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author | jkummerow@chromium.org <jkummerow@chromium.org@0039d316-1c4b-4281-b951-d872f2087c98> | 2011-11-07 15:48:38 +0000 |
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committer | jkummerow@chromium.org <jkummerow@chromium.org@0039d316-1c4b-4281-b951-d872f2087c98> | 2011-11-07 15:48:38 +0000 |
commit | e22bd0de2f37b831db7c6a57543029a5aac9dd9d (patch) | |
tree | 2ecc8ce4489281caec57b777d5d794e78bd8aa6f /crypto/p224.cc | |
parent | f00c299976e4af12a0569275426780d5164f6899 (diff) | |
download | chromium_src-e22bd0de2f37b831db7c6a57543029a5aac9dd9d.zip chromium_src-e22bd0de2f37b831db7c6a57543029a5aac9dd9d.tar.gz chromium_src-e22bd0de2f37b831db7c6a57543029a5aac9dd9d.tar.bz2 |
Revert 108866 - crypto: add simple P224 implementation.
This is intended to be the underlying group for an EKE implementation for
Remoting.
BUG=none
TEST=crypto_unittests
Review URL: http://codereview.chromium.org/8431007
TBR=agl@chromium.org
Review URL: http://codereview.chromium.org/8467016
git-svn-id: svn://svn.chromium.org/chrome/trunk/src@108869 0039d316-1c4b-4281-b951-d872f2087c98
Diffstat (limited to 'crypto/p224.cc')
-rw-r--r-- | crypto/p224.cc | 652 |
1 files changed, 0 insertions, 652 deletions
diff --git a/crypto/p224.cc b/crypto/p224.cc deleted file mode 100644 index 0c87a5f..0000000 --- a/crypto/p224.cc +++ /dev/null @@ -1,652 +0,0 @@ -// Copyright (c) 2011 The Chromium Authors. All rights reserved. -// Use of this source code is governed by a BSD-style license that can be -// found in the LICENSE file. - -// This is an implementation of the P224 elliptic curve group. It's written to -// be short and simple rather than fast, although it's still constant-time. -// -// See http://www.imperialviolet.org/2010/12/04/ecc.html ([1]) for background. - -#include "crypto/p224.h" - -#include <string.h> - -#include "build/build_config.h" - -// For htonl and ntohl. -#if defined(OS_WIN) -#include <winsock2.h> -#else -#include <arpa/inet.h> -#endif - -namespace { - -// Field element functions. -// -// The field that we're dealing with is ℤ/pℤ where p = 2**224 - 2**96 + 1. -// -// Field elements are represented by a FieldElement, which is a typedef to an -// array of 8 uint32's. The value of a FieldElement, a, is: -// a[0] + 2**28·a[1] + 2**56·a[1] + ... + 2**196·a[7] -// -// Using 28-bit limbs means that there's only 4 bits of headroom, which is less -// than we would really like. But it has the useful feature that we hit 2**224 -// exactly, making the reflections during a reduce much nicer. - -using crypto::p224::FieldElement; - -// Add computes *out = a+b -// -// a[i] + b[i] < 2**32 -void Add(FieldElement* out, const FieldElement& a, const FieldElement& b) { - for (int i = 0; i < 8; i++) { - (*out)[i] = a[i] + b[i]; - } -} - -static const uint32 kTwo31p3 = (1u<<31) + (1u<<3); -static const uint32 kTwo31m3 = (1u<<31) - (1u<<3); -static const uint32 kTwo31m15m3 = (1u<<31) - (1u<<15) - (1u<<3); -// kZero31ModP is 0 mod p where bit 31 is set in all limbs so that we can -// subtract smaller amounts without underflow. See the section "Subtraction" in -// [1] for why. -static const FieldElement kZero31ModP = { - kTwo31p3, kTwo31m3, kTwo31m3, kTwo31m15m3, - kTwo31m3, kTwo31m3, kTwo31m3, kTwo31m3 -}; - -// Subtract computes *out = a-b -// -// a[i], b[i] < 2**30 -// out[i] < 2**32 -void Subtract(FieldElement* out, const FieldElement& a, const FieldElement& b) { - for (int i = 0; i < 8; i++) { - // See the section on "Subtraction" in [1] for details. - (*out)[i] = a[i] + kZero31ModP[i] - b[i]; - } -} - -static const uint64 kTwo63p35 = (1ull<<63) + (1ull<<35); -static const uint64 kTwo63m35 = (1ull<<63) - (1ull<<35); -static const uint64 kTwo63m35m19 = (1ull<<63) - (1ull<<35) - (1ull<<19); -// kZero63ModP is 0 mod p where bit 63 is set in all limbs. See the section -// "Subtraction" in [1] for why. -static const uint64 kZero63ModP[8] = { - kTwo63p35, kTwo63m35, kTwo63m35, kTwo63m35, - kTwo63m35m19, kTwo63m35, kTwo63m35, kTwo63m35, -}; - -static const uint32 kBottom28Bits = 0xfffffff; - -// LargeFieldElement also represents an element of the field. The limbs are -// still spaced 28-bits apart and in little-endian order. So the limbs are at -// 0, 28, 56, ..., 392 bits, each 64-bits wide. -typedef uint64 LargeFieldElement[15]; - -// ReduceLarge converts a LargeFieldElement to a FieldElement. -// -// in[i] < 2**62 -void ReduceLarge(FieldElement* out, LargeFieldElement* inptr) { - LargeFieldElement& in(*inptr); - - for (int i = 0; i < 8; i++) { - in[i] += kZero63ModP[i]; - } - - // Eliminate the coefficients at 2**224 and greater while maintaining the - // same value mod p. - for (int i = 14; i >= 8; i--) { - in[i-8] -= in[i]; // reflection off the "+1" term of p. - in[i-5] += (in[i] & 0xffff) << 12; // part of the "-2**96" reflection. - in[i-4] += in[i] >> 16; // the rest of the "-2**96" reflection. - } - in[8] = 0; - // in[0..8] < 2**64 - - // As the values become small enough, we start to store them in |out| and use - // 32-bit operations. - for (int i = 1; i < 8; i++) { - in[i+1] += in[i] >> 28; - (*out)[i] = static_cast<uint32>(in[i] & kBottom28Bits); - } - // Eliminate the term at 2*224 that we introduced while keeping the same - // value mod p. - in[0] -= in[8]; // reflection off the "+1" term of p. - (*out)[3] += static_cast<uint32>(in[8] & 0xffff) << 12; // "-2**96" term - (*out)[4] += static_cast<uint32>(in[8] >> 16); // rest of "-2**96" term - // in[0] < 2**64 - // out[3] < 2**29 - // out[4] < 2**29 - // out[1,2,5..7] < 2**28 - - (*out)[0] = static_cast<uint32>(in[0] & kBottom28Bits); - (*out)[1] += static_cast<uint32>((in[0] >> 28) & kBottom28Bits); - (*out)[2] += static_cast<uint32>(in[0] >> 56); - // out[0] < 2**28 - // out[1..4] < 2**29 - // out[5..7] < 2**28 -} - -// Mul computes *out = a*b -// -// a[i] < 2**29, b[i] < 2**30 (or vice versa) -// out[i] < 2**29 -void Mul(FieldElement* out, const FieldElement& a, const FieldElement& b) { - LargeFieldElement tmp; - memset(&tmp, 0, sizeof(tmp)); - - for (int i = 0; i < 8; i++) { - for (int j = 0; j < 8; j++) { - tmp[i+j] += static_cast<uint64>(a[i]) * static_cast<uint64>(b[j]); - } - } - - ReduceLarge(out, &tmp); -} - -// Square computes *out = a*a -// -// a[i] < 2**29 -// out[i] < 2**29 -void Square(FieldElement* out, const FieldElement& a) { - LargeFieldElement tmp; - memset(&tmp, 0, sizeof(tmp)); - - for (int i = 0; i < 8; i++) { - for (int j = 0; j <= i; j++) { - uint64 r = static_cast<uint64>(a[i]) * static_cast<uint64>(a[j]); - if (i == j) { - tmp[i+j] += r; - } else { - tmp[i+j] += r << 1; - } - } - } - - ReduceLarge(out, &tmp); -} - -// Reduce reduces the coefficients of in_out to smaller bounds. -// -// On entry: a[i] < 2**31 + 2**30 -// On exit: a[i] < 2**29 -void Reduce(FieldElement* in_out) { - FieldElement& a = *in_out; - - for (int i = 0; i < 7; i++) { - a[i+1] += a[i] >> 28; - a[i] &= kBottom28Bits; - } - uint32 top = a[7] >> 28; - a[7] &= kBottom28Bits; - - // top < 2**4 - // Constant-time: mask = (top != 0) ? 0xffffffff : 0 - uint32 mask = top; - mask |= mask >> 2; - mask |= mask >> 1; - mask <<= 31; - mask = static_cast<uint32>(static_cast<int32>(mask) >> 31); - - // Eliminate top while maintaining the same value mod p. - a[0] -= top; - a[3] += top << 12; - - // We may have just made a[0] negative but, if we did, then we must - // have added something to a[3], thus it's > 2**12. Therefore we can - // carry down to a[0]. - a[3] -= 1 & mask; - a[2] += mask & ((1<<28) - 1); - a[1] += mask & ((1<<28) - 1); - a[0] += mask & (1<<28); -} - -// Invert calcuates *out = in**-1 by computing in**(2**224 - 2**96 - 1), i.e. -// Fermat's little theorem. -void Invert(FieldElement* out, const FieldElement& in) { - FieldElement f1, f2, f3, f4; - - Square(&f1, in); // 2 - Mul(&f1, f1, in); // 2**2 - 1 - Square(&f1, f1); // 2**3 - 2 - Mul(&f1, f1, in); // 2**3 - 1 - Square(&f2, f1); // 2**4 - 2 - Square(&f2, f2); // 2**5 - 4 - Square(&f2, f2); // 2**6 - 8 - Mul(&f1, f1, f2); // 2**6 - 1 - Square(&f2, f1); // 2**7 - 2 - for (int i = 0; i < 5; i++) { // 2**12 - 2**6 - Square(&f2, f2); - } - Mul(&f2, f2, f1); // 2**12 - 1 - Square(&f3, f2); // 2**13 - 2 - for (int i = 0; i < 11; i++) { // 2**24 - 2**12 - Square(&f3, f3); - } - Mul(&f2, f3, f2); // 2**24 - 1 - Square(&f3, f2); // 2**25 - 2 - for (int i = 0; i < 23; i++) { // 2**48 - 2**24 - Square(&f3, f3); - } - Mul(&f3, f3, f2); // 2**48 - 1 - Square(&f4, f3); // 2**49 - 2 - for (int i = 0; i < 47; i++) { // 2**96 - 2**48 - Square(&f4, f4); - } - Mul(&f3, f3, f4); // 2**96 - 1 - Square(&f4, f3); // 2**97 - 2 - for (int i = 0; i < 23; i++) { // 2**120 - 2**24 - Square(&f4, f4); - } - Mul(&f2, f4, f2); // 2**120 - 1 - for (int i = 0; i < 6; i++) { // 2**126 - 2**6 - Square(&f2, f2); - } - Mul(&f1, f1, f2); // 2**126 - 1 - Square(&f1, f1); // 2**127 - 2 - Mul(&f1, f1, in); // 2**127 - 1 - for (int i = 0; i < 97; i++) { // 2**224 - 2**97 - Square(&f1, f1); - } - Mul(out, f1, f3); // 2**224 - 2**96 - 1 -} - -// Contract converts a FieldElement to its minimal, distinguished form. -// -// On entry, in[i] < 2**32 -// On exit, in[i] < 2**28 -void Contract(FieldElement* inout) { - FieldElement& out = *inout; - - // Reduce the coefficients to < 2**28. - for (int i = 0; i < 7; i++) { - out[i+1] += out[i] >> 28; - out[i] &= kBottom28Bits; - } - uint32 top = out[7] >> 28; - out[7] &= kBottom28Bits; - - // Eliminate top while maintaining the same value mod p. - out[0] -= top; - out[3] += top << 12; - - // We may just have made out[0] negative. So we carry down. If we made - // out[0] negative then we know that out[3] is sufficiently positive - // because we just added to it. - for (int i = 0; i < 3; i++) { - uint32 mask = static_cast<uint32>(static_cast<int32>(out[i]) >> 31); - out[i] += (1 << 28) & mask; - out[i+1] -= 1 & mask; - } - - // The value is < 2**224, but maybe greater than p. In order to reduce to a - // unique, minimal value we see if the value is >= p and, if so, subtract p. - - // First we build a mask from the top four limbs, which must all be - // equal to bottom28Bits if the whole value is >= p. If top4AllOnes - // ends up with any zero bits in the bottom 28 bits, then this wasn't - // true. - uint32 top4AllOnes = 0xffffffffu; - for (int i = 4; i < 8; i++) { - top4AllOnes &= (out[i] & kBottom28Bits) - 1; - } - top4AllOnes |= 0xf0000000; - // Now we replicate any zero bits to all the bits in top4AllOnes. - top4AllOnes &= top4AllOnes >> 16; - top4AllOnes &= top4AllOnes >> 8; - top4AllOnes &= top4AllOnes >> 4; - top4AllOnes &= top4AllOnes >> 2; - top4AllOnes &= top4AllOnes >> 1; - top4AllOnes = - static_cast<uint32>(static_cast<int32>(top4AllOnes << 31) >> 31); - - // Now we test whether the bottom three limbs are non-zero. - uint32 bottom3NonZero = out[0] | out[1] | out[2]; - bottom3NonZero |= bottom3NonZero >> 16; - bottom3NonZero |= bottom3NonZero >> 8; - bottom3NonZero |= bottom3NonZero >> 4; - bottom3NonZero |= bottom3NonZero >> 2; - bottom3NonZero |= bottom3NonZero >> 1; - bottom3NonZero = - static_cast<uint32>(static_cast<int32>(bottom3NonZero << 31) >> 31); - - // Everything depends on the value of out[3]. - // If it's > 0xffff000 and top4AllOnes != 0 then the whole value is >= p - // If it's = 0xffff000 and top4AllOnes != 0 and bottom3NonZero != 0, - // then the whole value is >= p - // If it's < 0xffff000, then the whole value is < p - uint32 n = out[3] - 0xffff000; - uint32 out3Equal = n; - out3Equal |= out3Equal >> 16; - out3Equal |= out3Equal >> 8; - out3Equal |= out3Equal >> 4; - out3Equal |= out3Equal >> 2; - out3Equal |= out3Equal >> 1; - out3Equal = - ~static_cast<uint32>(static_cast<int32>(out3Equal << 31) >> 31); - - // If out[3] > 0xffff000 then n's MSB will be zero. - uint32 out3GT = ~static_cast<uint32>(static_cast<int32>(n << 31) >> 31); - - uint32 mask = top4AllOnes & ((out3Equal & bottom3NonZero) | out3GT); - out[0] -= 1 & mask; - out[3] -= 0xffff000 & mask; - out[4] -= 0xfffffff & mask; - out[5] -= 0xfffffff & mask; - out[6] -= 0xfffffff & mask; - out[7] -= 0xfffffff & mask; -} - - -// Group element functions. -// -// These functions deal with group elements. The group is an elliptic curve -// group with a = -3 defined in FIPS 186-3, section D.2.2. - -using crypto::p224::Point; - -// kP is the P224 prime. -const FieldElement kP = { - 1, 0, 0, 268431360, - 268435455, 268435455, 268435455, 268435455, -}; - -// kB is parameter of the elliptic curve. -const FieldElement kB = { - 55967668, 11768882, 265861671, 185302395, - 39211076, 180311059, 84673715, 188764328, -}; - -// AddJacobian computes *out = a+b where a != b. -void AddJacobian(Point *out, - const Point& a, - const Point& b) { - // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl - FieldElement z1z1, z2z2, u1, u2, s1, s2, h, i, j, r, v; - - // Z1Z1 = Z1² - Square(&z1z1, a.z); - - // Z2Z2 = Z2² - Square(&z2z2, b.z); - - // U1 = X1*Z2Z2 - Mul(&u1, a.x, z2z2); - - // U2 = X2*Z1Z1 - Mul(&u2, b.x, z1z1); - - // S1 = Y1*Z2*Z2Z2 - Mul(&s1, b.z, z2z2); - Mul(&s1, a.y, s1); - - // S2 = Y2*Z1*Z1Z1 - Mul(&s2, a.z, z1z1); - Mul(&s2, b.y, s2); - - // H = U2-U1 - Subtract(&h, u2, u1); - Reduce(&h); - - // I = (2*H)² - for (int j = 0; j < 8; j++) { - i[j] = h[j] << 1; - } - Reduce(&i); - Square(&i, i); - - // J = H*I - Mul(&j, h, i); - // r = 2*(S2-S1) - Subtract(&r, s2, s1); - Reduce(&r); - for (int i = 0; i < 8; i++) { - r[i] <<= 1; - } - Reduce(&r); - - // V = U1*I - Mul(&v, u1, i); - - // Z3 = ((Z1+Z2)²-Z1Z1-Z2Z2)*H - Add(&z1z1, z1z1, z2z2); - Add(&z2z2, a.z, b.z); - Reduce(&z2z2); - Square(&z2z2, z2z2); - Subtract(&out->z, z2z2, z1z1); - Reduce(&out->z); - Mul(&out->z, out->z, h); - - // X3 = r²-J-2*V - for (int i = 0; i < 8; i++) { - z1z1[i] = v[i] << 1; - } - Add(&z1z1, j, z1z1); - Reduce(&z1z1); - Square(&out->x, r); - Subtract(&out->x, out->x, z1z1); - Reduce(&out->x); - - // Y3 = r*(V-X3)-2*S1*J - for (int i = 0; i < 8; i++) { - s1[i] <<= 1; - } - Mul(&s1, s1, j); - Subtract(&z1z1, v, out->x); - Reduce(&z1z1); - Mul(&z1z1, z1z1, r); - Subtract(&out->y, z1z1, s1); - Reduce(&out->y); -} - -// DoubleJacobian computes *out = a+a. -void DoubleJacobian(Point* out, const Point& a) { - // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b - FieldElement delta, gamma, beta, alpha, t; - - Square(&delta, a.z); - Square(&gamma, a.y); - Mul(&beta, a.x, gamma); - - // alpha = 3*(X1-delta)*(X1+delta) - Add(&t, a.x, delta); - for (int i = 0; i < 8; i++) { - t[i] += t[i] << 1; - } - Reduce(&t); - Subtract(&alpha, a.x, delta); - Reduce(&alpha); - Mul(&alpha, alpha, t); - - // Z3 = (Y1+Z1)²-gamma-delta - Add(&out->z, a.y, a.z); - Reduce(&out->z); - Square(&out->z, out->z); - Subtract(&out->z, out->z, gamma); - Reduce(&out->z); - Subtract(&out->z, out->z, delta); - Reduce(&out->z); - - // X3 = alpha²-8*beta - for (int i = 0; i < 8; i++) { - delta[i] = beta[i] << 3; - } - Reduce(&delta); - Square(&out->x, alpha); - Subtract(&out->x, out->x, delta); - Reduce(&out->x); - - // Y3 = alpha*(4*beta-X3)-8*gamma² - for (int i = 0; i < 8; i++) { - beta[i] <<= 2; - } - Reduce(&beta); - Subtract(&beta, beta, out->x); - Reduce(&beta); - Square(&gamma, gamma); - for (int i = 0; i < 8; i++) { - gamma[i] <<= 3; - } - Reduce(&gamma); - Mul(&out->y, alpha, beta); - Subtract(&out->y, out->y, gamma); - Reduce(&out->y); -} - -// CopyConditional sets *out=a if mask is 0xffffffff. mask must be either 0 of -// 0xffffffff. -void CopyConditional(Point* out, - const Point& a, - uint32 mask) { - for (int i = 0; i < 8; i++) { - out->x[i] ^= mask & (a.x[i] ^ out->x[i]); - out->y[i] ^= mask & (a.y[i] ^ out->y[i]); - out->z[i] ^= mask & (a.z[i] ^ out->z[i]); - } -} - -// ScalarMult calculates *out = a*scalar where scalar is a big-endian number of -// length scalar_len and != 0. -void ScalarMult(Point* out, const Point& a, - const uint8* scalar, size_t scalar_len) { - memset(out, 0, sizeof(*out)); - Point tmp; - - uint32 first_bit = 0xffffffff; - for (size_t i = 0; i < scalar_len; i++) { - for (unsigned int bit_num = 0; bit_num < 8; bit_num++) { - DoubleJacobian(out, *out); - uint32 bit = static_cast<uint32>(static_cast<int32>( - (((scalar[i] >> (7 - bit_num)) & 1) << 31) >> 31)); - AddJacobian(&tmp, a, *out); - CopyConditional(out, a, first_bit & bit); - CopyConditional(out, tmp, ~first_bit & bit); - first_bit = first_bit & ~bit; - } - } -} - -// Get224Bits reads 7 words from in and scatters their contents in -// little-endian form into 8 words at out, 28 bits per output word. -void Get224Bits(uint32* out, const uint32* in) { - out[0] = ntohl(in[6]) & kBottom28Bits; - out[1] = ((ntohl(in[5]) << 4) | (ntohl(in[6]) >> 28)) & kBottom28Bits; - out[2] = ((ntohl(in[4]) << 8) | (ntohl(in[5]) >> 24)) & kBottom28Bits; - out[3] = ((ntohl(in[3]) << 12) | (ntohl(in[4]) >> 20)) & kBottom28Bits; - out[4] = ((ntohl(in[2]) << 16) | (ntohl(in[3]) >> 16)) & kBottom28Bits; - out[5] = ((ntohl(in[1]) << 20) | (ntohl(in[2]) >> 12)) & kBottom28Bits; - out[6] = ((ntohl(in[0]) << 24) | (ntohl(in[1]) >> 8)) & kBottom28Bits; - out[7] = (ntohl(in[0]) >> 4) & kBottom28Bits; -} - -// Put224Bits performs the inverse operation to Get224Bits: taking 28 bits from -// each of 8 input words and writing them in big-endian order to 7 words at -// out. -void Put224Bits(uint32* out, const uint32* in) { - out[6] = htonl((in[0] >> 0) | (in[1] << 28)); - out[5] = htonl((in[1] >> 4) | (in[2] << 24)); - out[4] = htonl((in[2] >> 8) | (in[3] << 20)); - out[3] = htonl((in[3] >> 12) | (in[4] << 16)); - out[2] = htonl((in[4] >> 16) | (in[5] << 12)); - out[1] = htonl((in[5] >> 20) | (in[6] << 8)); - out[0] = htonl((in[6] >> 24) | (in[7] << 4)); -} - -} // anonymous namespace - -namespace crypto { - -namespace p224 { - -bool Point::SetFromString(const base::StringPiece& in) { - if (in.size() != 2*28) - return false; - const uint32* inwords = reinterpret_cast<const uint32*>(in.data()); - Get224Bits(x, inwords); - Get224Bits(y, inwords + 7); - memset(&z, 0, sizeof(z)); - z[0] = 1; - - // Check that the point is on the curve, i.e. that y² = x³ - 3x + b. - FieldElement lhs; - Square(&lhs, y); - Contract(&lhs); - - FieldElement rhs; - Square(&rhs, x); - Mul(&rhs, x, rhs); - - FieldElement three_x; - for (int i = 0; i < 8; i++) { - three_x[i] = x[i] * 3; - } - Reduce(&three_x); - Subtract(&rhs, rhs, three_x); - Reduce(&rhs); - - ::Add(&rhs, rhs, kB); - Contract(&rhs); - return memcmp(&lhs, &rhs, sizeof(lhs)) == 0; -} - -std::string Point::ToString() const { - FieldElement zinv, zinv_sq, x, y; - - Invert(&zinv, this->z); - Square(&zinv_sq, zinv); - Mul(&x, this->x, zinv_sq); - Mul(&zinv_sq, zinv_sq, zinv); - Mul(&y, this->y, zinv_sq); - - Contract(&x); - Contract(&y); - - uint32 outwords[14]; - Put224Bits(outwords, x); - Put224Bits(outwords + 7, y); - return std::string(reinterpret_cast<const char*>(outwords), sizeof(outwords)); -} - -void ScalarMult(const Point& in, const uint8* scalar, Point* out) { - ::ScalarMult(out, in, scalar, 28); -} - -// kBasePoint is the base point (generator) of the elliptic curve group. -static const Point kBasePoint = { - {22813985, 52956513, 34677300, 203240812, - 12143107, 133374265, 225162431, 191946955}, - {83918388, 223877528, 122119236, 123340192, - 266784067, 263504429, 146143011, 198407736}, - {1, 0, 0, 0, 0, 0, 0, 0}, -}; - -void ScalarBaseMult(const uint8* scalar, Point* out) { - ::ScalarMult(out, kBasePoint, scalar, 28); -} - -void Add(const Point& a, const Point& b, Point* out) { - AddJacobian(out, a, b); -} - -void Negate(const Point& in, Point* out) { - // Guide to elliptic curve cryptography, page 89 suggests that (X : X+Y : Z) - // is the negative in Jacobian coordinates, but it doesn't actually appear to - // be true in testing so this performs the negation in affine coordinates. - FieldElement zinv, zinv_sq, y; - Invert(&zinv, in.z); - Square(&zinv_sq, zinv); - Mul(&out->x, in.x, zinv_sq); - Mul(&zinv_sq, zinv_sq, zinv); - Mul(&y, in.y, zinv_sq); - - Subtract(&out->y, kP, y); - Reduce(&out->y); - - memset(&out->z, 0, sizeof(out->z)); - out->z[0] = 1; -} - -} // namespace p224 - -} // namespace crypto |