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diff --git a/thirdparty/openssl/crypto/ec/ecp_nistp256.c b/thirdparty/openssl/crypto/ec/ecp_nistp256.c
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-/* crypto/ec/ecp_nistp256.c */
-/*
- * Written by Adam Langley (Google) for the OpenSSL project
- */
-/* Copyright 2011 Google Inc.
- *
- * Licensed under the Apache License, Version 2.0 (the "License");
- *
- * you may not use this file except in compliance with the License.
- * You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-/*
- * A 64-bit implementation of the NIST P-256 elliptic curve point multiplication
- *
- * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c.
- * Otherwise based on Emilia's P224 work, which was inspired by my curve25519
- * work which got its smarts from Daniel J. Bernstein's work on the same.
- */
-
-#include <openssl/opensslconf.h>
-#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
-
-# ifndef OPENSSL_SYS_VMS
-# include <stdint.h>
-# else
-# include <inttypes.h>
-# endif
-
-# include <string.h>
-# include <openssl/err.h>
-# include "ec_lcl.h"
-
-# if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
- /* even with gcc, the typedef won't work for 32-bit platforms */
-typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit
- * platforms */
-typedef __int128_t int128_t;
-# else
-# error "Need GCC 3.1 or later to define type uint128_t"
-# endif
-
-typedef uint8_t u8;
-typedef uint32_t u32;
-typedef uint64_t u64;
-typedef int64_t s64;
-
-/*
- * The underlying field. P256 operates over GF(2^256-2^224+2^192+2^96-1). We
- * can serialise an element of this field into 32 bytes. We call this an
- * felem_bytearray.
- */
-
-typedef u8 felem_bytearray[32];
-
-/*
- * These are the parameters of P256, taken from FIPS 186-3, page 86. These
- * values are big-endian.
- */
-static const felem_bytearray nistp256_curve_params[5] = {
- {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
- 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
- {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
- 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */
- {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7,
- 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc,
- 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6,
- 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b},
- {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */
- 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2,
- 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0,
- 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96},
- {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */
- 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16,
- 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce,
- 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5}
-};
-
-/*-
- * The representation of field elements.
- * ------------------------------------
- *
- * We represent field elements with either four 128-bit values, eight 128-bit
- * values, or four 64-bit values. The field element represented is:
- * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p)
- * or:
- * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p)
- *
- * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits
- * apart, but are 128-bits wide, the most significant bits of each limb overlap
- * with the least significant bits of the next.
- *
- * A field element with four limbs is an 'felem'. One with eight limbs is a
- * 'longfelem'
- *
- * A field element with four, 64-bit values is called a 'smallfelem'. Small
- * values are used as intermediate values before multiplication.
- */
-
-# define NLIMBS 4
-
-typedef uint128_t limb;
-typedef limb felem[NLIMBS];
-typedef limb longfelem[NLIMBS * 2];
-typedef u64 smallfelem[NLIMBS];
-
-/* This is the value of the prime as four 64-bit words, little-endian. */
-static const u64 kPrime[4] =
- { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul };
-static const u64 bottom63bits = 0x7ffffffffffffffful;
-
-/*
- * bin32_to_felem takes a little-endian byte array and converts it into felem
- * form. This assumes that the CPU is little-endian.
- */
-static void bin32_to_felem(felem out, const u8 in[32])
-{
- out[0] = *((u64 *)&in[0]);
- out[1] = *((u64 *)&in[8]);
- out[2] = *((u64 *)&in[16]);
- out[3] = *((u64 *)&in[24]);
-}
-
-/*
- * smallfelem_to_bin32 takes a smallfelem and serialises into a little
- * endian, 32 byte array. This assumes that the CPU is little-endian.
- */
-static void smallfelem_to_bin32(u8 out[32], const smallfelem in)
-{
- *((u64 *)&out[0]) = in[0];
- *((u64 *)&out[8]) = in[1];
- *((u64 *)&out[16]) = in[2];
- *((u64 *)&out[24]) = in[3];
-}
-
-/* To preserve endianness when using BN_bn2bin and BN_bin2bn */
-static void flip_endian(u8 *out, const u8 *in, unsigned len)
-{
- unsigned i;
- for (i = 0; i < len; ++i)
- out[i] = in[len - 1 - i];
-}
-
-/* BN_to_felem converts an OpenSSL BIGNUM into an felem */
-static int BN_to_felem(felem out, const BIGNUM *bn)
-{
- felem_bytearray b_in;
- felem_bytearray b_out;
- unsigned num_bytes;
-
- /* BN_bn2bin eats leading zeroes */
- memset(b_out, 0, sizeof b_out);
- num_bytes = BN_num_bytes(bn);
- if (num_bytes > sizeof b_out) {
- ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
- return 0;
- }
- if (BN_is_negative(bn)) {
- ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
- return 0;
- }
- num_bytes = BN_bn2bin(bn, b_in);
- flip_endian(b_out, b_in, num_bytes);
- bin32_to_felem(out, b_out);
- return 1;
-}
-
-/* felem_to_BN converts an felem into an OpenSSL BIGNUM */
-static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in)
-{
- felem_bytearray b_in, b_out;
- smallfelem_to_bin32(b_in, in);
- flip_endian(b_out, b_in, sizeof b_out);
- return BN_bin2bn(b_out, sizeof b_out, out);
-}
-
-/*-
- * Field operations
- * ----------------
- */
-
-static void smallfelem_one(smallfelem out)
-{
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
-}
-
-static void smallfelem_assign(smallfelem out, const smallfelem in)
-{
- out[0] = in[0];
- out[1] = in[1];
- out[2] = in[2];
- out[3] = in[3];
-}
-
-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];
-}
-
-/* felem_sum sets out = 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];
-}
-
-/* felem_small_sum sets out = out + in. */
-static void felem_small_sum(felem out, const smallfelem in)
-{
- out[0] += in[0];
- out[1] += in[1];
- out[2] += in[2];
- out[3] += in[3];
-}
-
-/* felem_scalar sets out = out * scalar */
-static void felem_scalar(felem out, const u64 scalar)
-{
- out[0] *= scalar;
- out[1] *= scalar;
- out[2] *= scalar;
- out[3] *= scalar;
-}
-
-/* longfelem_scalar sets out = out * scalar */
-static void longfelem_scalar(longfelem out, const u64 scalar)
-{
- out[0] *= scalar;
- out[1] *= scalar;
- out[2] *= scalar;
- out[3] *= scalar;
- out[4] *= scalar;
- out[5] *= scalar;
- out[6] *= scalar;
- out[7] *= scalar;
-}
-
-# define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9)
-# define two105 (((limb)1) << 105)
-# define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9)
-
-/* zero105 is 0 mod p */
-static const felem zero105 =
- { two105m41m9, two105, two105m41p9, two105m41p9 };
-
-/*-
- * smallfelem_neg sets |out| to |-small|
- * On exit:
- * out[i] < out[i] + 2^105
- */
-static void smallfelem_neg(felem out, const smallfelem small)
-{
- /* In order to prevent underflow, we subtract from 0 mod p. */
- out[0] = zero105[0] - small[0];
- out[1] = zero105[1] - small[1];
- out[2] = zero105[2] - small[2];
- out[3] = zero105[3] - small[3];
-}
-
-/*-
- * felem_diff subtracts |in| from |out|
- * On entry:
- * in[i] < 2^104
- * On exit:
- * out[i] < out[i] + 2^105
- */
-static void felem_diff(felem out, const felem in)
-{
- /*
- * In order to prevent underflow, we add 0 mod p before subtracting.
- */
- out[0] += zero105[0];
- out[1] += zero105[1];
- out[2] += zero105[2];
- out[3] += zero105[3];
-
- out[0] -= in[0];
- out[1] -= in[1];
- out[2] -= in[2];
- out[3] -= in[3];
-}
-
-# define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11)
-# define two107 (((limb)1) << 107)
-# define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11)
-
-/* zero107 is 0 mod p */
-static const felem zero107 =
- { two107m43m11, two107, two107m43p11, two107m43p11 };
-
-/*-
- * An alternative felem_diff for larger inputs |in|
- * felem_diff_zero107 subtracts |in| from |out|
- * On entry:
- * in[i] < 2^106
- * On exit:
- * out[i] < out[i] + 2^107
- */
-static void felem_diff_zero107(felem out, const felem in)
-{
- /*
- * In order to prevent underflow, we add 0 mod p before subtracting.
- */
- out[0] += zero107[0];
- out[1] += zero107[1];
- out[2] += zero107[2];
- out[3] += zero107[3];
-
- out[0] -= in[0];
- out[1] -= in[1];
- out[2] -= in[2];
- out[3] -= in[3];
-}
-
-/*-
- * longfelem_diff subtracts |in| from |out|
- * On entry:
- * in[i] < 7*2^67
- * On exit:
- * out[i] < out[i] + 2^70 + 2^40
- */
-static void longfelem_diff(longfelem out, const longfelem in)
-{
- static const limb two70m8p6 =
- (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6);
- static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40);
- static const limb two70 = (((limb) 1) << 70);
- static const limb two70m40m38p6 =
- (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) +
- (((limb) 1) << 6);
- static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6);
-
- /* add 0 mod p to avoid underflow */
- out[0] += two70m8p6;
- out[1] += two70p40;
- out[2] += two70;
- out[3] += two70m40m38p6;
- out[4] += two70m6;
- out[5] += two70m6;
- out[6] += two70m6;
- out[7] += two70m6;
-
- /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */
- 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];
- out[7] -= in[7];
-}
-
-# define two64m0 (((limb)1) << 64) - 1
-# define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1
-# define two64m46 (((limb)1) << 64) - (((limb)1) << 46)
-# define two64m32 (((limb)1) << 64) - (((limb)1) << 32)
-
-/* zero110 is 0 mod p */
-static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 };
-
-/*-
- * felem_shrink converts an felem into a smallfelem. The result isn't quite
- * minimal as the value may be greater than p.
- *
- * On entry:
- * in[i] < 2^109
- * On exit:
- * out[i] < 2^64
- */
-static void felem_shrink(smallfelem out, const felem in)
-{
- felem tmp;
- u64 a, b, mask;
- s64 high, low;
- static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */
-
- /* Carry 2->3 */
- tmp[3] = zero110[3] + in[3] + ((u64)(in[2] >> 64));
- /* tmp[3] < 2^110 */
-
- tmp[2] = zero110[2] + (u64)in[2];
- tmp[0] = zero110[0] + in[0];
- tmp[1] = zero110[1] + in[1];
- /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */
-
- /*
- * We perform two partial reductions where we eliminate the high-word of
- * tmp[3]. We don't update the other words till the end.
- */
- a = tmp[3] >> 64; /* a < 2^46 */
- tmp[3] = (u64)tmp[3];
- tmp[3] -= a;
- tmp[3] += ((limb) a) << 32;
- /* tmp[3] < 2^79 */
-
- b = a;
- a = tmp[3] >> 64; /* a < 2^15 */
- b += a; /* b < 2^46 + 2^15 < 2^47 */
- tmp[3] = (u64)tmp[3];
- tmp[3] -= a;
- tmp[3] += ((limb) a) << 32;
- /* tmp[3] < 2^64 + 2^47 */
-
- /*
- * This adjusts the other two words to complete the two partial
- * reductions.
- */
- tmp[0] += b;
- tmp[1] -= (((limb) b) << 32);
-
- /*
- * In order to make space in tmp[3] for the carry from 2 -> 3, we
- * conditionally subtract kPrime if tmp[3] is large enough.
- */
- high = tmp[3] >> 64;
- /* As tmp[3] < 2^65, high is either 1 or 0 */
- high <<= 63;
- high >>= 63;
- /*-
- * high is:
- * all ones if the high word of tmp[3] is 1
- * all zeros if the high word of tmp[3] if 0 */
- low = tmp[3];
- mask = low >> 63;
- /*-
- * mask is:
- * all ones if the MSB of low is 1
- * all zeros if the MSB of low if 0 */
- low &= bottom63bits;
- low -= kPrime3Test;
- /* if low was greater than kPrime3Test then the MSB is zero */
- low = ~low;
- low >>= 63;
- /*-
- * low is:
- * all ones if low was > kPrime3Test
- * all zeros if low was <= kPrime3Test */
- mask = (mask & low) | high;
- tmp[0] -= mask & kPrime[0];
- tmp[1] -= mask & kPrime[1];
- /* kPrime[2] is zero, so omitted */
- tmp[3] -= mask & kPrime[3];
- /* tmp[3] < 2**64 - 2**32 + 1 */
-
- tmp[1] += ((u64)(tmp[0] >> 64));
- tmp[0] = (u64)tmp[0];
- tmp[2] += ((u64)(tmp[1] >> 64));
- tmp[1] = (u64)tmp[1];
- tmp[3] += ((u64)(tmp[2] >> 64));
- tmp[2] = (u64)tmp[2];
- /* tmp[i] < 2^64 */
-
- out[0] = tmp[0];
- out[1] = tmp[1];
- out[2] = tmp[2];
- out[3] = tmp[3];
-}
-
-/* smallfelem_expand converts a smallfelem to an felem */
-static void smallfelem_expand(felem out, const smallfelem in)
-{
- out[0] = in[0];
- out[1] = in[1];
- out[2] = in[2];
- out[3] = in[3];
-}
-
-/*-
- * smallfelem_square sets |out| = |small|^2
- * On entry:
- * small[i] < 2^64
- * On exit:
- * out[i] < 7 * 2^64 < 2^67
- */
-static void smallfelem_square(longfelem out, const smallfelem small)
-{
- limb a;
- u64 high, low;
-
- a = ((uint128_t) small[0]) * small[0];
- low = a;
- high = a >> 64;
- out[0] = low;
- out[1] = high;
-
- a = ((uint128_t) small[0]) * small[1];
- low = a;
- high = a >> 64;
- out[1] += low;
- out[1] += low;
- out[2] = high;
-
- a = ((uint128_t) small[0]) * small[2];
- low = a;
- high = a >> 64;
- out[2] += low;
- out[2] *= 2;
- out[3] = high;
-
- a = ((uint128_t) small[0]) * small[3];
- low = a;
- high = a >> 64;
- out[3] += low;
- out[4] = high;
-
- a = ((uint128_t) small[1]) * small[2];
- low = a;
- high = a >> 64;
- out[3] += low;
- out[3] *= 2;
- out[4] += high;
-
- a = ((uint128_t) small[1]) * small[1];
- low = a;
- high = a >> 64;
- out[2] += low;
- out[3] += high;
-
- a = ((uint128_t) small[1]) * small[3];
- low = a;
- high = a >> 64;
- out[4] += low;
- out[4] *= 2;
- out[5] = high;
-
- a = ((uint128_t) small[2]) * small[3];
- low = a;
- high = a >> 64;
- out[5] += low;
- out[5] *= 2;
- out[6] = high;
- out[6] += high;
-
- a = ((uint128_t) small[2]) * small[2];
- low = a;
- high = a >> 64;
- out[4] += low;
- out[5] += high;
-
- a = ((uint128_t) small[3]) * small[3];
- low = a;
- high = a >> 64;
- out[6] += low;
- out[7] = high;
-}
-
-/*-
- * felem_square sets |out| = |in|^2
- * On entry:
- * in[i] < 2^109
- * On exit:
- * out[i] < 7 * 2^64 < 2^67
- */
-static void felem_square(longfelem out, const felem in)
-{
- u64 small[4];
- felem_shrink(small, in);
- smallfelem_square(out, small);
-}
-
-/*-
- * smallfelem_mul sets |out| = |small1| * |small2|
- * On entry:
- * small1[i] < 2^64
- * small2[i] < 2^64
- * On exit:
- * out[i] < 7 * 2^64 < 2^67
- */
-static void smallfelem_mul(longfelem out, const smallfelem small1,
- const smallfelem small2)
-{
- limb a;
- u64 high, low;
-
- a = ((uint128_t) small1[0]) * small2[0];
- low = a;
- high = a >> 64;
- out[0] = low;
- out[1] = high;
-
- a = ((uint128_t) small1[0]) * small2[1];
- low = a;
- high = a >> 64;
- out[1] += low;
- out[2] = high;
-
- a = ((uint128_t) small1[1]) * small2[0];
- low = a;
- high = a >> 64;
- out[1] += low;
- out[2] += high;
-
- a = ((uint128_t) small1[0]) * small2[2];
- low = a;
- high = a >> 64;
- out[2] += low;
- out[3] = high;
-
- a = ((uint128_t) small1[1]) * small2[1];
- low = a;
- high = a >> 64;
- out[2] += low;
- out[3] += high;
-
- a = ((uint128_t) small1[2]) * small2[0];
- low = a;
- high = a >> 64;
- out[2] += low;
- out[3] += high;
-
- a = ((uint128_t) small1[0]) * small2[3];
- low = a;
- high = a >> 64;
- out[3] += low;
- out[4] = high;
-
- a = ((uint128_t) small1[1]) * small2[2];
- low = a;
- high = a >> 64;
- out[3] += low;
- out[4] += high;
-
- a = ((uint128_t) small1[2]) * small2[1];
- low = a;
- high = a >> 64;
- out[3] += low;
- out[4] += high;
-
- a = ((uint128_t) small1[3]) * small2[0];
- low = a;
- high = a >> 64;
- out[3] += low;
- out[4] += high;
-
- a = ((uint128_t) small1[1]) * small2[3];
- low = a;
- high = a >> 64;
- out[4] += low;
- out[5] = high;
-
- a = ((uint128_t) small1[2]) * small2[2];
- low = a;
- high = a >> 64;
- out[4] += low;
- out[5] += high;
-
- a = ((uint128_t) small1[3]) * small2[1];
- low = a;
- high = a >> 64;
- out[4] += low;
- out[5] += high;
-
- a = ((uint128_t) small1[2]) * small2[3];
- low = a;
- high = a >> 64;
- out[5] += low;
- out[6] = high;
-
- a = ((uint128_t) small1[3]) * small2[2];
- low = a;
- high = a >> 64;
- out[5] += low;
- out[6] += high;
-
- a = ((uint128_t) small1[3]) * small2[3];
- low = a;
- high = a >> 64;
- out[6] += low;
- out[7] = high;
-}
-
-/*-
- * felem_mul sets |out| = |in1| * |in2|
- * On entry:
- * in1[i] < 2^109
- * in2[i] < 2^109
- * On exit:
- * out[i] < 7 * 2^64 < 2^67
- */
-static void felem_mul(longfelem out, const felem in1, const felem in2)
-{
- smallfelem small1, small2;
- felem_shrink(small1, in1);
- felem_shrink(small2, in2);
- smallfelem_mul(out, small1, small2);
-}
-
-/*-
- * felem_small_mul sets |out| = |small1| * |in2|
- * On entry:
- * small1[i] < 2^64
- * in2[i] < 2^109
- * On exit:
- * out[i] < 7 * 2^64 < 2^67
- */
-static void felem_small_mul(longfelem out, const smallfelem small1,
- const felem in2)
-{
- smallfelem small2;
- felem_shrink(small2, in2);
- smallfelem_mul(out, small1, small2);
-}
-
-# define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4)
-# define two100 (((limb)1) << 100)
-# define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4)
-/* zero100 is 0 mod p */
-static const felem zero100 =
- { two100m36m4, two100, two100m36p4, two100m36p4 };
-
-/*-
- * Internal function for the different flavours of felem_reduce.
- * felem_reduce_ reduces the higher coefficients in[4]-in[7].
- * On entry:
- * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7]
- * out[1] >= in[7] + 2^32*in[4]
- * out[2] >= in[5] + 2^32*in[5]
- * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6]
- * On exit:
- * out[0] <= out[0] + in[4] + 2^32*in[5]
- * out[1] <= out[1] + in[5] + 2^33*in[6]
- * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7]
- * out[3] <= out[3] + 2^32*in[4] + 3*in[7]
- */
-static void felem_reduce_(felem out, const longfelem in)
-{
- int128_t c;
- /* combine common terms from below */
- c = in[4] + (in[5] << 32);
- out[0] += c;
- out[3] -= c;
-
- c = in[5] - in[7];
- out[1] += c;
- out[2] -= c;
-
- /* the remaining terms */
- /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */
- out[1] -= (in[4] << 32);
- out[3] += (in[4] << 32);
-
- /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */
- out[2] -= (in[5] << 32);
-
- /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */
- out[0] -= in[6];
- out[0] -= (in[6] << 32);
- out[1] += (in[6] << 33);
- out[2] += (in[6] * 2);
- out[3] -= (in[6] << 32);
-
- /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */
- out[0] -= in[7];
- out[0] -= (in[7] << 32);
- out[2] += (in[7] << 33);
- out[3] += (in[7] * 3);
-}
-
-/*-
- * felem_reduce converts a longfelem into an felem.
- * To be called directly after felem_square or felem_mul.
- * On entry:
- * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64
- * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64
- * On exit:
- * out[i] < 2^101
- */
-static void felem_reduce(felem out, const longfelem in)
-{
- out[0] = zero100[0] + in[0];
- out[1] = zero100[1] + in[1];
- out[2] = zero100[2] + in[2];
- out[3] = zero100[3] + in[3];
-
- felem_reduce_(out, in);
-
- /*-
- * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0
- * out[1] > 2^100 - 2^64 - 7*2^96 > 0
- * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0
- * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0
- *
- * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101
- * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101
- * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101
- * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101
- */
-}
-
-/*-
- * felem_reduce_zero105 converts a larger longfelem into an felem.
- * On entry:
- * in[0] < 2^71
- * On exit:
- * out[i] < 2^106
- */
-static void felem_reduce_zero105(felem out, const longfelem in)
-{
- out[0] = zero105[0] + in[0];
- out[1] = zero105[1] + in[1];
- out[2] = zero105[2] + in[2];
- out[3] = zero105[3] + in[3];
-
- felem_reduce_(out, in);
-
- /*-
- * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0
- * out[1] > 2^105 - 2^71 - 2^103 > 0
- * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0
- * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0
- *
- * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106
- * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106
- * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106
- * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106
- */
-}
-
-/*
- * subtract_u64 sets *result = *result - v and *carry to one if the
- * subtraction underflowed.
- */
-static void subtract_u64(u64 *result, u64 *carry, u64 v)
-{
- uint128_t r = *result;
- r -= v;
- *carry = (r >> 64) & 1;
- *result = (u64)r;
-}
-
-/*
- * felem_contract converts |in| to its unique, minimal representation. On
- * entry: in[i] < 2^109
- */
-static void felem_contract(smallfelem out, const felem in)
-{
- unsigned i;
- u64 all_equal_so_far = 0, result = 0, carry;
-
- felem_shrink(out, in);
- /* small is minimal except that the value might be > p */
-
- all_equal_so_far--;
- /*
- * We are doing a constant time test if out >= kPrime. We need to compare
- * each u64, from most-significant to least significant. For each one, if
- * all words so far have been equal (m is all ones) then a non-equal
- * result is the answer. Otherwise we continue.
- */
- for (i = 3; i < 4; i--) {
- u64 equal;
- uint128_t a = ((uint128_t) kPrime[i]) - out[i];
- /*
- * if out[i] > kPrime[i] then a will underflow and the high 64-bits
- * will all be set.
- */
- result |= all_equal_so_far & ((u64)(a >> 64));
-
- /*
- * if kPrime[i] == out[i] then |equal| will be all zeros and the
- * decrement will make it all ones.
- */
- equal = kPrime[i] ^ out[i];
- equal--;
- equal &= equal << 32;
- equal &= equal << 16;
- equal &= equal << 8;
- equal &= equal << 4;
- equal &= equal << 2;
- equal &= equal << 1;
- equal = ((s64) equal) >> 63;
-
- all_equal_so_far &= equal;
- }
-
- /*
- * if all_equal_so_far is still all ones then the two values are equal
- * and so out >= kPrime is true.
- */
- result |= all_equal_so_far;
-
- /* if out >= kPrime then we subtract kPrime. */
- subtract_u64(&out[0], &carry, result & kPrime[0]);
- subtract_u64(&out[1], &carry, carry);
- subtract_u64(&out[2], &carry, carry);
- subtract_u64(&out[3], &carry, carry);
-
- subtract_u64(&out[1], &carry, result & kPrime[1]);
- subtract_u64(&out[2], &carry, carry);
- subtract_u64(&out[3], &carry, carry);
-
- subtract_u64(&out[2], &carry, result & kPrime[2]);
- subtract_u64(&out[3], &carry, carry);
-
- subtract_u64(&out[3], &carry, result & kPrime[3]);
-}
-
-static void smallfelem_square_contract(smallfelem out, const smallfelem in)
-{
- longfelem longtmp;
- felem tmp;
-
- smallfelem_square(longtmp, in);
- felem_reduce(tmp, longtmp);
- felem_contract(out, tmp);
-}
-
-static void smallfelem_mul_contract(smallfelem out, const smallfelem in1,
- const smallfelem in2)
-{
- longfelem longtmp;
- felem tmp;
-
- smallfelem_mul(longtmp, in1, in2);
- felem_reduce(tmp, longtmp);
- felem_contract(out, tmp);
-}
-
-/*-
- * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0
- * otherwise.
- * On entry:
- * small[i] < 2^64
- */
-static limb smallfelem_is_zero(const smallfelem small)
-{
- limb result;
- u64 is_p;
-
- u64 is_zero = small[0] | small[1] | small[2] | small[3];
- is_zero--;
- is_zero &= is_zero << 32;
- 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_zero = ((s64) is_zero) >> 63;
-
- is_p = (small[0] ^ kPrime[0]) |
- (small[1] ^ kPrime[1]) |
- (small[2] ^ kPrime[2]) | (small[3] ^ kPrime[3]);
- is_p--;
- is_p &= is_p << 32;
- 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;
- is_p = ((s64) is_p) >> 63;
-
- is_zero |= is_p;
-
- result = is_zero;
- result |= ((limb) is_zero) << 64;
- return result;
-}
-
-static int smallfelem_is_zero_int(const void *small)
-{
- return (int)(smallfelem_is_zero(small) & ((limb) 1));
-}
-
-/*-
- * felem_inv calculates |out| = |in|^{-1}
- *
- * Based on Fermat's Little Theorem:
- * a^p = a (mod p)
- * a^{p-1} = 1 (mod p)
- * a^{p-2} = a^{-1} (mod p)
- */
-static void felem_inv(felem out, const felem in)
-{
- felem ftmp, ftmp2;
- /* each e_I will hold |in|^{2^I - 1} */
- felem e2, e4, e8, e16, e32, e64;
- longfelem tmp;
- unsigned i;
-
- felem_square(tmp, in);
- felem_reduce(ftmp, tmp); /* 2^1 */
- felem_mul(tmp, in, ftmp);
- felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */
- felem_assign(e2, ftmp);
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */
- felem_mul(tmp, ftmp, e2);
- felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */
- felem_assign(e4, ftmp);
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */
- felem_mul(tmp, ftmp, e4);
- felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */
- felem_assign(e8, ftmp);
- for (i = 0; i < 8; i++) {
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp);
- } /* 2^16 - 2^8 */
- felem_mul(tmp, ftmp, e8);
- felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */
- felem_assign(e16, ftmp);
- for (i = 0; i < 16; i++) {
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp);
- } /* 2^32 - 2^16 */
- felem_mul(tmp, ftmp, e16);
- felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */
- felem_assign(e32, ftmp);
- for (i = 0; i < 32; i++) {
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp);
- } /* 2^64 - 2^32 */
- felem_assign(e64, ftmp);
- felem_mul(tmp, ftmp, in);
- felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */
- for (i = 0; i < 192; i++) {
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp);
- } /* 2^256 - 2^224 + 2^192 */
-
- felem_mul(tmp, e64, e32);
- felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */
- for (i = 0; i < 16; i++) {
- felem_square(tmp, ftmp2);
- felem_reduce(ftmp2, tmp);
- } /* 2^80 - 2^16 */
- felem_mul(tmp, ftmp2, e16);
- felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */
- for (i = 0; i < 8; i++) {
- felem_square(tmp, ftmp2);
- felem_reduce(ftmp2, tmp);
- } /* 2^88 - 2^8 */
- felem_mul(tmp, ftmp2, e8);
- felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */
- for (i = 0; i < 4; i++) {
- felem_square(tmp, ftmp2);
- felem_reduce(ftmp2, tmp);
- } /* 2^92 - 2^4 */
- felem_mul(tmp, ftmp2, e4);
- felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */
- felem_square(tmp, ftmp2);
- felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */
- felem_square(tmp, ftmp2);
- felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */
- felem_mul(tmp, ftmp2, e2);
- felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */
- felem_square(tmp, ftmp2);
- felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */
- felem_square(tmp, ftmp2);
- felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */
- felem_mul(tmp, ftmp2, in);
- felem_reduce(ftmp2, tmp); /* 2^96 - 3 */
-
- felem_mul(tmp, ftmp2, ftmp);
- felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */
-}
-
-static void smallfelem_inv_contract(smallfelem out, const smallfelem in)
-{
- felem tmp;
-
- smallfelem_expand(tmp, in);
- felem_inv(tmp, tmp);
- felem_contract(out, tmp);
-}
-
-/*-
- * Group operations
- * ----------------
- *
- * Building on top of the field operations we have the operations on the
- * elliptic curve group itself. Points on the curve are represented in Jacobian
- * coordinates
- */
-
-/*-
- * point_double calculates 2*(x_in, y_in, z_in)
- *
- * The method is taken from:
- * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
- *
- * 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)
-{
- longfelem tmp, tmp2;
- felem delta, gamma, beta, alpha, ftmp, ftmp2;
- smallfelem small1, small2;
-
- felem_assign(ftmp, x_in);
- /* ftmp[i] < 2^106 */
- felem_assign(ftmp2, x_in);
- /* ftmp2[i] < 2^106 */
-
- /* delta = z^2 */
- felem_square(tmp, z_in);
- felem_reduce(delta, tmp);
- /* delta[i] < 2^101 */
-
- /* gamma = y^2 */
- felem_square(tmp, y_in);
- felem_reduce(gamma, tmp);
- /* gamma[i] < 2^101 */
- felem_shrink(small1, gamma);
-
- /* beta = x*gamma */
- felem_small_mul(tmp, small1, x_in);
- felem_reduce(beta, tmp);
- /* beta[i] < 2^101 */
-
- /* alpha = 3*(x-delta)*(x+delta) */
- felem_diff(ftmp, delta);
- /* ftmp[i] < 2^105 + 2^106 < 2^107 */
- felem_sum(ftmp2, delta);
- /* ftmp2[i] < 2^105 + 2^106 < 2^107 */
- felem_scalar(ftmp2, 3);
- /* ftmp2[i] < 3 * 2^107 < 2^109 */
- felem_mul(tmp, ftmp, ftmp2);
- felem_reduce(alpha, tmp);
- /* alpha[i] < 2^101 */
- felem_shrink(small2, alpha);
-
- /* x' = alpha^2 - 8*beta */
- smallfelem_square(tmp, small2);
- felem_reduce(x_out, tmp);
- felem_assign(ftmp, beta);
- felem_scalar(ftmp, 8);
- /* ftmp[i] < 8 * 2^101 = 2^104 */
- felem_diff(x_out, ftmp);
- /* x_out[i] < 2^105 + 2^101 < 2^106 */
-
- /* z' = (y + z)^2 - gamma - delta */
- felem_sum(delta, gamma);
- /* delta[i] < 2^101 + 2^101 = 2^102 */
- felem_assign(ftmp, y_in);
- felem_sum(ftmp, z_in);
- /* ftmp[i] < 2^106 + 2^106 = 2^107 */
- felem_square(tmp, ftmp);
- felem_reduce(z_out, tmp);
- felem_diff(z_out, delta);
- /* z_out[i] < 2^105 + 2^101 < 2^106 */
-
- /* y' = alpha*(4*beta - x') - 8*gamma^2 */
- felem_scalar(beta, 4);
- /* beta[i] < 4 * 2^101 = 2^103 */
- felem_diff_zero107(beta, x_out);
- /* beta[i] < 2^107 + 2^103 < 2^108 */
- felem_small_mul(tmp, small2, beta);
- /* tmp[i] < 7 * 2^64 < 2^67 */
- smallfelem_square(tmp2, small1);
- /* tmp2[i] < 7 * 2^64 */
- longfelem_scalar(tmp2, 8);
- /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */
- longfelem_diff(tmp, tmp2);
- /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
- felem_reduce_zero105(y_out, tmp);
- /* y_out[i] < 2^106 */
-}
-
-/*
- * point_double_small is the same as point_double, except that it operates on
- * smallfelems
- */
-static void
-point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out,
- const smallfelem x_in, const smallfelem y_in,
- const smallfelem z_in)
-{
- felem felem_x_out, felem_y_out, felem_z_out;
- felem felem_x_in, felem_y_in, felem_z_in;
-
- smallfelem_expand(felem_x_in, x_in);
- smallfelem_expand(felem_y_in, y_in);
- smallfelem_expand(felem_z_in, z_in);
- point_double(felem_x_out, felem_y_out, felem_z_out,
- felem_x_in, felem_y_in, felem_z_in);
- felem_shrink(x_out, felem_x_out);
- felem_shrink(y_out, felem_y_out);
- felem_shrink(z_out, felem_z_out);
-}
-
-/* copy_conditional copies in to out iff mask is all ones. */
-static void copy_conditional(felem out, const felem in, limb mask)
-{
- unsigned i;
- for (i = 0; i < NLIMBS; ++i) {
- const limb tmp = mask & (in[i] ^ out[i]);
- out[i] ^= tmp;
- }
-}
-
-/* copy_small_conditional copies in to out iff mask is all ones. */
-static void copy_small_conditional(felem out, const smallfelem in, limb mask)
-{
- unsigned i;
- const u64 mask64 = mask;
- for (i = 0; i < NLIMBS; ++i) {
- out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask);
- }
-}
-
-/*-
- * point_add calcuates (x1, y1, z1) + (x2, y2, z2)
- *
- * The method is taken from:
- * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl,
- * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity).
- *
- * This function 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 smallfelem x2,
- const smallfelem y2, const smallfelem z2)
-{
- felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
- longfelem tmp, tmp2;
- smallfelem small1, small2, small3, small4, small5;
- limb x_equal, y_equal, z1_is_zero, z2_is_zero;
-
- felem_shrink(small3, z1);
-
- z1_is_zero = smallfelem_is_zero(small3);
- z2_is_zero = smallfelem_is_zero(z2);
-
- /* ftmp = z1z1 = z1**2 */
- smallfelem_square(tmp, small3);
- felem_reduce(ftmp, tmp);
- /* ftmp[i] < 2^101 */
- felem_shrink(small1, ftmp);
-
- if (!mixed) {
- /* ftmp2 = z2z2 = z2**2 */
- smallfelem_square(tmp, z2);
- felem_reduce(ftmp2, tmp);
- /* ftmp2[i] < 2^101 */
- felem_shrink(small2, ftmp2);
-
- felem_shrink(small5, x1);
-
- /* u1 = ftmp3 = x1*z2z2 */
- smallfelem_mul(tmp, small5, small2);
- felem_reduce(ftmp3, tmp);
- /* ftmp3[i] < 2^101 */
-
- /* ftmp5 = z1 + z2 */
- felem_assign(ftmp5, z1);
- felem_small_sum(ftmp5, z2);
- /* ftmp5[i] < 2^107 */
-
- /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */
- felem_square(tmp, ftmp5);
- felem_reduce(ftmp5, tmp);
- /* ftmp2 = z2z2 + z1z1 */
- felem_sum(ftmp2, ftmp);
- /* ftmp2[i] < 2^101 + 2^101 = 2^102 */
- felem_diff(ftmp5, ftmp2);
- /* ftmp5[i] < 2^105 + 2^101 < 2^106 */
-
- /* ftmp2 = z2 * z2z2 */
- smallfelem_mul(tmp, small2, z2);
- felem_reduce(ftmp2, tmp);
-
- /* s1 = ftmp2 = y1 * z2**3 */
- felem_mul(tmp, y1, ftmp2);
- felem_reduce(ftmp6, tmp);
- /* ftmp6[i] < 2^101 */
- } else {
- /*
- * We'll assume z2 = 1 (special case z2 = 0 is handled later)
- */
-
- /* u1 = ftmp3 = x1*z2z2 */
- felem_assign(ftmp3, x1);
- /* ftmp3[i] < 2^106 */
-
- /* ftmp5 = 2z1z2 */
- felem_assign(ftmp5, z1);
- felem_scalar(ftmp5, 2);
- /* ftmp5[i] < 2*2^106 = 2^107 */
-
- /* s1 = ftmp2 = y1 * z2**3 */
- felem_assign(ftmp6, y1);
- /* ftmp6[i] < 2^106 */
- }
-
- /* u2 = x2*z1z1 */
- smallfelem_mul(tmp, x2, small1);
- felem_reduce(ftmp4, tmp);
-
- /* h = ftmp4 = u2 - u1 */
- felem_diff_zero107(ftmp4, ftmp3);
- /* ftmp4[i] < 2^107 + 2^101 < 2^108 */
- felem_shrink(small4, ftmp4);
-
- x_equal = smallfelem_is_zero(small4);
-
- /* z_out = ftmp5 * h */
- felem_small_mul(tmp, small4, ftmp5);
- felem_reduce(z_out, tmp);
- /* z_out[i] < 2^101 */
-
- /* ftmp = z1 * z1z1 */
- smallfelem_mul(tmp, small1, small3);
- felem_reduce(ftmp, tmp);
-
- /* s2 = tmp = y2 * z1**3 */
- felem_small_mul(tmp, y2, ftmp);
- felem_reduce(ftmp5, tmp);
-
- /* r = ftmp5 = (s2 - s1)*2 */
- felem_diff_zero107(ftmp5, ftmp6);
- /* ftmp5[i] < 2^107 + 2^107 = 2^108 */
- felem_scalar(ftmp5, 2);
- /* ftmp5[i] < 2^109 */
- felem_shrink(small1, ftmp5);
- y_equal = smallfelem_is_zero(small1);
-
- if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
- point_double(x3, y3, z3, x1, y1, z1);
- return;
- }
-
- /* I = ftmp = (2h)**2 */
- felem_assign(ftmp, ftmp4);
- felem_scalar(ftmp, 2);
- /* ftmp[i] < 2*2^108 = 2^109 */
- felem_square(tmp, ftmp);
- felem_reduce(ftmp, tmp);
-
- /* J = ftmp2 = h * I */
- felem_mul(tmp, ftmp4, ftmp);
- felem_reduce(ftmp2, tmp);
-
- /* V = ftmp4 = U1 * I */
- felem_mul(tmp, ftmp3, ftmp);
- felem_reduce(ftmp4, tmp);
-
- /* x_out = r**2 - J - 2V */
- smallfelem_square(tmp, small1);
- felem_reduce(x_out, tmp);
- felem_assign(ftmp3, ftmp4);
- felem_scalar(ftmp4, 2);
- felem_sum(ftmp4, ftmp2);
- /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */
- felem_diff(x_out, ftmp4);
- /* x_out[i] < 2^105 + 2^101 */
-
- /* y_out = r(V-x_out) - 2 * s1 * J */
- felem_diff_zero107(ftmp3, x_out);
- /* ftmp3[i] < 2^107 + 2^101 < 2^108 */
- felem_small_mul(tmp, small1, ftmp3);
- felem_mul(tmp2, ftmp6, ftmp2);
- longfelem_scalar(tmp2, 2);
- /* tmp2[i] < 2*2^67 = 2^68 */
- longfelem_diff(tmp, tmp2);
- /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
- felem_reduce_zero105(y_out, tmp);
- /* y_out[i] < 2^106 */
-
- copy_small_conditional(x_out, x2, z1_is_zero);
- copy_conditional(x_out, x1, z2_is_zero);
- copy_small_conditional(y_out, y2, z1_is_zero);
- copy_conditional(y_out, y1, z2_is_zero);
- copy_small_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);
-}
-
-/*
- * point_add_small is the same as point_add, except that it operates on
- * smallfelems
- */
-static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3,
- smallfelem x1, smallfelem y1, smallfelem z1,
- smallfelem x2, smallfelem y2, smallfelem z2)
-{
- felem felem_x3, felem_y3, felem_z3;
- felem felem_x1, felem_y1, felem_z1;
- smallfelem_expand(felem_x1, x1);
- smallfelem_expand(felem_y1, y1);
- smallfelem_expand(felem_z1, z1);
- point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0,
- x2, y2, z2);
- felem_shrink(x3, felem_x3);
- felem_shrink(y3, felem_y3);
- felem_shrink(z3, felem_z3);
-}
-
-/*-
- * Base point pre computation
- * --------------------------
- *
- * Two different sorts of precomputed tables are used in the following code.
- * Each contain various points on the curve, where each point is three field
- * elements (x, y, z).
- *
- * For the base point table, z is usually 1 (0 for the point at infinity).
- * This 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 | 2^64G
- * 3 | 0 0 1 1 | (2^64 + 1)G
- * 4 | 0 1 0 0 | 2^128G
- * 5 | 0 1 0 1 | (2^128 + 1)G
- * 6 | 0 1 1 0 | (2^128 + 2^64)G
- * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G
- * 8 | 1 0 0 0 | 2^192G
- * 9 | 1 0 0 1 | (2^192 + 1)G
- * 10 | 1 0 1 0 | (2^192 + 2^64)G
- * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G
- * 12 | 1 1 0 0 | (2^192 + 2^128)G
- * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G
- * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G
- * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G
- * followed by a copy of this with each element multiplied by 2^32.
- *
- * 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.
- *
- * Tables for other points have table[i] = iG for i in 0 .. 16. */
-
-/* gmul is the table of precomputed base points */
-static const smallfelem gmul[2][16][3] = {
- {{{0, 0, 0, 0},
- {0, 0, 0, 0},
- {0, 0, 0, 0}},
- {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2,
- 0x6b17d1f2e12c4247},
- {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16,
- 0x4fe342e2fe1a7f9b},
- {1, 0, 0, 0}},
- {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de,
- 0x0fa822bc2811aaa5},
- {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b,
- 0xbff44ae8f5dba80d},
- {1, 0, 0, 0}},
- {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789,
- 0x300a4bbc89d6726f},
- {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f,
- 0x72aac7e0d09b4644},
- {1, 0, 0, 0}},
- {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e,
- 0x447d739beedb5e67},
- {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7,
- 0x2d4825ab834131ee},
- {1, 0, 0, 0}},
- {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60,
- 0xef9519328a9c72ff},
- {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c,
- 0x611e9fc37dbb2c9b},
- {1, 0, 0, 0}},
- {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf,
- 0x550663797b51f5d8},
- {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5,
- 0x157164848aecb851},
- {1, 0, 0, 0}},
- {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391,
- 0xeb5d7745b21141ea},
- {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee,
- 0xeafd72ebdbecc17b},
- {1, 0, 0, 0}},
- {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5,
- 0xa6d39677a7849276},
- {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf,
- 0x674f84749b0b8816},
- {1, 0, 0, 0}},
- {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb,
- 0x4e769e7672c9ddad},
- {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281,
- 0x42b99082de830663},
- {1, 0, 0, 0}},
- {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478,
- 0x78878ef61c6ce04d},
- {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def,
- 0xb6cb3f5d7b72c321},
- {1, 0, 0, 0}},
- {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae,
- 0x0c88bc4d716b1287},
- {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa,
- 0xdd5ddea3f3901dc6},
- {1, 0, 0, 0}},
- {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3,
- 0x68f344af6b317466},
- {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3,
- 0x31b9c405f8540a20},
- {1, 0, 0, 0}},
- {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0,
- 0x4052bf4b6f461db9},
- {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8,
- 0xfecf4d5190b0fc61},
- {1, 0, 0, 0}},
- {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a,
- 0x1eddbae2c802e41a},
- {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0,
- 0x43104d86560ebcfc},
- {1, 0, 0, 0}},
- {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a,
- 0xb48e26b484f7a21c},
- {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668,
- 0xfac015404d4d3dab},
- {1, 0, 0, 0}}},
- {{{0, 0, 0, 0},
- {0, 0, 0, 0},
- {0, 0, 0, 0}},
- {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da,
- 0x7fe36b40af22af89},
- {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1,
- 0xe697d45825b63624},
- {1, 0, 0, 0}},
- {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902,
- 0x4a5b506612a677a6},
- {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40,
- 0xeb13461ceac089f1},
- {1, 0, 0, 0}},
- {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857,
- 0x0781b8291c6a220a},
- {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434,
- 0x690cde8df0151593},
- {1, 0, 0, 0}},
- {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326,
- 0x8a535f566ec73617},
- {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf,
- 0x0455c08468b08bd7},
- {1, 0, 0, 0}},
- {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279,
- 0x06bada7ab77f8276},
- {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70,
- 0x5b476dfd0e6cb18a},
- {1, 0, 0, 0}},
- {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8,
- 0x3e29864e8a2ec908},
- {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed,
- 0x239b90ea3dc31e7e},
- {1, 0, 0, 0}},
- {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4,
- 0x820f4dd949f72ff7},
- {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3,
- 0x140406ec783a05ec},
- {1, 0, 0, 0}},
- {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe,
- 0x68f6b8542783dfee},
- {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028,
- 0xcbe1feba92e40ce6},
- {1, 0, 0, 0}},
- {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927,
- 0xd0b2f94d2f420109},
- {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a,
- 0x971459828b0719e5},
- {1, 0, 0, 0}},
- {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687,
- 0x961610004a866aba},
- {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c,
- 0x7acb9fadcee75e44},
- {1, 0, 0, 0}},
- {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea,
- 0x24eb9acca333bf5b},
- {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d,
- 0x69f891c5acd079cc},
- {1, 0, 0, 0}},
- {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514,
- 0xe51f547c5972a107},
- {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06,
- 0x1c309a2b25bb1387},
- {1, 0, 0, 0}},
- {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828,
- 0x20b87b8aa2c4e503},
- {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044,
- 0xf5c6fa49919776be},
- {1, 0, 0, 0}},
- {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56,
- 0x1ed7d1b9332010b9},
- {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24,
- 0x3a2b03f03217257a},
- {1, 0, 0, 0}},
- {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b,
- 0x15fee545c78dd9f6},
- {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb,
- 0x4ab5b6b2b8753f81},
- {1, 0, 0, 0}}}
-};
-
-/*
- * select_point selects the |idx|th point from a precomputation table and
- * copies it to out.
- */
-static void select_point(const u64 idx, unsigned int size,
- const smallfelem pre_comp[16][3], smallfelem out[3])
-{
- unsigned i, j;
- u64 *outlimbs = &out[0][0];
- memset(outlimbs, 0, 3 * sizeof(smallfelem));
-
- for (i = 0; i < size; i++) {
- const u64 *inlimbs = (u64 *)&pre_comp[i][0][0];
- u64 mask = i ^ idx;
- mask |= mask >> 4;
- mask |= mask >> 2;
- mask |= mask >> 1;
- mask &= 1;
- mask--;
- for (j = 0; j < NLIMBS * 3; j++)
- outlimbs[j] |= inlimbs[j] & mask;
- }
-}
-
-/* get_bit returns the |i|th bit in |in| */
-static char get_bit(const felem_bytearray in, int i)
-{
- if ((i < 0) || (i >= 256))
- return 0;
- return (in[i >> 3] >> (i & 7)) & 1;
-}
-
-/*
- * Interleaved point multiplication using precomputed point multiples: The
- * small point multiples 0*P, 1*P, ..., 17*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 unsigned num_points, const u8 *g_scalar,
- const int mixed, const smallfelem pre_comp[][17][3],
- const smallfelem g_pre_comp[2][16][3])
-{
- int i, skip;
- unsigned num, gen_mul = (g_scalar != NULL);
- felem nq[3], ftmp;
- smallfelem tmp[3];
- u64 bits;
- u8 sign, digit;
-
- /* set nq to the point at infinity */
- 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 32 rounds) and additions of
- * other points multiples (every 5th round).
- */
- skip = 1; /* save two point operations in the first
- * round */
- for (i = (num_points ? 255 : 31); i >= 0; --i) {
- /* double */
- if (!skip)
- point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
-
- /* add multiples of the generator */
- if (gen_mul && (i <= 31)) {
- /* first, look 32 bits upwards */
- bits = get_bit(g_scalar, i + 224) << 3;
- bits |= get_bit(g_scalar, i + 160) << 2;
- bits |= get_bit(g_scalar, i + 96) << 1;
- bits |= get_bit(g_scalar, i + 32);
- /* select the point to add, in constant time */
- select_point(bits, 16, g_pre_comp[1], tmp);
-
- if (!skip) {
- /* Arg 1 below is for "mixed" */
- point_add(nq[0], nq[1], nq[2],
- nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]);
- } else {
- smallfelem_expand(nq[0], tmp[0]);
- smallfelem_expand(nq[1], tmp[1]);
- smallfelem_expand(nq[2], tmp[2]);
- skip = 0;
- }
-
- /* second, look at the current position */
- bits = get_bit(g_scalar, i + 192) << 3;
- bits |= get_bit(g_scalar, i + 128) << 2;
- bits |= get_bit(g_scalar, i + 64) << 1;
- bits |= get_bit(g_scalar, i);
- /* select the point to add, in constant time */
- select_point(bits, 16, g_pre_comp[0], tmp);
- /* Arg 1 below is for "mixed" */
- point_add(nq[0], nq[1], nq[2],
- nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]);
- }
-
- /* do other additions every 5 doublings */
- if (num_points && (i % 5 == 0)) {
- /* loop over all scalars */
- 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, in constant time
- */
- select_point(digit, 17, pre_comp[num], tmp);
- smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative
- * point */
- copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1));
- felem_contract(tmp[1], ftmp);
-
- if (!skip) {
- point_add(nq[0], nq[1], nq[2],
- nq[0], nq[1], nq[2],
- mixed, tmp[0], tmp[1], tmp[2]);
- } else {
- smallfelem_expand(nq[0], tmp[0]);
- smallfelem_expand(nq[1], tmp[1]);
- smallfelem_expand(nq[2], tmp[2]);
- skip = 0;
- }
- }
- }
- }
- felem_assign(x_out, nq[0]);
- felem_assign(y_out, nq[1]);
- felem_assign(z_out, nq[2]);
-}
-
-/* Precomputation for the group generator. */
-typedef struct {
- smallfelem g_pre_comp[2][16][3];
- int references;
-} NISTP256_PRE_COMP;
-
-const EC_METHOD *EC_GFp_nistp256_method(void)
-{
- static const EC_METHOD ret = {
- EC_FLAGS_DEFAULT_OCT,
- NID_X9_62_prime_field,
- ec_GFp_nistp256_group_init,
- ec_GFp_simple_group_finish,
- ec_GFp_simple_group_clear_finish,
- ec_GFp_nist_group_copy,
- ec_GFp_nistp256_group_set_curve,
- ec_GFp_simple_group_get_curve,
- ec_GFp_simple_group_get_degree,
- ec_GFp_simple_group_check_discriminant,
- ec_GFp_simple_point_init,
- ec_GFp_simple_point_finish,
- ec_GFp_simple_point_clear_finish,
- ec_GFp_simple_point_copy,
- ec_GFp_simple_point_set_to_infinity,
- ec_GFp_simple_set_Jprojective_coordinates_GFp,
- ec_GFp_simple_get_Jprojective_coordinates_GFp,
- ec_GFp_simple_point_set_affine_coordinates,
- ec_GFp_nistp256_point_get_affine_coordinates,
- 0 /* point_set_compressed_coordinates */ ,
- 0 /* point2oct */ ,
- 0 /* oct2point */ ,
- ec_GFp_simple_add,
- ec_GFp_simple_dbl,
- ec_GFp_simple_invert,
- ec_GFp_simple_is_at_infinity,
- ec_GFp_simple_is_on_curve,
- ec_GFp_simple_cmp,
- ec_GFp_simple_make_affine,
- ec_GFp_simple_points_make_affine,
- ec_GFp_nistp256_points_mul,
- ec_GFp_nistp256_precompute_mult,
- ec_GFp_nistp256_have_precompute_mult,
- ec_GFp_nist_field_mul,
- ec_GFp_nist_field_sqr,
- 0 /* field_div */ ,
- 0 /* field_encode */ ,
- 0 /* field_decode */ ,
- 0 /* field_set_to_one */
- };
-
- return &ret;
-}
-
-/******************************************************************************/
-/*
- * FUNCTIONS TO MANAGE PRECOMPUTATION
- */
-
-static NISTP256_PRE_COMP *nistp256_pre_comp_new()
-{
- NISTP256_PRE_COMP *ret = NULL;
- ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret);
- if (!ret) {
- ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
- return ret;
- }
- memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
- ret->references = 1;
- return ret;
-}
-
-static void *nistp256_pre_comp_dup(void *src_)
-{
- NISTP256_PRE_COMP *src = src_;
-
- /* no need to actually copy, these objects never change! */
- CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
-
- return src_;
-}
-
-static void nistp256_pre_comp_free(void *pre_)
-{
- int i;
- NISTP256_PRE_COMP *pre = pre_;
-
- if (!pre)
- return;
-
- i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
- if (i > 0)
- return;
-
- OPENSSL_free(pre);
-}
-
-static void nistp256_pre_comp_clear_free(void *pre_)
-{
- int i;
- NISTP256_PRE_COMP *pre = pre_;
-
- if (!pre)
- return;
-
- i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
- if (i > 0)
- return;
-
- OPENSSL_cleanse(pre, sizeof *pre);
- OPENSSL_free(pre);
-}
-
-/******************************************************************************/
-/*
- * OPENSSL EC_METHOD FUNCTIONS
- */
-
-int ec_GFp_nistp256_group_init(EC_GROUP *group)
-{
- int ret;
- ret = ec_GFp_simple_group_init(group);
- group->a_is_minus3 = 1;
- return ret;
-}
-
-int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
- const BIGNUM *a, const BIGNUM *b,
- BN_CTX *ctx)
-{
- int ret = 0;
- BN_CTX *new_ctx = NULL;
- BIGNUM *curve_p, *curve_a, *curve_b;
-
- if (ctx == NULL)
- if ((ctx = new_ctx = BN_CTX_new()) == NULL)
- return 0;
- BN_CTX_start(ctx);
- if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
- ((curve_a = BN_CTX_get(ctx)) == NULL) ||
- ((curve_b = BN_CTX_get(ctx)) == NULL))
- goto err;
- BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p);
- BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a);
- BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b);
- if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) {
- ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE,
- EC_R_WRONG_CURVE_PARAMETERS);
- goto err;
- }
- group->field_mod_func = BN_nist_mod_256;
- ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
- err:
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
-}
-
-/*
- * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') =
- * (X/Z^2, Y/Z^3)
- */
-int ec_GFp_nistp256_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;
- smallfelem x_out, y_out;
- longfelem tmp;
-
- if (EC_POINT_is_at_infinity(group, point)) {
- ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
- 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) {
- if (!smallfelem_to_BN(x, x_out)) {
- ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
- 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) {
- if (!smallfelem_to_BN(y, y_out)) {
- ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
- ERR_R_BN_LIB);
- return 0;
- }
- }
- return 1;
-}
-
-/* points below is of size |num|, and tmp_smallfelems is of size |num+1| */
-static void make_points_affine(size_t num, smallfelem points[][3],
- smallfelem tmp_smallfelems[])
-{
- /*
- * Runs in constant time, unless an input is the point at infinity (which
- * normally shouldn't happen).
- */
- ec_GFp_nistp_points_make_affine_internal(num,
- points,
- sizeof(smallfelem),
- tmp_smallfelems,
- (void (*)(void *))smallfelem_one,
- smallfelem_is_zero_int,
- (void (*)(void *, const void *))
- smallfelem_assign,
- (void (*)(void *, const void *))
- smallfelem_square_contract,
- (void (*)
- (void *, const void *,
- const void *))
- smallfelem_mul_contract,
- (void (*)(void *, const void *))
- smallfelem_inv_contract,
- /* nothing to contract */
- (void (*)(void *, const void *))
- smallfelem_assign);
-}
-
-/*
- * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL
- * values Result is stored in r (r can equal one of the inputs).
- */
-int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
- const BIGNUM *scalar, size_t num,
- const EC_POINT *points[],
- const BIGNUM *scalars[], BN_CTX *ctx)
-{
- int ret = 0;
- int j;
- int mixed = 0;
- BN_CTX *new_ctx = NULL;
- BIGNUM *x, *y, *z, *tmp_scalar;
- felem_bytearray g_secret;
- felem_bytearray *secrets = NULL;
- smallfelem(*pre_comp)[17][3] = NULL;
- smallfelem *tmp_smallfelems = NULL;
- felem_bytearray tmp;
- unsigned i, num_bytes;
- int have_pre_comp = 0;
- size_t num_points = num;
- smallfelem x_in, y_in, z_in;
- felem x_out, y_out, z_out;
- NISTP256_PRE_COMP *pre = NULL;
- const smallfelem(*g_pre_comp)[16][3] = NULL;
- EC_POINT *generator = NULL;
- const EC_POINT *p = NULL;
- const BIGNUM *p_scalar = NULL;
-
- if (ctx == NULL)
- if ((ctx = new_ctx = BN_CTX_new()) == 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 (scalar != NULL) {
- pre = EC_EX_DATA_get_data(group->extra_data,
- nistp256_pre_comp_dup,
- nistp256_pre_comp_free,
- nistp256_pre_comp_clear_free);
- if (pre)
- /* we have precomputation, try to use it */
- g_pre_comp = (const smallfelem(*)[16][3])pre->g_pre_comp;
- else
- /* try to use the standard precomputation */
- g_pre_comp = &gmul[0];
- generator = EC_POINT_new(group);
- if (generator == NULL)
- goto err;
- /* get the generator from precomputation */
- if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) ||
- !smallfelem_to_BN(y, g_pre_comp[0][1][1]) ||
- !smallfelem_to_BN(z, g_pre_comp[0][1][2])) {
- ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
- goto err;
- }
- if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
- generator, x, y, z,
- ctx))
- goto err;
- if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
- /* precomputation matches generator */
- have_pre_comp = 1;
- else
- /*
- * we don't have valid precomputation: treat the generator as a
- * random point
- */
- num_points++;
- }
- if (num_points > 0) {
- if (num_points >= 3) {
- /*
- * unless we precompute multiples for just one or two points,
- * converting those into affine form is time well spent
- */
- mixed = 1;
- }
- secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
- pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(smallfelem));
- if (mixed)
- tmp_smallfelems =
- OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem));
- if ((secrets == NULL) || (pre_comp == NULL)
- || (mixed && (tmp_smallfelems == NULL))) {
- ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, 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
- */
- memset(secrets, 0, num_points * sizeof(felem_bytearray));
- memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem));
- for (i = 0; i < num_points; ++i) {
- if (i == num)
- /*
- * we didn't have a valid precomputation, so we pick the
- * generator
- */
- {
- p = EC_GROUP_get0_generator(group);
- p_scalar = scalar;
- } else
- /* the i^th point */
- {
- p = points[i];
- p_scalar = scalars[i];
- }
- if ((p_scalar != NULL) && (p != NULL)) {
- /* reduce scalar to 0 <= scalar < 2^256 */
- if ((BN_num_bits(p_scalar) > 256)
- || (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)) {
- ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, 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_shrink(pre_comp[i][1][0], x_out);
- felem_shrink(pre_comp[i][1][1], y_out);
- felem_shrink(pre_comp[i][1][2], z_out);
- for (j = 2; j <= 16; ++j) {
- if (j & 1) {
- point_add_small(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],
- pre_comp[i][j - 1][0],
- pre_comp[i][j - 1][1],
- pre_comp[i][j - 1][2]);
- } else {
- point_double_small(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 (mixed)
- make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems);
- }
-
- /* the scalar for the generator */
- if ((scalar != NULL) && (have_pre_comp)) {
- memset(g_secret, 0, sizeof(g_secret));
- /* reduce scalar to 0 <= scalar < 2^256 */
- if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) {
- /*
- * this is an unusual input, and we don't guarantee
- * constant-timeness
- */
- if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
- ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
- goto err;
- }
- num_bytes = BN_bn2bin(tmp_scalar, tmp);
- } else
- num_bytes = BN_bn2bin(scalar, tmp);
- flip_endian(g_secret, tmp, num_bytes);
- /* do the multiplication with generator precomputation */
- batch_mul(x_out, y_out, z_out,
- (const felem_bytearray(*))secrets, num_points,
- g_secret,
- mixed, (const smallfelem(*)[17][3])pre_comp, g_pre_comp);
- } else
- /* do the multiplication without generator precomputation */
- batch_mul(x_out, y_out, z_out,
- (const felem_bytearray(*))secrets, num_points,
- NULL, mixed, (const smallfelem(*)[17][3])pre_comp, NULL);
- /* 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 ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) ||
- (!smallfelem_to_BN(z, z_in))) {
- ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
- goto err;
- }
- ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
-
- err:
- BN_CTX_end(ctx);
- if (generator != NULL)
- EC_POINT_free(generator);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- if (secrets != NULL)
- OPENSSL_free(secrets);
- if (pre_comp != NULL)
- OPENSSL_free(pre_comp);
- if (tmp_smallfelems != NULL)
- OPENSSL_free(tmp_smallfelems);
- return ret;
-}
-
-int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
-{
- int ret = 0;
- NISTP256_PRE_COMP *pre = NULL;
- int i, j;
- BN_CTX *new_ctx = NULL;
- BIGNUM *x, *y;
- EC_POINT *generator = NULL;
- smallfelem tmp_smallfelems[32];
- felem x_tmp, y_tmp, z_tmp;
-
- /* throw away old precomputation */
- EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup,
- nistp256_pre_comp_free,
- nistp256_pre_comp_clear_free);
- if (ctx == NULL)
- if ((ctx = new_ctx = BN_CTX_new()) == NULL)
- return 0;
- BN_CTX_start(ctx);
- if (((x = BN_CTX_get(ctx)) == NULL) || ((y = BN_CTX_get(ctx)) == NULL))
- goto err;
- /* get the generator */
- if (group->generator == NULL)
- goto err;
- generator = EC_POINT_new(group);
- if (generator == NULL)
- goto err;
- BN_bin2bn(nistp256_curve_params[3], sizeof(felem_bytearray), x);
- BN_bin2bn(nistp256_curve_params[4], sizeof(felem_bytearray), y);
- if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
- goto err;
- if ((pre = nistp256_pre_comp_new()) == NULL)
- goto err;
- /*
- * if the generator is the standard one, use built-in precomputation
- */
- if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) {
- memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
- goto done;
- }
- if ((!BN_to_felem(x_tmp, &group->generator->X)) ||
- (!BN_to_felem(y_tmp, &group->generator->Y)) ||
- (!BN_to_felem(z_tmp, &group->generator->Z)))
- goto err;
- felem_shrink(pre->g_pre_comp[0][1][0], x_tmp);
- felem_shrink(pre->g_pre_comp[0][1][1], y_tmp);
- felem_shrink(pre->g_pre_comp[0][1][2], z_tmp);
- /*
- * compute 2^64*G, 2^128*G, 2^192*G for the first table, 2^32*G, 2^96*G,
- * 2^160*G, 2^224*G for the second one
- */
- for (i = 1; i <= 8; i <<= 1) {
- point_double_small(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1],
- pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0],
- pre->g_pre_comp[0][i][1],
- pre->g_pre_comp[0][i][2]);
- for (j = 0; j < 31; ++j) {
- point_double_small(pre->g_pre_comp[1][i][0],
- pre->g_pre_comp[1][i][1],
- pre->g_pre_comp[1][i][2],
- pre->g_pre_comp[1][i][0],
- pre->g_pre_comp[1][i][1],
- pre->g_pre_comp[1][i][2]);
- }
- if (i == 8)
- break;
- point_double_small(pre->g_pre_comp[0][2 * i][0],
- pre->g_pre_comp[0][2 * i][1],
- pre->g_pre_comp[0][2 * i][2],
- pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1],
- pre->g_pre_comp[1][i][2]);
- for (j = 0; j < 31; ++j) {
- point_double_small(pre->g_pre_comp[0][2 * i][0],
- pre->g_pre_comp[0][2 * i][1],
- pre->g_pre_comp[0][2 * i][2],
- pre->g_pre_comp[0][2 * i][0],
- pre->g_pre_comp[0][2 * i][1],
- pre->g_pre_comp[0][2 * i][2]);
- }
- }
- for (i = 0; i < 2; i++) {
- /* g_pre_comp[i][0] is the point at infinity */
- memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0]));
- /* the remaining multiples */
- /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */
- point_add_small(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1],
- pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0],
- pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2],
- pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
- pre->g_pre_comp[i][2][2]);
- /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */
- point_add_small(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1],
- pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0],
- pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
- pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
- pre->g_pre_comp[i][2][2]);
- /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */
- point_add_small(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1],
- pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0],
- pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
- pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1],
- pre->g_pre_comp[i][4][2]);
- /*
- * 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G
- */
- point_add_small(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1],
- pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0],
- pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
- pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
- pre->g_pre_comp[i][2][2]);
- for (j = 1; j < 8; ++j) {
- /* odd multiples: add G resp. 2^32*G */
- point_add_small(pre->g_pre_comp[i][2 * j + 1][0],
- pre->g_pre_comp[i][2 * j + 1][1],
- pre->g_pre_comp[i][2 * j + 1][2],
- pre->g_pre_comp[i][2 * j][0],
- pre->g_pre_comp[i][2 * j][1],
- pre->g_pre_comp[i][2 * j][2],
- pre->g_pre_comp[i][1][0],
- pre->g_pre_comp[i][1][1],
- pre->g_pre_comp[i][1][2]);
- }
- }
- make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems);
-
- done:
- if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup,
- nistp256_pre_comp_free,
- nistp256_pre_comp_clear_free))
- goto err;
- ret = 1;
- pre = NULL;
- err:
- BN_CTX_end(ctx);
- if (generator != NULL)
- EC_POINT_free(generator);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- if (pre)
- nistp256_pre_comp_free(pre);
- return ret;
-}
-
-int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group)
-{
- if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup,
- nistp256_pre_comp_free,
- nistp256_pre_comp_clear_free)
- != NULL)
- return 1;
- else
- return 0;
-}
-#else
-static void *dummy = &dummy;
-#endif
generated by cgit v1.2.3 (git 2.25.1) at 2024-12-02 11:54:29 +0000