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boringssl/crypto/ec/p224-64.c
David Benjamin 17cf2cb1d2 Work around language and compiler bug in memcpy, etc. 
Most C standard library functions are undefined if passed NULL, even
when the corresponding length is zero. This gives them (and, in turn,
all functions which call them) surprising behavior on empty arrays.
Some compilers will miscompile code due to this rule. See also
https://www.imperialviolet.org/2016/06/26/nonnull.html

Add OPENSSL_memcpy, etc., wrappers which avoid this problem.

BUG=23

Change-Id: I95f42b23e92945af0e681264fffaf578e7f8465e
Reviewed-on: https://boringssl-review.googlesource.com/12928
Commit-Queue: David Benjamin <davidben@google.com>
Reviewed-by: Adam Langley <agl@google.com>
2016-12-21 20:34:47 +00:00

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/* Copyright (c) 2015, Google Inc.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
/* A 64-bit implementation of the NIST P-224 elliptic curve point multiplication
*
* Inspired by Daniel J. Bernstein's public domain nistp224 implementation
* and Adam Langley's public domain 64-bit C implementation of curve25519. */
#include <openssl/base.h>
#if defined(OPENSSL_64_BIT) && !defined(OPENSSL_WINDOWS) && \
!defined(OPENSSL_SMALL)
#include <openssl/bn.h>
#include <openssl/ec.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include <string.h>
#include "internal.h"
#include "../internal.h"
typedef uint8_t u8;
typedef uint64_t u64;
typedef int64_t s64;
/* Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
* using 64-bit coefficients called 'limbs', and sometimes (for multiplication
* results) as b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 +
* 2^336*b_6 using 128-bit coefficients called 'widelimbs'. A 4-limb
* representation is an 'felem'; a 7-widelimb representation is a 'widefelem'.
* Even within felems, bits of adjacent limbs overlap, and we don't always
* reduce the representations: we ensure that inputs to each felem
* multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, and
* fit into a 128-bit word without overflow. The coefficients are then again
* partially reduced to obtain an felem satisfying a_i < 2^57. We only reduce
* to the unique minimal representation at the end of the computation. */
typedef uint64_t limb;
typedef uint128_t widelimb;
typedef limb felem[4];
typedef widelimb widefelem[7];
/* Field element represented as a byte arrary. 28*8 = 224 bits is also the
* group order size for the elliptic curve, and we also use this type for
* scalars for point multiplication. */
typedef u8 felem_bytearray[28];
/* Precomputed multiples of the standard generator
* Points are given in coordinates (X, Y, Z) where Z normally is 1
* (0 for the point at infinity).
* For each field element, slice a_0 is word 0, etc.
*
* The table has 2 * 16 elements, starting with the following:
* index | bits | point
* ------+---------+------------------------------
* 0 | 0 0 0 0 | 0G
* 1 | 0 0 0 1 | 1G
* 2 | 0 0 1 0 | 2^56G
* 3 | 0 0 1 1 | (2^56 + 1)G
* 4 | 0 1 0 0 | 2^112G
* 5 | 0 1 0 1 | (2^112 + 1)G
* 6 | 0 1 1 0 | (2^112 + 2^56)G
* 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G
* 8 | 1 0 0 0 | 2^168G
* 9 | 1 0 0 1 | (2^168 + 1)G
* 10 | 1 0 1 0 | (2^168 + 2^56)G
* 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G
* 12 | 1 1 0 0 | (2^168 + 2^112)G
* 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G
* 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G
* 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G
* followed by a copy of this with each element multiplied by 2^28.
*
* The reason for this is so that we can clock bits into four different
* locations when doing simple scalar multiplies against the base point,
* and then another four locations using the second 16 elements. */
static const felem g_pre_comp[2][16][3] = {
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf},
{0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723},
{1, 0, 0, 0}},
{{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5},
{0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321},
{1, 0, 0, 0}},
{{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748},
{0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17},
{1, 0, 0, 0}},
{{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe},
{0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b},
{1, 0, 0, 0}},
{{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3},
{0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a},
{1, 0, 0, 0}},
{{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c},
{0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244},
{1, 0, 0, 0}},
{{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849},
{0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112},
{1, 0, 0, 0}},
{{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47},
{0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394},
{1, 0, 0, 0}},
{{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d},
{0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7},
{1, 0, 0, 0}},
{{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24},
{0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881},
{1, 0, 0, 0}},
{{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984},
{0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369},
{1, 0, 0, 0}},
{{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3},
{0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60},
{1, 0, 0, 0}},
{{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057},
{0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9},
{1, 0, 0, 0}},
{{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9},
{0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc},
{1, 0, 0, 0}},
{{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58},
{0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558},
{1, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31},
{0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d},
{1, 0, 0, 0}},
{{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3},
{0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a},
{1, 0, 0, 0}},
{{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33},
{0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100},
{1, 0, 0, 0}},
{{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5},
{0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea},
{1, 0, 0, 0}},
{{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be},
{0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51},
{1, 0, 0, 0}},
{{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1},
{0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb},
{1, 0, 0, 0}},
{{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233},
{0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def},
{1, 0, 0, 0}},
{{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae},
{0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45},
{1, 0, 0, 0}},
{{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e},
{0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb},
{1, 0, 0, 0}},
{{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de},
{0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3},
{1, 0, 0, 0}},
{{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05},
{0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58},
{1, 0, 0, 0}},
{{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb},
{0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0},
{1, 0, 0, 0}},
{{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9},
{0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea},
{1, 0, 0, 0}},
{{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba},
{0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405},
{1, 0, 0, 0}},
{{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e},
{0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e},
{1, 0, 0, 0}}}};
/* Helper functions to convert field elements to/from internal representation */
static void bin28_to_felem(felem out, const u8 in[28]) {
out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff;
out[1] = (*((const uint64_t *)(in + 7))) & 0x00ffffffffffffff;
out[2] = (*((const uint64_t *)(in + 14))) & 0x00ffffffffffffff;
out[3] = (*((const uint64_t *)(in + 20))) >> 8;
}
static void felem_to_bin28(u8 out[28], const felem in) {
for (size_t i = 0; i < 7; ++i) {
out[i] = in[0] >> (8 * i);
out[i + 7] = in[1] >> (8 * i);
out[i + 14] = in[2] >> (8 * i);
out[i + 21] = in[3] >> (8 * i);
}
}
/* To preserve endianness when using BN_bn2bin and BN_bin2bn */
static void flip_endian(u8 *out, const u8 *in, size_t len) {
for (size_t i = 0; i < len; ++i) {
out[i] = in[len - 1 - i];
}
}
/* From OpenSSL BIGNUM to internal representation */
static int BN_to_felem(felem out, const BIGNUM *bn) {
/* BN_bn2bin eats leading zeroes */
felem_bytearray b_out;
OPENSSL_memset(b_out, 0, sizeof(b_out));
size_t num_bytes = BN_num_bytes(bn);
if (num_bytes > sizeof(b_out) ||
BN_is_negative(bn)) {
OPENSSL_PUT_ERROR(EC, EC_R_BIGNUM_OUT_OF_RANGE);
return 0;
}
felem_bytearray b_in;
num_bytes = BN_bn2bin(bn, b_in);
flip_endian(b_out, b_in, num_bytes);
bin28_to_felem(out, b_out);
return 1;
}
/* From internal representation to OpenSSL BIGNUM */
static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) {
felem_bytearray b_in, b_out;
felem_to_bin28(b_in, in);
flip_endian(b_out, b_in, sizeof(b_out));
return BN_bin2bn(b_out, sizeof(b_out), out);
}
/* Field operations, using the internal representation of field elements.
* NB! These operations are specific to our point multiplication and cannot be
* expected to be correct in general - e.g., multiplication with a large scalar
* will cause an overflow. */
static void felem_assign(felem out, const felem in) {
out[0] = in[0];
out[1] = in[1];
out[2] = in[2];
out[3] = in[3];
}
/* Sum two field elements: out += in */
static void felem_sum(felem out, const felem in) {
out[0] += in[0];
out[1] += in[1];
out[2] += in[2];
out[3] += in[3];
}
/* Get negative value: out = -in */
/* Assumes in[i] < 2^57 */
static void felem_neg(felem out, const felem in) {
static const limb two58p2 = (((limb)1) << 58) + (((limb)1) << 2);
static const limb two58m2 = (((limb)1) << 58) - (((limb)1) << 2);
static const limb two58m42m2 =
(((limb)1) << 58) - (((limb)1) << 42) - (((limb)1) << 2);
/* Set to 0 mod 2^224-2^96+1 to ensure out > in */
out[0] = two58p2 - in[0];
out[1] = two58m42m2 - in[1];
out[2] = two58m2 - in[2];
out[3] = two58m2 - in[3];
}
/* Subtract field elements: out -= in */
/* Assumes in[i] < 2^57 */
static void felem_diff(felem out, const felem in) {
static const limb two58p2 = (((limb)1) << 58) + (((limb)1) << 2);
static const limb two58m2 = (((limb)1) << 58) - (((limb)1) << 2);
static const limb two58m42m2 =
(((limb)1) << 58) - (((limb)1) << 42) - (((limb)1) << 2);
/* Add 0 mod 2^224-2^96+1 to ensure out > in */
out[0] += two58p2;
out[1] += two58m42m2;
out[2] += two58m2;
out[3] += two58m2;
out[0] -= in[0];
out[1] -= in[1];
out[2] -= in[2];
out[3] -= in[3];
}
/* Subtract in unreduced 128-bit mode: out -= in */
/* Assumes in[i] < 2^119 */
static void widefelem_diff(widefelem out, const widefelem in) {
static const widelimb two120 = ((widelimb)1) << 120;
static const widelimb two120m64 =
(((widelimb)1) << 120) - (((widelimb)1) << 64);
static const widelimb two120m104m64 =
(((widelimb)1) << 120) - (((widelimb)1) << 104) - (((widelimb)1) << 64);
/* Add 0 mod 2^224-2^96+1 to ensure out > in */
out[0] += two120;
out[1] += two120m64;
out[2] += two120m64;
out[3] += two120;
out[4] += two120m104m64;
out[5] += two120m64;
out[6] += two120m64;
out[0] -= in[0];
out[1] -= in[1];
out[2] -= in[2];
out[3] -= in[3];
out[4] -= in[4];
out[5] -= in[5];
out[6] -= in[6];
}
/* Subtract in mixed mode: out128 -= in64 */
/* in[i] < 2^63 */
static void felem_diff_128_64(widefelem out, const felem in) {
static const widelimb two64p8 = (((widelimb)1) << 64) + (((widelimb)1) << 8);
static const widelimb two64m8 = (((widelimb)1) << 64) - (((widelimb)1) << 8);
static const widelimb two64m48m8 =
(((widelimb)1) << 64) - (((widelimb)1) << 48) - (((widelimb)1) << 8);
/* Add 0 mod 2^224-2^96+1 to ensure out > in */
out[0] += two64p8;
out[1] += two64m48m8;
out[2] += two64m8;
out[3] += two64m8;
out[0] -= in[0];
out[1] -= in[1];
out[2] -= in[2];
out[3] -= in[3];
}
/* Multiply a field element by a scalar: out = out * scalar
* The scalars we actually use are small, so results fit without overflow */
static void felem_scalar(felem out, const limb scalar) {
out[0] *= scalar;
out[1] *= scalar;
out[2] *= scalar;
out[3] *= scalar;
}
/* Multiply an unreduced field element by a scalar: out = out * scalar
* The scalars we actually use are small, so results fit without overflow */
static void widefelem_scalar(widefelem out, const widelimb scalar) {
out[0] *= scalar;
out[1] *= scalar;
out[2] *= scalar;
out[3] *= scalar;
out[4] *= scalar;
out[5] *= scalar;
out[6] *= scalar;
}
/* Square a field element: out = in^2 */
static void felem_square(widefelem out, const felem in) {
limb tmp0, tmp1, tmp2;
tmp0 = 2 * in[0];
tmp1 = 2 * in[1];
tmp2 = 2 * in[2];
out[0] = ((widelimb)in[0]) * in[0];
out[1] = ((widelimb)in[0]) * tmp1;
out[2] = ((widelimb)in[0]) * tmp2 + ((widelimb)in[1]) * in[1];
out[3] = ((widelimb)in[3]) * tmp0 + ((widelimb)in[1]) * tmp2;
out[4] = ((widelimb)in[3]) * tmp1 + ((widelimb)in[2]) * in[2];
out[5] = ((widelimb)in[3]) * tmp2;
out[6] = ((widelimb)in[3]) * in[3];
}
/* Multiply two field elements: out = in1 * in2 */
static void felem_mul(widefelem out, const felem in1, const felem in2) {
out[0] = ((widelimb)in1[0]) * in2[0];
out[1] = ((widelimb)in1[0]) * in2[1] + ((widelimb)in1[1]) * in2[0];
out[2] = ((widelimb)in1[0]) * in2[2] + ((widelimb)in1[1]) * in2[1] +
((widelimb)in1[2]) * in2[0];
out[3] = ((widelimb)in1[0]) * in2[3] + ((widelimb)in1[1]) * in2[2] +
((widelimb)in1[2]) * in2[1] + ((widelimb)in1[3]) * in2[0];
out[4] = ((widelimb)in1[1]) * in2[3] + ((widelimb)in1[2]) * in2[2] +
((widelimb)in1[3]) * in2[1];
out[5] = ((widelimb)in1[2]) * in2[3] + ((widelimb)in1[3]) * in2[2];
out[6] = ((widelimb)in1[3]) * in2[3];
}
/* Reduce seven 128-bit coefficients to four 64-bit coefficients.
* Requires in[i] < 2^126,
* ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */
static void felem_reduce(felem out, const widefelem in) {
static const widelimb two127p15 =
(((widelimb)1) << 127) + (((widelimb)1) << 15);
static const widelimb two127m71 =
(((widelimb)1) << 127) - (((widelimb)1) << 71);
static const widelimb two127m71m55 =
(((widelimb)1) << 127) - (((widelimb)1) << 71) - (((widelimb)1) << 55);
widelimb output[5];
/* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
output[0] = in[0] + two127p15;
output[1] = in[1] + two127m71m55;
output[2] = in[2] + two127m71;
output[3] = in[3];
output[4] = in[4];
/* Eliminate in[4], in[5], in[6] */
output[4] += in[6] >> 16;
output[3] += (in[6] & 0xffff) << 40;
output[2] -= in[6];
output[3] += in[5] >> 16;
output[2] += (in[5] & 0xffff) << 40;
output[1] -= in[5];
output[2] += output[4] >> 16;
output[1] += (output[4] & 0xffff) << 40;
output[0] -= output[4];
/* Carry 2 -> 3 -> 4 */
output[3] += output[2] >> 56;
output[2] &= 0x00ffffffffffffff;
output[4] = output[3] >> 56;
output[3] &= 0x00ffffffffffffff;
/* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */
/* Eliminate output[4] */
output[2] += output[4] >> 16;
/* output[2] < 2^56 + 2^56 = 2^57 */
output[1] += (output[4] & 0xffff) << 40;
output[0] -= output[4];
/* Carry 0 -> 1 -> 2 -> 3 */
output[1] += output[0] >> 56;
out[0] = output[0] & 0x00ffffffffffffff;
output[2] += output[1] >> 56;
/* output[2] < 2^57 + 2^72 */
out[1] = output[1] & 0x00ffffffffffffff;
output[3] += output[2] >> 56;
/* output[3] <= 2^56 + 2^16 */
out[2] = output[2] & 0x00ffffffffffffff;
/* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
* out[3] <= 2^56 + 2^16 (due to final carry),
* so out < 2*p */
out[3] = output[3];
}
/* Reduce to unique minimal representation.
* Requires 0 <= in < 2*p (always call felem_reduce first) */
static void felem_contract(felem out, const felem in) {
static const int64_t two56 = ((limb)1) << 56;
/* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */
/* if in > p , reduce in = in - 2^224 + 2^96 - 1 */
int64_t tmp[4], a;
tmp[0] = in[0];
tmp[1] = in[1];
tmp[2] = in[2];
tmp[3] = in[3];
/* Case 1: a = 1 iff in >= 2^224 */
a = (in[3] >> 56);
tmp[0] -= a;
tmp[1] += a << 40;
tmp[3] &= 0x00ffffffffffffff;
/* Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 and
* the lower part is non-zero */
a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) |
(((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63);
a &= 0x00ffffffffffffff;
/* turn a into an all-one mask (if a = 0) or an all-zero mask */
a = (a - 1) >> 63;
/* subtract 2^224 - 2^96 + 1 if a is all-one */
tmp[3] &= a ^ 0xffffffffffffffff;
tmp[2] &= a ^ 0xffffffffffffffff;
tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
tmp[0] -= 1 & a;
/* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must
* be non-zero, so we only need one step */
a = tmp[0] >> 63;
tmp[0] += two56 & a;
tmp[1] -= 1 & a;
/* carry 1 -> 2 -> 3 */
tmp[2] += tmp[1] >> 56;
tmp[1] &= 0x00ffffffffffffff;
tmp[3] += tmp[2] >> 56;
tmp[2] &= 0x00ffffffffffffff;
/* Now 0 <= out < p */
out[0] = tmp[0];
out[1] = tmp[1];
out[2] = tmp[2];
out[3] = tmp[3];
}
/* Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field
* elements are reduced to in < 2^225, so we only need to check three cases: 0,
* 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 */
static limb felem_is_zero(const felem in) {
limb zero = in[0] | in[1] | in[2] | in[3];
zero = (((int64_t)(zero)-1) >> 63) & 1;
limb two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) |
(in[2] ^ 0x00ffffffffffffff) |
(in[3] ^ 0x00ffffffffffffff);
two224m96p1 = (((int64_t)(two224m96p1)-1) >> 63) & 1;
limb two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) |
(in[2] ^ 0x00ffffffffffffff) |
(in[3] ^ 0x01ffffffffffffff);
two225m97p2 = (((int64_t)(two225m97p2)-1) >> 63) & 1;
return (zero | two224m96p1 | two225m97p2);
}
/* Invert a field element */
/* Computation chain copied from djb's code */
static void felem_inv(felem out, const felem in) {
felem ftmp, ftmp2, ftmp3, ftmp4;
widefelem tmp;
felem_square(tmp, in);
felem_reduce(ftmp, tmp); /* 2 */
felem_mul(tmp, in, ftmp);
felem_reduce(ftmp, tmp); /* 2^2 - 1 */
felem_square(tmp, ftmp);
felem_reduce(ftmp, tmp); /* 2^3 - 2 */
felem_mul(tmp, in, ftmp);
felem_reduce(ftmp, tmp); /* 2^3 - 1 */
felem_square(tmp, ftmp);
felem_reduce(ftmp2, tmp); /* 2^4 - 2 */
felem_square(tmp, ftmp2);
felem_reduce(ftmp2, tmp); /* 2^5 - 4 */
felem_square(tmp, ftmp2);
felem_reduce(ftmp2, tmp); /* 2^6 - 8 */
felem_mul(tmp, ftmp2, ftmp);
felem_reduce(ftmp, tmp); /* 2^6 - 1 */
felem_square(tmp, ftmp);
felem_reduce(ftmp2, tmp); /* 2^7 - 2 */
for (size_t i = 0; i < 5; ++i) { /* 2^12 - 2^6 */
felem_square(tmp, ftmp2);
felem_reduce(ftmp2, tmp);
}
felem_mul(tmp, ftmp2, ftmp);
felem_reduce(ftmp2, tmp); /* 2^12 - 1 */
felem_square(tmp, ftmp2);
felem_reduce(ftmp3, tmp); /* 2^13 - 2 */
for (size_t i = 0; i < 11; ++i) {/* 2^24 - 2^12 */
felem_square(tmp, ftmp3);
felem_reduce(ftmp3, tmp);
}
felem_mul(tmp, ftmp3, ftmp2);
felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
felem_square(tmp, ftmp2);
felem_reduce(ftmp3, tmp); /* 2^25 - 2 */
for (size_t i = 0; i < 23; ++i) {/* 2^48 - 2^24 */
felem_square(tmp, ftmp3);
felem_reduce(ftmp3, tmp);
}
felem_mul(tmp, ftmp3, ftmp2);
felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
felem_square(tmp, ftmp3);
felem_reduce(ftmp4, tmp); /* 2^49 - 2 */
for (size_t i = 0; i < 47; ++i) {/* 2^96 - 2^48 */
felem_square(tmp, ftmp4);
felem_reduce(ftmp4, tmp);
}
felem_mul(tmp, ftmp3, ftmp4);
felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
felem_square(tmp, ftmp3);
felem_reduce(ftmp4, tmp); /* 2^97 - 2 */
for (size_t i = 0; i < 23; ++i) {/* 2^120 - 2^24 */
felem_square(tmp, ftmp4);
felem_reduce(ftmp4, tmp);
}
felem_mul(tmp, ftmp2, ftmp4);
felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
for (size_t i = 0; i < 6; ++i) { /* 2^126 - 2^6 */
felem_square(tmp, ftmp2);
felem_reduce(ftmp2, tmp);
}
felem_mul(tmp, ftmp2, ftmp);
felem_reduce(ftmp, tmp); /* 2^126 - 1 */
felem_square(tmp, ftmp);
felem_reduce(ftmp, tmp); /* 2^127 - 2 */
felem_mul(tmp, ftmp, in);
felem_reduce(ftmp, tmp); /* 2^127 - 1 */
for (size_t i = 0; i < 97; ++i) {/* 2^224 - 2^97 */
felem_square(tmp, ftmp);
felem_reduce(ftmp, tmp);
}
felem_mul(tmp, ftmp, ftmp3);
felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */
}
/* Copy in constant time:
* if icopy == 1, copy in to out,
* if icopy == 0, copy out to itself. */
static void copy_conditional(felem out, const felem in, limb icopy) {
/* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
const limb copy = -icopy;
for (size_t i = 0; i < 4; ++i) {
const limb tmp = copy & (in[i] ^ out[i]);
out[i] ^= tmp;
}
}
/* ELLIPTIC CURVE POINT OPERATIONS
*
* Points are represented in Jacobian projective coordinates:
* (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
* or to the point at infinity if Z == 0. */
/* Double an elliptic curve point:
* (X', Y', Z') = 2 * (X, Y, Z), where
* X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
* Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
* Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
* Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
* while x_out == y_in is not (maybe this works, but it's not tested). */
static void point_double(felem x_out, felem y_out, felem z_out,
const felem x_in, const felem y_in, const felem z_in) {
widefelem tmp, tmp2;
felem delta, gamma, beta, alpha, ftmp, ftmp2;
felem_assign(ftmp, x_in);
felem_assign(ftmp2, x_in);
/* delta = z^2 */
felem_square(tmp, z_in);
felem_reduce(delta, tmp);
/* gamma = y^2 */
felem_square(tmp, y_in);
felem_reduce(gamma, tmp);
/* beta = x*gamma */
felem_mul(tmp, x_in, gamma);
felem_reduce(beta, tmp);
/* alpha = 3*(x-delta)*(x+delta) */
felem_diff(ftmp, delta);
/* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
felem_sum(ftmp2, delta);
/* ftmp2[i] < 2^57 + 2^57 = 2^58 */
felem_scalar(ftmp2, 3);
/* ftmp2[i] < 3 * 2^58 < 2^60 */
felem_mul(tmp, ftmp, ftmp2);
/* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
felem_reduce(alpha, tmp);
/* x' = alpha^2 - 8*beta */
felem_square(tmp, alpha);
/* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
felem_assign(ftmp, beta);
felem_scalar(ftmp, 8);
/* ftmp[i] < 8 * 2^57 = 2^60 */
felem_diff_128_64(tmp, ftmp);
/* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
felem_reduce(x_out, tmp);
/* z' = (y + z)^2 - gamma - delta */
felem_sum(delta, gamma);
/* delta[i] < 2^57 + 2^57 = 2^58 */
felem_assign(ftmp, y_in);
felem_sum(ftmp, z_in);
/* ftmp[i] < 2^57 + 2^57 = 2^58 */
felem_square(tmp, ftmp);
/* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
felem_diff_128_64(tmp, delta);
/* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
felem_reduce(z_out, tmp);
/* y' = alpha*(4*beta - x') - 8*gamma^2 */
felem_scalar(beta, 4);
/* beta[i] < 4 * 2^57 = 2^59 */
felem_diff(beta, x_out);
/* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
felem_mul(tmp, alpha, beta);
/* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
felem_square(tmp2, gamma);
/* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
widefelem_scalar(tmp2, 8);
/* tmp2[i] < 8 * 2^116 = 2^119 */
widefelem_diff(tmp, tmp2);
/* tmp[i] < 2^119 + 2^120 < 2^121 */
felem_reduce(y_out, tmp);
}
/* Add two elliptic curve points:
* (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
* X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
* 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
* Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 *
* X_1)^2 - X_3) -
* Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
* Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2)
*
* This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. */
/* This function is not entirely constant-time: it includes a branch for
* checking whether the two input points are equal, (while not equal to the
* point at infinity). This case never happens during single point
* multiplication, so there is no timing leak for ECDH or ECDSA signing. */
static void point_add(felem x3, felem y3, felem z3, const felem x1,
const felem y1, const felem z1, const int mixed,
const felem x2, const felem y2, const felem z2) {
felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out;
widefelem tmp, tmp2;
limb z1_is_zero, z2_is_zero, x_equal, y_equal;
if (!mixed) {
/* ftmp2 = z2^2 */
felem_square(tmp, z2);
felem_reduce(ftmp2, tmp);
/* ftmp4 = z2^3 */
felem_mul(tmp, ftmp2, z2);
felem_reduce(ftmp4, tmp);
/* ftmp4 = z2^3*y1 */
felem_mul(tmp2, ftmp4, y1);
felem_reduce(ftmp4, tmp2);
/* ftmp2 = z2^2*x1 */
felem_mul(tmp2, ftmp2, x1);
felem_reduce(ftmp2, tmp2);
} else {
/* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
/* ftmp4 = z2^3*y1 */
felem_assign(ftmp4, y1);
/* ftmp2 = z2^2*x1 */
felem_assign(ftmp2, x1);
}
/* ftmp = z1^2 */
felem_square(tmp, z1);
felem_reduce(ftmp, tmp);
/* ftmp3 = z1^3 */
felem_mul(tmp, ftmp, z1);
felem_reduce(ftmp3, tmp);
/* tmp = z1^3*y2 */
felem_mul(tmp, ftmp3, y2);
/* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
/* ftmp3 = z1^3*y2 - z2^3*y1 */
felem_diff_128_64(tmp, ftmp4);
/* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
felem_reduce(ftmp3, tmp);
/* tmp = z1^2*x2 */
felem_mul(tmp, ftmp, x2);
/* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
/* ftmp = z1^2*x2 - z2^2*x1 */
felem_diff_128_64(tmp, ftmp2);
/* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
felem_reduce(ftmp, tmp);
/* the formulae are incorrect if the points are equal
* so we check for this and do doubling if this happens */
x_equal = felem_is_zero(ftmp);
y_equal = felem_is_zero(ftmp3);
z1_is_zero = felem_is_zero(z1);
z2_is_zero = felem_is_zero(z2);
/* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
point_double(x3, y3, z3, x1, y1, z1);
return;
}
/* ftmp5 = z1*z2 */
if (!mixed) {
felem_mul(tmp, z1, z2);
felem_reduce(ftmp5, tmp);
} else {
/* special case z2 = 0 is handled later */
felem_assign(ftmp5, z1);
}
/* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */
felem_mul(tmp, ftmp, ftmp5);
felem_reduce(z_out, tmp);
/* ftmp = (z1^2*x2 - z2^2*x1)^2 */
felem_assign(ftmp5, ftmp);
felem_square(tmp, ftmp);
felem_reduce(ftmp, tmp);
/* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
felem_mul(tmp, ftmp, ftmp5);
felem_reduce(ftmp5, tmp);
/* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
felem_mul(tmp, ftmp2, ftmp);
felem_reduce(ftmp2, tmp);
/* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
felem_mul(tmp, ftmp4, ftmp5);
/* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
/* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
felem_square(tmp2, ftmp3);
/* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
/* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
felem_diff_128_64(tmp2, ftmp5);
/* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
/* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
felem_assign(ftmp5, ftmp2);
felem_scalar(ftmp5, 2);
/* ftmp5[i] < 2 * 2^57 = 2^58 */
/* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
felem_diff_128_64(tmp2, ftmp5);
/* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
felem_reduce(x_out, tmp2);
/* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */
felem_diff(ftmp2, x_out);
/* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
/* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */
felem_mul(tmp2, ftmp3, ftmp2);
/* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
/* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) -
z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
widefelem_diff(tmp2, tmp);
/* tmp2[i] < 2^118 + 2^120 < 2^121 */
felem_reduce(y_out, tmp2);
/* the result (x_out, y_out, z_out) is incorrect if one of the inputs is
* the point at infinity, so we need to check for this separately */
/* if point 1 is at infinity, copy point 2 to output, and vice versa */
copy_conditional(x_out, x2, z1_is_zero);
copy_conditional(x_out, x1, z2_is_zero);
copy_conditional(y_out, y2, z1_is_zero);
copy_conditional(y_out, y1, z2_is_zero);
copy_conditional(z_out, z2, z1_is_zero);
copy_conditional(z_out, z1, z2_is_zero);
felem_assign(x3, x_out);
felem_assign(y3, y_out);
felem_assign(z3, z_out);
}
/* select_point selects the |idx|th point from a precomputation table and
* copies it to out. */
static void select_point(const u64 idx, size_t size,
const felem pre_comp[/*size*/][3], felem out[3]) {
limb *outlimbs = &out[0][0];
OPENSSL_memset(outlimbs, 0, 3 * sizeof(felem));
for (size_t i = 0; i < size; i++) {
const limb *inlimbs = &pre_comp[i][0][0];
u64 mask = i ^ idx;
mask |= mask >> 4;
mask |= mask >> 2;
mask |= mask >> 1;
mask &= 1;
mask--;
for (size_t j = 0; j < 4 * 3; j++) {
outlimbs[j] |= inlimbs[j] & mask;
}
}
}
/* get_bit returns the |i|th bit in |in| */
static char get_bit(const felem_bytearray in, size_t i) {
if (i >= 224) {
return 0;
}
return (in[i >> 3] >> (i & 7)) & 1;
}
/* Interleaved point multiplication using precomputed point multiples:
* The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[],
* the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
* of the generator, using certain (large) precomputed multiples in g_pre_comp.
* Output point (X, Y, Z) is stored in x_out, y_out, z_out */
static void batch_mul(felem x_out, felem y_out, felem z_out,
const felem_bytearray scalars[],
const size_t num_points, const u8 *g_scalar,
const felem pre_comp[][17][3]) {
felem nq[3], tmp[4];
u64 bits;
u8 sign, digit;
/* set nq to the point at infinity */
OPENSSL_memset(nq, 0, 3 * sizeof(felem));
/* Loop over all scalars msb-to-lsb, interleaving additions
* of multiples of the generator (two in each of the last 28 rounds)
* and additions of other points multiples (every 5th round). */
int skip = 1; /* save two point operations in the first round */
size_t i = num_points != 0 ? 220 : 27;
for (;;) {
/* double */
if (!skip) {
point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
}
/* add multiples of the generator */
if (g_scalar != NULL && i <= 27) {
/* first, look 28 bits upwards */
bits = get_bit(g_scalar, i + 196) << 3;
bits |= get_bit(g_scalar, i + 140) << 2;
bits |= get_bit(g_scalar, i + 84) << 1;
bits |= get_bit(g_scalar, i + 28);
/* select the point to add, in constant time */
select_point(bits, 16, g_pre_comp[1], tmp);
if (!skip) {
point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */,
tmp[0], tmp[1], tmp[2]);
} else {
OPENSSL_memcpy(nq, tmp, 3 * sizeof(felem));
skip = 0;
}
/* second, look at the current position */
bits = get_bit(g_scalar, i + 168) << 3;
bits |= get_bit(g_scalar, i + 112) << 2;
bits |= get_bit(g_scalar, i + 56) << 1;
bits |= get_bit(g_scalar, i);
/* select the point to add, in constant time */
select_point(bits, 16, g_pre_comp[0], tmp);
point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, tmp[0],
tmp[1], tmp[2]);
}
/* do other additions every 5 doublings */
if (num_points != 0 && i % 5 == 0) {
/* loop over all scalars */
size_t num;
for (num = 0; num < num_points; ++num) {
bits = get_bit(scalars[num], i + 4) << 5;
bits |= get_bit(scalars[num], i + 3) << 4;
bits |= get_bit(scalars[num], i + 2) << 3;
bits |= get_bit(scalars[num], i + 1) << 2;
bits |= get_bit(scalars[num], i) << 1;
bits |= get_bit(scalars[num], i - 1);
ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
/* select the point to add or subtract */
select_point(digit, 17, pre_comp[num], tmp);
felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */
copy_conditional(tmp[1], tmp[3], sign);
if (!skip) {
point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */,
tmp[0], tmp[1], tmp[2]);
} else {
OPENSSL_memcpy(nq, tmp, 3 * sizeof(felem));
skip = 0;
}
}
}
if (i == 0) {
break;
}
--i;
}
felem_assign(x_out, nq[0]);
felem_assign(y_out, nq[1]);
felem_assign(z_out, nq[2]);
}
/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
* (X', Y') = (X/Z^2, Y/Z^3) */
static int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
const EC_POINT *point,
BIGNUM *x, BIGNUM *y,
BN_CTX *ctx) {
felem z1, z2, x_in, y_in, x_out, y_out;
widefelem tmp;
if (EC_POINT_is_at_infinity(group, point)) {
OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
return 0;
}
if (!BN_to_felem(x_in, &point->X) ||
!BN_to_felem(y_in, &point->Y) ||
!BN_to_felem(z1, &point->Z)) {
return 0;
}
felem_inv(z2, z1);
felem_square(tmp, z2);
felem_reduce(z1, tmp);
felem_mul(tmp, x_in, z1);
felem_reduce(x_in, tmp);
felem_contract(x_out, x_in);
if (x != NULL && !felem_to_BN(x, x_out)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
return 0;
}
felem_mul(tmp, z1, z2);
felem_reduce(z1, tmp);
felem_mul(tmp, y_in, z1);
felem_reduce(y_in, tmp);
felem_contract(y_out, y_in);
if (y != NULL && !felem_to_BN(y, y_out)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
return 0;
}
return 1;
}
static int ec_GFp_nistp224_points_mul(const EC_GROUP *group,
EC_POINT *r,
const BIGNUM *g_scalar,
const EC_POINT *p_,
const BIGNUM *p_scalar_,
BN_CTX *ctx) {
/* TODO: This function used to take |points| and |scalars| as arrays of
* |num| elements. The code below should be simplified to work in terms of
* |p_| and |p_scalar_|. */
size_t num = p_ != NULL ? 1 : 0;
const EC_POINT **points = p_ != NULL ? &p_ : NULL;
BIGNUM const *const *scalars = p_ != NULL ? &p_scalar_ : NULL;
int ret = 0;
BN_CTX *new_ctx = NULL;
BIGNUM *x, *y, *z, *tmp_scalar;
felem_bytearray g_secret;
felem_bytearray *secrets = NULL;
felem(*pre_comp)[17][3] = NULL;
felem_bytearray tmp;
size_t num_points = num;
felem x_in, y_in, z_in, x_out, y_out, z_out;
const EC_POINT *p = NULL;
const BIGNUM *p_scalar = NULL;
if (ctx == NULL) {
ctx = BN_CTX_new();
new_ctx = ctx;
if (ctx == NULL) {
return 0;
}
}
BN_CTX_start(ctx);
if ((x = BN_CTX_get(ctx)) == NULL ||
(y = BN_CTX_get(ctx)) == NULL ||
(z = BN_CTX_get(ctx)) == NULL ||
(tmp_scalar = BN_CTX_get(ctx)) == NULL) {
goto err;
}
if (num_points > 0) {
secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
pre_comp = OPENSSL_malloc(num_points * sizeof(felem[17][3]));
if (secrets == NULL ||
pre_comp == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
/* we treat NULL scalars as 0, and NULL points as points at infinity,
* i.e., they contribute nothing to the linear combination */
OPENSSL_memset(secrets, 0, num_points * sizeof(felem_bytearray));
OPENSSL_memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem));
for (size_t i = 0; i < num_points; ++i) {
if (i == num) {
/* the generator */
p = EC_GROUP_get0_generator(group);
p_scalar = g_scalar;
} else {
/* the i^th point */
p = points[i];
p_scalar = scalars[i];
}
if (p_scalar != NULL && p != NULL) {
size_t num_bytes;
/* reduce g_scalar to 0 <= g_scalar < 2^224 */
if (BN_num_bits(p_scalar) > 224 || BN_is_negative(p_scalar)) {
/* this is an unusual input, and we don't guarantee
* constant-timeness */
if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
}
num_bytes = BN_bn2bin(tmp_scalar, tmp);
} else {
num_bytes = BN_bn2bin(p_scalar, tmp);
}
flip_endian(secrets[i], tmp, num_bytes);
/* precompute multiples */
if (!BN_to_felem(x_out, &p->X) ||
!BN_to_felem(y_out, &p->Y) ||
!BN_to_felem(z_out, &p->Z)) {
goto err;
}
felem_assign(pre_comp[i][1][0], x_out);
felem_assign(pre_comp[i][1][1], y_out);
felem_assign(pre_comp[i][1][2], z_out);
for (size_t j = 2; j <= 16; ++j) {
if (j & 1) {
point_add(pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1],
pre_comp[i][j - 1][2]);
} else {
point_double(pre_comp[i][j][0], pre_comp[i][j][1],
pre_comp[i][j][2], pre_comp[i][j / 2][0],
pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]);
}
}
}
}
}
if (g_scalar != NULL) {
OPENSSL_memset(g_secret, 0, sizeof(g_secret));
size_t num_bytes;
/* reduce g_scalar to 0 <= g_scalar < 2^224 */
if (BN_num_bits(g_scalar) > 224 || BN_is_negative(g_scalar)) {
/* this is an unusual input, and we don't guarantee constant-timeness */
if (!BN_nnmod(tmp_scalar, g_scalar, &group->order, ctx)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
}
num_bytes = BN_bn2bin(tmp_scalar, tmp);
} else {
num_bytes = BN_bn2bin(g_scalar, tmp);
}
flip_endian(g_secret, tmp, num_bytes);
}
batch_mul(x_out, y_out, z_out, (const felem_bytearray(*))secrets,
num_points, g_scalar != NULL ? g_secret : NULL,
(const felem(*)[17][3])pre_comp);
/* reduce the output to its unique minimal representation */
felem_contract(x_in, x_out);
felem_contract(y_in, y_out);
felem_contract(z_in, z_out);
if (!felem_to_BN(x, x_in) ||
!felem_to_BN(y, y_in) ||
!felem_to_BN(z, z_in)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
}
ret = ec_point_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
err:
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
OPENSSL_free(secrets);
OPENSSL_free(pre_comp);
return ret;
}
const EC_METHOD EC_GFp_nistp224_method = {
ec_GFp_simple_group_init,
ec_GFp_simple_group_finish,
ec_GFp_simple_group_copy,
ec_GFp_simple_group_set_curve,
ec_GFp_nistp224_point_get_affine_coordinates,
ec_GFp_nistp224_points_mul,
ec_GFp_simple_field_mul,
ec_GFp_simple_field_sqr,
NULL /* field_encode */,
NULL /* field_decode */,
};
#endif /* 64_BIT && !WINDOWS && !SMALL */
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