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Unified Diff: crypto/p224.cc

Issue 1841863002: Update monet. (Closed) Base URL: https://github.com/domokit/monet.git@master
Patch Set: Created 4 years, 9 months ago
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Index: crypto/p224.cc
diff --git a/crypto/p224.cc b/crypto/p224.cc
new file mode 100644
index 0000000000000000000000000000000000000000..11946a9413c5b06fe20601a99be19cc8327d1d2f
--- /dev/null
+++ b/crypto/p224.cc
@@ -0,0 +1,758 @@
+// Copyright (c) 2012 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 "base/sys_byteorder.h"
+
+namespace {
+
+using base::HostToNet32;
+using base::NetToHost32;
+
+// 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;
+
+// kP is the P224 prime.
+const FieldElement kP = {
+ 1, 0, 0, 268431360,
+ 268435455, 268435455, 268435455, 268435455,
+};
+
+void Contract(FieldElement* inout);
+
+// IsZero returns 0xffffffff if a == 0 mod p and 0 otherwise.
+uint32 IsZero(const FieldElement& a) {
+ FieldElement minimal;
+ memcpy(&minimal, &a, sizeof(minimal));
+ Contract(&minimal);
+
+ uint32 is_zero = 0, is_p = 0;
+ for (unsigned i = 0; i < 8; i++) {
+ is_zero |= minimal[i];
+ is_p |= minimal[i] - kP[i];
+ }
+
+ // If either is_zero or is_p is 0, then we should return 1.
+ is_zero |= is_zero >> 16;
+ is_zero |= is_zero >> 8;
+ is_zero |= is_zero >> 4;
+ is_zero |= is_zero >> 2;
+ is_zero |= is_zero >> 1;
+
+ is_p |= is_p >> 16;
+ is_p |= is_p >> 8;
+ is_p |= is_p >> 4;
+ is_p |= is_p >> 2;
+ is_p |= is_p >> 1;
+
+ // For is_zero and is_p, the LSB is 0 iff all the bits are zero.
+ is_zero &= is_p & 1;
+ is_zero = (~is_zero) << 31;
+ is_zero = static_cast<int32>(is_zero) >> 31;
+ return is_zero;
+}
+
+// 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
+
+// GCC 4.9 incorrectly vectorizes the first coefficient elimination loop, so
+// disable that optimization via pragma. Don't use the pragma under Clang, since
+// clang doesn't understand it.
+// TODO(wez): Remove this when crbug.com/439566 is fixed.
+#if defined(__GNUC__) && !defined(__clang__)
+#pragma GCC optimize("no-tree-vectorize")
+#endif
+
+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
+}
+
+// TODO(wez): Remove this when crbug.com/439566 is fixed.
+#if defined(__GNUC__) && !defined(__clang__)
+// Reenable "tree-vectorize" optimization if it got disabled for ReduceLarge.
+#pragma GCC reset_options
+#endif
+
+// 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**29
+// 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;
+ }
+
+ // We might have pushed out[3] over 2**28 so we perform another, partial
+ // carry chain.
+ for (int i = 3; i < 7; i++) {
+ out[i+1] += out[i] >> 28;
+ out[i] &= kBottom28Bits;
+ }
+ top = out[7] >> 28;
+ out[7] &= kBottom28Bits;
+
+ // Eliminate top while maintaining the same value mod p.
+ out[0] -= top;
+ out[3] += top << 12;
+
+ // There are two cases to consider for out[3]:
+ // 1) The first time that we eliminated top, we didn't push out[3] over
+ // 2**28. In this case, the partial carry chain didn't change any values
+ // and top is zero.
+ // 2) We did push out[3] over 2**28 the first time that we eliminated top.
+ // The first value of top was in [0..16), therefore, prior to eliminating
+ // the first top, 0xfff1000 <= out[3] <= 0xfffffff. Therefore, after
+ // overflowing and being reduced by the second carry chain, out[3] <=
+ // 0xf000. Thus it cannot have overflowed when we eliminated top for the
+ // second time.
+
+ // Again, we may just have made out[0] negative, so do the same carry down.
+ // As before, if we made out[0] negative then we know that out[3] is
+ // sufficiently positive.
+ 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 top_4_all_ones
+ // ends up with any zero bits in the bottom 28 bits, then this wasn't
+ // true.
+ uint32 top_4_all_ones = 0xffffffffu;
+ for (int i = 4; i < 8; i++) {
+ top_4_all_ones &= out[i];
+ }
+ top_4_all_ones |= 0xf0000000;
+ // Now we replicate any zero bits to all the bits in top_4_all_ones.
+ top_4_all_ones &= top_4_all_ones >> 16;
+ top_4_all_ones &= top_4_all_ones >> 8;
+ top_4_all_ones &= top_4_all_ones >> 4;
+ top_4_all_ones &= top_4_all_ones >> 2;
+ top_4_all_ones &= top_4_all_ones >> 1;
+ top_4_all_ones =
+ static_cast<uint32>(static_cast<int32>(top_4_all_ones << 31) >> 31);
+
+ // Now we test whether the bottom three limbs are non-zero.
+ uint32 bottom_3_non_zero = out[0] | out[1] | out[2];
+ bottom_3_non_zero |= bottom_3_non_zero >> 16;
+ bottom_3_non_zero |= bottom_3_non_zero >> 8;
+ bottom_3_non_zero |= bottom_3_non_zero >> 4;
+ bottom_3_non_zero |= bottom_3_non_zero >> 2;
+ bottom_3_non_zero |= bottom_3_non_zero >> 1;
+ bottom_3_non_zero =
+ static_cast<uint32>(static_cast<int32>(bottom_3_non_zero) >> 31);
+
+ // Everything depends on the value of out[3].
+ // If it's > 0xffff000 and top_4_all_ones != 0 then the whole value is >= p
+ // If it's = 0xffff000 and top_4_all_ones != 0 and bottom_3_non_zero != 0,
+ // then the whole value is >= p
+ // If it's < 0xffff000, then the whole value is < p
+ uint32 n = out[3] - 0xffff000;
+ uint32 out_3_equal = n;
+ out_3_equal |= out_3_equal >> 16;
+ out_3_equal |= out_3_equal >> 8;
+ out_3_equal |= out_3_equal >> 4;
+ out_3_equal |= out_3_equal >> 2;
+ out_3_equal |= out_3_equal >> 1;
+ out_3_equal =
+ ~static_cast<uint32>(static_cast<int32>(out_3_equal << 31) >> 31);
+
+ // If out[3] > 0xffff000 then n's MSB will be zero.
+ uint32 out_3_gt = ~static_cast<uint32>(static_cast<int32>(n << 31) >> 31);
+
+ uint32 mask = top_4_all_ones & ((out_3_equal & bottom_3_non_zero) | out_3_gt);
+ 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;
+
+// kB is parameter of the elliptic curve.
+const FieldElement kB = {
+ 55967668, 11768882, 265861671, 185302395,
+ 39211076, 180311059, 84673715, 188764328,
+};
+
+void CopyConditional(Point* out, const Point& a, uint32 mask);
+void DoubleJacobian(Point* out, const Point& a);
+
+// 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;
+
+ uint32 z1_is_zero = IsZero(a.z);
+ uint32 z2_is_zero = IsZero(b.z);
+
+ // 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);
+ uint32 x_equal = IsZero(h);
+
+ // I = (2*H)²
+ for (int k = 0; k < 8; k++) {
+ i[k] = h[k] << 1;
+ }
+ Reduce(&i);
+ Square(&i, i);
+
+ // J = H*I
+ Mul(&j, h, i);
+ // r = 2*(S2-S1)
+ Subtract(&r, s2, s1);
+ Reduce(&r);
+ uint32 y_equal = IsZero(r);
+
+ if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
+ // The two input points are the same therefore we must use the dedicated
+ // doubling function as the slope of the line is undefined.
+ DoubleJacobian(out, a);
+ return;
+ }
+
+ for (int k = 0; k < 8; k++) {
+ r[k] <<= 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 k = 0; k < 8; k++) {
+ z1z1[k] = v[k] << 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 k = 0; k < 8; k++) {
+ s1[k] <<= 1;
+ }
+ Mul(&s1, s1, j);
+ Subtract(&z1z1, v, out->x);
+ Reduce(&z1z1);
+ Mul(&z1z1, z1z1, r);
+ Subtract(&out->y, z1z1, s1);
+ Reduce(&out->y);
+
+ CopyConditional(out, a, z2_is_zero);
+ CopyConditional(out, b, z1_is_zero);
+}
+
+// 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;
+
+ 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, tmp, 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] = NetToHost32(in[6]) & kBottom28Bits;
+ out[1] = ((NetToHost32(in[5]) << 4) |
+ (NetToHost32(in[6]) >> 28)) & kBottom28Bits;
+ out[2] = ((NetToHost32(in[4]) << 8) |
+ (NetToHost32(in[5]) >> 24)) & kBottom28Bits;
+ out[3] = ((NetToHost32(in[3]) << 12) |
+ (NetToHost32(in[4]) >> 20)) & kBottom28Bits;
+ out[4] = ((NetToHost32(in[2]) << 16) |
+ (NetToHost32(in[3]) >> 16)) & kBottom28Bits;
+ out[5] = ((NetToHost32(in[1]) << 20) |
+ (NetToHost32(in[2]) >> 12)) & kBottom28Bits;
+ out[6] = ((NetToHost32(in[0]) << 24) |
+ (NetToHost32(in[1]) >> 8)) & kBottom28Bits;
+ out[7] = (NetToHost32(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] = HostToNet32((in[0] >> 0) | (in[1] << 28));
+ out[5] = HostToNet32((in[1] >> 4) | (in[2] << 24));
+ out[4] = HostToNet32((in[2] >> 8) | (in[3] << 20));
+ out[3] = HostToNet32((in[3] >> 12) | (in[4] << 16));
+ out[2] = HostToNet32((in[4] >> 16) | (in[5] << 12));
+ out[1] = HostToNet32((in[5] >> 20) | (in[6] << 8));
+ out[0] = HostToNet32((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, xx, yy;
+
+ // If this is the point at infinity we return a string of all zeros.
+ if (IsZero(this->z)) {
+ static const char zeros[56] = {0};
+ return std::string(zeros, sizeof(zeros));
+ }
+
+ Invert(&zinv, this->z);
+ Square(&zinv_sq, zinv);
+ Mul(&xx, x, zinv_sq);
+ Mul(&zinv_sq, zinv_sq, zinv);
+ Mul(&yy, y, zinv_sq);
+
+ Contract(&xx);
+ Contract(&yy);
+
+ uint32 outwords[14];
+ Put224Bits(outwords, xx);
+ Put224Bits(outwords + 7, yy);
+ 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
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