp_worksp_gfp_el)[5]; + + if (mZ != *(mC.get_mres_one())) + { + //z = mY * mZ; + (*mp_worksp_gfp_el)[0].share_assign(mY); + (*mp_worksp_gfp_el)[0] *= mZ; + + } + else + { + //z = mY; + (*mp_worksp_gfp_el)[0].share_assign(mY); + + } + //z = z + z; + (*mp_worksp_gfp_el)[6].share_assign((*mp_worksp_gfp_el)[0]); + (*mp_worksp_gfp_el)[0] += (*mp_worksp_gfp_el)[6]; + + //mX = x; + //mY = y; + //mZ = z; + mX = (*mp_worksp_gfp_el)[2]; + mY = (*mp_worksp_gfp_el)[3]; + mZ = (*mp_worksp_gfp_el)[0]; + + mZpow2_set = false; + mZpow3_set = false; + mAZpow4_set = false; + return *this; + } + +void PointGFp::turn_on_sp_red_mul() const + { + mX.turn_on_sp_red_mul(); + mY.turn_on_sp_red_mul(); + mZ.turn_on_sp_red_mul(); + + // also pretransform, otherwise + // we might have bad results with respect to + // performance because + // additions/subtractions in mult2_in_place() + // and op+= spread untransformed GFpElements + mX.get_mres(); + mY.get_mres(); + mZ.get_mres(); + + mZpow2.turn_on_sp_red_mul(); + mZpow3.turn_on_sp_red_mul(); + mAZpow4.turn_on_sp_red_mul(); + } +// getters + +/** +* returns a point equivalent to *this but were +* Z has value one, i.e. x and y correspond to +* their values in affine coordinates +* +* Distributed under the terms of the Botan license +*/ +PointGFp const PointGFp::get_z_to_one() const + { + return PointGFp(*this).set_z_to_one(); + } + +/** +* changes the representation of *this so that +* Z has value one, i.e. x and y correspond to +* their values in affine coordinates. +* returns *this. +*/ +const PointGFp& PointGFp::set_z_to_one() const + { + if (!(mZ.get_value() == BigInt(1)) && !(mZ.get_value() == BigInt(0))) + { + GFpElement z = inverse(mZ); + GFpElement z2 = z * z; + z *= z2; + GFpElement x = mX * z2; + GFpElement y = mY * z; + mZ = GFpElement(mC.get_p(), BigInt(1)); + mX = x; + mY = y; + } + else + { + if (mZ.get_value() == BigInt(0)) + { + throw Illegal_Transformation("cannot convert Z to one"); + } + } + return *this; // mZ = 1 already + } + +const CurveGFp PointGFp::get_curve() const + { + return mC; + } + +GFpElement const PointGFp::get_affine_x() const + { + + if (is_zero()) + { + throw Illegal_Transformation("cannot convert to affine"); + + } + /*if(!mZpow2_set) + {*/ + mZpow2 = mZ * mZ; + mZpow2_set = true; + //} + //assert(mZpow2 == mZ*mZ); + GFpElement z2 = mZpow2; + return mX * z2.inverse_in_place(); + } + +GFpElement const PointGFp::get_affine_y() const + { + + if (is_zero()) + { + throw Illegal_Transformation("cannot convert to affine"); + + } + /*if(!mZpow3_set ) + {*/ + mZpow3 = mZ * mZ * mZ; + mZpow3_set = true; + //} + //assert(mZpow3 == mZ * mZ *mZ); + GFpElement z3 = mZpow3; + return mY * z3.inverse_in_place(); + } + +GFpElement const PointGFp::get_jac_proj_x() const + { + return GFpElement(mX); + } + +GFpElement const PointGFp::get_jac_proj_y() const + { + return GFpElement(mY); + } + +GFpElement const PointGFp::get_jac_proj_z() const + { + return GFpElement(mZ); + } + +// Is this the point at infinity? +bool PointGFp::is_zero() const + { + return(mX.is_zero() && mZ.is_zero()); + //NOTE: the calls to GFpElement::is_zero() instead of getting the value and + // and comparing it are import because they do not provoke backtransformations + // to the ordinary residue. + } + +// Is the point still on the curve?? +// (If everything is correct, the point is always on its curve; then the +// function will return silently. If Oskar managed to corrupt this object's state, +// then it will throw an exception.) + +void PointGFp::check_invariants() const + { + if (is_zero()) + { + return; + } + const GFpElement y2 = mY * mY; + const GFpElement x3 = mX * mX * mX; + + if (mZ.get_value() == BigInt(1)) + { + GFpElement ax = mC.get_a() * mX; + if(y2 != (x3 + ax + mC.get_b())) + { + throw Illegal_Point(); + } + + } + + mZpow2 = mZ * mZ; + mZpow2_set = true; + mZpow3 = mZpow2 * mZ; + mZpow3_set = true; + mAZpow4 = mZpow3 * mZ * mC.get_a(); + mAZpow4_set = true; + const GFpElement aXZ4 = mAZpow4 * mX; + const GFpElement bZ6 = mC.get_b() * mZpow3 * mZpow3; + + if (y2 != (x3 + aXZ4 + bZ6)) + throw Illegal_Point(); + } + +// swaps the states of *this and other, does not throw! +void PointGFp::swap(PointGFp& other) + { + mC.swap(other.mC); + mX.swap(other.mX); + mY.swap(other.mY); + mZ.swap(other.mZ); + mZpow2.swap(other.mZpow2); + mZpow3.swap(other.mZpow3); + mAZpow4.swap(other.mAZpow4); + std::swap<bool>(mZpow2_set, other.mZpow2_set); + std::swap<bool>(mZpow3_set, other.mZpow3_set); + std::swap<bool>(mAZpow4_set, other.mAZpow4_set); + } + +PointGFp const mult2(const PointGFp& point) + { + return (PointGFp(point)).mult2_in_place(); + } + +bool operator==(const PointGFp& lhs, PointGFp const& rhs) + { + if (lhs.is_zero() && rhs.is_zero()) + { + return true; + } + if ((lhs.is_zero() && !rhs.is_zero()) || (!lhs.is_zero() && rhs.is_zero())) + { + return false; + } + // neither operand is zero, so we can call get_z_to_one() + //assert(!lhs.is_zero()); + //assert(!rhs.is_zero()); + PointGFp aff_lhs = lhs.get_z_to_one(); + PointGFp aff_rhs = rhs.get_z_to_one(); + return (aff_lhs.get_curve() == aff_rhs.get_curve() && + aff_lhs.get_jac_proj_x() == aff_rhs.get_jac_proj_x() && + aff_lhs.get_jac_proj_y() == aff_rhs.get_jac_proj_y()); + } + +// arithmetic operators +PointGFp operator+(const PointGFp& lhs, PointGFp const& rhs) + { + PointGFp tmp(lhs); + return tmp += rhs; + } + +PointGFp operator-(const PointGFp& lhs, PointGFp const& rhs) + { + PointGFp tmp(lhs); + return tmp -= rhs; + } + +PointGFp operator-(const PointGFp& lhs) + { + return PointGFp(lhs).negate(); + } + +PointGFp operator*(const BigInt& scalar, const PointGFp& point) + { + PointGFp result(point); + return result *= scalar; + } + +PointGFp operator*(const PointGFp& point, const BigInt& scalar) + { + PointGFp result(point); + return result *= scalar; + } + +PointGFp mult_point_secure(const PointGFp& point, const BigInt& scalar, + const BigInt& point_order, const BigInt& max_secret) + { + PointGFp result(point); + result.mult_this_secure(scalar, point_order, max_secret); + return result; + } + +// encoding and decoding +SecureVector<byte> EC2OSP(const PointGFp& point, byte format) + { + SecureVector<byte> result; + if (format == PointGFp::UNCOMPRESSED) + { + result = encode_uncompressed(point); + } + else if (format == PointGFp::COMPRESSED) + { + result = encode_compressed(point); + + } + else if (format == PointGFp::HYBRID) + { + result = encode_hybrid(point); + } + else + { + throw Format_Error("illegal point encoding format specification"); + } + return result; + } +SecureVector<byte> encode_compressed(const PointGFp& point) + { + + + if (point.is_zero()) + { + SecureVector<byte> result (1); + result[0] = 0; + return result; + + } + u32bit l = point.get_curve().get_p().bits(); + int dummy = l & 7; + if (dummy != 0) + { + l += 8 - dummy; + } + l /= 8; + SecureVector<byte> result (l+1); + result[0] = 2; + BigInt x = point.get_affine_x().get_value(); + SecureVector<byte> bX = BigInt::encode_1363(x, l); + result.copy(1, bX.begin(), bX.size()); + BigInt y = point.get_affine_y().get_value(); + if (y.get_bit(0)) + { + result[0] |= 1; + } + return result; + } + + +SecureVector<byte> encode_uncompressed(const PointGFp& point) + { + if (point.is_zero()) + { + SecureVector<byte> result (1); + result[0] = 0; + return result; + } + u32bit l = point.get_curve().get_p().bits(); + int dummy = l & 7; + if (dummy != 0) + { + l += 8 - dummy; + } + l /= 8; + SecureVector<byte> result (2*l+1); + result[0] = 4; + BigInt x = point.get_affine_x().get_value(); + BigInt y = point.get_affine_y().get_value(); + SecureVector<byte> bX = BigInt::encode_1363(x, l); + SecureVector<byte> bY = BigInt::encode_1363(y, l); + result.copy(1, bX.begin(), l); + result.copy(l+1, bY.begin(), l); + return result; + + } + +SecureVector<byte> encode_hybrid(const PointGFp& point) + { + if (point.is_zero()) + { + SecureVector<byte> result (1); + result[0] = 0; + return result; + } + u32bit l = point.get_curve().get_p().bits(); + int dummy = l & 7; + if (dummy != 0) + { + l += 8 - dummy; + } + l /= 8; + SecureVector<byte> result (2*l+1); + result[0] = 6; + BigInt x = point.get_affine_x().get_value(); + BigInt y = point.get_affine_y().get_value(); + SecureVector<byte> bX = BigInt::encode_1363(x, l); + SecureVector<byte> bY = BigInt::encode_1363(y, l); + result.copy(1, bX.begin(), bX.size()); + result.copy(l+1, bY.begin(), bY.size()); + if (y.get_bit(0)) + { + result[0] |= 1; + } + return result; + } + +PointGFp OS2ECP(MemoryRegion<byte> const& os, const CurveGFp& curve) + { + if (os.size() == 1 && os[0] == 0) + { + return PointGFp(curve); // return zero + } + SecureVector<byte> bX; + SecureVector<byte> bY; + + GFpElement x(1,0); + GFpElement y(1,0); + GFpElement z(1,0); + + const byte pc = os[0]; + BigInt bi_dec_x; + BigInt bi_dec_y; + switch (pc) + { + case 2: + case 3: + //compressed form + bX = SecureVector<byte>(os.size() - 1); + bX.copy(os.begin()+1, os.size()-1); + + /* Problem wäre, wenn decode() das erste bit als Vorzeichen interpretiert. + *--------------------- + * AW(FS): decode() interpretiert das erste Bit nicht als Vorzeichen + */ + bi_dec_x = BigInt::decode(bX, bX.size()); + x = GFpElement(curve.get_p(), bi_dec_x); + bool yMod2; + yMod2 = (pc & 1) == 1; + y = PointGFp::decompress(yMod2, x, curve); + break; + case 4: + // uncompressed form + int l; + l = (os.size() -1)/2; + bX = SecureVector<byte>(l); + bY = SecureVector<byte>(l); + bX.copy(os.begin()+1, l); + bY.copy(os.begin()+1+l, l); + bi_dec_x = BigInt::decode(bX.begin(), bX.size()); + + bi_dec_y = BigInt::decode(bY.begin(),bY.size()); + x = GFpElement(curve.get_p(), bi_dec_x); + y = GFpElement(curve.get_p(), bi_dec_y); + break; + + case 6: + case 7: + //hybrid form + l = (os.size() - 1)/2; + bX = SecureVector<byte>(l); + bY = SecureVector<byte>(l); + bX.copy(os.begin() + 1, l); + bY.copy(os.begin()+1+l, l); + yMod2 = (pc & 0x01) == 1; + if (!(PointGFp::decompress(yMod2, x, curve) == y)) + { + throw Illegal_Point("error during decoding hybrid format"); + } + break; + default: + throw Format_Error("encountered illegal format specification while decoding point"); + } + z = GFpElement(curve.get_p(), BigInt(1)); + //assert((x.is_trf_to_mres() && x.is_use_montgm()) || !x.is_trf_to_mres()); + //assert((y.is_trf_to_mres() && y.is_use_montgm()) || !y.is_trf_to_mres()); + //assert((z.is_trf_to_mres() && z.is_use_montgm()) || !z.is_trf_to_mres()); + PointGFp result(curve, x, y, z); + result.check_invariants(); + //assert((result.get_jac_proj_x().is_trf_to_mres() && result.get_jac_proj_x().is_use_montgm()) || !result.get_jac_proj_x().is_trf_to_mres()); + //assert((result.get_jac_proj_y().is_trf_to_mres() && result.get_jac_proj_y().is_use_montgm()) || !result.get_jac_proj_y().is_trf_to_mres()); + //assert((result.get_jac_proj_z().is_trf_to_mres() && result.get_jac_proj_z().is_use_montgm()) || !result.get_jac_proj_z().is_trf_to_mres()); + return result; + } + +GFpElement PointGFp::decompress(bool yMod2, const GFpElement& x, + const CurveGFp& curve) + { + BigInt xVal = x.get_value(); + BigInt xpow3 = xVal * xVal * xVal; + BigInt g = curve.get_a().get_value() * xVal; + g += xpow3; + g += curve.get_b().get_value(); + g = g%curve.get_p(); + BigInt z = ressol(g, curve.get_p()); + + if(z < 0) + throw Illegal_Point("error during decompression"); + + bool zMod2 = z.get_bit(0); + if ((zMod2 && ! yMod2) || (!zMod2 && yMod2)) + { + z = curve.get_p() - z; + } + return GFpElement(curve.get_p(),z); + } + +PointGFp const create_random_point(RandomNumberGenerator& rng, + const CurveGFp& curve) + { + + // create a random point + GFpElement mX(1,1); + GFpElement mY(1,1); + GFpElement mZ(1,1); + GFpElement minusOne(curve.get_p(), BigInt(BigInt::Negative,1)); + mY = minusOne; + GFpElement y2(1,1); + GFpElement x(1,1); + + while (mY == minusOne) + { + BigInt value(rng, curve.get_p().bits()); + mX = GFpElement(curve.get_p(),value); + y2 = curve.get_a() * mX; + x = mX * mX; + x *= mX; + y2 += (x + curve.get_b()); + + value = ressol(y2.get_value(), curve.get_p()); + + if(value < 0) + mY = minusOne; + else + mY = GFpElement(curve.get_p(), value); + } + mZ = GFpElement(curve.get_p(), BigInt(1)); + + return PointGFp(curve, mX, mY, mZ); + } + +} // namespace Botan diff --git a/old/botan/src/math/gfpmath/point_gfp.h b/old/botan/src/math/gfpmath/point_gfp.h new file mode 100644 index 0000000..771605e --- /dev/null +++ b/old/botan/src/math/gfpmath/point_gfp.h @@ -0,0 +1,315 @@ +/* +* Arithmetic over GF(p) +* +* (C) 2007 Martin Doering +* Christoph Ludwig +* Falko Strenzke +* (C) 2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_POINT_GFP_H__ +#define BOTAN_POINT_GFP_H__ + +#include <botan/curve_gfp.h> +#include <botan/gfp_element.h> +#include <botan/bigint.h> +#include <botan/exceptn.h> +#include <vector> + +namespace Botan { + +struct Illegal_Point : public Exception + { + Illegal_Point(const std::string& err = "") : Exception(err) {} + }; + +/** +* This class represents one point on a curve of GF(p). +*/ +class BOTAN_DLL PointGFp + { + public: + /** + * uncompressed encoding byte value + */ + static const int UNCOMPRESSED = 0; + + /** + * compressed encoding byte value + */ + static const int COMPRESSED = 1; + + /** + * hybrid encoding byte value + */ + static const int HYBRID = 2; + + /** + * Construct the point O + * @param curve The base curve + */ + explicit PointGFp(const CurveGFp& curve); + + /** + * Construct a point given its affine coordinates + * @param curve the base curve + * @param x affine x coordinate + * @param y affine y coordinate + */ + explicit PointGFp(const CurveGFp& curve, GFpElement const& x, + GFpElement const& y); + + /** + * Construct a point given its jacobian projective coordinates + * @param curve the base curve + * @param x jacobian projective x coordinate + * @param y jacobian projective y coordinate + * @param z jacobian projective y coordinate + */ + explicit PointGFp(const CurveGFp& curve, GFpElement const& x, + GFpElement const& y, GFpElement const& z); + + /** + * copy constructor + * @param other the value to clone + */ + PointGFp(const PointGFp& other); + + /** + * assignment operator + * @param other The point to use as source for the assignment + */ + const PointGFp& operator=(const PointGFp& other); + + /** + * assign another point which is on the same curve as *this + * @param other The point to use as source for the assignment + */ + const PointGFp& assign_within_same_curve(const PointGFp& other); + + + + /** + * += Operator + * @param rhs the PointGFp to add to the local value + * @result resulting PointGFp + */ + PointGFp& operator+=(const PointGFp& rhs); + + /** + * -= Operator + * @param rhs the PointGFp to subtract from the local value + * @result resulting PointGFp + */ + PointGFp& operator-=(const PointGFp& rhs); + + /** + * *= Operator + * This function turns on the the special reduction multiplication + * itself for fast computation, turns it off again when finished. + * @param scalar the PointGFp to multiply with *this + * @result resulting PointGFp + */ + PointGFp& operator*=(const BigInt& scalar); + + /** + * the equivalent to operator*= with countermeasures against + * sidechannel attacks, using the randomized exponent + * and add-and-double-always + * countermeasures (suitable for ECDSA and ECKAEG) + * @param scalar the scalar to multiply the point with + * @param point_order a multiple of the order of the point + *(= n * k in the general case; k is the cofactor) + * @param max_secr the maximal size of the scalar + * (will usually be n-1 ) + * @result resulting PointGFp + */ + PointGFp& mult_this_secure(const BigInt& scalar, + const BigInt& point_order, + const BigInt& max_secr + ); + + /** + * Negate internal value(*this *= -1 ) + * @return *this + */ + PointGFp& negate(); + + /** + * Multiply the point by two(*this *= 2 ) + * @return *this + */ + PointGFp& mult2_in_place(); + + /** + * Set z coordinate to one. + * @return *this + */ + const PointGFp& set_z_to_one() const; + + /** + * Turn on the special reduction multiplication (i.e. the + * Montgomery multiplication in the current implementation) for + * the coordinates. This enables fast execution of mult2_in_place() + * and operator+=(). + */ + void turn_on_sp_red_mul() const; + + /** + * Return a point + * where the coordinates are transformed + * so that z equals one, + * thus x and y have just the affine values. + * @result *this + */ + PointGFp const get_z_to_one() const; + + /** + * Return base curve of this point + * @result the curve over GF(p) of this point + */ + CurveGFp const get_curve() const; + + /** + * get affine x coordinate + * @result affine x coordinate + */ + GFpElement const get_affine_x() const; + + /** + * get affine y coordinate + * @result affine y coordinate + */ + GFpElement const get_affine_y() const; + + /** + * get the jacobian projective x coordinate + * @result jacobian projective x coordinate + */ + GFpElement const get_jac_proj_x() const; + + /** + * get the jacobian projective y coordinate + * @result jacobian projective y coordinate + */ + GFpElement const get_jac_proj_y() const; + + /** + * get the jacobian projective z coordinate + * @result jacobian projective z coordinate + */ + GFpElement const get_jac_proj_z() const; + + /** + * Is this the point at infinity? + * @result true, if this point is at infinity, false otherwise. + */ + bool is_zero() const; + + /** + * Checks whether the point is to be found on the underlying curve. + * Throws an Invalid_Point exception in case of detecting that the point + * does not satisfy the curve equation. + * To be used to ensure against fault attacks. + */ + void check_invariants() const; + + + /** + * swaps the states of *this and other, does not throw! + * @param other the object to swap values with + */ + void swap(PointGFp& other); + + /** + * Sets the shared pointer to the GFpModulus that will be + * held in *this, specifically the various members of *this. + * Warning: do not use this function unless you know in detail about + * the implications of using + * the shared GFpModulus objects! + * Do NOT spread a shared pointer to GFpModulus over different + * threads! + * @param mod a shared pointer to a GFpModulus that will + * be held in the members *this + */ + void set_shrd_mod(std::tr1::shared_ptr<GFpModulus> p_mod); + + static GFpElement decompress(bool yMod2, GFpElement const& x, const CurveGFp& curve); + + private: + static const u32bit GFPEL_WKSP_SIZE = 9; + void ensure_worksp() const; + + inline std::tr1::shared_ptr<PointGFp> mult_loop(int l, const BigInt& m, + std::tr1::shared_ptr<PointGFp> H, + std::tr1::shared_ptr<PointGFp> tmp, + const PointGFp& P); + + CurveGFp mC; + mutable GFpElement mX; // NOTE: these values must be mutable (affine<->proj) + mutable GFpElement mY; + mutable GFpElement mZ; + mutable GFpElement mZpow2; // mZ^2 + mutable GFpElement mZpow3; // mZ^3 + mutable GFpElement mAZpow4; // mA*mZ^4 + mutable bool mZpow2_set; + mutable bool mZpow3_set; + mutable bool mAZpow4_set; + mutable std::tr1::shared_ptr<std::vector<GFpElement> > mp_worksp_gfp_el; + + }; + +// relational operators +bool operator==(const PointGFp& lhs, const PointGFp& rhs); +inline bool operator!=(const PointGFp& lhs, const PointGFp& rhs ) + { + return !operator==(lhs, rhs); + } + +// arithmetic operators +PointGFp operator+(const PointGFp& lhs, const PointGFp& rhs); +PointGFp operator-(const PointGFp& lhs, const PointGFp& rhs); +PointGFp operator-(const PointGFp& lhs); + +PointGFp operator*(const BigInt& scalar, const PointGFp& point); +PointGFp operator*(const PointGFp& point, const BigInt& scalar); +PointGFp mult_point_secure(const PointGFp& point, + const BigInt& scalar, + const BigInt& point_order, + const BigInt& max_secret); + +PointGFp const mult2(const PointGFp& point); + +PointGFp const create_random_point(RandomNumberGenerator& rng, + const CurveGFp& curve); + +// encoding and decoding +SecureVector<byte> EC2OSP(const PointGFp& point, byte format); +PointGFp OS2ECP(MemoryRegion<byte> const& os, const CurveGFp& curve); + +SecureVector<byte> encode_uncompressed(const PointGFp& point); // maybe make private +SecureVector<byte> encode_hybrid(const PointGFp& point); // maybe make private +SecureVector<byte> encode_compressed(const PointGFp& point); // maybe make private + +// swaps the states of point1 and point2, does not throw! +// cf. Meyers, Item 25 +inline +void swap(PointGFp& point1, PointGFp& point2 ) + { + point1.swap(point2); + } + +} // namespace Botan + +namespace std { + +// swaps the states of point1 and point2, does not throw! +// cf. Meyers, Item 25 +template<> inline void +swap<Botan::PointGFp>(Botan::PointGFp& x, Botan::PointGFp& y) { x.swap(y); } + +} // namespace std + +#endif diff --git a/old/botan/src/math/numbertheory/blinding.cpp b/old/botan/src/math/numbertheory/blinding.cpp new file mode 100644 index 0000000..c6a3fd1 --- /dev/null +++ b/old/botan/src/math/numbertheory/blinding.cpp @@ -0,0 +1,49 @@ +/* +* Blinder +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/blinding.h> +#include <botan/numthry.h> + +namespace Botan { + +/* +* Blinder Constructor +*/ +Blinder::Blinder(const BigInt& e, const BigInt& d, const BigInt& n) + { + if(e < 1 || d < 1 || n < 1) + throw Invalid_Argument("Blinder: Arguments too small"); + + reducer = Modular_Reducer(n); + this->e = e; + this->d = d; + } + +/* +* Blind a number +*/ +BigInt Blinder::blind(const BigInt& i) const + { + if(!reducer.initialized()) + return i; + + e = reducer.square(e); + d = reducer.square(d); + return reducer.multiply(i, e); + } + +/* +* Unblind a number +*/ +BigInt Blinder::unblind(const BigInt& i) const + { + if(!reducer.initialized()) + return i; + return reducer.multiply(i, d); + } + +} diff --git a/old/botan/src/math/numbertheory/blinding.h b/old/botan/src/math/numbertheory/blinding.h new file mode 100644 index 0000000..5f7f9e6 --- /dev/null +++ b/old/botan/src/math/numbertheory/blinding.h @@ -0,0 +1,34 @@ +/* +* Blinder +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_BLINDER_H__ +#define BOTAN_BLINDER_H__ + +#include <botan/bigint.h> +#include <botan/reducer.h> + +namespace Botan { + +/* +* Blinding Function Object +*/ +class BOTAN_DLL Blinder + { + public: + BigInt blind(const BigInt&) const; + BigInt unblind(const BigInt&) const; + + Blinder() {} + Blinder(const BigInt&, const BigInt&, const BigInt&); + private: + Modular_Reducer reducer; + mutable BigInt e, d; + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/def_powm.h b/old/botan/src/math/numbertheory/def_powm.h new file mode 100644 index 0000000..472c865 --- /dev/null +++ b/old/botan/src/math/numbertheory/def_powm.h @@ -0,0 +1,64 @@ +/* +* Modular Exponentiation +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#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 BOTAN_DLL Fixed_Window_Exponentiator : public Modular_Exponentiator + { + public: + void set_exponent(const BigInt&); + void set_base(const BigInt&); + BigInt execute() const; + + Modular_Exponentiator* copy() const + { return new Fixed_Window_Exponentiator(*this); } + + Fixed_Window_Exponentiator(const BigInt&, Power_Mod::Usage_Hints); + private: + Modular_Reducer reducer; + BigInt exp; + u32bit window_bits; + std::vector<BigInt> g; + Power_Mod::Usage_Hints hints; + }; + +/* +* Montgomery Exponentiator +*/ +class BOTAN_DLL Montgomery_Exponentiator : public Modular_Exponentiator + { + public: + void set_exponent(const BigInt&); + void set_base(const BigInt&); + BigInt execute() const; + + Modular_Exponentiator* copy() const + { return new Montgomery_Exponentiator(*this); } + + Montgomery_Exponentiator(const BigInt&, Power_Mod::Usage_Hints); + private: + BigInt exp, modulus; + BigInt R2, R_mod; + std::vector<BigInt> g; + word mod_prime; + u32bit mod_words, exp_bits, window_bits; + Power_Mod::Usage_Hints hints; + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/dsa_gen.cpp b/old/botan/src/math/numbertheory/dsa_gen.cpp new file mode 100644 index 0000000..83646e5 --- /dev/null +++ b/old/botan/src/math/numbertheory/dsa_gen.cpp @@ -0,0 +1,135 @@ +/* +* DSA Parameter Generation +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> +#include <botan/algo_factory.h> +#include <botan/hash.h> +#include <botan/parsing.h> +#include <algorithm> +#include <memory> + +namespace Botan { + +namespace { + +/* +* Check if this size is allowed by FIPS 186-3 +*/ +bool fips186_3_valid_size(u32bit pbits, u32bit qbits) + { + if(qbits == 160) + return (pbits == 512 || pbits == 768 || 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, + Algorithm_Factory& af, + BigInt& p, BigInt& q, + u32bit pbits, u32bit qbits, + const MemoryRegion<byte>& seed_c) + { + if(!fips186_3_valid_size(pbits, qbits)) + throw Invalid_Argument( + "FIPS 186-3 does not allow DSA domain parameters of " + + to_string(pbits) + "/" + to_string(qbits) + " bits long"); + + if(seed_c.size() * 8 < qbits) + throw Invalid_Argument( + "Generating a DSA parameter set with a " + to_string(qbits) + + "long q requires a seed at least as many bits long"); + + std::auto_ptr<HashFunction> hash( + af.make_hash_function("SHA-" + to_string(qbits))); + + const u32bit HASH_SIZE = hash->OUTPUT_LENGTH; + + class Seed + { + public: + Seed(const MemoryRegion<byte>& s) : seed(s) {} + + operator MemoryRegion<byte>& () { return seed; } + + Seed& operator++() + { + for(u32bit j = seed.size(); j > 0; --j) + if(++seed[j-1]) + break; + return (*this); + } + private: + SecureVector<byte> seed; + }; + + Seed seed(seed_c); + + q.binary_decode(hash->process(seed)); + q.set_bit(qbits-1); + q.set_bit(0); + + if(!is_prime(q, rng)) + return false; + + const u32bit n = (pbits-1) / (HASH_SIZE * 8), + b = (pbits-1) % (HASH_SIZE * 8); + + BigInt X; + SecureVector<byte> V(HASH_SIZE * (n+1)); + + for(u32bit j = 0; j != 4096; ++j) + { + for(u32bit k = 0; k <= n; ++k) + { + ++seed; + hash->update(seed); + hash->final(V + HASH_SIZE * (n-k)); + } + + X.binary_decode(V + (HASH_SIZE - 1 - b/8), + V.size() - (HASH_SIZE - 1 - b/8)); + X.set_bit(pbits-1); + + p = X - (X % (2*q) - 1); + + if(p.bits() == pbits && is_prime(p, rng)) + return true; + } + return false; + } + +/* +* Generate DSA Primes +*/ +SecureVector<byte> generate_dsa_primes(RandomNumberGenerator& rng, + Algorithm_Factory& af, + BigInt& p, BigInt& q, + u32bit pbits, u32bit qbits) + { + SecureVector<byte> seed(qbits/8); + + while(true) + { + rng.randomize(seed, seed.size()); + + if(generate_dsa_primes(rng, af, p, q, pbits, qbits, seed)) + return seed; + } + } + +} diff --git a/old/botan/src/math/numbertheory/info.txt b/old/botan/src/math/numbertheory/info.txt new file mode 100644 index 0000000..1595c73 --- /dev/null +++ b/old/botan/src/math/numbertheory/info.txt @@ -0,0 +1,33 @@ +realname "Math Functions" + +load_on auto + +define BIGINT_MATH + +<add> +blinding.cpp +blinding.h +def_powm.h +dsa_gen.cpp +jacobi.cpp +make_prm.cpp +mp_numth.cpp +numthry.cpp +numthry.h +pow_mod.cpp +pow_mod.h +powm_fw.cpp +powm_mnt.cpp +primes.cpp +reducer.cpp +reducer.h +ressol.cpp +</add> + +<requires> +algo_factory +bigint +hash +libstate +rng +</requires> diff --git a/old/botan/src/math/numbertheory/jacobi.cpp b/old/botan/src/math/numbertheory/jacobi.cpp new file mode 100644 index 0000000..2ad05ff --- /dev/null +++ b/old/botan/src/math/numbertheory/jacobi.cpp @@ -0,0 +1,53 @@ +/* +* Jacobi Function +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> + +namespace Botan { + +/* +* Calculate the Jacobi symbol +*/ +s32bit 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; + s32bit 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; + + u32bit 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/old/botan/src/math/numbertheory/make_prm.cpp b/old/botan/src/math/numbertheory/make_prm.cpp new file mode 100644 index 0000000..b136b6d --- /dev/null +++ b/old/botan/src/math/numbertheory/make_prm.cpp @@ -0,0 +1,97 @@ +/* +* Prime Generation +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> +#include <botan/parsing.h> +#include <algorithm> + +namespace Botan { + +/* +* Generate a random prime +*/ +BigInt random_prime(RandomNumberGenerator& rng, + u32bit bits, const BigInt& coprime, + u32bit equiv, u32bit modulo) + { + if(bits <= 1) + throw Invalid_Argument("random_prime: Can't make a prime of " + + 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); + + if(coprime <= 0) + throw Invalid_Argument("random_prime: coprime must be > 0"); + if(modulo % 2 == 1 || modulo == 0) + throw Invalid_Argument("random_prime: Invalid modulo value"); + if(equiv >= modulo || equiv % 2 == 0) + throw Invalid_Argument("random_prime: equiv must be < modulo, and odd"); + + while(true) + { + BigInt p(rng, bits); + p.set_bit(bits - 2); + p.set_bit(0); + + if(p % modulo != equiv) + p += (modulo - p % modulo) + equiv; + + const u32bit sieve_size = std::min(bits / 2, PRIME_TABLE_SIZE); + SecureVector<u32bit> sieve(sieve_size); + + for(u32bit j = 0; j != sieve.size(); ++j) + sieve[j] = p % PRIMES[j]; + + u32bit counter = 0; + while(true) + { + if(counter == 4096 || p.bits() > bits) + break; + + bool passes_sieve = true; + ++counter; + p += modulo; + + if(p.bits() > bits) + break; + + for(u32bit j = 0; j != sieve.size(); ++j) + { + sieve[j] = (sieve[j] + modulo) % PRIMES[j]; + if(sieve[j] == 0) + passes_sieve = false; + } + + if(!passes_sieve || gcd(p - 1, coprime) != 1) + continue; + if(passes_mr_tests(rng, p)) + return p; + } + } + } + +/* +* Generate a random safe prime +*/ +BigInt random_safe_prime(RandomNumberGenerator& rng, u32bit bits) + { + if(bits <= 64) + throw Invalid_Argument("random_safe_prime: Can't make a prime of " + + to_string(bits) + " bits"); + + BigInt p; + do + p = (random_prime(rng, bits - 1) << 1) + 1; + while(!is_prime(p, rng)); + return p; + } + +} diff --git a/old/botan/src/math/numbertheory/mp_numth.cpp b/old/botan/src/math/numbertheory/mp_numth.cpp new file mode 100644 index 0000000..45a3984 --- /dev/null +++ b/old/botan/src/math/numbertheory/mp_numth.cpp @@ -0,0 +1,71 @@ +/* +* Fused and Important MP Algorithms +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> +#include <botan/mp_core.h> +#include <botan/util.h> +#include <algorithm> + +namespace Botan { + +/* +* Square a BigInt +*/ +BigInt square(const BigInt& x) + { + const u32bit x_sw = x.sig_words(); + + BigInt z(BigInt::Positive, round_up(2*x_sw, 16)); + SecureVector<word> workspace(z.size()); + + bigint_sqr(z.get_reg(), z.size(), workspace, + x.data(), x.size(), x_sw); + return z; + } + +/* +* Multiply-Add Operation +*/ +BigInt mul_add(const BigInt& a, const BigInt& b, const BigInt& c) + { + if(c.is_negative() || c.is_zero()) + throw Invalid_Argument("mul_add: Third argument must be > 0"); + + BigInt::Sign sign = BigInt::Positive; + if(a.sign() != b.sign()) + sign = BigInt::Negative; + + const u32bit a_sw = a.sig_words(); + const u32bit b_sw = b.sig_words(); + const u32bit c_sw = c.sig_words(); + + BigInt r(sign, std::max(a.size() + b.size(), c_sw) + 1); + SecureVector<word> workspace(r.size()); + + bigint_mul(r.get_reg(), r.size(), workspace, + a.data(), a.size(), a_sw, + b.data(), b.size(), b_sw); + const u32bit r_size = std::max(r.sig_words(), c_sw); + bigint_add2(r.get_reg(), 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; + } + +} diff --git a/old/botan/src/math/numbertheory/numthry.cpp b/old/botan/src/math/numbertheory/numthry.cpp new file mode 100644 index 0000000..4486813 --- /dev/null +++ b/old/botan/src/math/numbertheory/numthry.cpp @@ -0,0 +1,346 @@ +/* +* Number Theory Functions +* (C) 1999-2009 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> +#include <botan/bit_ops.h> +#include <algorithm> + +namespace Botan { + +namespace { + +/* +* Miller-Rabin Iterations +*/ +u32bit miller_rabin_test_iterations(u32bit bits, bool verify) + { + struct mapping { u32bit bits; u32bit verify_iter; u32bit check_iter; }; + + static const mapping tests[] = { + { 50, 55, 25 }, + { 100, 38, 22 }, + { 160, 32, 18 }, + { 163, 31, 17 }, + { 168, 30, 16 }, + { 177, 29, 16 }, + { 181, 28, 15 }, + { 185, 27, 15 }, + { 190, 26, 15 }, + { 195, 25, 14 }, + { 201, 24, 14 }, + { 208, 23, 14 }, + { 215, 22, 13 }, + { 222, 21, 13 }, + { 231, 20, 13 }, + { 241, 19, 12 }, + { 252, 18, 12 }, + { 264, 17, 12 }, + { 278, 16, 11 }, + { 294, 15, 10 }, + { 313, 14, 9 }, + { 334, 13, 8 }, + { 360, 12, 8 }, + { 392, 11, 7 }, + { 430, 10, 7 }, + { 479, 9, 6 }, + { 542, 8, 6 }, + { 626, 7, 5 }, + { 746, 6, 4 }, + { 926, 5, 3 }, + { 1232, 4, 2 }, + { 1853, 3, 2 }, + { 0, 0, 0 } + }; + + for(u32bit i = 0; tests[i].bits; ++i) + { + if(bits <= tests[i].bits) + { + if(verify) + return tests[i].verify_iter; + else + return tests[i].check_iter; + } + } + return 2; + } + +} + +/* +* Return the number of 0 bits at the end of n +*/ +u32bit low_zero_bits(const BigInt& n) + { + if(n.is_negative() || n.is_zero()) return 0; + + u32bit low_zero = 0; + + if(n.is_positive() && n.is_nonzero()) + { + for(u32bit i = 0; i != n.size(); ++i) + { + word x = n[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 = a, y = b; + x.set_sign(BigInt::Positive); + y.set_sign(BigInt::Positive); + u32bit shift = std::min(low_zero_bits(x), low_zero_bits(y)); + + x >>= shift; + y >>= shift; + + while(x.is_nonzero()) + { + x >>= low_zero_bits(x); + y >>= low_zero_bits(y); + if(x >= y) { x -= y; x >>= 1; } + else { y -= x; y >>= 1; } + } + + return (y << shift); + } + +/* +* Calculate the LCM +*/ +BigInt lcm(const BigInt& a, const BigInt& b) + { + return ((a * b) / gcd(a, b)); + } + +/* +* 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; + + BigInt x = mod, y = n, u = mod, v = n; + BigInt A = 1, B = 0, C = 0, D = 1; + + while(u.is_nonzero()) + { + u32bit zero_bits = low_zero_bits(u); + u >>= zero_bits; + for(u32bit i = 0; i != zero_bits; ++i) + { + if(A.is_odd() || B.is_odd()) + { A += y; B -= x; } + A >>= 1; B >>= 1; + } + + zero_bits = low_zero_bits(v); + v >>= zero_bits; + for(u32bit i = 0; i != zero_bits; ++i) + { + if(C.is_odd() || D.is_odd()) + { C += y; D -= x; } + 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; + + while(D.is_negative()) D += mod; + while(D >= mod) D -= mod; + + return D; + } + +/* +* Modular Exponentiation +*/ +BigInt power_mod(const BigInt& base, const BigInt& exp, const BigInt& mod) + { + Power_Mod pow_mod(mod); + pow_mod.set_base(base); + pow_mod.set_exponent(exp); + return pow_mod.execute(); + } + +/* +* Do simple tests of primality +*/ +s32bit simple_primality_tests(const BigInt& n) + { + const s32bit NOT_PRIME = -1, UNKNOWN = 0, PRIME = 1; + + if(n == 2) + return PRIME; + if(n <= 1 || n.is_even()) + return NOT_PRIME; + + if(n <= PRIMES[PRIME_TABLE_SIZE-1]) + { + const word num = n.word_at(0); + for(u32bit i = 0; PRIMES[i]; ++i) + { + if(num == PRIMES[i]) return PRIME; + if(num < PRIMES[i]) return NOT_PRIME; + } + return NOT_PRIME; + } + + u32bit check_first = std::min(n.bits() / 32, PRIME_PRODUCTS_TABLE_SIZE); + for(u32bit i = 0; i != check_first; ++i) + if(gcd(n, PRIME_PRODUCTS[i]) != 1) + return NOT_PRIME; + + return UNKNOWN; + } + +/* +* Fast check of primality +*/ +bool check_prime(const BigInt& n, RandomNumberGenerator& rng) + { + return run_primality_tests(rng, n, 0); + } + +/* +* Test for primality +*/ +bool is_prime(const BigInt& n, RandomNumberGenerator& rng) + { + return run_primality_tests(rng, n, 1); + } + +/* +* Verify primality +*/ +bool verify_prime(const BigInt& n, RandomNumberGenerator& rng) + { + return run_primality_tests(rng, n, 2); + } + +/* +* Verify primality +*/ +bool run_primality_tests(RandomNumberGenerator& rng, + const BigInt& n, u32bit level) + { + s32bit simple_tests = simple_primality_tests(n); + if(simple_tests) return (simple_tests == 1) ? true : false; + return passes_mr_tests(rng, n, level); + } + +/* +* Test for primaility using Miller-Rabin +*/ +bool passes_mr_tests(RandomNumberGenerator& rng, + const BigInt& n, u32bit level) + { + const u32bit PREF_NONCE_BITS = 40; + + if(level > 2) + level = 2; + + MillerRabin_Test mr(n); + + if(!mr.passes_test(2)) + return false; + + if(level == 0) + return true; + + const u32bit NONCE_BITS = std::min(n.bits() - 1, PREF_NONCE_BITS); + + const bool verify = (level == 2); + + u32bit tests = miller_rabin_test_iterations(n.bits(), verify); + + BigInt nonce; + for(u32bit i = 0; i != tests; ++i) + { + if(!verify && PRIMES[i] < (n-1)) + nonce = PRIMES[i]; + else + { + while(nonce < 2 || nonce >= (n-1)) + nonce.randomize(rng, NONCE_BITS); + } + + if(!mr.passes_test(nonce)) + return false; + } + return true; + } + +/* +* Miller-Rabin Test +*/ +bool MillerRabin_Test::passes_test(const BigInt& a) + { + if(a < 2 || a >= n_minus_1) + throw Invalid_Argument("Bad size for nonce in Miller-Rabin test"); + + BigInt y = pow_mod(a); + if(y == 1 || y == n_minus_1) + return true; + + for(u32bit i = 1; i != s; ++i) + { + y = reducer.square(y); + + if(y == 1) + return false; + if(y == n_minus_1) + return true; + } + return false; + } + +/* +* Miller-Rabin Constructor +*/ +MillerRabin_Test::MillerRabin_Test(const BigInt& num) + { + if(num.is_even() || num < 3) + throw Invalid_Argument("MillerRabin_Test: Invalid number for testing"); + + n = num; + n_minus_1 = n - 1; + s = low_zero_bits(n_minus_1); + r = n_minus_1 >> s; + + pow_mod = Fixed_Exponent_Power_Mod(r, n); + reducer = Modular_Reducer(n); + } + +} diff --git a/old/botan/src/math/numbertheory/numthry.h b/old/botan/src/math/numbertheory/numthry.h new file mode 100644 index 0000000..e4c0437 --- /dev/null +++ b/old/botan/src/math/numbertheory/numthry.h @@ -0,0 +1,120 @@ +/* +* Number Theory Functions +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_NUMBER_THEORY_H__ +#define BOTAN_NUMBER_THEORY_H__ + +#include <botan/bigint.h> +#include <botan/reducer.h> +#include <botan/pow_mod.h> +#include <botan/rng.h> + +namespace Botan { + +/* +* Fused Arithmetic Operations +*/ +BigInt BOTAN_DLL mul_add(const BigInt&, const BigInt&, const BigInt&); +BigInt BOTAN_DLL sub_mul(const BigInt&, const BigInt&, const BigInt&); + +/* +* Number Theory Functions +*/ +inline BigInt abs(const BigInt& n) { return n.abs(); } + +void BOTAN_DLL divide(const BigInt&, const BigInt&, BigInt&, BigInt&); + +BigInt BOTAN_DLL gcd(const BigInt&, const BigInt&); +BigInt BOTAN_DLL lcm(const BigInt&, const BigInt&); + +BigInt BOTAN_DLL square(const BigInt&); +BigInt BOTAN_DLL inverse_mod(const BigInt&, const BigInt&); +s32bit BOTAN_DLL jacobi(const BigInt&, const BigInt&); + +BigInt BOTAN_DLL power_mod(const BigInt&, const BigInt&, const BigInt&); + +/* +* Compute the square root of x modulo a prime +* using the Shanks-Tonnelli algorithm +*/ +BigInt ressol(const BigInt& x, const BigInt& p); + +/* +* Utility Functions +*/ +u32bit BOTAN_DLL low_zero_bits(const BigInt&); + +/* +* Primality Testing +*/ +bool BOTAN_DLL check_prime(const BigInt&, RandomNumberGenerator&); +bool BOTAN_DLL is_prime(const BigInt&, RandomNumberGenerator&); +bool BOTAN_DLL verify_prime(const BigInt&, RandomNumberGenerator&); + +s32bit BOTAN_DLL simple_primality_tests(const BigInt&); + +bool BOTAN_DLL passes_mr_tests(RandomNumberGenerator&, + const BigInt&, u32bit = 1); + +bool BOTAN_DLL run_primality_tests(RandomNumberGenerator&, + const BigInt&, u32bit = 1); + +/* +* Random Number Generation +*/ +BigInt BOTAN_DLL random_prime(RandomNumberGenerator&, + u32bit bits, const BigInt& coprime = 1, + u32bit equiv = 1, u32bit equiv_mod = 2); + +BigInt BOTAN_DLL random_safe_prime(RandomNumberGenerator&, + u32bit); + +/* +* DSA Parameter Generation +*/ +class Algorithm_Factory; + +SecureVector<byte> BOTAN_DLL +generate_dsa_primes(RandomNumberGenerator& rng, + Algorithm_Factory& af, + BigInt& p, BigInt& q, + u32bit pbits, u32bit qbits); + +bool BOTAN_DLL +generate_dsa_primes(RandomNumberGenerator& rng, + Algorithm_Factory& af, + BigInt& p_out, BigInt& q_out, + u32bit p_bits, u32bit q_bits, + const MemoryRegion<byte>& seed); + +/* +* Prime Numbers +*/ +const u32bit PRIME_TABLE_SIZE = 6541; +const u32bit PRIME_PRODUCTS_TABLE_SIZE = 256; + +extern const u16bit BOTAN_DLL PRIMES[]; +extern const u64bit PRIME_PRODUCTS[]; + +/* +* Miller-Rabin Primality Tester +*/ +class BOTAN_DLL MillerRabin_Test + { + public: + bool passes_test(const BigInt&); + MillerRabin_Test(const BigInt&); + private: + BigInt n, r, n_minus_1; + u32bit s; + Fixed_Exponent_Power_Mod pow_mod; + Modular_Reducer reducer; + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/pow_mod.cpp b/old/botan/src/math/numbertheory/pow_mod.cpp new file mode 100644 index 0000000..fd9b8e9 --- /dev/null +++ b/old/botan/src/math/numbertheory/pow_mod.cpp @@ -0,0 +1,157 @@ +/* +* Modular Exponentiation Proxy +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/pow_mod.h> +#include <botan/pk_engine.h> + +namespace Botan { + +/* +* Power_Mod Constructor +*/ +Power_Mod::Power_Mod(const BigInt& n, Usage_Hints hints) + { + core = 0; + set_modulus(n, hints); + } + +/* +* Power_Mod Copy Constructor +*/ +Power_Mod::Power_Mod(const Power_Mod& other) + { + core = 0; + if(other.core) + core = other.core->copy(); + } + +/* +* Power_Mod Assignment Operator +*/ +Power_Mod& Power_Mod::operator=(const Power_Mod& other) + { + delete core; + core = 0; + if(other.core) + core = other.core->copy(); + return (*this); + } + +/* +* Power_Mod Destructor +*/ +Power_Mod::~Power_Mod() + { + delete core; + } + +/* +* Set the modulus +*/ +void Power_Mod::set_modulus(const BigInt& n, Usage_Hints hints) const + { + delete core; + core = ((n == 0) ? 0 : Engine_Core::mod_exp(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(!core) + throw Internal_Error("Power_Mod::set_base: core was NULL"); + 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(!core) + throw Internal_Error("Power_Mod::set_exponent: core was NULL"); + core->set_exponent(e); + } + +/* +* Compute the result +*/ +BigInt Power_Mod::execute() const + { + if(!core) + throw Internal_Error("Power_Mod::execute: core was NULL"); + return core->execute(); + } + +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 u32bit b_bits = b.bits(); + const u32bit 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 u32bit e_bits = e.bits(); + const u32bit 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/old/botan/src/math/numbertheory/pow_mod.h b/old/botan/src/math/numbertheory/pow_mod.h new file mode 100644 index 0000000..6952dcd --- /dev/null +++ b/old/botan/src/math/numbertheory/pow_mod.h @@ -0,0 +1,93 @@ +/* +* Modular Exponentiator +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_POWER_MOD_H__ +#define BOTAN_POWER_MOD_H__ + +#include <botan/bigint.h> + +namespace Botan { + +/* +* Modular Exponentiator Interface +*/ +class BOTAN_DLL 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; + virtual ~Modular_Exponentiator() {} + }; + +/* +* Modular Exponentiator Proxy +*/ +class BOTAN_DLL 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 + }; + + void set_modulus(const BigInt&, Usage_Hints = NO_HINTS) const; + void set_base(const BigInt&) const; + void set_exponent(const BigInt&) const; + + BigInt execute() const; + + Power_Mod& operator=(const Power_Mod&); + + Power_Mod(const BigInt& = 0, Usage_Hints = NO_HINTS); + Power_Mod(const Power_Mod&); + ~Power_Mod(); + private: + mutable Modular_Exponentiator* core; + Usage_Hints hints; + }; + +/* +* Fixed Exponent Modular Exponentiator Proxy +*/ +class BOTAN_DLL Fixed_Exponent_Power_Mod : public Power_Mod + { + public: + BigInt operator()(const BigInt& b) const + { set_base(b); return execute(); } + + Fixed_Exponent_Power_Mod() {} + Fixed_Exponent_Power_Mod(const BigInt&, const BigInt&, + Usage_Hints = NO_HINTS); + }; + +/* +* Fixed Base Modular Exponentiator Proxy +*/ +class BOTAN_DLL Fixed_Base_Power_Mod : public Power_Mod + { + public: + BigInt operator()(const BigInt& e) const + { set_exponent(e); return execute(); } + + Fixed_Base_Power_Mod() {} + Fixed_Base_Power_Mod(const BigInt&, const BigInt&, + Usage_Hints = NO_HINTS); + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/powm_fw.cpp b/old/botan/src/math/numbertheory/powm_fw.cpp new file mode 100644 index 0000000..b764ee7 --- /dev/null +++ b/old/botan/src/math/numbertheory/powm_fw.cpp @@ -0,0 +1,104 @@ +/* +* Fixed Window Exponentiation +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/def_powm.h> +#include <botan/numthry.h> +#include <vector> + +namespace Botan { + +namespace { + +/* +* Try to choose a good window size +*/ +u32bit choose_window_bits(u32bit exp_bits, u32bit, + Power_Mod::Usage_Hints hints) + { + static const u32bit wsize[][2] = { + { 2048, 7 }, { 1024, 6 }, { 256, 5 }, { 128, 4 }, { 64, 3 }, { 0, 0 } + }; + + u32bit window_bits = 3; + + if(exp_bits) + { + for(u32bit j = 0; wsize[j][0]; ++j) + { + if(exp_bits >= wsize[j][0]) + { + window_bits += wsize[j][1]; + break; + } + } + } + + if(hints & Power_Mod::EXP_IS_FIXED) + window_bits += 2; + if(hints & Power_Mod::EXP_IS_LARGE) + window_bits += 2; + if(hints & Power_Mod::BASE_IS_FIXED) + ++window_bits; + + return window_bits; + } + +} + +/* +* Set the exponent +*/ +void Fixed_Window_Exponentiator::set_exponent(const BigInt& e) + { + exp = e; + } + +/* +* Set the base +*/ +void Fixed_Window_Exponentiator::set_base(const BigInt& base) + { + window_bits = choose_window_bits(exp.bits(), base.bits(), hints); + + g.resize((1 << window_bits) - 1); + g[0] = base; + for(u32bit j = 1; j != g.size(); ++j) + g[j] = reducer.multiply(g[j-1], g[0]); + } + +/* +* Compute the result +*/ +BigInt Fixed_Window_Exponentiator::execute() const + { + const u32bit exp_nibbles = (exp.bits() + window_bits - 1) / window_bits; + + BigInt x = 1; + for(u32bit j = exp_nibbles; j > 0; --j) + { + for(u32bit k = 0; k != window_bits; ++k) + x = reducer.square(x); + + u32bit nibble = exp.get_substring(window_bits*(j-1), window_bits); + if(nibble) + x = reducer.multiply(x, g[nibble-1]); + } + return x; + } + +/* +* Fixed_Window_Exponentiator Constructor +*/ +Fixed_Window_Exponentiator::Fixed_Window_Exponentiator(const BigInt& n, + Power_Mod::Usage_Hints hints) + { + reducer = Modular_Reducer(n); + this->hints = hints; + window_bits = 0; + } + +} diff --git a/old/botan/src/math/numbertheory/powm_mnt.cpp b/old/botan/src/math/numbertheory/powm_mnt.cpp new file mode 100644 index 0000000..e6d8cc3 --- /dev/null +++ b/old/botan/src/math/numbertheory/powm_mnt.cpp @@ -0,0 +1,180 @@ +/* +* Montgomery Exponentiation +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/def_powm.h> +#include <botan/numthry.h> +#include <botan/mp_core.h> + +namespace Botan { + +namespace { + +/* +* Try to choose a good window size +*/ +u32bit choose_window_bits(u32bit exp_bits, u32bit, + Power_Mod::Usage_Hints hints) + { + static const u32bit wsize[][2] = { + { 2048, 4 }, { 1024, 3 }, { 256, 2 }, { 128, 1 }, { 0, 0 } + }; + + u32bit window_bits = 1; + + if(exp_bits) + { + for(u32bit 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; + } + +/* +* Montgomery Reduction +*/ +inline void montgomery_reduce(BigInt& out, MemoryRegion<word>& z_buf, + const BigInt& x_bn, u32bit x_size, word u) + { + const word* x = x_bn.data(); + word* z = z_buf.begin(); + u32bit z_size = z_buf.size(); + + bigint_monty_redc(z, z_size, x, x_size, u); + + out.get_reg().set(z + x_size, x_size + 1); + } + +} + +/* +* Set the exponent +*/ +void Montgomery_Exponentiator::set_exponent(const BigInt& exp) + { + this->exp = exp; + exp_bits = exp.bits(); + } + +/* +* Set the base +*/ +void Montgomery_Exponentiator::set_base(const BigInt& base) + { + window_bits = choose_window_bits(exp.bits(), base.bits(), hints); + + g.resize((1 << window_bits) - 1); + + SecureVector<word> z(2 * (mod_words + 1)); + SecureVector<word> workspace(z.size()); + + g[0] = (base >= modulus) ? (base % modulus) : base; + bigint_mul(z.begin(), z.size(), workspace, + g[0].data(), g[0].size(), g[0].sig_words(), + R2.data(), R2.size(), R2.sig_words()); + + montgomery_reduce(g[0], z, modulus, mod_words, mod_prime); + + const BigInt& x = g[0]; + const u32bit x_sig = x.sig_words(); + + for(u32bit j = 1; j != g.size(); ++j) + { + const BigInt& y = g[j-1]; + const u32bit y_sig = y.sig_words(); + + z.clear(); + bigint_mul(z.begin(), z.size(), workspace, + x.data(), x.size(), x_sig, + y.data(), y.size(), y_sig); + + montgomery_reduce(g[j], z, modulus, mod_words, mod_prime); + } + } + +/* +* Compute the result +*/ +BigInt Montgomery_Exponentiator::execute() const + { + const u32bit exp_nibbles = (exp_bits + window_bits - 1) / window_bits; + + BigInt x = R_mod; + SecureVector<word> z(2 * (mod_words + 1)); + SecureVector<word> workspace(2 * (mod_words + 1)); + + for(u32bit j = exp_nibbles; j > 0; --j) + { + for(u32bit k = 0; k != window_bits; ++k) + { + z.clear(); + bigint_sqr(z.begin(), z.size(), workspace, + x.data(), x.size(), x.sig_words()); + + montgomery_reduce(x, z, modulus, mod_words, mod_prime); + } + + u32bit nibble = exp.get_substring(window_bits*(j-1), window_bits); + if(nibble) + { + const BigInt& y = g[nibble-1]; + + z.clear(); + bigint_mul(z.begin(), z.size(), workspace, + x.data(), x.size(), x.sig_words(), + y.data(), y.size(), y.sig_words()); + + montgomery_reduce(x, z, modulus, mod_words, mod_prime); + } + } + + z.clear(); + z.copy(x.data(), x.size()); + + montgomery_reduce(x, z, modulus, mod_words, mod_prime); + return x; + } + +/* +* Montgomery_Exponentiator Constructor +*/ +Montgomery_Exponentiator::Montgomery_Exponentiator(const BigInt& mod, + Power_Mod::Usage_Hints hints) + { + if(!mod.is_positive()) + throw Exception("Montgomery_Exponentiator: modulus must be positive"); + if(mod.is_even()) + throw Exception("Montgomery_Exponentiator: modulus must be odd"); + + window_bits = 0; + this->hints = hints; + modulus = mod; + + mod_words = modulus.sig_words(); + + BigInt mod_prime_bn(BigInt::Power2, MP_WORD_BITS); + mod_prime = (mod_prime_bn - inverse_mod(modulus, mod_prime_bn)).word_at(0); + + R_mod = BigInt(BigInt::Power2, MP_WORD_BITS * mod_words); + R_mod %= modulus; + + R2 = BigInt(BigInt::Power2, 2 * MP_WORD_BITS * mod_words); + R2 %= modulus; + } + +} diff --git a/old/botan/src/math/numbertheory/primes.cpp b/old/botan/src/math/numbertheory/primes.cpp new file mode 100644 index 0000000..a9c8ab5 --- /dev/null +++ b/old/botan/src/math/numbertheory/primes.cpp @@ -0,0 +1,676 @@ +/* +* Small Primes Table +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> + +namespace Botan { + +const u16bit 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, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, + 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, + 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, + 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, + 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, + 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, + 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, + 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, + 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, + 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, + 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, + 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, + 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, + 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, + 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, + 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, + 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, + 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, + 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, + 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, + 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, + 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, + 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, + 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, + 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, + 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, + 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, + 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, + 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, + 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, + 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, + 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, + 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, + 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, + 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, + 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, + 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, + 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, + 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, + 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, + 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, + 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, + 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, + 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, + 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, + 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, + 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, + 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, + 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, + 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, + 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, + 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, + 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, + 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, + 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, + 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, + 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, + 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, + 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, + 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, + 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, + 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, + 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, + 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, + 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, + 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, + 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, + 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, + 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, + 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, + 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, + 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, + 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, + 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, + 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, + 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, + 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, + 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, +10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, +10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, +10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, +10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, +10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, +10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, +10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, +10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, +10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, +10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, +11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, +11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, +11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, +11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, +11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, +11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, +11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, +11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, +11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, +12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, +12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, +12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, +12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, +12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, +12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, +12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, +12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, +12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, +12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, +13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, +13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, +13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, +13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, +13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, +13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, +13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, +13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, +13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997, +13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, +14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, +14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, +14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, +14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, +14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, +14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, +14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, +14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, +14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, +15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, +15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, +15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, +15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, +15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, +15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, +15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, +15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, +15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, +15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, +16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, +16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, +16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, +16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, +16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, +16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, +16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, +16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, +16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, +17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, +17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, +17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, 17417, +17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, +17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, +17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, +17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, +17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, +17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, +18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, +18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, +18253, 18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313, 18329, 18341, +18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, +18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, +18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, +18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, +18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, +18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, +19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, +19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, +19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, +19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489, +19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, +19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, +19751, 19753, 19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, +19853, 19861, 19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, +19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, +20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, +20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, +20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, +20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 20477, +20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593, +20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, +20731, 20743, 20747, 20749, 20753, 20759, 20771, 20773, 20789, 20807, 20809, +20849, 20857, 20873, 20879, 20887, 20897, 20899, 20903, 20921, 20929, 20939, +20947, 20959, 20963, 20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, +21031, 21059, 21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, +21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247, +21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341, 21347, 21377, 21379, +21383, 21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, +21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 21569, +21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 21649, 21661, +21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 21757, 21767, 21773, +21787, 21799, 21803, 21817, 21821, 21839, 21841, 21851, 21859, 21863, 21871, +21881, 21893, 21911, 21929, 21937, 21943, 21961, 21977, 21991, 21997, 22003, +22013, 22027, 22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, +22093, 22109, 22111, 22123, 22129, 22133, 22147, 22153, 22157, 22159, 22171, +22189, 22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, +22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, +22441, 22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, +22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 22643, 22651, +22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 22739, 22741, +22751, 22769, 22777, 22783, 22787, 22807, 22811, 22817, 22853, 22859, 22861, +22871, 22877, 22901, 22907, 22921, 22937, 22943, 22961, 22963, 22973, 22993, +23003, 23011, 23017, 23021, 23027, 23029, 23039, 23041, 23053, 23057, 23059, +23063, 23071, 23081, 23087, 23099, 23117, 23131, 23143, 23159, 23167, 23173, +23189, 23197, 23201, 23203, 23209, 23227, 23251, 23269, 23279, 23291, 23293, +23297, 23311, 23321, 23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417, +23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557, +23561, 23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623, 23627, 23629, +23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743, 23747, +23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 23827, 23831, 23833, +23857, 23869, 23873, 23879, 23887, 23893, 23899, 23909, 23911, 23917, 23929, +23957, 23971, 23977, 23981, 23993, 24001, 24007, 24019, 24023, 24029, 24043, +24049, 24061, 24071, 24077, 24083, 24091, 24097, 24103, 24107, 24109, 24113, +24121, 24133, 24137, 24151, 24169, 24179, 24181, 24197, 24203, 24223, 24229, +24239, 24247, 24251, 24281, 24317, 24329, 24337, 24359, 24371, 24373, 24379, +24391, 24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499, +24509, 24517, 24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, +24659, 24671, 24677, 24683, 24691, 24697, 24709, 24733, 24749, 24763, 24767, +24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851, 24859, 24877, 24889, +24907, 24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977, 24979, 24989, +25013, 25031, 25033, 25037, 25057, 25073, 25087, 25097, 25111, 25117, 25121, +25127, 25147, 25153, 25163, 25169, 25171, 25183, 25189, 25219, 25229, 25237, +25243, 25247, 25253, 25261, 25301, 25303, 25307, 25309, 25321, 25339, 25343, +25349, 25357, 25367, 25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, +25457, 25463, 25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583, +25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, +25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771, 25793, +25799, 25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889, 25903, 25913, +25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999, 26003, +26017, 26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 26113, 26119, +26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203, 26209, 26227, 26237, +26249, 26251, 26261, 26263, 26267, 26293, 26297, 26309, 26317, 26321, 26339, +26347, 26357, 26371, 26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, +26449, 26459, 26479, 26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573, +26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693, +26699, 26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, +26783, 26801, 26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879, 26881, +26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, +26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077, 27091, +27103, 27107, 27109, 27127, 27143, 27179, 27191, 27197, 27211, 27239, 27241, +27253, 27259, 27271, 27277, 27281, 27283, 27299, 27329, 27337, 27361, 27367, +27397, 27407, 27409, 27427, 27431, 27437, 27449, 27457, 27479, 27481, 27487, +27509, 27527, 27529, 27539, 27541, 27551, 27581, 27583, 27611, 27617, 27631, +27647, 27653, 27673, 27689, 27691, 27697, 27701, 27733, 27737, 27739, 27743, +27749, 27751, 27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803, 27809, +27817, 27823, 27827, 27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941, +27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001, 28019, 28027, 28031, +28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, +28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 28289, +28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 28403, 28409, 28411, +28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 28513, 28517, 28537, +28541, 28547, 28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 28607, +28619, 28621, 28627, 28631, 28643, 28649, 28657, 28661, 28663, 28669, 28687, +28697, 28703, 28711, 28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793, +28807, 28813, 28817, 28837, 28843, 28859, 28867, 28871, 28879, 28901, 28909, +28921, 28927, 28933, 28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027, +29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, +29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, +29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339, 29347, 29363, 29383, +29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443, 29453, 29473, +29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587, 29599, +29611, 29629, 29633, 29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741, +29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837, 29851, 29863, 29867, +29873, 29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, +30013, 30029, 30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, +30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, +30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, +30341, 30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469, +30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559, 30577, +30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703, +30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809, 30817, 30829, +30839, 30841, 30851, 30853, 30859, 30869, 30871, 30881, 30893, 30911, 30931, +30937, 30941, 30949, 30971, 30977, 30983, 31013, 31019, 31033, 31039, 31051, +31063, 31069, 31079, 31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, +31159, 31177, 31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237, 31247, +31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333, +31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, +31511, 31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, +31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687, 31699, 31721, 31723, +31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817, 31847, 31849, +31859, 31873, 31883, 31891, 31907, 31957, 31963, 31973, 31981, 31991, 32003, +32009, 32027, 32029, 32051, 32057, 32059, 32063, 32069, 32077, 32083, 32089, +32099, 32117, 32119, 32141, 32143, 32159, 32173, 32183, 32189, 32191, 32203, +32213, 32233, 32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309, 32321, +32323, 32327, 32341, 32353, 32359, 32363, 32369, 32371, 32377, 32381, 32401, +32411, 32413, 32423, 32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503, +32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587, 32603, +32609, 32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707, 32713, 32717, +32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831, 32833, +32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 32939, 32941, 32957, +32969, 32971, 32983, 32987, 32993, 32999, 33013, 33023, 33029, 33037, 33049, +33053, 33071, 33073, 33083, 33091, 33107, 33113, 33119, 33149, 33151, 33161, +33179, 33181, 33191, 33199, 33203, 33211, 33223, 33247, 33287, 33289, 33301, +33311, 33317, 33329, 33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391, +33403, 33409, 33413, 33427, 33457, 33461, 33469, 33479, 33487, 33493, 33503, +33521, 33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599, +33601, 33613, 33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, +33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773, 33791, 33797, +33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871, 33889, 33893, 33911, +33923, 33931, 33937, 33941, 33961, 33967, 33997, 34019, 34031, 34033, 34039, +34057, 34061, 34123, 34127, 34129, 34141, 34147, 34157, 34159, 34171, 34183, +34211, 34213, 34217, 34231, 34253, 34259, 34261, 34267, 34273, 34283, 34297, +34301, 34303, 34313, 34319, 34327, 34337, 34351, 34361, 34367, 34369, 34381, +34403, 34421, 34429, 34439, 34457, 34469, 34471, 34483, 34487, 34499, 34501, +34511, 34513, 34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603, 34607, +34613, 34631, 34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721, +34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807, 34819, 34841, 34843, +34847, 34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939, 34949, 34961, +34963, 34981, 35023, 35027, 35051, 35053, 35059, 35069, 35081, 35083, 35089, +35099, 35107, 35111, 35117, 35129, 35141, 35149, 35153, 35159, 35171, 35201, +35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291, 35311, 35317, 35323, +35327, 35339, 35353, 35363, 35381, 35393, 35401, 35407, 35419, 35423, 35437, +35447, 35449, 35461, 35491, 35507, 35509, 35521, 35527, 35531, 35533, 35537, +35543, 35569, 35573, 35591, 35593, 35597, 35603, 35617, 35671, 35677, 35729, +35731, 35747, 35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837, +35839, 35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951, +35963, 35969, 35977, 35983, 35993, 35999, 36007, 36011, 36013, 36017, 36037, +36061, 36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161, +36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 36277, 36293, +36299, 36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 36389, 36433, +36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497, 36523, 36527, 36529, +36541, 36551, 36559, 36563, 36571, 36583, 36587, 36599, 36607, 36629, 36637, +36643, 36653, 36671, 36677, 36683, 36691, 36697, 36709, 36713, 36721, 36739, +36749, 36761, 36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833, +36847, 36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923, 36929, +36931, 36943, 36947, 36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039, +37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171, 37181, +37189, 37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, +37313, 37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397, 37409, +37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501, 37507, 37511, 37517, +37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573, 37579, 37589, 37591, +37607, 37619, 37633, 37643, 37649, 37657, 37663, 37691, 37693, 37699, 37717, +37747, 37781, 37783, 37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871, +37879, 37889, 37897, 37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993, +37997, 38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153, +38167, 38177, 38183, 38189, 38197, 38201, 38219, 38231, 38237, 38239, 38261, +38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, +38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543, +38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611, 38629, 38639, 38651, +38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713, 38723, 38729, +38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 38833, 38839, 38851, +38861, 38867, 38873, 38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959, +38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047, 39079, 39089, 39097, +39103, 39107, 39113, 39119, 39133, 39139, 39157, 39161, 39163, 39181, 39191, +39199, 39209, 39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, +39313, 39317, 39323, 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, +39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, +39541, 39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, +39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769, 39779, +39791, 39799, 39821, 39827, 39829, 39839, 39841, 39847, 39857, 39863, 39869, +39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 39979, 39983, 39989, +40009, 40013, 40031, 40037, 40039, 40063, 40087, 40093, 40099, 40111, 40123, +40127, 40129, 40151, 40153, 40163, 40169, 40177, 40189, 40193, 40213, 40231, +40237, 40241, 40253, 40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387, +40423, 40427, 40429, 40433, 40459, 40471, 40483, 40487, 40493, 40499, 40507, +40519, 40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627, +40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, +40787, 40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, +40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 40973, 40993, +41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 41113, 41117, +41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 41189, 41201, 41203, +41213, 41221, 41227, 41231, 41233, 41243, 41257, 41263, 41269, 41281, 41299, +41333, 41341, 41351, 41357, 41381, 41387, 41389, 41399, 41411, 41413, 41443, +41453, 41467, 41479, 41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, +41579, 41593, 41597, 41603, 41609, 41611, 41617, 41621, 41627, 41641, 41647, +41651, 41659, 41669, 41681, 41687, 41719, 41729, 41737, 41759, 41761, 41771, +41777, 41801, 41809, 41813, 41843, 41849, 41851, 41863, 41879, 41887, 41893, +41897, 41903, 41911, 41927, 41941, 41947, 41953, 41957, 41959, 41969, 41981, +41983, 41999, 42013, 42017, 42019, 42023, 42043, 42061, 42071, 42073, 42083, +42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 42187, 42193, 42197, +42209, 42221, 42223, 42227, 42239, 42257, 42281, 42283, 42293, 42299, 42307, +42323, 42331, 42337, 42349, 42359, 42373, 42379, 42391, 42397, 42403, 42407, +42409, 42433, 42437, 42443, 42451, 42457, 42461, 42463, 42467, 42473, 42487, +42491, 42499, 42509, 42533, 42557, 42569, 42571, 42577, 42589, 42611, 42641, +42643, 42649, 42667, 42677, 42683, 42689, 42697, 42701, 42703, 42709, 42719, +42727, 42737, 42743, 42751, 42767, 42773, 42787, 42793, 42797, 42821, 42829, +42839, 42841, 42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, +42953, 42961, 42967, 42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051, +43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177, 43189, 43201, +43207, 43223, 43237, 43261, 43271, 43283, 43291, 43313, 43319, 43321, 43331, +43391, 43397, 43399, 43403, 43411, 43427, 43441, 43451, 43457, 43481, 43487, +43499, 43517, 43541, 43543, 43573, 43577, 43579, 43591, 43597, 43607, 43609, +43613, 43627, 43633, 43649, 43651, 43661, 43669, 43691, 43711, 43717, 43721, +43753, 43759, 43777, 43781, 43783, 43787, 43789, 43793, 43801, 43853, 43867, +43889, 43891, 43913, 43933, 43943, 43951, 43961, 43963, 43969, 43973, 43987, +43991, 43997, 44017, 44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087, +44089, 44101, 44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179, 44189, +44201, 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269, 44273, 44279, +44281, 44293, 44351, 44357, 44371, 44381, 44383, 44389, 44417, 44449, 44453, +44483, 44491, 44497, 44501, 44507, 44519, 44531, 44533, 44537, 44543, 44549, +44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641, 44647, 44651, 44657, +44683, 44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771, 44773, 44777, +44789, 44797, 44809, 44819, 44839, 44843, 44851, 44867, 44879, 44887, 44893, +44909, 44917, 44927, 44939, 44953, 44959, 44963, 44971, 44983, 44987, 45007, +45013, 45053, 45061, 45077, 45083, 45119, 45121, 45127, 45131, 45137, 45139, +45161, 45179, 45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, +45293, 45307, 45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377, 45389, +45403, 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533, +45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 45659, +45667, 45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757, 45763, 45767, +45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 45863, 45869, 45887, +45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989, 46021, 46027, 46049, +46051, 46061, 46073, 46091, 46093, 46099, 46103, 46133, 46141, 46147, 46153, +46171, 46181, 46183, 46187, 46199, 46219, 46229, 46237, 46261, 46271, 46273, +46279, 46301, 46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411, +46439, 46441, 46447, 46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511, +46523, 46549, 46559, 46567, 46573, 46589, 46591, 46601, 46619, 46633, 46639, +46643, 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723, 46727, 46747, +46751, 46757, 46769, 46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, +46861, 46867, 46877, 46889, 46901, 46919, 46933, 46957, 46993, 46997, 47017, +47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119, 47123, 47129, 47137, +47143, 47147, 47149, 47161, 47189, 47207, 47221, 47237, 47251, 47269, 47279, +47287, 47293, 47297, 47303, 47309, 47317, 47339, 47351, 47353, 47363, 47381, +47387, 47389, 47407, 47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501, +47507, 47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581, 47591, 47599, +47609, 47623, 47629, 47639, 47653, 47657, 47659, 47681, 47699, 47701, 47711, +47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, +47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, +47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023, 48029, 48049, 48073, +48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179, 48187, 48193, +48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, +48341, 48353, 48371, 48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, +48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541, +48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, +48677, 48679, 48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, +48799, 48809, 48817, 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883, +48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, +49033, 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, +49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211, 49223, +49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 49363, 49367, +49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 49459, 49463, +49477, 49481, 49499, 49523, 49529, 49531, 49537, 49547, 49549, 49559, 49597, +49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681, 49697, 49711, +49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, +49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919, 49921, 49927, 49937, +49939, 49943, 49957, 49991, 49993, 49999, 50021, 50023, 50033, 50047, 50051, +50053, 50069, 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129, 50131, +50147, 50153, 50159, 50177, 50207, 50221, 50227, 50231, 50261, 50263, 50273, +50287, 50291, 50311, 50321, 50329, 50333, 50341, 50359, 50363, 50377, 50383, +50387, 50411, 50417, 50423, 50441, 50459, 50461, 50497, 50503, 50513, 50527, +50539, 50543, 50549, 50551, 50581, 50587, 50591, 50593, 50599, 50627, 50647, +50651, 50671, 50683, 50707, 50723, 50741, 50753, 50767, 50773, 50777, 50789, +50821, 50833, 50839, 50849, 50857, 50867, 50873, 50891, 50893, 50909, 50923, +50929, 50951, 50957, 50969, 50971, 50989, 50993, 51001, 51031, 51043, 51047, +51059, 51061, 51071, 51109, 51131, 51133, 51137, 51151, 51157, 51169, 51193, +51197, 51199, 51203, 51217, 51229, 51239, 51241, 51257, 51263, 51283, 51287, +51307, 51329, 51341, 51343, 51347, 51349, 51361, 51383, 51407, 51413, 51419, +51421, 51427, 51431, 51437, 51439, 51449, 51461, 51473, 51479, 51481, 51487, +51503, 51511, 51517, 51521, 51539, 51551, 51563, 51577, 51581, 51593, 51599, +51607, 51613, 51631, 51637, 51647, 51659, 51673, 51679, 51683, 51691, 51713, +51719, 51721, 51749, 51767, 51769, 51787, 51797, 51803, 51817, 51827, 51829, +51839, 51853, 51859, 51869, 51871, 51893, 51899, 51907, 51913, 51929, 51941, +51949, 51971, 51973, 51977, 51991, 52009, 52021, 52027, 52051, 52057, 52067, +52069, 52081, 52103, 52121, 52127, 52147, 52153, 52163, 52177, 52181, 52183, +52189, 52201, 52223, 52237, 52249, 52253, 52259, 52267, 52289, 52291, 52301, +52313, 52321, 52361, 52363, 52369, 52379, 52387, 52391, 52433, 52453, 52457, +52489, 52501, 52511, 52517, 52529, 52541, 52543, 52553, 52561, 52567, 52571, +52579, 52583, 52609, 52627, 52631, 52639, 52667, 52673, 52691, 52697, 52709, +52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783, 52807, 52813, 52817, +52837, 52859, 52861, 52879, 52883, 52889, 52901, 52903, 52919, 52937, 52951, +52957, 52963, 52967, 52973, 52981, 52999, 53003, 53017, 53047, 53051, 53069, +53077, 53087, 53089, 53093, 53101, 53113, 53117, 53129, 53147, 53149, 53161, +53171, 53173, 53189, 53197, 53201, 53231, 53233, 53239, 53267, 53269, 53279, +53281, 53299, 53309, 53323, 53327, 53353, 53359, 53377, 53381, 53401, 53407, +53411, 53419, 53437, 53441, 53453, 53479, 53503, 53507, 53527, 53549, 53551, +53569, 53591, 53593, 53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639, +53653, 53657, 53681, 53693, 53699, 53717, 53719, 53731, 53759, 53773, 53777, +53783, 53791, 53813, 53819, 53831, 53849, 53857, 53861, 53881, 53887, 53891, +53897, 53899, 53917, 53923, 53927, 53939, 53951, 53959, 53987, 53993, 54001, +54011, 54013, 54037, 54049, 54059, 54083, 54091, 54101, 54121, 54133, 54139, +54151, 54163, 54167, 54181, 54193, 54217, 54251, 54269, 54277, 54287, 54293, +54311, 54319, 54323, 54331, 54347, 54361, 54367, 54371, 54377, 54401, 54403, +54409, 54413, 54419, 54421, 54437, 54443, 54449, 54469, 54493, 54497, 54499, +54503, 54517, 54521, 54539, 54541, 54547, 54559, 54563, 54577, 54581, 54583, +54601, 54617, 54623, 54629, 54631, 54647, 54667, 54673, 54679, 54709, 54713, +54721, 54727, 54751, 54767, 54773, 54779, 54787, 54799, 54829, 54833, 54851, +54869, 54877, 54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973, 54979, +54983, 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073, 55079, 55103, +55109, 55117, 55127, 55147, 55163, 55171, 55201, 55207, 55213, 55217, 55219, +55229, 55243, 55249, 55259, 55291, 55313, 55331, 55333, 55337, 55339, 55343, +55351, 55373, 55381, 55399, 55411, 55439, 55441, 55457, 55469, 55487, 55501, +55511, 55529, 55541, 55547, 55579, 55589, 55603, 55609, 55619, 55621, 55631, +55633, 55639, 55661, 55663, 55667, 55673, 55681, 55691, 55697, 55711, 55717, +55721, 55733, 55763, 55787, 55793, 55799, 55807, 55813, 55817, 55819, 55823, +55829, 55837, 55843, 55849, 55871, 55889, 55897, 55901, 55903, 55921, 55927, +55931, 55933, 55949, 55967, 55987, 55997, 56003, 56009, 56039, 56041, 56053, +56081, 56087, 56093, 56099, 56101, 56113, 56123, 56131, 56149, 56167, 56171, +56179, 56197, 56207, 56209, 56237, 56239, 56249, 56263, 56267, 56269, 56299, +56311, 56333, 56359, 56369, 56377, 56383, 56393, 56401, 56417, 56431, 56437, +56443, 56453, 56467, 56473, 56477, 56479, 56489, 56501, 56503, 56509, 56519, +56527, 56531, 56533, 56543, 56569, 56591, 56597, 56599, 56611, 56629, 56633, +56659, 56663, 56671, 56681, 56687, 56701, 56711, 56713, 56731, 56737, 56747, +56767, 56773, 56779, 56783, 56807, 56809, 56813, 56821, 56827, 56843, 56857, +56873, 56891, 56893, 56897, 56909, 56911, 56921, 56923, 56929, 56941, 56951, +56957, 56963, 56983, 56989, 56993, 56999, 57037, 57041, 57047, 57059, 57073, +57077, 57089, 57097, 57107, 57119, 57131, 57139, 57143, 57149, 57163, 57173, +57179, 57191, 57193, 57203, 57221, 57223, 57241, 57251, 57259, 57269, 57271, +57283, 57287, 57301, 57329, 57331, 57347, 57349, 57367, 57373, 57383, 57389, +57397, 57413, 57427, 57457, 57467, 57487, 57493, 57503, 57527, 57529, 57557, +57559, 57571, 57587, 57593, 57601, 57637, 57641, 57649, 57653, 57667, 57679, +57689, 57697, 57709, 57713, 57719, 57727, 57731, 57737, 57751, 57773, 57781, +57787, 57791, 57793, 57803, 57809, 57829, 57839, 57847, 57853, 57859, 57881, +57899, 57901, 57917, 57923, 57943, 57947, 57973, 57977, 57991, 58013, 58027, +58031, 58043, 58049, 58057, 58061, 58067, 58073, 58099, 58109, 58111, 58129, +58147, 58151, 58153, 58169, 58171, 58189, 58193, 58199, 58207, 58211, 58217, +58229, 58231, 58237, 58243, 58271, 58309, 58313, 58321, 58337, 58363, 58367, +58369, 58379, 58391, 58393, 58403, 58411, 58417, 58427, 58439, 58441, 58451, +58453, 58477, 58481, 58511, 58537, 58543, 58549, 58567, 58573, 58579, 58601, +58603, 58613, 58631, 58657, 58661, 58679, 58687, 58693, 58699, 58711, 58727, +58733, 58741, 58757, 58763, 58771, 58787, 58789, 58831, 58889, 58897, 58901, +58907, 58909, 58913, 58921, 58937, 58943, 58963, 58967, 58979, 58991, 58997, +59009, 59011, 59021, 59023, 59029, 59051, 59053, 59063, 59069, 59077, 59083, +59093, 59107, 59113, 59119, 59123, 59141, 59149, 59159, 59167, 59183, 59197, +59207, 59209, 59219, 59221, 59233, 59239, 59243, 59263, 59273, 59281, 59333, +59341, 59351, 59357, 59359, 59369, 59377, 59387, 59393, 59399, 59407, 59417, +59419, 59441, 59443, 59447, 59453, 59467, 59471, 59473, 59497, 59509, 59513, +59539, 59557, 59561, 59567, 59581, 59611, 59617, 59621, 59627, 59629, 59651, +59659, 59663, 59669, 59671, 59693, 59699, 59707, 59723, 59729, 59743, 59747, +59753, 59771, 59779, 59791, 59797, 59809, 59833, 59863, 59879, 59887, 59921, +59929, 59951, 59957, 59971, 59981, 59999, 60013, 60017, 60029, 60037, 60041, +60077, 60083, 60089, 60091, 60101, 60103, 60107, 60127, 60133, 60139, 60149, +60161, 60167, 60169, 60209, 60217, 60223, 60251, 60257, 60259, 60271, 60289, +60293, 60317, 60331, 60337, 60343, 60353, 60373, 60383, 60397, 60413, 60427, +60443, 60449, 60457, 60493, 60497, 60509, 60521, 60527, 60539, 60589, 60601, +60607, 60611, 60617, 60623, 60631, 60637, 60647, 60649, 60659, 60661, 60679, +60689, 60703, 60719, 60727, 60733, 60737, 60757, 60761, 60763, 60773, 60779, +60793, 60811, 60821, 60859, 60869, 60887, 60889, 60899, 60901, 60913, 60917, +60919, 60923, 60937, 60943, 60953, 60961, 61001, 61007, 61027, 61031, 61043, +61051, 61057, 61091, 61099, 61121, 61129, 61141, 61151, 61153, 61169, 61211, +61223, 61231, 61253, 61261, 61283, 61291, 61297, 61331, 61333, 61339, 61343, +61357, 61363, 61379, 61381, 61403, 61409, 61417, 61441, 61463, 61469, 61471, +61483, 61487, 61493, 61507, 61511, 61519, 61543, 61547, 61553, 61559, 61561, +61583, 61603, 61609, 61613, 61627, 61631, 61637, 61643, 61651, 61657, 61667, +61673, 61681, 61687, 61703, 61717, 61723, 61729, 61751, 61757, 61781, 61813, +61819, 61837, 61843, 61861, 61871, 61879, 61909, 61927, 61933, 61949, 61961, +61967, 61979, 61981, 61987, 61991, 62003, 62011, 62017, 62039, 62047, 62053, +62057, 62071, 62081, 62099, 62119, 62129, 62131, 62137, 62141, 62143, 62171, +62189, 62191, 62201, 62207, 62213, 62219, 62233, 62273, 62297, 62299, 62303, +62311, 62323, 62327, 62347, 62351, 62383, 62401, 62417, 62423, 62459, 62467, +62473, 62477, 62483, 62497, 62501, 62507, 62533, 62539, 62549, 62563, 62581, +62591, 62597, 62603, 62617, 62627, 62633, 62639, 62653, 62659, 62683, 62687, +62701, 62723, 62731, 62743, 62753, 62761, 62773, 62791, 62801, 62819, 62827, +62851, 62861, 62869, 62873, 62897, 62903, 62921, 62927, 62929, 62939, 62969, +62971, 62981, 62983, 62987, 62989, 63029, 63031, 63059, 63067, 63073, 63079, +63097, 63103, 63113, 63127, 63131, 63149, 63179, 63197, 63199, 63211, 63241, +63247, 63277, 63281, 63299, 63311, 63313, 63317, 63331, 63337, 63347, 63353, +63361, 63367, 63377, 63389, 63391, 63397, 63409, 63419, 63421, 63439, 63443, +63463, 63467, 63473, 63487, 63493, 63499, 63521, 63527, 63533, 63541, 63559, +63577, 63587, 63589, 63599, 63601, 63607, 63611, 63617, 63629, 63647, 63649, +63659, 63667, 63671, 63689, 63691, 63697, 63703, 63709, 63719, 63727, 63737, +63743, 63761, 63773, 63781, 63793, 63799, 63803, 63809, 63823, 63839, 63841, +63853, 63857, 63863, 63901, 63907, 63913, 63929, 63949, 63977, 63997, 64007, +64013, 64019, 64033, 64037, 64063, 64067, 64081, 64091, 64109, 64123, 64151, +64153, 64157, 64171, 64187, 64189, 64217, 64223, 64231, 64237, 64271, 64279, +64283, 64301, 64303, 64319, 64327, 64333, 64373, 64381, 64399, 64403, 64433, +64439, 64451, 64453, 64483, 64489, 64499, 64513, 64553, 64567, 64577, 64579, +64591, 64601, 64609, 64613, 64621, 64627, 64633, 64661, 64663, 64667, 64679, +64693, 64709, 64717, 64747, 64763, 64781, 64783, 64793, 64811, 64817, 64849, +64853, 64871, 64877, 64879, 64891, 64901, 64919, 64921, 64927, 64937, 64951, +64969, 64997, 65003, 65011, 65027, 65029, 65033, 65053, 65063, 65071, 65089, +65099, 65101, 65111, 65119, 65123, 65129, 65141, 65147, 65167, 65171, 65173, +65179, 65183, 65203, 65213, 65239, 65257, 65267, 65269, 65287, 65293, 65309, +65323, 65327, 65353, 65357, 65371, 65381, 65393, 65407, 65413, 65419, 65423, +65437, 65447, 65449, 65479, 65497, 65519, 65521, 0 }; + +const u64bit PRIME_PRODUCTS[PRIME_PRODUCTS_TABLE_SIZE] = { +(u64bit) 0xFF658BDE2F2A43DFULL, (u64bit) 0xFEEB94CD535119EDULL, (u64bit) 0xFA921839EC24DDD5ULL, (u64bit) 0xFDDA766C77E1E605ULL, +(u64bit) 0xFF3024B0EB4EE333ULL, (u64bit) 0xFEEE350BBC92F4DFULL, (u64bit) 0xFFC724B7D011D01BULL, (u64bit) 0xFEED34B826C33B05ULL, +(u64bit) 0xFE69D8DE3F85C6E3ULL, (u64bit) 0xFE3B48909250918FULL, (u64bit) 0xFF8EC0CE9C632429ULL, (u64bit) 0xFFD92A5C78226D6BULL, +(u64bit) 0xFFB4BFB0C65133CFULL, (u64bit) 0xFE77113704902C57ULL, (u64bit) 0xFF8A21D222EA81FDULL, (u64bit) 0xFEDA1299661CF5ABULL, +(u64bit) 0xFF4CE86187737D0DULL, (u64bit) 0xFFD26443A07F519DULL, (u64bit) 0xFFA817B7191D7967ULL, (u64bit) 0xFF00EDC142868873ULL, +(u64bit) 0xFFB9C6D7F7A239B7ULL, (u64bit) 0xFFE76D3481E98E39ULL, (u64bit) 0xFF76D5432584120DULL, (u64bit) 0xFFAA499F071EC705ULL, +(u64bit) 0xFEB5198F05722E59ULL, (u64bit) 0xFF7E0431CA41107FULL, (u64bit) 0xFFCFD52FEDDC928FULL, (u64bit) 0xFE0EA42537BC6ABFULL, +(u64bit) 0xFF64937896876925ULL, (u64bit) 0xFC6FC87E811607D3ULL, (u64bit) 0xFFBF600E6CDD0F4FULL, (u64bit) 0xFF022700FE658243ULL, +(u64bit) 0xFF2E21166779D6B9ULL, (u64bit) 0xFFC224624C665C33ULL, (u64bit) 0xFF1372F41FF177ADULL, (u64bit) 0xFF31E57E972D0C13ULL, +(u64bit) 0xFFA891F866404D23ULL, (u64bit) 0xFF7BF13EF716E9A3ULL, (u64bit) 0xFE51CAFD9466E733ULL, (u64bit) 0xFDA1CF55F6D6336FULL, +(u64bit) 0xFFAF6C040ED0950FULL, (u64bit) 0xFFAA1725F40BA269ULL, (u64bit) 0xFEC593BC3570BEEBULL, (u64bit) 0xFEE05B35B426F413ULL, +(u64bit) 0xFFCA5209A08890F9ULL, (u64bit) 0xFFED8AF70EB0CC89ULL, (u64bit) 0xFF3F98E3E27860A5ULL, (u64bit) 0xFF92FECD017FF9F7ULL, +(u64bit) 0xFEFA655B2609018FULL, (u64bit) 0xFFFC51D15AAC7B77ULL, (u64bit) 0xFEF5007E71420DB1ULL, (u64bit) 0xFFEC4784141332D1ULL, +(u64bit) 0xFE8384ED4E1D21CDULL, (u64bit) 0xFFD3FF614D3ECC47ULL, (u64bit) 0xFFDE5166FD540313ULL, (u64bit) 0xFF5320ECED04B26FULL, +(u64bit) 0xFF223980F122FF75ULL, (u64bit) 0xFF19C1F27CB1B4A5ULL, (u64bit) 0xFF0F1DFC9DA9523BULL, (u64bit) 0xFF82DE7B387F5427ULL, +(u64bit) 0xFF9A026BA87314E3ULL, (u64bit) 0xFFAC7FF3ACE64E77ULL, (u64bit) 0xFF808EB2FD5873C3ULL, (u64bit) 0xFE983ED5BB363301ULL, +(u64bit) 0xFF714856DB2CFE95ULL, (u64bit) 0xFF84E1510CF3EB9FULL, (u64bit) 0xFF29D04C1DA0B115ULL, (u64bit) 0xFFBCF3BF9433552FULL, +(u64bit) 0xFF32203D58A4C473ULL, (u64bit) 0xFFF00910A15021C3ULL, (u64bit) 0xFDE93041F28240ADULL, (u64bit) 0xFFC518BCD81C03C5ULL, +(u64bit) 0xFEF504CD8BB9CBDDULL, (u64bit) 0xFEB8FFBFFF116A6BULL, (u64bit) 0xFF7642E0785ADA23ULL, (u64bit) 0xFFECF068800FD50DULL, +(u64bit) 0xFFD703577CA247A7ULL, (u64bit) 0xFF54C0ECAD2C9691ULL, (u64bit) 0xFFC031706B8C72F5ULL, (u64bit) 0xFFE59E5CA58BBDF5ULL, +(u64bit) 0xFFF31FAFFD3B331DULL, (u64bit) 0xFF64DDF32349FF6DULL, (u64bit) 0xFFE38309D0BD4A51ULL, (u64bit) 0xFF8C934F76B3C737ULL, +(u64bit) 0xFFDC80B4BAEAFC1FULL, (u64bit) 0xFFCC1FE4C856FBD9ULL, (u64bit) 0xFFDB5976DDF601FDULL, (u64bit) 0xFFD3DD25F424433DULL, +(u64bit) 0xFFC00FA367E746C7ULL, (u64bit) 0xFFE08BF011CC854FULL, (u64bit) 0xFFC3F21982468F6DULL, (u64bit) 0xFFDA6C52478A76DFULL, +(u64bit) 0xFFC67D95AADED363ULL, (u64bit) 0xFFD605D18C3AFC65ULL, (u64bit) 0xFFE828C9D698F1DFULL, (u64bit) 0xFFBE5098D83B7737ULL, +(u64bit) 0xFF79EB34474ABFB9ULL, (u64bit) 0xFFD27AEED0786363ULL, (u64bit) 0xFFD0FE27B77C271FULL, (u64bit) 0xFFFBB6563BD065EFULL, +(u64bit) 0xFFF3638F8635E1EBULL, (u64bit) 0xFFBE862C22C9F065ULL, (u64bit) 0xFF44712D8488A01DULL, (u64bit) 0xFF7EEC97F9913111ULL, +(u64bit) 0xFFC23CC78CB12AB1ULL, (u64bit) 0xFFF390FE85F81D3DULL, (u64bit) 0xFFE8EA21A0FB9931ULL, (u64bit) 0xFFB9D42D17A93385ULL, +(u64bit) 0xFFCDB63AB21E904DULL, (u64bit) 0xFF5EB7F2210D33DFULL, (u64bit) 0xFFE6F6C7BB60C9DFULL, (u64bit) 0xFFAD4CA8DC26D699ULL, +(u64bit) 0xFF7BE75BD21DCA51ULL, (u64bit) 0xFEF89CE23CB61789ULL, (u64bit) 0xFF40ECA3CCA22CE5ULL, (u64bit) 0xF52BDF080F7ABA6FULL, +(u64bit) 0xEC8F38C8B28E0493ULL, (u64bit) 0xE68E732A2ABED62FULL, (u64bit) 0xE21A13779E0CCDC7ULL, (u64bit) 0xD823C075C325191BULL, +(u64bit) 0xD1B284C91EED248BULL, (u64bit) 0xCBA5A08068E8C1F7ULL, (u64bit) 0xC483EE5A2228985DULL, (u64bit) 0xBCAEE9F787AC75EBULL, +(u64bit) 0xB782DAB1B77D3E09ULL, (u64bit) 0xB0D77226F15E387BULL, (u64bit) 0xAA2A8727D47941CDULL, (u64bit) 0xA4A45682E9CE533DULL, +(u64bit) 0x9CAF15AF4CE7FCF7ULL, (u64bit) 0x94C051DD15537305ULL, (u64bit) 0x9006D2FBD933A297ULL, (u64bit) 0x8C4DED05F19B7399ULL, +(u64bit) 0x884FD7A270AD1B1BULL, (u64bit) 0x83C687D33F238D4BULL, (u64bit) 0xFF62E2BAE50C6C16ULL, (u64bit) 0x7A59E1FD9D203DBBULL, +(u64bit) 0x764F1DC07B0E442DULL, (u64bit) 0x72732FE1F2023153ULL, (u64bit) 0x6E373B550764872FULL, (u64bit) 0x680FFFD267C5F3FFULL, +(u64bit) 0x6206BFEC14F1CFC5ULL, (u64bit) 0x5FA6F70CFD587265ULL, (u64bit) 0x5CC7A1B4F6DF9823ULL, (u64bit) 0x599291B29311407FULL, +(u64bit) 0xFF3CEBD359B67EF9ULL, (u64bit) 0x51C573C14F289F6DULL, (u64bit) 0x4FA265B31B73C6DFULL, (u64bit) 0x4B3154ACBD077DEDULL, +(u64bit) 0x4785C96B29A1E437ULL, (u64bit) 0x451F887F646CF763ULL, (u64bit) 0x429DC254C5490571ULL, (u64bit) 0x408410840EAE2883ULL, +(u64bit) 0x3E12CC83606624F3ULL, (u64bit) 0x3A70D774B821DA71ULL, (u64bit) 0x37A21449A196A825ULL, (u64bit) 0x34C5D056E2278B81ULL, +(u64bit) 0xFA0C6CAB29D8E297ULL, (u64bit) 0x2FA5AEC982A5972BULL, (u64bit) 0x2D6831749426068FULL, (u64bit) 0x2B7F876418155CA7ULL, +(u64bit) 0x2A1B897ED2AB433DULL, (u64bit) 0x28C9430D0F92132FULL, (u64bit) 0x26DF879EBF12E103ULL, (u64bit) 0xFD2FAB4CA364D43BULL, +(u64bit) 0x22B5B4FC40D4C35FULL, (u64bit) 0x209298AA84D7E6A1ULL, (u64bit) 0x1ED4B9F11445F1E7ULL, (u64bit) 0x1DC6D2DD416CC91DULL, +(u64bit) 0x1C1517A52E37C3EFULL, (u64bit) 0x1A808916125AEF2FULL, (u64bit) 0x197A2FB2938FF13DULL, (u64bit) 0x1814AA6C087B561DULL, +(u64bit) 0xFB3B173E72947609ULL, (u64bit) 0x1571187A8E3D4D6BULL, (u64bit) 0x13D306D29263C139ULL, (u64bit) 0xF8AEC6ADA137E865ULL, +(u64bit) 0x123EA204BAB48731ULL, (u64bit) 0x11012099D202F297ULL, (u64bit) 0x10290E15797C21BDULL, (u64bit) 0x0F3AB38E679D6317ULL, +(u64bit) 0xF50B5505D593FCF9ULL, (u64bit) 0xFF23754F7F2052B5ULL, (u64bit) 0x0CC52D96BC2E5A2DULL, (u64bit) 0x0BF80EAD87B228E5ULL, +(u64bit) 0x0B59A623082C9171ULL, (u64bit) 0xF44E28B9221A433BULL, (u64bit) 0x09DB5CDD2505EABDULL, (u64bit) 0x09638C123BCAB351ULL, +(u64bit) 0xFDB9AE6935254CD3ULL, (u64bit) 0xFFE30D7E4F02F163ULL, (u64bit) 0x07CF1FC053B9C61FULL, (u64bit) 0x0789244FF1705821ULL, +(u64bit) 0x06FBD05649B0B9C7ULL, (u64bit) 0xEF9713EC6A0C250BULL, (u64bit) 0xF47691AD6AA9F0DBULL, (u64bit) 0xF2A8EB02CB08CA51ULL, +(u64bit) 0xF9559D40380A20E1ULL, (u64bit) 0x04E15138A5B9BF43ULL, (u64bit) 0xEECD739EA48F3ABBULL, (u64bit) 0xF76E7E7530574E79ULL, +(u64bit) 0xF8393D2E42D7D277ULL, (u64bit) 0xF666F9AD3A16D173ULL, (u64bit) 0xF403C629749F3ED5ULL, (u64bit) 0xFBD7EC45F220A473ULL, +(u64bit) 0xFA8AFF7491B234FDULL, (u64bit) 0xFF471CE534D1F537ULL, (u64bit) 0xF4BEBFDD9C54CEC9ULL, (u64bit) 0xDD04722310A6CE9DULL, +(u64bit) 0xFD8071236214FA05ULL, (u64bit) 0xFBCA07B399A482DDULL, (u64bit) 0xFD9642C104864C17ULL, (u64bit) 0xFA525105AADEFA39ULL, +(u64bit) 0xF71122156406E645ULL, (u64bit) 0xFF415FDFD1247539ULL, (u64bit) 0xFB709936F52446AFULL, (u64bit) 0xFF7734CCB806CDA7ULL, +(u64bit) 0xF801E9A88CD3D70DULL, (u64bit) 0xFC0C00AC9BCC5491ULL, (u64bit) 0xFF462CD8E52ED221ULL, (u64bit) 0xFC97426300FCE331ULL, +(u64bit) 0xFEB3049C5E37A059ULL, (u64bit) 0xFFFC8AB1E05051CDULL, (u64bit) 0xFE5F4621F2D9FE63ULL, (u64bit) 0xFE931DB54FC5D521ULL, +(u64bit) 0xFFDE43D960FE42A5ULL, (u64bit) 0xFFDBFAD1B802BDB5ULL, (u64bit) 0xFF23C485F6B7BF53ULL, (u64bit) 0xFFC98F169C8DF21BULL, +(u64bit) 0xF1609D0E2E564D01ULL, (u64bit) 0xCB10B976C333834BULL, (u64bit) 0x9B52037A38DAB8F9ULL, (u64bit) 0x800E88FF5E929095ULL, +(u64bit) 0x55A9AD1C21F5E173ULL, (u64bit) 0x3D1A64E4E555D699ULL, (u64bit) 0x2A5D1D73694F7B93ULL, (u64bit) 0x198F4260D8807623ULL, +(u64bit) 0x140D45BB525C35EBULL, (u64bit) 0x102F4743FF914EEBULL, (u64bit) 0x0CB114936A734FBFULL, (u64bit) 0x096D97150B7B0A71ULL, +(u64bit) 0x06F06B90B850C2E5ULL, (u64bit) 0x053B17A0D7F7386BULL, (u64bit) 0xE3AD1CE3C82FE6A5ULL, (u64bit) 0xDAE968B4B710E857ULL, +(u64bit) 0xFA2DC15B2C96BE77ULL, (u64bit) 0xF1FF5F22AF135BD9ULL, (u64bit) 0xFC65C5CAAA878A13ULL, (u64bit) 0xFB9427EB08CF9C11ULL, +(u64bit) 0xCCB12B6FEBFE285DULL, (u64bit) 0x5BAADA462B48F999ULL, (u64bit) 0x2E53167EC64B703BULL, (u64bit) 0x1264ED670CD61961ULL, +(u64bit) 0x071F216A9AB74E2DULL, (u64bit) 0xEE26503C1266CE55ULL, (u64bit) 0x4C6004C7E404E4B5ULL, (u64bit) 0xCB649E41ECE95F85ULL +}; + +} diff --git a/old/botan/src/math/numbertheory/reducer.cpp b/old/botan/src/math/numbertheory/reducer.cpp new file mode 100644 index 0000000..fbd675e --- /dev/null +++ b/old/botan/src/math/numbertheory/reducer.cpp @@ -0,0 +1,97 @@ +/* +* Modular Reducer +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/reducer.h> +#include <botan/numthry.h> +#include <botan/mp_core.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"); + + modulus = mod; + mod_words = modulus.sig_words(); + + modulus_2 = Botan::square(modulus); + mod2_words = modulus_2.sig_words(); + + mu = BigInt(BigInt::Power2, 2 * MP_WORD_BITS * mod_words) / modulus; + mu_words = mu.sig_words(); + } + +/* +* Barrett Reduction +*/ +BigInt Modular_Reducer::reduce(const BigInt& x) const + { + if(mod_words == 0) + throw Invalid_State("Modular_Reducer: Never initalized"); + + BigInt t1 = x; + t1.set_sign(BigInt::Positive); + + if(t1 < modulus) + { + if(x.is_negative() && t1.is_nonzero()) + return modulus - t1; + return x; + } + + if(t1 >= modulus_2) + return (x % modulus); + + t1 >>= (MP_WORD_BITS * (mod_words - 1)); + t1 *= mu; + t1 >>= (MP_WORD_BITS * (mod_words + 1)); + + t1 *= modulus; + t1.mask_bits(MP_WORD_BITS * (mod_words+1)); + + BigInt t2 = x; + t2.set_sign(BigInt::Positive); + t2.mask_bits(MP_WORD_BITS * (mod_words+1)); + + t1 = t2 - t1; + + if(t1.is_negative()) + { + BigInt b_to_k1(BigInt::Power2, MP_WORD_BITS * (mod_words+1)); + t1 += b_to_k1; + } + + while(t1 >= modulus) + t1 -= modulus; + + if(x.is_negative() && t1.is_nonzero()) + t1 = modulus - t1; + + return t1; + } + +/* +* Multiply, followed by a reduction +*/ +BigInt Modular_Reducer::multiply(const BigInt& x, const BigInt& y) const + { + return reduce(x * y); + } + +/* +* Square, followed by a reduction +*/ +BigInt Modular_Reducer::square(const BigInt& x) const + { + return reduce(Botan::square(x)); + } + +} diff --git a/old/botan/src/math/numbertheory/reducer.h b/old/botan/src/math/numbertheory/reducer.h new file mode 100644 index 0000000..d234e07 --- /dev/null +++ b/old/botan/src/math/numbertheory/reducer.h @@ -0,0 +1,36 @@ +/* +* Modular Reducer +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MODARITH_H__ +#define BOTAN_MODARITH_H__ + +#include <botan/bigint.h> + +namespace Botan { + +/* +* Modular Reducer +*/ +class BOTAN_DLL Modular_Reducer + { + public: + BigInt multiply(const BigInt&, const BigInt&) const; + BigInt square(const BigInt&) const; + BigInt reduce(const BigInt&) const; + + bool initialized() const { return (mod_words != 0); } + + Modular_Reducer() { mod_words = 0; } + Modular_Reducer(const BigInt&); + private: + BigInt modulus, modulus_2, mu; + u32bit mod_words, mod2_words, mu_words; + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/ressol.cpp b/old/botan/src/math/numbertheory/ressol.cpp new file mode 100644 index 0000000..d51acb8 --- /dev/null +++ b/old/botan/src/math/numbertheory/ressol.cpp @@ -0,0 +1,82 @@ +/* +* Shanks-Tonnelli (RESSOL) +* (C) 2007-2008 Falko Strenzke, FlexSecure GmbH +* (C) 2008 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> +#include <botan/reducer.h> + +namespace Botan { + +/* +* Shanks-Tonnelli algorithm +*/ +BigInt ressol(const BigInt& a, const BigInt& p) + { + if(a < 0) + throw Invalid_Argument("ressol(): a to solve for must be positive"); + if(p <= 1) + throw Invalid_Argument("ressol(): prime must be > 1"); + + if(a == 0) + return 0; + if(p == 2) + return a; + + if(jacobi(a, p) != 1) // not a quadratic residue + return -BigInt(1); + + if(p % 4 == 3) + return power_mod(a, ((p+1) >> 2), p); + + u32bit 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; + + u32bit i = 0; + while(q != 1) + { + q = mod_p.square(q); + ++i; + } + u32bit t = s; + + if(t <= i) + return -BigInt(1); + + c = power_mod(c, BigInt(BigInt::Power2, t-i-1), p); + r = mod_p.multiply(r, c); + c = mod_p.square(c); + n = mod_p.multiply(n, c); + s = i; + } + + return r; + } + +} |