aboutsummaryrefslogtreecommitdiff
path: root/third_party/openssl-nistp256c64/ecp_nistp256.c
diff options
context:
space:
mode:
Diffstat (limited to 'third_party/openssl-nistp256c64/ecp_nistp256.c')
-rw-r--r--third_party/openssl-nistp256c64/ecp_nistp256.c1314
1 files changed, 0 insertions, 1314 deletions
diff --git a/third_party/openssl-nistp256c64/ecp_nistp256.c b/third_party/openssl-nistp256c64/ecp_nistp256.c
deleted file mode 100644
index 9d5f36905..000000000
--- a/third_party/openssl-nistp256c64/ecp_nistp256.c
+++ /dev/null
@@ -1,1314 +0,0 @@
-/*
- * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved.
- *
- * Licensed under the OpenSSL license (the "License"). You may not use
- * this file except in compliance with the License. You can obtain a copy
- * in the file LICENSE in the source distribution or at
- * https://www.openssl.org/source/license.html
- */
-
-/* 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 <stdint.h>
-# include <string.h>
-# include <openssl/err.h>
-# include "ecp_nistp256.h"
-
-
-/*
- * 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}
-};
-
-/*-
-
-/* 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];
-}
-
-/*-
- * 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 smallfelem 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 calculates (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.
- */
-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);
-}
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-18 07:55:12 +0000