From 54e403c650b9bc99056211d37580fa30780c2b34 Mon Sep 17 00:00:00 2001 From: Andres Erbsen Date: Sat, 1 Jul 2017 01:01:49 -0400 Subject: benchmark OpenSSL p256 C code --- third_party/openssl-nistp256c64/LICENSE | 125 +++ third_party/openssl-nistp256c64/bench_madd.c | 16 + third_party/openssl-nistp256c64/compiler.sh | 4 + third_party/openssl-nistp256c64/ecp_nistp256.c | 1314 ++++++++++++++++++++++++ third_party/openssl-nistp256c64/ecp_nistp256.h | 55 + 5 files changed, 1514 insertions(+) create mode 100644 third_party/openssl-nistp256c64/LICENSE create mode 100644 third_party/openssl-nistp256c64/bench_madd.c create mode 100755 third_party/openssl-nistp256c64/compiler.sh create mode 100644 third_party/openssl-nistp256c64/ecp_nistp256.c create mode 100644 third_party/openssl-nistp256c64/ecp_nistp256.h (limited to 'third_party') diff --git a/third_party/openssl-nistp256c64/LICENSE b/third_party/openssl-nistp256c64/LICENSE new file mode 100644 index 000000000..8fbabd8af --- /dev/null +++ b/third_party/openssl-nistp256c64/LICENSE @@ -0,0 +1,125 @@ + + LICENSE ISSUES + ============== + + The OpenSSL toolkit stays under a double license, i.e. both the conditions of + the OpenSSL License and the original SSLeay license apply to the toolkit. + See below for the actual license texts. + + OpenSSL License + --------------- + +/* ==================================================================== + * Copyright (c) 1998-2017 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ + + Original SSLeay License + ----------------------- + +/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) + * All rights reserved. + * + * This package is an SSL implementation written + * by Eric Young (eay@cryptsoft.com). + * The implementation was written so as to conform with Netscapes SSL. + * + * This library is free for commercial and non-commercial use as long as + * the following conditions are aheared to. The following conditions + * apply to all code found in this distribution, be it the RC4, RSA, + * lhash, DES, etc., code; not just the SSL code. The SSL documentation + * included with this distribution is covered by the same copyright terms + * except that the holder is Tim Hudson (tjh@cryptsoft.com). + * + * Copyright remains Eric Young's, and as such any Copyright notices in + * the code are not to be removed. + * If this package is used in a product, Eric Young should be given attribution + * as the author of the parts of the library used. + * This can be in the form of a textual message at program startup or + * in documentation (online or textual) provided with the package. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * "This product includes cryptographic software written by + * Eric Young (eay@cryptsoft.com)" + * The word 'cryptographic' can be left out if the rouines from the library + * being used are not cryptographic related :-). + * 4. If you include any Windows specific code (or a derivative thereof) from + * the apps directory (application code) you must include an acknowledgement: + * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" + * + * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * The licence and distribution terms for any publically available version or + * derivative of this code cannot be changed. i.e. this code cannot simply be + * copied and put under another distribution licence + * [including the GNU Public Licence.] + */ + diff --git a/third_party/openssl-nistp256c64/bench_madd.c b/third_party/openssl-nistp256c64/bench_madd.c new file mode 100644 index 000000000..e2dc8e880 --- /dev/null +++ b/third_party/openssl-nistp256c64/bench_madd.c @@ -0,0 +1,16 @@ +#include +#include "ecp_nistp256.h" + +void bench_madd(unsigned char* buf) { + uint128_t* x3 = (uint128_t*) buf; + uint128_t* y3 = (uint128_t*) (buf + 1*sizeof(felem)); + uint128_t* z3 = (uint128_t*) (buf + 2*sizeof(felem)); + uint128_t* x1 = (uint128_t*) (buf + 3*sizeof(felem)); + uint128_t* y1 = (uint128_t*) (buf + 4*sizeof(felem)); + uint128_t* z1 = (uint128_t*) (buf + 5*sizeof(felem)); + int mixed = 1; + uint64_t* x2 = (uint64_t*) (buf + 6*sizeof(felem)); + uint64_t* y2 = (uint64_t*) (buf + 6*sizeof(felem) + sizeof(smallfelem)); + smallfelem z2 = {1, 0, 0, 0}; + point_add(x3, y3, z3, x1, y1, z1, mixed, x2, y2, z2); +} diff --git a/third_party/openssl-nistp256c64/compiler.sh b/third_party/openssl-nistp256c64/compiler.sh new file mode 100755 index 000000000..e64df574a --- /dev/null +++ b/third_party/openssl-nistp256c64/compiler.sh @@ -0,0 +1,4 @@ +#!/bin/sh +set -eu + +gcc -march=native -mtune=native -std=gnu11 -O3 -flto -fomit-frame-pointer -fwrapv -Wno-attributes $@ diff --git a/third_party/openssl-nistp256c64/ecp_nistp256.c b/third_party/openssl-nistp256c64/ecp_nistp256.c new file mode 100644 index 000000000..9d5f36905 --- /dev/null +++ b/third_party/openssl-nistp256c64/ecp_nistp256.c @@ -0,0 +1,1314 @@ +/* + * 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 +# include +# include +# 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); +} diff --git a/third_party/openssl-nistp256c64/ecp_nistp256.h b/third_party/openssl-nistp256c64/ecp_nistp256.h new file mode 100644 index 000000000..190b81b61 --- /dev/null +++ b/third_party/openssl-nistp256c64/ecp_nistp256.h @@ -0,0 +1,55 @@ +#include + +# 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 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]; + +/* + * 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]; +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); -- cgit v1.2.3