diff options
Diffstat (limited to 'src/libs/3rdparty/botan/src/lib/pubkey/ec_group/point_gfp.cpp')
-rw-r--r-- | src/libs/3rdparty/botan/src/lib/pubkey/ec_group/point_gfp.cpp | 727 |
1 files changed, 0 insertions, 727 deletions
diff --git a/src/libs/3rdparty/botan/src/lib/pubkey/ec_group/point_gfp.cpp b/src/libs/3rdparty/botan/src/lib/pubkey/ec_group/point_gfp.cpp deleted file mode 100644 index 77803de78f..0000000000 --- a/src/libs/3rdparty/botan/src/lib/pubkey/ec_group/point_gfp.cpp +++ /dev/null @@ -1,727 +0,0 @@ -/* -* Point arithmetic on elliptic curves over GF(p) -* -* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke -* 2008-2011,2012,2014,2015 Jack Lloyd -* -* Botan is released under the Simplified BSD License (see license.txt) -*/ - -#include <botan/point_gfp.h> -#include <botan/numthry.h> -#include <botan/rng.h> -#include <botan/internal/rounding.h> - -namespace Botan { - -PointGFp::PointGFp(const CurveGFp& curve) : - m_curve(curve), - m_coord_x(0), - m_coord_y(curve.get_1_rep()), - m_coord_z(0) - { - // Assumes Montgomery rep of zero is zero - } - -PointGFp::PointGFp(const CurveGFp& curve, const BigInt& x, const BigInt& y) : - m_curve(curve), - m_coord_x(x), - m_coord_y(y), - m_coord_z(m_curve.get_1_rep()) - { - if(x <= 0 || x >= curve.get_p()) - throw Invalid_Argument("Invalid PointGFp affine x"); - if(y <= 0 || y >= curve.get_p()) - throw Invalid_Argument("Invalid PointGFp affine y"); - - secure_vector<word> monty_ws(m_curve.get_ws_size()); - m_curve.to_rep(m_coord_x, monty_ws); - m_curve.to_rep(m_coord_y, monty_ws); - } - -void PointGFp::randomize_repr(RandomNumberGenerator& rng) - { - secure_vector<word> ws(m_curve.get_ws_size()); - randomize_repr(rng, ws); - } - -void PointGFp::randomize_repr(RandomNumberGenerator& rng, secure_vector<word>& ws) - { - const BigInt mask = BigInt::random_integer(rng, 2, m_curve.get_p()); - - /* - * No reason to convert this to Montgomery representation first, - * just pretend the random mask was chosen as Redc(mask) and the - * random mask we generated above is in the Montgomery - * representation. - * //m_curve.to_rep(mask, ws); - */ - const BigInt mask2 = m_curve.sqr_to_tmp(mask, ws); - const BigInt mask3 = m_curve.mul_to_tmp(mask2, mask, ws); - - m_coord_x = m_curve.mul_to_tmp(m_coord_x, mask2, ws); - m_coord_y = m_curve.mul_to_tmp(m_coord_y, mask3, ws); - m_coord_z = m_curve.mul_to_tmp(m_coord_z, mask, ws); - } - -namespace { - -inline void resize_ws(std::vector<BigInt>& ws_bn, size_t cap_size) - { - BOTAN_ASSERT(ws_bn.size() >= PointGFp::WORKSPACE_SIZE, - "Expected size for PointGFp workspace"); - - for(size_t i = 0; i != ws_bn.size(); ++i) - if(ws_bn[i].size() < cap_size) - ws_bn[i].get_word_vector().resize(cap_size); - } - -inline bool all_zeros(const word x[], size_t len) - { - word z = 0; - for(size_t i = 0; i != len; ++i) - z |= x[i]; - return (z == 0); - } - -} - -void PointGFp::add_affine(const word x_words[], size_t x_size, - const word y_words[], size_t y_size, - std::vector<BigInt>& ws_bn) - { - if(all_zeros(x_words, x_size) && all_zeros(y_words, y_size)) - return; - - if(is_zero()) - { - m_coord_x.set_words(x_words, x_size); - m_coord_y.set_words(y_words, y_size); - m_coord_z = m_curve.get_1_rep(); - return; - } - - resize_ws(ws_bn, m_curve.get_ws_size()); - - secure_vector<word>& ws = ws_bn[0].get_word_vector(); - secure_vector<word>& sub_ws = ws_bn[1].get_word_vector(); - - BigInt& T0 = ws_bn[2]; - BigInt& T1 = ws_bn[3]; - BigInt& T2 = ws_bn[4]; - BigInt& T3 = ws_bn[5]; - BigInt& T4 = ws_bn[6]; - - /* - https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2 - simplified with Z2 = 1 - */ - - const BigInt& p = m_curve.get_p(); - - m_curve.sqr(T3, m_coord_z, ws); // z1^2 - m_curve.mul(T4, x_words, x_size, T3, ws); // x2*z1^2 - - m_curve.mul(T2, m_coord_z, T3, ws); // z1^3 - m_curve.mul(T0, y_words, y_size, T2, ws); // y2*z1^3 - - T4.mod_sub(m_coord_x, p, sub_ws); // x2*z1^2 - x1*z2^2 - - T0.mod_sub(m_coord_y, p, sub_ws); - - if(T4.is_zero()) - { - if(T0.is_zero()) - { - mult2(ws_bn); - return; - } - - // setting to zero: - m_coord_x = 0; - m_coord_y = m_curve.get_1_rep(); - m_coord_z = 0; - return; - } - - m_curve.sqr(T2, T4, ws); - - m_curve.mul(T3, m_coord_x, T2, ws); - - m_curve.mul(T1, T2, T4, ws); - - m_curve.sqr(m_coord_x, T0, ws); - m_coord_x.mod_sub(T1, p, sub_ws); - m_coord_x.mod_sub(T3, p, sub_ws); - m_coord_x.mod_sub(T3, p, sub_ws); - - T3.mod_sub(m_coord_x, p, sub_ws); - - T2 = m_coord_y; - m_curve.mul(T2, T0, T3, ws); - m_curve.mul(T3, m_coord_y, T1, ws); - T2.mod_sub(T3, p, sub_ws); - m_coord_y = T2; - - m_curve.mul(T3, m_coord_z, T4, ws); - m_coord_z = T3; - } - -void PointGFp::add(const word x_words[], size_t x_size, - const word y_words[], size_t y_size, - const word z_words[], size_t z_size, - std::vector<BigInt>& ws_bn) - { - if(all_zeros(x_words, x_size) && all_zeros(z_words, z_size)) - return; - - if(is_zero()) - { - m_coord_x.set_words(x_words, x_size); - m_coord_y.set_words(y_words, y_size); - m_coord_z.set_words(z_words, z_size); - return; - } - - resize_ws(ws_bn, m_curve.get_ws_size()); - - secure_vector<word>& ws = ws_bn[0].get_word_vector(); - secure_vector<word>& sub_ws = ws_bn[1].get_word_vector(); - - BigInt& T0 = ws_bn[2]; - BigInt& T1 = ws_bn[3]; - BigInt& T2 = ws_bn[4]; - BigInt& T3 = ws_bn[5]; - BigInt& T4 = ws_bn[6]; - BigInt& T5 = ws_bn[7]; - - /* - https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2 - */ - - const BigInt& p = m_curve.get_p(); - - m_curve.sqr(T0, z_words, z_size, ws); // z2^2 - m_curve.mul(T1, m_coord_x, T0, ws); // x1*z2^2 - m_curve.mul(T3, z_words, z_size, T0, ws); // z2^3 - m_curve.mul(T2, m_coord_y, T3, ws); // y1*z2^3 - - m_curve.sqr(T3, m_coord_z, ws); // z1^2 - m_curve.mul(T4, x_words, x_size, T3, ws); // x2*z1^2 - - m_curve.mul(T5, m_coord_z, T3, ws); // z1^3 - m_curve.mul(T0, y_words, y_size, T5, ws); // y2*z1^3 - - T4.mod_sub(T1, p, sub_ws); // x2*z1^2 - x1*z2^2 - - T0.mod_sub(T2, p, sub_ws); - - if(T4.is_zero()) - { - if(T0.is_zero()) - { - mult2(ws_bn); - return; - } - - // setting to zero: - m_coord_x = 0; - m_coord_y = m_curve.get_1_rep(); - m_coord_z = 0; - return; - } - - m_curve.sqr(T5, T4, ws); - - m_curve.mul(T3, T1, T5, ws); - - m_curve.mul(T1, T5, T4, ws); - - m_curve.sqr(m_coord_x, T0, ws); - m_coord_x.mod_sub(T1, p, sub_ws); - m_coord_x.mod_sub(T3, p, sub_ws); - m_coord_x.mod_sub(T3, p, sub_ws); - - T3.mod_sub(m_coord_x, p, sub_ws); - - m_curve.mul(m_coord_y, T0, T3, ws); - m_curve.mul(T3, T2, T1, ws); - - m_coord_y.mod_sub(T3, p, sub_ws); - - m_curve.mul(T3, z_words, z_size, m_coord_z, ws); - m_curve.mul(m_coord_z, T3, T4, ws); - } - -void PointGFp::mult2i(size_t iterations, std::vector<BigInt>& ws_bn) - { - if(iterations == 0) - return; - - if(m_coord_y.is_zero()) - { - *this = PointGFp(m_curve); // setting myself to zero - return; - } - - /* - TODO we can save 2 squarings per iteration by computing - a*Z^4 using values cached from previous iteration - */ - for(size_t i = 0; i != iterations; ++i) - mult2(ws_bn); - } - -// *this *= 2 -void PointGFp::mult2(std::vector<BigInt>& ws_bn) - { - if(is_zero()) - return; - - if(m_coord_y.is_zero()) - { - *this = PointGFp(m_curve); // setting myself to zero - return; - } - - resize_ws(ws_bn, m_curve.get_ws_size()); - - secure_vector<word>& ws = ws_bn[0].get_word_vector(); - secure_vector<word>& sub_ws = ws_bn[1].get_word_vector(); - - BigInt& T0 = ws_bn[2]; - BigInt& T1 = ws_bn[3]; - BigInt& T2 = ws_bn[4]; - BigInt& T3 = ws_bn[5]; - BigInt& T4 = ws_bn[6]; - - /* - https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-1986-cc - */ - const BigInt& p = m_curve.get_p(); - - m_curve.sqr(T0, m_coord_y, ws); - - m_curve.mul(T1, m_coord_x, T0, ws); - T1 <<= 2; // * 4 - m_curve.redc_mod_p(T1, sub_ws); - - if(m_curve.a_is_zero()) - { - // if a == 0 then 3*x^2 + a*z^4 is just 3*x^2 - m_curve.sqr(T4, m_coord_x, ws); // x^2 - T4 *= 3; // 3*x^2 - m_curve.redc_mod_p(T4, sub_ws); - } - else if(m_curve.a_is_minus_3()) - { - /* - if a == -3 then - 3*x^2 + a*z^4 == 3*x^2 - 3*z^4 == 3*(x^2-z^4) == 3*(x-z^2)*(x+z^2) - */ - m_curve.sqr(T3, m_coord_z, ws); // z^2 - - // (x-z^2) - T2 = m_coord_x; - T2.mod_sub(T3, p, sub_ws); - - // (x+z^2) - T3.mod_add(m_coord_x, p, sub_ws); - - m_curve.mul(T4, T2, T3, ws); // (x-z^2)*(x+z^2) - - T4 *= 3; // 3*(x-z^2)*(x+z^2) - m_curve.redc_mod_p(T4, sub_ws); - } - else - { - m_curve.sqr(T3, m_coord_z, ws); // z^2 - m_curve.sqr(T4, T3, ws); // z^4 - m_curve.mul(T3, m_curve.get_a_rep(), T4, ws); // a*z^4 - - m_curve.sqr(T4, m_coord_x, ws); // x^2 - T4 *= 3; // 3*x^2 - T4.mod_add(T3, p, sub_ws); // 3*x^2 + a*z^4 - } - - m_curve.sqr(T2, T4, ws); - T2.mod_sub(T1, p, sub_ws); - T2.mod_sub(T1, p, sub_ws); - - m_curve.sqr(T3, T0, ws); - T3 <<= 3; - m_curve.redc_mod_p(T3, sub_ws); - - T1.mod_sub(T2, p, sub_ws); - - m_curve.mul(T0, T4, T1, ws); - T0.mod_sub(T3, p, sub_ws); - - m_coord_x = T2; - - m_curve.mul(T2, m_coord_y, m_coord_z, ws); - T2 <<= 1; - m_curve.redc_mod_p(T2, sub_ws); - - m_coord_y = T0; - m_coord_z = T2; - } - -// arithmetic operators -PointGFp& PointGFp::operator+=(const PointGFp& rhs) - { - std::vector<BigInt> ws(PointGFp::WORKSPACE_SIZE); - add(rhs, ws); - 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::operator*=(const BigInt& scalar) - { - *this = scalar * *this; - return *this; - } - -PointGFp operator*(const BigInt& scalar, const PointGFp& point) - { - BOTAN_DEBUG_ASSERT(point.on_the_curve()); - - const size_t scalar_bits = scalar.bits(); - - std::vector<BigInt> ws(PointGFp::WORKSPACE_SIZE); - - PointGFp R[2] = { point.zero(), point }; - - for(size_t i = scalar_bits; i > 0; i--) - { - const size_t b = scalar.get_bit(i - 1); - R[b ^ 1].add(R[b], ws); - R[b].mult2(ws); - } - - if(scalar.is_negative()) - R[0].negate(); - - BOTAN_DEBUG_ASSERT(R[0].on_the_curve()); - - return R[0]; - } - -//static -void PointGFp::force_all_affine(std::vector<PointGFp>& points, - secure_vector<word>& ws) - { - if(points.size() <= 1) - { - for(size_t i = 0; i != points.size(); ++i) - points[i].force_affine(); - return; - } - - /* - For >= 2 points use Montgomery's trick - - See Algorithm 2.26 in "Guide to Elliptic Curve Cryptography" - (Hankerson, Menezes, Vanstone) - - TODO is it really necessary to save all k points in c? - */ - - const CurveGFp& curve = points[0].m_curve; - const BigInt& rep_1 = curve.get_1_rep(); - - if(ws.size() < curve.get_ws_size()) - ws.resize(curve.get_ws_size()); - - std::vector<BigInt> c(points.size()); - c[0] = points[0].m_coord_z; - - for(size_t i = 1; i != points.size(); ++i) - { - curve.mul(c[i], c[i-1], points[i].m_coord_z, ws); - } - - BigInt s_inv = curve.invert_element(c[c.size()-1], ws); - - BigInt z_inv, z2_inv, z3_inv; - - for(size_t i = points.size() - 1; i != 0; i--) - { - PointGFp& point = points[i]; - - curve.mul(z_inv, s_inv, c[i-1], ws); - - s_inv = curve.mul_to_tmp(s_inv, point.m_coord_z, ws); - - curve.sqr(z2_inv, z_inv, ws); - curve.mul(z3_inv, z2_inv, z_inv, ws); - point.m_coord_x = curve.mul_to_tmp(point.m_coord_x, z2_inv, ws); - point.m_coord_y = curve.mul_to_tmp(point.m_coord_y, z3_inv, ws); - point.m_coord_z = rep_1; - } - - curve.sqr(z2_inv, s_inv, ws); - curve.mul(z3_inv, z2_inv, s_inv, ws); - points[0].m_coord_x = curve.mul_to_tmp(points[0].m_coord_x, z2_inv, ws); - points[0].m_coord_y = curve.mul_to_tmp(points[0].m_coord_y, z3_inv, ws); - points[0].m_coord_z = rep_1; - } - -void PointGFp::force_affine() - { - if(is_zero()) - throw Invalid_State("Cannot convert zero ECC point to affine"); - - secure_vector<word> ws; - - const BigInt z_inv = m_curve.invert_element(m_coord_z, ws); - const BigInt z2_inv = m_curve.sqr_to_tmp(z_inv, ws); - const BigInt z3_inv = m_curve.mul_to_tmp(z_inv, z2_inv, ws); - m_coord_x = m_curve.mul_to_tmp(m_coord_x, z2_inv, ws); - m_coord_y = m_curve.mul_to_tmp(m_coord_y, z3_inv, ws); - m_coord_z = m_curve.get_1_rep(); - } - -bool PointGFp::is_affine() const - { - return m_curve.is_one(m_coord_z); - } - -BigInt PointGFp::get_affine_x() const - { - if(is_zero()) - throw Illegal_Transformation("Cannot convert zero point to affine"); - - secure_vector<word> monty_ws; - - if(is_affine()) - return m_curve.from_rep(m_coord_x, monty_ws); - - BigInt z2 = m_curve.sqr_to_tmp(m_coord_z, monty_ws); - z2 = m_curve.invert_element(z2, monty_ws); - - BigInt r; - m_curve.mul(r, m_coord_x, z2, monty_ws); - m_curve.from_rep(r, monty_ws); - return r; - } - -BigInt PointGFp::get_affine_y() const - { - if(is_zero()) - throw Illegal_Transformation("Cannot convert zero point to affine"); - - secure_vector<word> monty_ws; - - if(is_affine()) - return m_curve.from_rep(m_coord_y, monty_ws); - - const BigInt z2 = m_curve.sqr_to_tmp(m_coord_z, monty_ws); - const BigInt z3 = m_curve.mul_to_tmp(m_coord_z, z2, monty_ws); - const BigInt z3_inv = m_curve.invert_element(z3, monty_ws); - - BigInt r; - m_curve.mul(r, m_coord_y, z3_inv, monty_ws); - m_curve.from_rep(r, monty_ws); - return r; - } - -bool PointGFp::on_the_curve() const - { - /* - Is the point still on the curve?? (If everything is correct, the - point is always on its curve; then the function will return true. - If somehow the state is corrupted, which suggests a fault attack - (or internal computational error), then return false. - */ - if(is_zero()) - return true; - - secure_vector<word> monty_ws; - - const BigInt y2 = m_curve.from_rep(m_curve.sqr_to_tmp(m_coord_y, monty_ws), monty_ws); - const BigInt x3 = m_curve.mul_to_tmp(m_coord_x, m_curve.sqr_to_tmp(m_coord_x, monty_ws), monty_ws); - const BigInt ax = m_curve.mul_to_tmp(m_coord_x, m_curve.get_a_rep(), monty_ws); - const BigInt z2 = m_curve.sqr_to_tmp(m_coord_z, monty_ws); - - if(m_coord_z == z2) // Is z equal to 1 (in Montgomery form)? - { - if(y2 != m_curve.from_rep(x3 + ax + m_curve.get_b_rep(), monty_ws)) - return false; - } - - const BigInt z3 = m_curve.mul_to_tmp(m_coord_z, z2, monty_ws); - const BigInt ax_z4 = m_curve.mul_to_tmp(ax, m_curve.sqr_to_tmp(z2, monty_ws), monty_ws); - const BigInt b_z6 = m_curve.mul_to_tmp(m_curve.get_b_rep(), m_curve.sqr_to_tmp(z3, monty_ws), monty_ws); - - if(y2 != m_curve.from_rep(x3 + ax_z4 + b_z6, monty_ws)) - return false; - - return true; - } - -// swaps the states of *this and other, does not throw! -void PointGFp::swap(PointGFp& other) - { - m_curve.swap(other.m_curve); - m_coord_x.swap(other.m_coord_x); - m_coord_y.swap(other.m_coord_y); - m_coord_z.swap(other.m_coord_z); - } - -bool PointGFp::operator==(const PointGFp& other) const - { - if(m_curve != other.m_curve) - return false; - - // If this is zero, only equal if other is also zero - if(is_zero()) - return other.is_zero(); - - return (get_affine_x() == other.get_affine_x() && - get_affine_y() == other.get_affine_y()); - } - -// encoding and decoding -std::vector<uint8_t> PointGFp::encode(PointGFp::Compression_Type format) const - { - if(is_zero()) - return std::vector<uint8_t>(1); // single 0 byte - - const size_t p_bytes = m_curve.get_p().bytes(); - - const BigInt x = get_affine_x(); - const BigInt y = get_affine_y(); - - std::vector<uint8_t> result; - - if(format == PointGFp::UNCOMPRESSED) - { - result.resize(1 + 2*p_bytes); - result[0] = 0x04; - BigInt::encode_1363(&result[1], p_bytes, x); - BigInt::encode_1363(&result[1+p_bytes], p_bytes, y); - } - else if(format == PointGFp::COMPRESSED) - { - result.resize(1 + p_bytes); - result[0] = 0x02 | static_cast<uint8_t>(y.get_bit(0)); - BigInt::encode_1363(&result[1], p_bytes, x); - } - else if(format == PointGFp::HYBRID) - { - result.resize(1 + 2*p_bytes); - result[0] = 0x06 | static_cast<uint8_t>(y.get_bit(0)); - BigInt::encode_1363(&result[1], p_bytes, x); - BigInt::encode_1363(&result[1+p_bytes], p_bytes, y); - } - else - throw Invalid_Argument("EC2OSP illegal point encoding"); - - return result; - } - -namespace { - -BigInt decompress_point(bool yMod2, - const BigInt& x, - const BigInt& curve_p, - const BigInt& curve_a, - const BigInt& curve_b) - { - BigInt xpow3 = x * x * x; - - BigInt g = curve_a * x; - g += xpow3; - g += curve_b; - g = g % curve_p; - - BigInt z = ressol(g, curve_p); - - if(z < 0) - throw Illegal_Point("error during EC point decompression"); - - if(z.get_bit(0) != yMod2) - z = curve_p - z; - - return z; - } - -} - -PointGFp OS2ECP(const uint8_t data[], size_t data_len, - const CurveGFp& curve) - { - // Should we really be doing this? - if(data_len <= 1) - return PointGFp(curve); // return zero - - std::pair<BigInt, BigInt> xy = OS2ECP(data, data_len, curve.get_p(), curve.get_a(), curve.get_b()); - - PointGFp point(curve, xy.first, xy.second); - - if(!point.on_the_curve()) - throw Illegal_Point("OS2ECP: Decoded point was not on the curve"); - - return point; - } - -std::pair<BigInt, BigInt> OS2ECP(const uint8_t data[], size_t data_len, - const BigInt& curve_p, - const BigInt& curve_a, - const BigInt& curve_b) - { - if(data_len <= 1) - throw Decoding_Error("OS2ECP invalid point"); - - const uint8_t pc = data[0]; - - BigInt x, y; - - if(pc == 2 || pc == 3) - { - //compressed form - x = BigInt::decode(&data[1], data_len - 1); - - const bool y_mod_2 = ((pc & 0x01) == 1); - y = decompress_point(y_mod_2, x, curve_p, curve_a, curve_b); - } - else if(pc == 4) - { - const size_t l = (data_len - 1) / 2; - - // uncompressed form - x = BigInt::decode(&data[1], l); - y = BigInt::decode(&data[l+1], l); - } - else if(pc == 6 || pc == 7) - { - const size_t l = (data_len - 1) / 2; - - // hybrid form - x = BigInt::decode(&data[1], l); - y = BigInt::decode(&data[l+1], l); - - const bool y_mod_2 = ((pc & 0x01) == 1); - - if(decompress_point(y_mod_2, x, curve_p, curve_a, curve_b) != y) - throw Illegal_Point("OS2ECP: Decoding error in hybrid format"); - } - else - throw Invalid_Argument("OS2ECP: Unknown format type " + std::to_string(pc)); - - return std::make_pair(x, y); - } - -} |