diff options
author | Robert Sloan <varomodt@google.com> | 2017-12-18 11:26:17 -0800 |
---|---|---|
committer | Robert Sloan <varomodt@google.com> | 2017-12-18 11:26:23 -0800 |
commit | 558181089d69085101510906bd46e51ade9e20e9 (patch) | |
tree | e57121bbdd758b4b17aba72bf5d90559acfd0e4d /src/third_party | |
parent | cd79cdebdcdadadb156e037973c927abf3dac79d (diff) | |
download | boringssl-558181089d69085101510906bd46e51ade9e20e9.tar.gz |
external/boringssl: Sync to ea52ec98a56a40879b37493f3d1da1a1679e1fba.
This includes the following changes:
https://boringssl.googlesource.com/boringssl/+log/21baf6421a7e1e03f85cf2243c3c2404f5765072..ea52ec98a56a40879b37493f3d1da1a1679e1fba
Test: BoringSSL CTS Presubmits.
Change-Id: I6ebeb5f2aa7daa462c9d8933d9d5388011054fac
Diffstat (limited to 'src/third_party')
-rw-r--r-- | src/third_party/fiat/p256.c | 1725 |
1 files changed, 1725 insertions, 0 deletions
diff --git a/src/third_party/fiat/p256.c b/src/third_party/fiat/p256.c new file mode 100644 index 00000000..25ef3830 --- /dev/null +++ b/src/third_party/fiat/p256.c @@ -0,0 +1,1725 @@ +// The MIT License (MIT) +// +// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file). +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions: +// +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. + +// The field arithmetic code is generated by Fiat +// (https://github.com/mit-plv/fiat-crypto), which is MIT licensed. +// +// An implementation of the NIST P-256 elliptic curve point multiplication. +// 256-bit Montgomery form, generated using fiat-crypto, for 64 and 32-bit. +// Field operations with inputs in [0,p) return outputs in [0,p). + +#include <openssl/base.h> + +#include <openssl/bn.h> +#include <openssl/ec.h> +#include <openssl/err.h> +#include <openssl/mem.h> + +#include <string.h> + +#include "../../crypto/fipsmodule/delocate.h" +#include "../../crypto/fipsmodule/ec/internal.h" +#include "../../crypto/internal.h" + + +// MSVC does not implement uint128_t, and crashes with intrinsics +#if defined(BORINGSSL_HAS_UINT128) +#define BORINGSSL_NISTP256_64BIT 1 +#endif + +// "intrinsics" + +#if defined(BORINGSSL_NISTP256_64BIT) + +static uint64_t mulx_u64(uint64_t a, uint64_t b, uint64_t *high) { + uint128_t x = (uint128_t)a * b; + *high = (uint64_t) (x >> 64); + return (uint64_t) x; +} + +static uint64_t addcarryx_u64(uint8_t c, uint64_t a, uint64_t b, uint64_t *low) { + uint128_t x = (uint128_t)a + b + c; + *low = (uint64_t) x; + return (uint64_t) (x>>64); +} + +static uint64_t subborrow_u64(uint8_t c, uint64_t a, uint64_t b, uint64_t *low) { + uint128_t t = ((uint128_t) b + c); + uint128_t x = a-t; + *low = (uint64_t) x; + return (uint8_t) (x>>127); +} + +static uint64_t cmovznz_u64(uint64_t t, uint64_t z, uint64_t nz) { + t = -!!t; // all set if nonzero, 0 if 0 + return (t&nz) | ((~t)&z); +} + +#else + +static uint32_t mulx_u32(uint32_t a, uint32_t b, uint32_t *high) { + uint64_t x = (uint64_t)a * b; + *high = (uint32_t) (x >> 32); + return (uint32_t) x; +} + +static uint32_t addcarryx_u32(uint8_t c, uint32_t a, uint32_t b, uint32_t *low) { + uint64_t x = (uint64_t)a + b + c; + *low = (uint32_t) x; + return (uint32_t) (x>>32); +} + +static uint32_t subborrow_u32(uint8_t c, uint32_t a, uint32_t b, uint32_t *low) { + uint64_t t = ((uint64_t) b + c); + uint64_t x = a-t; + *low = (uint32_t) x; + return (uint8_t) (x>>63); +} + +static uint32_t cmovznz_u32(uint32_t t, uint32_t z, uint32_t nz) { + t = -!!t; // all set if nonzero, 0 if 0 + return (t&nz) | ((~t)&z); +} + +#endif + +// fiat-crypto generated code + +#if defined(BORINGSSL_NISTP256_64BIT) + +static void fe_add(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { + { const uint64_t x8 = in1[3]; + { const uint64_t x9 = in1[2]; + { const uint64_t x7 = in1[1]; + { const uint64_t x5 = in1[0]; + { const uint64_t x14 = in2[3]; + { const uint64_t x15 = in2[2]; + { const uint64_t x13 = in2[1]; + { const uint64_t x11 = in2[0]; + { uint64_t x17; uint8_t x18 = addcarryx_u64(0x0, x5, x11, &x17); + { uint64_t x20; uint8_t x21 = addcarryx_u64(x18, x7, x13, &x20); + { uint64_t x23; uint8_t x24 = addcarryx_u64(x21, x9, x15, &x23); + { uint64_t x26; uint8_t x27 = addcarryx_u64(x24, x8, x14, &x26); + { uint64_t x29; uint8_t x30 = subborrow_u64(0x0, x17, 0xffffffffffffffffL, &x29); + { uint64_t x32; uint8_t x33 = subborrow_u64(x30, x20, 0xffffffff, &x32); + { uint64_t x35; uint8_t x36 = subborrow_u64(x33, x23, 0x0, &x35); + { uint64_t x38; uint8_t x39 = subborrow_u64(x36, x26, 0xffffffff00000001L, &x38); + { uint64_t _1; uint8_t x42 = subborrow_u64(x39, x27, 0x0, &_1); + { uint64_t x43 = cmovznz_u64(x42, x38, x26); + { uint64_t x44 = cmovznz_u64(x42, x35, x23); + { uint64_t x45 = cmovznz_u64(x42, x32, x20); + { uint64_t x46 = cmovznz_u64(x42, x29, x17); + out[0] = x46; + out[1] = x45; + out[2] = x44; + out[3] = x43; + }}}}}}}}}}}}}}}}}}}}} +} + +// fe_op sets out = -in +static void fe_opp(uint64_t out[4], const uint64_t in1[4]) { + const uint64_t x5 = in1[3]; + const uint64_t x6 = in1[2]; + const uint64_t x4 = in1[1]; + const uint64_t x2 = in1[0]; + uint64_t x8; uint8_t x9 = subborrow_u64(0x0, 0x0, x2, &x8); + uint64_t x11; uint8_t x12 = subborrow_u64(x9, 0x0, x4, &x11); + uint64_t x14; uint8_t x15 = subborrow_u64(x12, 0x0, x6, &x14); + uint64_t x17; uint8_t x18 = subborrow_u64(x15, 0x0, x5, &x17); + uint64_t x19 = (uint64_t)cmovznz_u64(x18, 0x0, 0xffffffffffffffffL); + uint64_t x20 = (x19 & 0xffffffffffffffffL); + uint64_t x22; uint8_t x23 = addcarryx_u64(0x0, x8, x20, &x22); + uint64_t x24 = (x19 & 0xffffffff); + uint64_t x26; uint8_t x27 = addcarryx_u64(x23, x11, x24, &x26); + uint64_t x29; uint8_t x30 = addcarryx_u64(x27, x14, 0x0, &x29); + uint64_t x31 = (x19 & 0xffffffff00000001L); + uint64_t x33; addcarryx_u64(x30, x17, x31, &x33); + out[0] = x22; + out[1] = x26; + out[2] = x29; + out[3] = x33; +} + +static void fe_mul(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { + const uint64_t x8 = in1[3]; + const uint64_t x9 = in1[2]; + const uint64_t x7 = in1[1]; + const uint64_t x5 = in1[0]; + const uint64_t x14 = in2[3]; + const uint64_t x15 = in2[2]; + const uint64_t x13 = in2[1]; + const uint64_t x11 = in2[0]; + uint64_t x18; uint64_t x17 = mulx_u64(x5, x11, &x18); + uint64_t x21; uint64_t x20 = mulx_u64(x5, x13, &x21); + uint64_t x24; uint64_t x23 = mulx_u64(x5, x15, &x24); + uint64_t x27; uint64_t x26 = mulx_u64(x5, x14, &x27); + uint64_t x29; uint8_t x30 = addcarryx_u64(0x0, x18, x20, &x29); + uint64_t x32; uint8_t x33 = addcarryx_u64(x30, x21, x23, &x32); + uint64_t x35; uint8_t x36 = addcarryx_u64(x33, x24, x26, &x35); + uint64_t x38; addcarryx_u64(0x0, x36, x27, &x38); + uint64_t x42; uint64_t x41 = mulx_u64(x17, 0xffffffffffffffffL, &x42); + uint64_t x45; uint64_t x44 = mulx_u64(x17, 0xffffffff, &x45); + uint64_t x48; uint64_t x47 = mulx_u64(x17, 0xffffffff00000001L, &x48); + uint64_t x50; uint8_t x51 = addcarryx_u64(0x0, x42, x44, &x50); + uint64_t x53; uint8_t x54 = addcarryx_u64(x51, x45, 0x0, &x53); + uint64_t x56; uint8_t x57 = addcarryx_u64(x54, 0x0, x47, &x56); + uint64_t x59; addcarryx_u64(0x0, x57, x48, &x59); + uint64_t _2; uint8_t x63 = addcarryx_u64(0x0, x17, x41, &_2); + uint64_t x65; uint8_t x66 = addcarryx_u64(x63, x29, x50, &x65); + uint64_t x68; uint8_t x69 = addcarryx_u64(x66, x32, x53, &x68); + uint64_t x71; uint8_t x72 = addcarryx_u64(x69, x35, x56, &x71); + uint64_t x74; uint8_t x75 = addcarryx_u64(x72, x38, x59, &x74); + uint64_t x78; uint64_t x77 = mulx_u64(x7, x11, &x78); + uint64_t x81; uint64_t x80 = mulx_u64(x7, x13, &x81); + uint64_t x84; uint64_t x83 = mulx_u64(x7, x15, &x84); + uint64_t x87; uint64_t x86 = mulx_u64(x7, x14, &x87); + uint64_t x89; uint8_t x90 = addcarryx_u64(0x0, x78, x80, &x89); + uint64_t x92; uint8_t x93 = addcarryx_u64(x90, x81, x83, &x92); + uint64_t x95; uint8_t x96 = addcarryx_u64(x93, x84, x86, &x95); + uint64_t x98; addcarryx_u64(0x0, x96, x87, &x98); + uint64_t x101; uint8_t x102 = addcarryx_u64(0x0, x65, x77, &x101); + uint64_t x104; uint8_t x105 = addcarryx_u64(x102, x68, x89, &x104); + uint64_t x107; uint8_t x108 = addcarryx_u64(x105, x71, x92, &x107); + uint64_t x110; uint8_t x111 = addcarryx_u64(x108, x74, x95, &x110); + uint64_t x113; uint8_t x114 = addcarryx_u64(x111, x75, x98, &x113); + uint64_t x117; uint64_t x116 = mulx_u64(x101, 0xffffffffffffffffL, &x117); + uint64_t x120; uint64_t x119 = mulx_u64(x101, 0xffffffff, &x120); + uint64_t x123; uint64_t x122 = mulx_u64(x101, 0xffffffff00000001L, &x123); + uint64_t x125; uint8_t x126 = addcarryx_u64(0x0, x117, x119, &x125); + uint64_t x128; uint8_t x129 = addcarryx_u64(x126, x120, 0x0, &x128); + uint64_t x131; uint8_t x132 = addcarryx_u64(x129, 0x0, x122, &x131); + uint64_t x134; addcarryx_u64(0x0, x132, x123, &x134); + uint64_t _3; uint8_t x138 = addcarryx_u64(0x0, x101, x116, &_3); + uint64_t x140; uint8_t x141 = addcarryx_u64(x138, x104, x125, &x140); + uint64_t x143; uint8_t x144 = addcarryx_u64(x141, x107, x128, &x143); + uint64_t x146; uint8_t x147 = addcarryx_u64(x144, x110, x131, &x146); + uint64_t x149; uint8_t x150 = addcarryx_u64(x147, x113, x134, &x149); + uint8_t x151 = (x150 + x114); + uint64_t x154; uint64_t x153 = mulx_u64(x9, x11, &x154); + uint64_t x157; uint64_t x156 = mulx_u64(x9, x13, &x157); + uint64_t x160; uint64_t x159 = mulx_u64(x9, x15, &x160); + uint64_t x163; uint64_t x162 = mulx_u64(x9, x14, &x163); + uint64_t x165; uint8_t x166 = addcarryx_u64(0x0, x154, x156, &x165); + uint64_t x168; uint8_t x169 = addcarryx_u64(x166, x157, x159, &x168); + uint64_t x171; uint8_t x172 = addcarryx_u64(x169, x160, x162, &x171); + uint64_t x174; addcarryx_u64(0x0, x172, x163, &x174); + uint64_t x177; uint8_t x178 = addcarryx_u64(0x0, x140, x153, &x177); + uint64_t x180; uint8_t x181 = addcarryx_u64(x178, x143, x165, &x180); + uint64_t x183; uint8_t x184 = addcarryx_u64(x181, x146, x168, &x183); + uint64_t x186; uint8_t x187 = addcarryx_u64(x184, x149, x171, &x186); + uint64_t x189; uint8_t x190 = addcarryx_u64(x187, x151, x174, &x189); + uint64_t x193; uint64_t x192 = mulx_u64(x177, 0xffffffffffffffffL, &x193); + uint64_t x196; uint64_t x195 = mulx_u64(x177, 0xffffffff, &x196); + uint64_t x199; uint64_t x198 = mulx_u64(x177, 0xffffffff00000001L, &x199); + uint64_t x201; uint8_t x202 = addcarryx_u64(0x0, x193, x195, &x201); + uint64_t x204; uint8_t x205 = addcarryx_u64(x202, x196, 0x0, &x204); + uint64_t x207; uint8_t x208 = addcarryx_u64(x205, 0x0, x198, &x207); + uint64_t x210; addcarryx_u64(0x0, x208, x199, &x210); + uint64_t _4; uint8_t x214 = addcarryx_u64(0x0, x177, x192, &_4); + uint64_t x216; uint8_t x217 = addcarryx_u64(x214, x180, x201, &x216); + uint64_t x219; uint8_t x220 = addcarryx_u64(x217, x183, x204, &x219); + uint64_t x222; uint8_t x223 = addcarryx_u64(x220, x186, x207, &x222); + uint64_t x225; uint8_t x226 = addcarryx_u64(x223, x189, x210, &x225); + uint8_t x227 = (x226 + x190); + uint64_t x230; uint64_t x229 = mulx_u64(x8, x11, &x230); + uint64_t x233; uint64_t x232 = mulx_u64(x8, x13, &x233); + uint64_t x236; uint64_t x235 = mulx_u64(x8, x15, &x236); + uint64_t x239; uint64_t x238 = mulx_u64(x8, x14, &x239); + uint64_t x241; uint8_t x242 = addcarryx_u64(0x0, x230, x232, &x241); + uint64_t x244; uint8_t x245 = addcarryx_u64(x242, x233, x235, &x244); + uint64_t x247; uint8_t x248 = addcarryx_u64(x245, x236, x238, &x247); + uint64_t x250; addcarryx_u64(0x0, x248, x239, &x250); + uint64_t x253; uint8_t x254 = addcarryx_u64(0x0, x216, x229, &x253); + uint64_t x256; uint8_t x257 = addcarryx_u64(x254, x219, x241, &x256); + uint64_t x259; uint8_t x260 = addcarryx_u64(x257, x222, x244, &x259); + uint64_t x262; uint8_t x263 = addcarryx_u64(x260, x225, x247, &x262); + uint64_t x265; uint8_t x266 = addcarryx_u64(x263, x227, x250, &x265); + uint64_t x269; uint64_t x268 = mulx_u64(x253, 0xffffffffffffffffL, &x269); + uint64_t x272; uint64_t x271 = mulx_u64(x253, 0xffffffff, &x272); + uint64_t x275; uint64_t x274 = mulx_u64(x253, 0xffffffff00000001L, &x275); + uint64_t x277; uint8_t x278 = addcarryx_u64(0x0, x269, x271, &x277); + uint64_t x280; uint8_t x281 = addcarryx_u64(x278, x272, 0x0, &x280); + uint64_t x283; uint8_t x284 = addcarryx_u64(x281, 0x0, x274, &x283); + uint64_t x286; addcarryx_u64(0x0, x284, x275, &x286); + uint64_t _5; uint8_t x290 = addcarryx_u64(0x0, x253, x268, &_5); + uint64_t x292; uint8_t x293 = addcarryx_u64(x290, x256, x277, &x292); + uint64_t x295; uint8_t x296 = addcarryx_u64(x293, x259, x280, &x295); + uint64_t x298; uint8_t x299 = addcarryx_u64(x296, x262, x283, &x298); + uint64_t x301; uint8_t x302 = addcarryx_u64(x299, x265, x286, &x301); + uint8_t x303 = (x302 + x266); + uint64_t x305; uint8_t x306 = subborrow_u64(0x0, x292, 0xffffffffffffffffL, &x305); + uint64_t x308; uint8_t x309 = subborrow_u64(x306, x295, 0xffffffff, &x308); + uint64_t x311; uint8_t x312 = subborrow_u64(x309, x298, 0x0, &x311); + uint64_t x314; uint8_t x315 = subborrow_u64(x312, x301, 0xffffffff00000001L, &x314); + uint64_t _6; uint8_t x318 = subborrow_u64(x315, x303, 0x0, &_6); + uint64_t x319 = cmovznz_u64(x318, x314, x301); + uint64_t x320 = cmovznz_u64(x318, x311, x298); + uint64_t x321 = cmovznz_u64(x318, x308, x295); + uint64_t x322 = cmovznz_u64(x318, x305, x292); + out[0] = x322; + out[1] = x321; + out[2] = x320; + out[3] = x319; +} + +static void fe_sub(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { + const uint64_t x8 = in1[3]; + const uint64_t x9 = in1[2]; + const uint64_t x7 = in1[1]; + const uint64_t x5 = in1[0]; + const uint64_t x14 = in2[3]; + const uint64_t x15 = in2[2]; + const uint64_t x13 = in2[1]; + const uint64_t x11 = in2[0]; + uint64_t x17; uint8_t x18 = subborrow_u64(0x0, x5, x11, &x17); + uint64_t x20; uint8_t x21 = subborrow_u64(x18, x7, x13, &x20); + uint64_t x23; uint8_t x24 = subborrow_u64(x21, x9, x15, &x23); + uint64_t x26; uint8_t x27 = subborrow_u64(x24, x8, x14, &x26); + uint64_t x28 = (uint64_t)cmovznz_u64(x27, 0x0, 0xffffffffffffffffL); + uint64_t x29 = (x28 & 0xffffffffffffffffL); + uint64_t x31; uint8_t x32 = addcarryx_u64(0x0, x17, x29, &x31); + uint64_t x33 = (x28 & 0xffffffff); + uint64_t x35; uint8_t x36 = addcarryx_u64(x32, x20, x33, &x35); + uint64_t x38; uint8_t x39 = addcarryx_u64(x36, x23, 0x0, &x38); + uint64_t x40 = (x28 & 0xffffffff00000001L); + uint64_t x42; addcarryx_u64(x39, x26, x40, &x42); + out[0] = x31; + out[1] = x35; + out[2] = x38; + out[3] = x42; +} + +#else // 64BIT, else 32BIT + +static void fe_add(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { + const uint32_t x16 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x30 = in2[7]; + const uint32_t x31 = in2[6]; + const uint32_t x29 = in2[5]; + const uint32_t x27 = in2[4]; + const uint32_t x25 = in2[3]; + const uint32_t x23 = in2[2]; + const uint32_t x21 = in2[1]; + const uint32_t x19 = in2[0]; + uint32_t x33; uint8_t x34 = addcarryx_u32(0x0, x5, x19, &x33); + uint32_t x36; uint8_t x37 = addcarryx_u32(x34, x7, x21, &x36); + uint32_t x39; uint8_t x40 = addcarryx_u32(x37, x9, x23, &x39); + uint32_t x42; uint8_t x43 = addcarryx_u32(x40, x11, x25, &x42); + uint32_t x45; uint8_t x46 = addcarryx_u32(x43, x13, x27, &x45); + uint32_t x48; uint8_t x49 = addcarryx_u32(x46, x15, x29, &x48); + uint32_t x51; uint8_t x52 = addcarryx_u32(x49, x17, x31, &x51); + uint32_t x54; uint8_t x55 = addcarryx_u32(x52, x16, x30, &x54); + uint32_t x57; uint8_t x58 = subborrow_u32(0x0, x33, 0xffffffff, &x57); + uint32_t x60; uint8_t x61 = subborrow_u32(x58, x36, 0xffffffff, &x60); + uint32_t x63; uint8_t x64 = subborrow_u32(x61, x39, 0xffffffff, &x63); + uint32_t x66; uint8_t x67 = subborrow_u32(x64, x42, 0x0, &x66); + uint32_t x69; uint8_t x70 = subborrow_u32(x67, x45, 0x0, &x69); + uint32_t x72; uint8_t x73 = subborrow_u32(x70, x48, 0x0, &x72); + uint32_t x75; uint8_t x76 = subborrow_u32(x73, x51, 0x1, &x75); + uint32_t x78; uint8_t x79 = subborrow_u32(x76, x54, 0xffffffff, &x78); + uint32_t _; uint8_t x82 = subborrow_u32(x79, x55, 0x0, &_); + uint32_t x83 = cmovznz_u32(x82, x78, x54); + uint32_t x84 = cmovznz_u32(x82, x75, x51); + uint32_t x85 = cmovznz_u32(x82, x72, x48); + uint32_t x86 = cmovznz_u32(x82, x69, x45); + uint32_t x87 = cmovznz_u32(x82, x66, x42); + uint32_t x88 = cmovznz_u32(x82, x63, x39); + uint32_t x89 = cmovznz_u32(x82, x60, x36); + uint32_t x90 = cmovznz_u32(x82, x57, x33); + out[0] = x90; + out[1] = x89; + out[2] = x88; + out[3] = x87; + out[4] = x86; + out[5] = x85; + out[6] = x84; + out[7] = x83; +} + +static void fe_mul(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { + const uint32_t x16 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x30 = in2[7]; + const uint32_t x31 = in2[6]; + const uint32_t x29 = in2[5]; + const uint32_t x27 = in2[4]; + const uint32_t x25 = in2[3]; + const uint32_t x23 = in2[2]; + const uint32_t x21 = in2[1]; + const uint32_t x19 = in2[0]; + uint32_t x34; uint32_t x33 = mulx_u32(x5, x19, &x34); + uint32_t x37; uint32_t x36 = mulx_u32(x5, x21, &x37); + uint32_t x40; uint32_t x39 = mulx_u32(x5, x23, &x40); + uint32_t x43; uint32_t x42 = mulx_u32(x5, x25, &x43); + uint32_t x46; uint32_t x45 = mulx_u32(x5, x27, &x46); + uint32_t x49; uint32_t x48 = mulx_u32(x5, x29, &x49); + uint32_t x52; uint32_t x51 = mulx_u32(x5, x31, &x52); + uint32_t x55; uint32_t x54 = mulx_u32(x5, x30, &x55); + uint32_t x57; uint8_t x58 = addcarryx_u32(0x0, x34, x36, &x57); + uint32_t x60; uint8_t x61 = addcarryx_u32(x58, x37, x39, &x60); + uint32_t x63; uint8_t x64 = addcarryx_u32(x61, x40, x42, &x63); + uint32_t x66; uint8_t x67 = addcarryx_u32(x64, x43, x45, &x66); + uint32_t x69; uint8_t x70 = addcarryx_u32(x67, x46, x48, &x69); + uint32_t x72; uint8_t x73 = addcarryx_u32(x70, x49, x51, &x72); + uint32_t x75; uint8_t x76 = addcarryx_u32(x73, x52, x54, &x75); + uint32_t x78; addcarryx_u32(0x0, x76, x55, &x78); + uint32_t x82; uint32_t x81 = mulx_u32(x33, 0xffffffff, &x82); + uint32_t x85; uint32_t x84 = mulx_u32(x33, 0xffffffff, &x85); + uint32_t x88; uint32_t x87 = mulx_u32(x33, 0xffffffff, &x88); + uint32_t x91; uint32_t x90 = mulx_u32(x33, 0xffffffff, &x91); + uint32_t x93; uint8_t x94 = addcarryx_u32(0x0, x82, x84, &x93); + uint32_t x96; uint8_t x97 = addcarryx_u32(x94, x85, x87, &x96); + uint32_t x99; uint8_t x100 = addcarryx_u32(x97, x88, 0x0, &x99); + uint8_t x101 = (0x0 + 0x0); + uint32_t _1; uint8_t x104 = addcarryx_u32(0x0, x33, x81, &_1); + uint32_t x106; uint8_t x107 = addcarryx_u32(x104, x57, x93, &x106); + uint32_t x109; uint8_t x110 = addcarryx_u32(x107, x60, x96, &x109); + uint32_t x112; uint8_t x113 = addcarryx_u32(x110, x63, x99, &x112); + uint32_t x115; uint8_t x116 = addcarryx_u32(x113, x66, x100, &x115); + uint32_t x118; uint8_t x119 = addcarryx_u32(x116, x69, x101, &x118); + uint32_t x121; uint8_t x122 = addcarryx_u32(x119, x72, x33, &x121); + uint32_t x124; uint8_t x125 = addcarryx_u32(x122, x75, x90, &x124); + uint32_t x127; uint8_t x128 = addcarryx_u32(x125, x78, x91, &x127); + uint8_t x129 = (x128 + 0x0); + uint32_t x132; uint32_t x131 = mulx_u32(x7, x19, &x132); + uint32_t x135; uint32_t x134 = mulx_u32(x7, x21, &x135); + uint32_t x138; uint32_t x137 = mulx_u32(x7, x23, &x138); + uint32_t x141; uint32_t x140 = mulx_u32(x7, x25, &x141); + uint32_t x144; uint32_t x143 = mulx_u32(x7, x27, &x144); + uint32_t x147; uint32_t x146 = mulx_u32(x7, x29, &x147); + uint32_t x150; uint32_t x149 = mulx_u32(x7, x31, &x150); + uint32_t x153; uint32_t x152 = mulx_u32(x7, x30, &x153); + uint32_t x155; uint8_t x156 = addcarryx_u32(0x0, x132, x134, &x155); + uint32_t x158; uint8_t x159 = addcarryx_u32(x156, x135, x137, &x158); + uint32_t x161; uint8_t x162 = addcarryx_u32(x159, x138, x140, &x161); + uint32_t x164; uint8_t x165 = addcarryx_u32(x162, x141, x143, &x164); + uint32_t x167; uint8_t x168 = addcarryx_u32(x165, x144, x146, &x167); + uint32_t x170; uint8_t x171 = addcarryx_u32(x168, x147, x149, &x170); + uint32_t x173; uint8_t x174 = addcarryx_u32(x171, x150, x152, &x173); + uint32_t x176; addcarryx_u32(0x0, x174, x153, &x176); + uint32_t x179; uint8_t x180 = addcarryx_u32(0x0, x106, x131, &x179); + uint32_t x182; uint8_t x183 = addcarryx_u32(x180, x109, x155, &x182); + uint32_t x185; uint8_t x186 = addcarryx_u32(x183, x112, x158, &x185); + uint32_t x188; uint8_t x189 = addcarryx_u32(x186, x115, x161, &x188); + uint32_t x191; uint8_t x192 = addcarryx_u32(x189, x118, x164, &x191); + uint32_t x194; uint8_t x195 = addcarryx_u32(x192, x121, x167, &x194); + uint32_t x197; uint8_t x198 = addcarryx_u32(x195, x124, x170, &x197); + uint32_t x200; uint8_t x201 = addcarryx_u32(x198, x127, x173, &x200); + uint32_t x203; uint8_t x204 = addcarryx_u32(x201, x129, x176, &x203); + uint32_t x207; uint32_t x206 = mulx_u32(x179, 0xffffffff, &x207); + uint32_t x210; uint32_t x209 = mulx_u32(x179, 0xffffffff, &x210); + uint32_t x213; uint32_t x212 = mulx_u32(x179, 0xffffffff, &x213); + uint32_t x216; uint32_t x215 = mulx_u32(x179, 0xffffffff, &x216); + uint32_t x218; uint8_t x219 = addcarryx_u32(0x0, x207, x209, &x218); + uint32_t x221; uint8_t x222 = addcarryx_u32(x219, x210, x212, &x221); + uint32_t x224; uint8_t x225 = addcarryx_u32(x222, x213, 0x0, &x224); + uint8_t x226 = (0x0 + 0x0); + uint32_t _2; uint8_t x229 = addcarryx_u32(0x0, x179, x206, &_2); + uint32_t x231; uint8_t x232 = addcarryx_u32(x229, x182, x218, &x231); + uint32_t x234; uint8_t x235 = addcarryx_u32(x232, x185, x221, &x234); + uint32_t x237; uint8_t x238 = addcarryx_u32(x235, x188, x224, &x237); + uint32_t x240; uint8_t x241 = addcarryx_u32(x238, x191, x225, &x240); + uint32_t x243; uint8_t x244 = addcarryx_u32(x241, x194, x226, &x243); + uint32_t x246; uint8_t x247 = addcarryx_u32(x244, x197, x179, &x246); + uint32_t x249; uint8_t x250 = addcarryx_u32(x247, x200, x215, &x249); + uint32_t x252; uint8_t x253 = addcarryx_u32(x250, x203, x216, &x252); + uint8_t x254 = (x253 + x204); + uint32_t x257; uint32_t x256 = mulx_u32(x9, x19, &x257); + uint32_t x260; uint32_t x259 = mulx_u32(x9, x21, &x260); + uint32_t x263; uint32_t x262 = mulx_u32(x9, x23, &x263); + uint32_t x266; uint32_t x265 = mulx_u32(x9, x25, &x266); + uint32_t x269; uint32_t x268 = mulx_u32(x9, x27, &x269); + uint32_t x272; uint32_t x271 = mulx_u32(x9, x29, &x272); + uint32_t x275; uint32_t x274 = mulx_u32(x9, x31, &x275); + uint32_t x278; uint32_t x277 = mulx_u32(x9, x30, &x278); + uint32_t x280; uint8_t x281 = addcarryx_u32(0x0, x257, x259, &x280); + uint32_t x283; uint8_t x284 = addcarryx_u32(x281, x260, x262, &x283); + uint32_t x286; uint8_t x287 = addcarryx_u32(x284, x263, x265, &x286); + uint32_t x289; uint8_t x290 = addcarryx_u32(x287, x266, x268, &x289); + uint32_t x292; uint8_t x293 = addcarryx_u32(x290, x269, x271, &x292); + uint32_t x295; uint8_t x296 = addcarryx_u32(x293, x272, x274, &x295); + uint32_t x298; uint8_t x299 = addcarryx_u32(x296, x275, x277, &x298); + uint32_t x301; addcarryx_u32(0x0, x299, x278, &x301); + uint32_t x304; uint8_t x305 = addcarryx_u32(0x0, x231, x256, &x304); + uint32_t x307; uint8_t x308 = addcarryx_u32(x305, x234, x280, &x307); + uint32_t x310; uint8_t x311 = addcarryx_u32(x308, x237, x283, &x310); + uint32_t x313; uint8_t x314 = addcarryx_u32(x311, x240, x286, &x313); + uint32_t x316; uint8_t x317 = addcarryx_u32(x314, x243, x289, &x316); + uint32_t x319; uint8_t x320 = addcarryx_u32(x317, x246, x292, &x319); + uint32_t x322; uint8_t x323 = addcarryx_u32(x320, x249, x295, &x322); + uint32_t x325; uint8_t x326 = addcarryx_u32(x323, x252, x298, &x325); + uint32_t x328; uint8_t x329 = addcarryx_u32(x326, x254, x301, &x328); + uint32_t x332; uint32_t x331 = mulx_u32(x304, 0xffffffff, &x332); + uint32_t x335; uint32_t x334 = mulx_u32(x304, 0xffffffff, &x335); + uint32_t x338; uint32_t x337 = mulx_u32(x304, 0xffffffff, &x338); + uint32_t x341; uint32_t x340 = mulx_u32(x304, 0xffffffff, &x341); + uint32_t x343; uint8_t x344 = addcarryx_u32(0x0, x332, x334, &x343); + uint32_t x346; uint8_t x347 = addcarryx_u32(x344, x335, x337, &x346); + uint32_t x349; uint8_t x350 = addcarryx_u32(x347, x338, 0x0, &x349); + uint8_t x351 = (0x0 + 0x0); + uint32_t _3; uint8_t x354 = addcarryx_u32(0x0, x304, x331, &_3); + uint32_t x356; uint8_t x357 = addcarryx_u32(x354, x307, x343, &x356); + uint32_t x359; uint8_t x360 = addcarryx_u32(x357, x310, x346, &x359); + uint32_t x362; uint8_t x363 = addcarryx_u32(x360, x313, x349, &x362); + uint32_t x365; uint8_t x366 = addcarryx_u32(x363, x316, x350, &x365); + uint32_t x368; uint8_t x369 = addcarryx_u32(x366, x319, x351, &x368); + uint32_t x371; uint8_t x372 = addcarryx_u32(x369, x322, x304, &x371); + uint32_t x374; uint8_t x375 = addcarryx_u32(x372, x325, x340, &x374); + uint32_t x377; uint8_t x378 = addcarryx_u32(x375, x328, x341, &x377); + uint8_t x379 = (x378 + x329); + uint32_t x382; uint32_t x381 = mulx_u32(x11, x19, &x382); + uint32_t x385; uint32_t x384 = mulx_u32(x11, x21, &x385); + uint32_t x388; uint32_t x387 = mulx_u32(x11, x23, &x388); + uint32_t x391; uint32_t x390 = mulx_u32(x11, x25, &x391); + uint32_t x394; uint32_t x393 = mulx_u32(x11, x27, &x394); + uint32_t x397; uint32_t x396 = mulx_u32(x11, x29, &x397); + uint32_t x400; uint32_t x399 = mulx_u32(x11, x31, &x400); + uint32_t x403; uint32_t x402 = mulx_u32(x11, x30, &x403); + uint32_t x405; uint8_t x406 = addcarryx_u32(0x0, x382, x384, &x405); + uint32_t x408; uint8_t x409 = addcarryx_u32(x406, x385, x387, &x408); + uint32_t x411; uint8_t x412 = addcarryx_u32(x409, x388, x390, &x411); + uint32_t x414; uint8_t x415 = addcarryx_u32(x412, x391, x393, &x414); + uint32_t x417; uint8_t x418 = addcarryx_u32(x415, x394, x396, &x417); + uint32_t x420; uint8_t x421 = addcarryx_u32(x418, x397, x399, &x420); + uint32_t x423; uint8_t x424 = addcarryx_u32(x421, x400, x402, &x423); + uint32_t x426; addcarryx_u32(0x0, x424, x403, &x426); + uint32_t x429; uint8_t x430 = addcarryx_u32(0x0, x356, x381, &x429); + uint32_t x432; uint8_t x433 = addcarryx_u32(x430, x359, x405, &x432); + uint32_t x435; uint8_t x436 = addcarryx_u32(x433, x362, x408, &x435); + uint32_t x438; uint8_t x439 = addcarryx_u32(x436, x365, x411, &x438); + uint32_t x441; uint8_t x442 = addcarryx_u32(x439, x368, x414, &x441); + uint32_t x444; uint8_t x445 = addcarryx_u32(x442, x371, x417, &x444); + uint32_t x447; uint8_t x448 = addcarryx_u32(x445, x374, x420, &x447); + uint32_t x450; uint8_t x451 = addcarryx_u32(x448, x377, x423, &x450); + uint32_t x453; uint8_t x454 = addcarryx_u32(x451, x379, x426, &x453); + uint32_t x457; uint32_t x456 = mulx_u32(x429, 0xffffffff, &x457); + uint32_t x460; uint32_t x459 = mulx_u32(x429, 0xffffffff, &x460); + uint32_t x463; uint32_t x462 = mulx_u32(x429, 0xffffffff, &x463); + uint32_t x466; uint32_t x465 = mulx_u32(x429, 0xffffffff, &x466); + uint32_t x468; uint8_t x469 = addcarryx_u32(0x0, x457, x459, &x468); + uint32_t x471; uint8_t x472 = addcarryx_u32(x469, x460, x462, &x471); + uint32_t x474; uint8_t x475 = addcarryx_u32(x472, x463, 0x0, &x474); + uint8_t x476 = (0x0 + 0x0); + uint32_t _4; uint8_t x479 = addcarryx_u32(0x0, x429, x456, &_4); + uint32_t x481; uint8_t x482 = addcarryx_u32(x479, x432, x468, &x481); + uint32_t x484; uint8_t x485 = addcarryx_u32(x482, x435, x471, &x484); + uint32_t x487; uint8_t x488 = addcarryx_u32(x485, x438, x474, &x487); + uint32_t x490; uint8_t x491 = addcarryx_u32(x488, x441, x475, &x490); + uint32_t x493; uint8_t x494 = addcarryx_u32(x491, x444, x476, &x493); + uint32_t x496; uint8_t x497 = addcarryx_u32(x494, x447, x429, &x496); + uint32_t x499; uint8_t x500 = addcarryx_u32(x497, x450, x465, &x499); + uint32_t x502; uint8_t x503 = addcarryx_u32(x500, x453, x466, &x502); + uint8_t x504 = (x503 + x454); + uint32_t x507; uint32_t x506 = mulx_u32(x13, x19, &x507); + uint32_t x510; uint32_t x509 = mulx_u32(x13, x21, &x510); + uint32_t x513; uint32_t x512 = mulx_u32(x13, x23, &x513); + uint32_t x516; uint32_t x515 = mulx_u32(x13, x25, &x516); + uint32_t x519; uint32_t x518 = mulx_u32(x13, x27, &x519); + uint32_t x522; uint32_t x521 = mulx_u32(x13, x29, &x522); + uint32_t x525; uint32_t x524 = mulx_u32(x13, x31, &x525); + uint32_t x528; uint32_t x527 = mulx_u32(x13, x30, &x528); + uint32_t x530; uint8_t x531 = addcarryx_u32(0x0, x507, x509, &x530); + uint32_t x533; uint8_t x534 = addcarryx_u32(x531, x510, x512, &x533); + uint32_t x536; uint8_t x537 = addcarryx_u32(x534, x513, x515, &x536); + uint32_t x539; uint8_t x540 = addcarryx_u32(x537, x516, x518, &x539); + uint32_t x542; uint8_t x543 = addcarryx_u32(x540, x519, x521, &x542); + uint32_t x545; uint8_t x546 = addcarryx_u32(x543, x522, x524, &x545); + uint32_t x548; uint8_t x549 = addcarryx_u32(x546, x525, x527, &x548); + uint32_t x551; addcarryx_u32(0x0, x549, x528, &x551); + uint32_t x554; uint8_t x555 = addcarryx_u32(0x0, x481, x506, &x554); + uint32_t x557; uint8_t x558 = addcarryx_u32(x555, x484, x530, &x557); + uint32_t x560; uint8_t x561 = addcarryx_u32(x558, x487, x533, &x560); + uint32_t x563; uint8_t x564 = addcarryx_u32(x561, x490, x536, &x563); + uint32_t x566; uint8_t x567 = addcarryx_u32(x564, x493, x539, &x566); + uint32_t x569; uint8_t x570 = addcarryx_u32(x567, x496, x542, &x569); + uint32_t x572; uint8_t x573 = addcarryx_u32(x570, x499, x545, &x572); + uint32_t x575; uint8_t x576 = addcarryx_u32(x573, x502, x548, &x575); + uint32_t x578; uint8_t x579 = addcarryx_u32(x576, x504, x551, &x578); + uint32_t x582; uint32_t x581 = mulx_u32(x554, 0xffffffff, &x582); + uint32_t x585; uint32_t x584 = mulx_u32(x554, 0xffffffff, &x585); + uint32_t x588; uint32_t x587 = mulx_u32(x554, 0xffffffff, &x588); + uint32_t x591; uint32_t x590 = mulx_u32(x554, 0xffffffff, &x591); + uint32_t x593; uint8_t x594 = addcarryx_u32(0x0, x582, x584, &x593); + uint32_t x596; uint8_t x597 = addcarryx_u32(x594, x585, x587, &x596); + uint32_t x599; uint8_t x600 = addcarryx_u32(x597, x588, 0x0, &x599); + uint8_t x601 = (0x0 + 0x0); + uint32_t _5; uint8_t x604 = addcarryx_u32(0x0, x554, x581, &_5); + uint32_t x606; uint8_t x607 = addcarryx_u32(x604, x557, x593, &x606); + uint32_t x609; uint8_t x610 = addcarryx_u32(x607, x560, x596, &x609); + uint32_t x612; uint8_t x613 = addcarryx_u32(x610, x563, x599, &x612); + uint32_t x615; uint8_t x616 = addcarryx_u32(x613, x566, x600, &x615); + uint32_t x618; uint8_t x619 = addcarryx_u32(x616, x569, x601, &x618); + uint32_t x621; uint8_t x622 = addcarryx_u32(x619, x572, x554, &x621); + uint32_t x624; uint8_t x625 = addcarryx_u32(x622, x575, x590, &x624); + uint32_t x627; uint8_t x628 = addcarryx_u32(x625, x578, x591, &x627); + uint8_t x629 = (x628 + x579); + uint32_t x632; uint32_t x631 = mulx_u32(x15, x19, &x632); + uint32_t x635; uint32_t x634 = mulx_u32(x15, x21, &x635); + uint32_t x638; uint32_t x637 = mulx_u32(x15, x23, &x638); + uint32_t x641; uint32_t x640 = mulx_u32(x15, x25, &x641); + uint32_t x644; uint32_t x643 = mulx_u32(x15, x27, &x644); + uint32_t x647; uint32_t x646 = mulx_u32(x15, x29, &x647); + uint32_t x650; uint32_t x649 = mulx_u32(x15, x31, &x650); + uint32_t x653; uint32_t x652 = mulx_u32(x15, x30, &x653); + uint32_t x655; uint8_t x656 = addcarryx_u32(0x0, x632, x634, &x655); + uint32_t x658; uint8_t x659 = addcarryx_u32(x656, x635, x637, &x658); + uint32_t x661; uint8_t x662 = addcarryx_u32(x659, x638, x640, &x661); + uint32_t x664; uint8_t x665 = addcarryx_u32(x662, x641, x643, &x664); + uint32_t x667; uint8_t x668 = addcarryx_u32(x665, x644, x646, &x667); + uint32_t x670; uint8_t x671 = addcarryx_u32(x668, x647, x649, &x670); + uint32_t x673; uint8_t x674 = addcarryx_u32(x671, x650, x652, &x673); + uint32_t x676; addcarryx_u32(0x0, x674, x653, &x676); + uint32_t x679; uint8_t x680 = addcarryx_u32(0x0, x606, x631, &x679); + uint32_t x682; uint8_t x683 = addcarryx_u32(x680, x609, x655, &x682); + uint32_t x685; uint8_t x686 = addcarryx_u32(x683, x612, x658, &x685); + uint32_t x688; uint8_t x689 = addcarryx_u32(x686, x615, x661, &x688); + uint32_t x691; uint8_t x692 = addcarryx_u32(x689, x618, x664, &x691); + uint32_t x694; uint8_t x695 = addcarryx_u32(x692, x621, x667, &x694); + uint32_t x697; uint8_t x698 = addcarryx_u32(x695, x624, x670, &x697); + uint32_t x700; uint8_t x701 = addcarryx_u32(x698, x627, x673, &x700); + uint32_t x703; uint8_t x704 = addcarryx_u32(x701, x629, x676, &x703); + uint32_t x707; uint32_t x706 = mulx_u32(x679, 0xffffffff, &x707); + uint32_t x710; uint32_t x709 = mulx_u32(x679, 0xffffffff, &x710); + uint32_t x713; uint32_t x712 = mulx_u32(x679, 0xffffffff, &x713); + uint32_t x716; uint32_t x715 = mulx_u32(x679, 0xffffffff, &x716); + uint32_t x718; uint8_t x719 = addcarryx_u32(0x0, x707, x709, &x718); + uint32_t x721; uint8_t x722 = addcarryx_u32(x719, x710, x712, &x721); + uint32_t x724; uint8_t x725 = addcarryx_u32(x722, x713, 0x0, &x724); + uint8_t x726 = (0x0 + 0x0); + uint32_t _6; uint8_t x729 = addcarryx_u32(0x0, x679, x706, &_6); + uint32_t x731; uint8_t x732 = addcarryx_u32(x729, x682, x718, &x731); + uint32_t x734; uint8_t x735 = addcarryx_u32(x732, x685, x721, &x734); + uint32_t x737; uint8_t x738 = addcarryx_u32(x735, x688, x724, &x737); + uint32_t x740; uint8_t x741 = addcarryx_u32(x738, x691, x725, &x740); + uint32_t x743; uint8_t x744 = addcarryx_u32(x741, x694, x726, &x743); + uint32_t x746; uint8_t x747 = addcarryx_u32(x744, x697, x679, &x746); + uint32_t x749; uint8_t x750 = addcarryx_u32(x747, x700, x715, &x749); + uint32_t x752; uint8_t x753 = addcarryx_u32(x750, x703, x716, &x752); + uint8_t x754 = (x753 + x704); + uint32_t x757; uint32_t x756 = mulx_u32(x17, x19, &x757); + uint32_t x760; uint32_t x759 = mulx_u32(x17, x21, &x760); + uint32_t x763; uint32_t x762 = mulx_u32(x17, x23, &x763); + uint32_t x766; uint32_t x765 = mulx_u32(x17, x25, &x766); + uint32_t x769; uint32_t x768 = mulx_u32(x17, x27, &x769); + uint32_t x772; uint32_t x771 = mulx_u32(x17, x29, &x772); + uint32_t x775; uint32_t x774 = mulx_u32(x17, x31, &x775); + uint32_t x778; uint32_t x777 = mulx_u32(x17, x30, &x778); + uint32_t x780; uint8_t x781 = addcarryx_u32(0x0, x757, x759, &x780); + uint32_t x783; uint8_t x784 = addcarryx_u32(x781, x760, x762, &x783); + uint32_t x786; uint8_t x787 = addcarryx_u32(x784, x763, x765, &x786); + uint32_t x789; uint8_t x790 = addcarryx_u32(x787, x766, x768, &x789); + uint32_t x792; uint8_t x793 = addcarryx_u32(x790, x769, x771, &x792); + uint32_t x795; uint8_t x796 = addcarryx_u32(x793, x772, x774, &x795); + uint32_t x798; uint8_t x799 = addcarryx_u32(x796, x775, x777, &x798); + uint32_t x801; addcarryx_u32(0x0, x799, x778, &x801); + uint32_t x804; uint8_t x805 = addcarryx_u32(0x0, x731, x756, &x804); + uint32_t x807; uint8_t x808 = addcarryx_u32(x805, x734, x780, &x807); + uint32_t x810; uint8_t x811 = addcarryx_u32(x808, x737, x783, &x810); + uint32_t x813; uint8_t x814 = addcarryx_u32(x811, x740, x786, &x813); + uint32_t x816; uint8_t x817 = addcarryx_u32(x814, x743, x789, &x816); + uint32_t x819; uint8_t x820 = addcarryx_u32(x817, x746, x792, &x819); + uint32_t x822; uint8_t x823 = addcarryx_u32(x820, x749, x795, &x822); + uint32_t x825; uint8_t x826 = addcarryx_u32(x823, x752, x798, &x825); + uint32_t x828; uint8_t x829 = addcarryx_u32(x826, x754, x801, &x828); + uint32_t x832; uint32_t x831 = mulx_u32(x804, 0xffffffff, &x832); + uint32_t x835; uint32_t x834 = mulx_u32(x804, 0xffffffff, &x835); + uint32_t x838; uint32_t x837 = mulx_u32(x804, 0xffffffff, &x838); + uint32_t x841; uint32_t x840 = mulx_u32(x804, 0xffffffff, &x841); + uint32_t x843; uint8_t x844 = addcarryx_u32(0x0, x832, x834, &x843); + uint32_t x846; uint8_t x847 = addcarryx_u32(x844, x835, x837, &x846); + uint32_t x849; uint8_t x850 = addcarryx_u32(x847, x838, 0x0, &x849); + uint8_t x851 = (0x0 + 0x0); + uint32_t _7; uint8_t x854 = addcarryx_u32(0x0, x804, x831, &_7); + uint32_t x856; uint8_t x857 = addcarryx_u32(x854, x807, x843, &x856); + uint32_t x859; uint8_t x860 = addcarryx_u32(x857, x810, x846, &x859); + uint32_t x862; uint8_t x863 = addcarryx_u32(x860, x813, x849, &x862); + uint32_t x865; uint8_t x866 = addcarryx_u32(x863, x816, x850, &x865); + uint32_t x868; uint8_t x869 = addcarryx_u32(x866, x819, x851, &x868); + uint32_t x871; uint8_t x872 = addcarryx_u32(x869, x822, x804, &x871); + uint32_t x874; uint8_t x875 = addcarryx_u32(x872, x825, x840, &x874); + uint32_t x877; uint8_t x878 = addcarryx_u32(x875, x828, x841, &x877); + uint8_t x879 = (x878 + x829); + uint32_t x882; uint32_t x881 = mulx_u32(x16, x19, &x882); + uint32_t x885; uint32_t x884 = mulx_u32(x16, x21, &x885); + uint32_t x888; uint32_t x887 = mulx_u32(x16, x23, &x888); + uint32_t x891; uint32_t x890 = mulx_u32(x16, x25, &x891); + uint32_t x894; uint32_t x893 = mulx_u32(x16, x27, &x894); + uint32_t x897; uint32_t x896 = mulx_u32(x16, x29, &x897); + uint32_t x900; uint32_t x899 = mulx_u32(x16, x31, &x900); + uint32_t x903; uint32_t x902 = mulx_u32(x16, x30, &x903); + uint32_t x905; uint8_t x906 = addcarryx_u32(0x0, x882, x884, &x905); + uint32_t x908; uint8_t x909 = addcarryx_u32(x906, x885, x887, &x908); + uint32_t x911; uint8_t x912 = addcarryx_u32(x909, x888, x890, &x911); + uint32_t x914; uint8_t x915 = addcarryx_u32(x912, x891, x893, &x914); + uint32_t x917; uint8_t x918 = addcarryx_u32(x915, x894, x896, &x917); + uint32_t x920; uint8_t x921 = addcarryx_u32(x918, x897, x899, &x920); + uint32_t x923; uint8_t x924 = addcarryx_u32(x921, x900, x902, &x923); + uint32_t x926; addcarryx_u32(0x0, x924, x903, &x926); + uint32_t x929; uint8_t x930 = addcarryx_u32(0x0, x856, x881, &x929); + uint32_t x932; uint8_t x933 = addcarryx_u32(x930, x859, x905, &x932); + uint32_t x935; uint8_t x936 = addcarryx_u32(x933, x862, x908, &x935); + uint32_t x938; uint8_t x939 = addcarryx_u32(x936, x865, x911, &x938); + uint32_t x941; uint8_t x942 = addcarryx_u32(x939, x868, x914, &x941); + uint32_t x944; uint8_t x945 = addcarryx_u32(x942, x871, x917, &x944); + uint32_t x947; uint8_t x948 = addcarryx_u32(x945, x874, x920, &x947); + uint32_t x950; uint8_t x951 = addcarryx_u32(x948, x877, x923, &x950); + uint32_t x953; uint8_t x954 = addcarryx_u32(x951, x879, x926, &x953); + uint32_t x957; uint32_t x956 = mulx_u32(x929, 0xffffffff, &x957); + uint32_t x960; uint32_t x959 = mulx_u32(x929, 0xffffffff, &x960); + uint32_t x963; uint32_t x962 = mulx_u32(x929, 0xffffffff, &x963); + uint32_t x966; uint32_t x965 = mulx_u32(x929, 0xffffffff, &x966); + uint32_t x968; uint8_t x969 = addcarryx_u32(0x0, x957, x959, &x968); + uint32_t x971; uint8_t x972 = addcarryx_u32(x969, x960, x962, &x971); + uint32_t x974; uint8_t x975 = addcarryx_u32(x972, x963, 0x0, &x974); + uint8_t x976 = (0x0 + 0x0); + uint32_t _8; uint8_t x979 = addcarryx_u32(0x0, x929, x956, &_8); + uint32_t x981; uint8_t x982 = addcarryx_u32(x979, x932, x968, &x981); + uint32_t x984; uint8_t x985 = addcarryx_u32(x982, x935, x971, &x984); + uint32_t x987; uint8_t x988 = addcarryx_u32(x985, x938, x974, &x987); + uint32_t x990; uint8_t x991 = addcarryx_u32(x988, x941, x975, &x990); + uint32_t x993; uint8_t x994 = addcarryx_u32(x991, x944, x976, &x993); + uint32_t x996; uint8_t x997 = addcarryx_u32(x994, x947, x929, &x996); + uint32_t x999; uint8_t x1000 = addcarryx_u32(x997, x950, x965, &x999); + uint32_t x1002; uint8_t x1003 = addcarryx_u32(x1000, x953, x966, &x1002); + uint8_t x1004 = (x1003 + x954); + uint32_t x1006; uint8_t x1007 = subborrow_u32(0x0, x981, 0xffffffff, &x1006); + uint32_t x1009; uint8_t x1010 = subborrow_u32(x1007, x984, 0xffffffff, &x1009); + uint32_t x1012; uint8_t x1013 = subborrow_u32(x1010, x987, 0xffffffff, &x1012); + uint32_t x1015; uint8_t x1016 = subborrow_u32(x1013, x990, 0x0, &x1015); + uint32_t x1018; uint8_t x1019 = subborrow_u32(x1016, x993, 0x0, &x1018); + uint32_t x1021; uint8_t x1022 = subborrow_u32(x1019, x996, 0x0, &x1021); + uint32_t x1024; uint8_t x1025 = subborrow_u32(x1022, x999, 0x1, &x1024); + uint32_t x1027; uint8_t x1028 = subborrow_u32(x1025, x1002, 0xffffffff, &x1027); + uint32_t _9; uint8_t x1031 = subborrow_u32(x1028, x1004, 0x0, &_9); + uint32_t x1032 = cmovznz_u32(x1031, x1027, x1002); + uint32_t x1033 = cmovznz_u32(x1031, x1024, x999); + uint32_t x1034 = cmovznz_u32(x1031, x1021, x996); + uint32_t x1035 = cmovznz_u32(x1031, x1018, x993); + uint32_t x1036 = cmovznz_u32(x1031, x1015, x990); + uint32_t x1037 = cmovznz_u32(x1031, x1012, x987); + uint32_t x1038 = cmovznz_u32(x1031, x1009, x984); + uint32_t x1039 = cmovznz_u32(x1031, x1006, x981); + out[0] = x1039; + out[1] = x1038; + out[2] = x1037; + out[3] = x1036; + out[4] = x1035; + out[5] = x1034; + out[6] = x1033; + out[7] = x1032; +} + +// NOTE: the following functions are generated from fiat-crypto, from the same +// template as their 64-bit counterparts above, but the correctness proof of +// the template was not composed with the correctness proof of the +// specialization pipeline. This is because Coq unexplainedly loops on trying +// to synthesize opp and sub using the normal pipeline. + +static void fe_sub(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { + const uint32_t x14 = in1[7]; + const uint32_t x15 = in1[6]; + const uint32_t x13 = in1[5]; + const uint32_t x11 = in1[4]; + const uint32_t x9 = in1[3]; + const uint32_t x7 = in1[2]; + const uint32_t x5 = in1[1]; + const uint32_t x3 = in1[0]; + const uint32_t x28 = in2[7]; + const uint32_t x29 = in2[6]; + const uint32_t x27 = in2[5]; + const uint32_t x25 = in2[4]; + const uint32_t x23 = in2[3]; + const uint32_t x21 = in2[2]; + const uint32_t x19 = in2[1]; + const uint32_t x17 = in2[0]; + uint32_t x31; uint8_t x32 = subborrow_u32(0x0, x3, x17, &x31); + uint32_t x34; uint8_t x35 = subborrow_u32(x32, x5, x19, &x34); + uint32_t x37; uint8_t x38 = subborrow_u32(x35, x7, x21, &x37); + uint32_t x40; uint8_t x41 = subborrow_u32(x38, x9, x23, &x40); + uint32_t x43; uint8_t x44 = subborrow_u32(x41, x11, x25, &x43); + uint32_t x46; uint8_t x47 = subborrow_u32(x44, x13, x27, &x46); + uint32_t x49; uint8_t x50 = subborrow_u32(x47, x15, x29, &x49); + uint32_t x52; uint8_t x53 = subborrow_u32(x50, x14, x28, &x52); + uint32_t x54 = cmovznz_u32(x53, 0x0, 0xffffffff); + uint32_t x56; uint8_t x57 = addcarryx_u32(0x0, x31, (x54 & 0xffffffff), &x56); + uint32_t x59; uint8_t x60 = addcarryx_u32(x57, x34, (x54 & 0xffffffff), &x59); + uint32_t x62; uint8_t x63 = addcarryx_u32(x60, x37, (x54 & 0xffffffff), &x62); + uint32_t x65; uint8_t x66 = addcarryx_u32(x63, x40, 0x0, &x65); + uint32_t x68; uint8_t x69 = addcarryx_u32(x66, x43, 0x0, &x68); + uint32_t x71; uint8_t x72 = addcarryx_u32(x69, x46, 0x0, &x71); + uint32_t x74; uint8_t x75 = addcarryx_u32(x72, x49, ((uint8_t)x54 & 0x1), &x74); + uint32_t x77; addcarryx_u32(x75, x52, (x54 & 0xffffffff), &x77); + out[0] = x56; + out[1] = x59; + out[2] = x62; + out[3] = x65; + out[4] = x68; + out[5] = x71; + out[6] = x74; + out[7] = x77; +} + +// fe_op sets out = -in +static void fe_opp(uint32_t out[8], const uint32_t in1[8]) { + const uint32_t x12 = in1[7]; + const uint32_t x13 = in1[6]; + const uint32_t x11 = in1[5]; + const uint32_t x9 = in1[4]; + const uint32_t x7 = in1[3]; + const uint32_t x5 = in1[2]; + const uint32_t x3 = in1[1]; + const uint32_t x1 = in1[0]; + uint32_t x15; uint8_t x16 = subborrow_u32(0x0, 0x0, x1, &x15); + uint32_t x18; uint8_t x19 = subborrow_u32(x16, 0x0, x3, &x18); + uint32_t x21; uint8_t x22 = subborrow_u32(x19, 0x0, x5, &x21); + uint32_t x24; uint8_t x25 = subborrow_u32(x22, 0x0, x7, &x24); + uint32_t x27; uint8_t x28 = subborrow_u32(x25, 0x0, x9, &x27); + uint32_t x30; uint8_t x31 = subborrow_u32(x28, 0x0, x11, &x30); + uint32_t x33; uint8_t x34 = subborrow_u32(x31, 0x0, x13, &x33); + uint32_t x36; uint8_t x37 = subborrow_u32(x34, 0x0, x12, &x36); + uint32_t x38 = cmovznz_u32(x37, 0x0, 0xffffffff); + uint32_t x40; uint8_t x41 = addcarryx_u32(0x0, x15, (x38 & 0xffffffff), &x40); + uint32_t x43; uint8_t x44 = addcarryx_u32(x41, x18, (x38 & 0xffffffff), &x43); + uint32_t x46; uint8_t x47 = addcarryx_u32(x44, x21, (x38 & 0xffffffff), &x46); + uint32_t x49; uint8_t x50 = addcarryx_u32(x47, x24, 0x0, &x49); + uint32_t x52; uint8_t x53 = addcarryx_u32(x50, x27, 0x0, &x52); + uint32_t x55; uint8_t x56 = addcarryx_u32(x53, x30, 0x0, &x55); + uint32_t x58; uint8_t x59 = addcarryx_u32(x56, x33, ((uint8_t)x38 & 0x1), &x58); + uint32_t x61; addcarryx_u32(x59, x36, (x38 & 0xffffffff), &x61); + out[0] = x40; + out[1] = x43; + out[2] = x46; + out[3] = x49; + out[4] = x52; + out[5] = x55; + out[6] = x58; + out[7] = x61; +} + +#endif + +// utility functions, handwritten + +#define NBYTES 32 + +#if defined(BORINGSSL_NISTP256_64BIT) + +#define NLIMBS 4 +typedef uint64_t limb_t; +#define cmovznz_limb cmovznz_u64 +typedef uint64_t fe[NLIMBS]; +#else // 64BIT; else 32BIT + +#define NLIMBS 8 +typedef uint32_t limb_t; +#define cmovznz_limb cmovznz_u32 +typedef uint32_t fe[NLIMBS]; + +#endif // 64BIT + +static limb_t fe_nz(const limb_t in1[NLIMBS]) { + limb_t ret = 0; + for (int i = 0; i < NLIMBS; i++) { + ret |= in1[i]; + } + return ret; +} + +static void fe_copy(limb_t out[NLIMBS], const limb_t in1[NLIMBS]) { + for (int i = 0; i < NLIMBS; i++) { + out[i] = in1[i]; + } +} + +static void fe_cmovznz(limb_t out[NLIMBS], limb_t t, const limb_t z[NLIMBS], + const limb_t nz[NLIMBS]) { + for (int i = 0; i < NLIMBS; i++) { + out[i] = cmovznz_limb(t, z[i], nz[i]); + } +} + +static void fe_sqr(fe out, const fe in) { + fe_mul(out, in, in); +} + +static void fe_tobytes(uint8_t out[NBYTES], const fe in) { + for (int i = 0; i<NBYTES; i++) { + out[i] = (uint8_t)(in[i/sizeof(in[0])] >> (8*(i%sizeof(in[0])))); + } +} + +static void fe_frombytes(fe out, const uint8_t in[NBYTES]) { + for (int i = 0; i<NLIMBS; i++) { + out[i] = 0; + } + for (int i = 0; i<NBYTES; i++) { + out[i/sizeof(out[0])] |= ((limb_t)in[i]) << (8*(i%sizeof(out[0]))); + } +} + +static void fe_from_montgomery(fe x) { + static const limb_t kOne[NLIMBS] = {1, 0}; + fe_mul(x, x, kOne); +} + +// BN_* compatability wrappers + +static int BN_to_fe(fe out, const BIGNUM *bn) { + uint8_t tmp[NBYTES]; + if (!BN_bn2le_padded(tmp, NBYTES, bn)) { + return 0; + } + fe_frombytes(out, tmp); + return 1; +} + +static BIGNUM *fe_to_BN(BIGNUM *out, const fe in) { + uint8_t tmp[NBYTES]; + fe_tobytes(tmp, in); + return BN_le2bn(tmp, NBYTES, out); +} + +// fe_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 fe_inv(fe out, const fe in) { + fe ftmp, ftmp2; + // each e_I will hold |in|^{2^I - 1} + fe e2, e4, e8, e16, e32, e64; + + fe_sqr(ftmp, in); // 2^1 + fe_mul(ftmp, in, ftmp); // 2^2 - 2^0 + fe_copy(e2, ftmp); + fe_sqr(ftmp, ftmp); // 2^3 - 2^1 + fe_sqr(ftmp, ftmp); // 2^4 - 2^2 + fe_mul(ftmp, ftmp, e2); // 2^4 - 2^0 + fe_copy(e4, ftmp); + fe_sqr(ftmp, ftmp); // 2^5 - 2^1 + fe_sqr(ftmp, ftmp); // 2^6 - 2^2 + fe_sqr(ftmp, ftmp); // 2^7 - 2^3 + fe_sqr(ftmp, ftmp); // 2^8 - 2^4 + fe_mul(ftmp, ftmp, e4); // 2^8 - 2^0 + fe_copy(e8, ftmp); + for (size_t i = 0; i < 8; i++) { + fe_sqr(ftmp, ftmp); + } // 2^16 - 2^8 + fe_mul(ftmp, ftmp, e8); // 2^16 - 2^0 + fe_copy(e16, ftmp); + for (size_t i = 0; i < 16; i++) { + fe_sqr(ftmp, ftmp); + } // 2^32 - 2^16 + fe_mul(ftmp, ftmp, e16); // 2^32 - 2^0 + fe_copy(e32, ftmp); + for (size_t i = 0; i < 32; i++) { + fe_sqr(ftmp, ftmp); + } // 2^64 - 2^32 + fe_copy(e64, ftmp); + fe_mul(ftmp, ftmp, in); // 2^64 - 2^32 + 2^0 + for (size_t i = 0; i < 192; i++) { + fe_sqr(ftmp, ftmp); + } // 2^256 - 2^224 + 2^192 + + fe_mul(ftmp2, e64, e32); // 2^64 - 2^0 + for (size_t i = 0; i < 16; i++) { + fe_sqr(ftmp2, ftmp2); + } // 2^80 - 2^16 + fe_mul(ftmp2, ftmp2, e16); // 2^80 - 2^0 + for (size_t i = 0; i < 8; i++) { + fe_sqr(ftmp2, ftmp2); + } // 2^88 - 2^8 + fe_mul(ftmp2, ftmp2, e8); // 2^88 - 2^0 + for (size_t i = 0; i < 4; i++) { + fe_sqr(ftmp2, ftmp2); + } // 2^92 - 2^4 + fe_mul(ftmp2, ftmp2, e4); // 2^92 - 2^0 + fe_sqr(ftmp2, ftmp2); // 2^93 - 2^1 + fe_sqr(ftmp2, ftmp2); // 2^94 - 2^2 + fe_mul(ftmp2, ftmp2, e2); // 2^94 - 2^0 + fe_sqr(ftmp2, ftmp2); // 2^95 - 2^1 + fe_sqr(ftmp2, ftmp2); // 2^96 - 2^2 + fe_mul(ftmp2, ftmp2, in); // 2^96 - 3 + + fe_mul(out, ftmp2, ftmp); // 2^256 - 2^224 + 2^192 + 2^96 - 3 +} + +// 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(fe x_out, fe y_out, fe z_out, + const fe x_in, const fe y_in, const fe z_in) { + fe delta, gamma, beta, ftmp, ftmp2, tmptmp, alpha, fourbeta; + // delta = z^2 + fe_sqr(delta, z_in); + // gamma = y^2 + fe_sqr(gamma, y_in); + // beta = x*gamma + fe_mul(beta, x_in, gamma); + + // alpha = 3*(x-delta)*(x+delta) + fe_sub(ftmp, x_in, delta); + fe_add(ftmp2, x_in, delta); + + fe_add(tmptmp, ftmp2, ftmp2); + fe_add(ftmp2, ftmp2, tmptmp); + fe_mul(alpha, ftmp, ftmp2); + + // x' = alpha^2 - 8*beta + fe_sqr(x_out, alpha); + fe_add(fourbeta, beta, beta); + fe_add(fourbeta, fourbeta, fourbeta); + fe_add(tmptmp, fourbeta, fourbeta); + fe_sub(x_out, x_out, tmptmp); + + // z' = (y + z)^2 - gamma - delta + fe_add(delta, gamma, delta); + fe_add(ftmp, y_in, z_in); + fe_sqr(z_out, ftmp); + fe_sub(z_out, z_out, delta); + + // y' = alpha*(4*beta - x') - 8*gamma^2 + fe_sub(y_out, fourbeta, x_out); + fe_add(gamma, gamma, gamma); + fe_sqr(gamma, gamma); + fe_mul(y_out, alpha, y_out); + fe_add(gamma, gamma, gamma); + fe_sub(y_out, y_out, gamma); +} + +// 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(fe x3, fe y3, fe z3, const fe x1, + const fe y1, const fe z1, const int mixed, + const fe x2, const fe y2, const fe z2) { + fe x_out, y_out, z_out; + limb_t z1nz = fe_nz(z1); + limb_t z2nz = fe_nz(z2); + + // z1z1 = z1z1 = z1**2 + fe z1z1; fe_sqr(z1z1, z1); + + fe u1, s1, two_z1z2; + if (!mixed) { + // ftmp2 = z2z2 = z2**2 + fe z2z2; fe_sqr(z2z2, z2); + + // u1 = ftmp3 = x1*z2z2 + fe_mul(u1, x1, z2z2); + + // two_z1z2 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 + fe_add(two_z1z2, z1, z2); + fe_sqr(two_z1z2, two_z1z2); + fe_sub(two_z1z2, two_z1z2, z1z1); + fe_sub(two_z1z2, two_z1z2, z2z2); + + // s1 = ftmp2 = y1 * z2**3 + fe_mul(s1, z2, z2z2); + fe_mul(s1, s1, y1); + } else { + // We'll assume z2 = 1 (special case z2 = 0 is handled later). + + // u1 = ftmp3 = x1*z2z2 + fe_copy(u1, x1); + // two_z1z2 = 2z1z2 + fe_add(two_z1z2, z1, z1); + // s1 = ftmp2 = y1 * z2**3 + fe_copy(s1, y1); + } + + // u2 = x2*z1z1 + fe u2; fe_mul(u2, x2, z1z1); + + // h = ftmp4 = u2 - u1 + fe h; fe_sub(h, u2, u1); + + limb_t xneq = fe_nz(h); + + // z_out = two_z1z2 * h + fe_mul(z_out, h, two_z1z2); + + // z1z1z1 = z1 * z1z1 + fe z1z1z1; fe_mul(z1z1z1, z1, z1z1); + + // s2 = tmp = y2 * z1**3 + fe s2; fe_mul(s2, y2, z1z1z1); + + // r = (s2 - s1)*2 + fe r; + fe_sub(r, s2, s1); + fe_add(r, r, r); + + limb_t yneq = fe_nz(r); + + if (!xneq && !yneq && z1nz && z2nz) { + point_double(x_out, y_out, z_out, x1, y1, z1); + return; + } + + // I = (2h)**2 + fe i; + fe_add(i, h, h); + fe_sqr(i, i); + + // J = ftmp2 = h * I + fe j; fe_mul(j, h, i); + + // V = ftmp4 = U1 * I + fe v; fe_mul(v, u1, i); + + // x_out = r**2 - J - 2V + fe_sqr(x_out, r); + fe_sub(x_out, x_out, j); + fe_sub(x_out, x_out, v); + fe_sub(x_out, x_out, v); + + // y_out = r(V-x_out) - 2 * s1 * J + fe_sub(y_out, v, x_out); + fe_mul(y_out, y_out, r); + fe s1j; + fe_mul(s1j, s1, j); + fe_sub(y_out, y_out, s1j); + fe_sub(y_out, y_out, s1j); + + fe_cmovznz(x_out, z1nz, x2, x_out); + fe_cmovznz(x3, z2nz, x1, x_out); + fe_cmovznz(y_out, z1nz, y2, y_out); + fe_cmovznz(y3, z2nz, y1, y_out); + fe_cmovznz(z_out, z1nz, z2, z_out); + fe_cmovznz(z3, z2nz, z1, z_out); +} + +// 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. + +// g_pre_comp is the table of precomputed base points +#if defined(BORINGSSL_NISTP256_64BIT) +static const fe g_pre_comp[2][16][3] = { + {{{0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}}, + {{0x79e730d418a9143c, 0x75ba95fc5fedb601, 0x79fb732b77622510, + 0x18905f76a53755c6}, + {0xddf25357ce95560a, 0x8b4ab8e4ba19e45c, 0xd2e88688dd21f325, + 0x8571ff1825885d85}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x4f922fc516a0d2bb, 0xd5cc16c1a623499, 0x9241cf3a57c62c8b, + 0x2f5e6961fd1b667f}, + {0x5c15c70bf5a01797, 0x3d20b44d60956192, 0x4911b37071fdb52, + 0xf648f9168d6f0f7b}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x9e566847e137bbbc, 0xe434469e8a6a0bec, 0xb1c4276179d73463, + 0x5abe0285133d0015}, + {0x92aa837cc04c7dab, 0x573d9f4c43260c07, 0xc93156278e6cc37, + 0x94bb725b6b6f7383}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x62a8c244bfe20925, 0x91c19ac38fdce867, 0x5a96a5d5dd387063, + 0x61d587d421d324f6}, + {0xe87673a2a37173ea, 0x2384800853778b65, 0x10f8441e05bab43e, + 0xfa11fe124621efbe}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x1c891f2b2cb19ffd, 0x1ba8d5bb1923c23, 0xb6d03d678ac5ca8e, + 0x586eb04c1f13bedc}, + {0xc35c6e527e8ed09, 0x1e81a33c1819ede2, 0x278fd6c056c652fa, + 0x19d5ac0870864f11}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x62577734d2b533d5, 0x673b8af6a1bdddc0, 0x577e7c9aa79ec293, + 0xbb6de651c3b266b1}, + {0xe7e9303ab65259b3, 0xd6a0afd3d03a7480, 0xc5ac83d19b3cfc27, + 0x60b4619a5d18b99b}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xbd6a38e11ae5aa1c, 0xb8b7652b49e73658, 0xb130014ee5f87ed, + 0x9d0f27b2aeebffcd}, + {0xca9246317a730a55, 0x9c955b2fddbbc83a, 0x7c1dfe0ac019a71, + 0x244a566d356ec48d}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x56f8410ef4f8b16a, 0x97241afec47b266a, 0xa406b8e6d9c87c1, + 0x803f3e02cd42ab1b}, + {0x7f0309a804dbec69, 0xa83b85f73bbad05f, 0xc6097273ad8e197f, + 0xc097440e5067adc1}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x846a56f2c379ab34, 0xa8ee068b841df8d1, 0x20314459176c68ef, + 0xf1af32d5915f1f30}, + {0x99c375315d75bd50, 0x837cffbaf72f67bc, 0x613a41848d7723f, + 0x23d0f130e2d41c8b}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xed93e225d5be5a2b, 0x6fe799835934f3c6, 0x4314092622626ffc, + 0x50bbb4d97990216a}, + {0x378191c6e57ec63e, 0x65422c40181dcdb2, 0x41a8099b0236e0f6, + 0x2b10011801fe49c3}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xfc68b5c59b391593, 0xc385f5a2598270fc, 0x7144f3aad19adcbb, + 0xdd55899983fbae0c}, + {0x93b88b8e74b82ff4, 0xd2e03c4071e734c9, 0x9a7a9eaf43c0322a, + 0xe6e4c551149d6041}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x5fe14bfe80ec21fe, 0xf6ce116ac255be82, 0x98bc5a072f4a5d67, + 0xfad27148db7e63af}, + {0x90c0b6ac29ab05b3, 0x37a9a83c4e251ae6, 0xa7dc875c2aade7d, + 0x77387de39f0e1a84}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x1e9ecc49a56c0dd7, 0xa5cffcd846086c74, 0x8f7a1408f505aece, + 0xb37b85c0bef0c47e}, + {0x3596b6e4cc0e6a8f, 0xfd6d4bbf6b388f23, 0xaba453fac39cef4e, + 0x9c135ac8f9f628d5}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xa1c729495c8f8be, 0x2961c4803bf362bf, 0x9e418403df63d4ac, + 0xc109f9cb91ece900}, + {0xc2d095d058945705, 0xb9083d96ddeb85c0, 0x84692b8d7a40449b, + 0x9bc3344f2eee1ee1}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xd5ae35642913074, 0x55491b2748a542b1, 0x469ca665b310732a, + 0x29591d525f1a4cc1}, + {0xe76f5b6bb84f983f, 0xbe7eef419f5f84e1, 0x1200d49680baa189, + 0x6376551f18ef332c}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}}, + {{{0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}}, + {{0x202886024147519a, 0xd0981eac26b372f0, 0xa9d4a7caa785ebc8, + 0xd953c50ddbdf58e9}, + {0x9d6361ccfd590f8f, 0x72e9626b44e6c917, 0x7fd9611022eb64cf, + 0x863ebb7e9eb288f3}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x4fe7ee31b0e63d34, 0xf4600572a9e54fab, 0xc0493334d5e7b5a4, + 0x8589fb9206d54831}, + {0xaa70f5cc6583553a, 0x879094ae25649e5, 0xcc90450710044652, + 0xebb0696d02541c4f}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xabbaa0c03b89da99, 0xa6f2d79eb8284022, 0x27847862b81c05e8, + 0x337a4b5905e54d63}, + {0x3c67500d21f7794a, 0x207005b77d6d7f61, 0xa5a378104cfd6e8, + 0xd65e0d5f4c2fbd6}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xd433e50f6d3549cf, 0x6f33696ffacd665e, 0x695bfdacce11fcb4, + 0x810ee252af7c9860}, + {0x65450fe17159bb2c, 0xf7dfbebe758b357b, 0x2b057e74d69fea72, + 0xd485717a92731745}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xce1f69bbe83f7669, 0x9f8ae8272877d6b, 0x9548ae543244278d, + 0x207755dee3c2c19c}, + {0x87bd61d96fef1945, 0x18813cefb12d28c3, 0x9fbcd1d672df64aa, + 0x48dc5ee57154b00d}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xef0f469ef49a3154, 0x3e85a5956e2b2e9a, 0x45aaec1eaa924a9c, + 0xaa12dfc8a09e4719}, + {0x26f272274df69f1d, 0xe0e4c82ca2ff5e73, 0xb9d8ce73b7a9dd44, + 0x6c036e73e48ca901}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xe1e421e1a47153f0, 0xb86c3b79920418c9, 0x93bdce87705d7672, + 0xf25ae793cab79a77}, + {0x1f3194a36d869d0c, 0x9d55c8824986c264, 0x49fb5ea3096e945e, + 0x39b8e65313db0a3e}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xe3417bc035d0b34a, 0x440b386b8327c0a7, 0x8fb7262dac0362d1, + 0x2c41114ce0cdf943}, + {0x2ba5cef1ad95a0b1, 0xc09b37a867d54362, 0x26d6cdd201e486c9, + 0x20477abf42ff9297}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xf121b41bc0a67d2, 0x62d4760a444d248a, 0xe044f1d659b4737, + 0x8fde365250bb4a8}, + {0xaceec3da848bf287, 0xc2a62182d3369d6e, 0x3582dfdc92449482, + 0x2f7e2fd2565d6cd7}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xa0122b5178a876b, 0x51ff96ff085104b4, 0x50b31ab14f29f76, + 0x84abb28b5f87d4e6}, + {0xd5ed439f8270790a, 0x2d6cb59d85e3f46b, 0x75f55c1b6c1e2212, + 0xe5436f6717655640}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xc2965ecc9aeb596d, 0x1ea03e7023c92b4, 0x4704b4b62e013961, + 0xca8fd3f905ea367}, + {0x92523a42551b2b61, 0x1eb7a89c390fcd06, 0xe7f1d2be0392a63e, + 0x96dca2644ddb0c33}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x231c210e15339848, 0xe87a28e870778c8d, 0x9d1de6616956e170, + 0x4ac3c9382bb09c0b}, + {0x19be05516998987d, 0x8b2376c4ae09f4d6, 0x1de0b7651a3f933d, + 0x380d94c7e39705f4}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x3685954b8c31c31d, 0x68533d005bf21a0c, 0xbd7626e75c79ec9, + 0xca17754742c69d54}, + {0xcc6edafff6d2dbb2, 0xfd0d8cbd174a9d18, 0x875e8793aa4578e8, + 0xa976a7139cab2ce6}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0xce37ab11b43ea1db, 0xa7ff1a95259d292, 0x851b02218f84f186, + 0xa7222beadefaad13}, + {0xa2ac78ec2b0a9144, 0x5a024051f2fa59c5, 0x91d1eca56147ce38, + 0xbe94d523bc2ac690}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, + {{0x2d8daefd79ec1a0f, 0x3bbcd6fdceb39c97, 0xf5575ffc58f61a95, + 0xdbd986c4adf7b420}, + {0x81aa881415f39eb7, 0x6ee2fcf5b98d976c, 0x5465475dcf2f717d, + 0x8e24d3c46860bbd0}, + {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}}}; +#else +static const fe g_pre_comp[2][16][3] = { + {{{0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, + {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, + {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}}, + {{0x18a9143c,0x79e730d4, 0x5fedb601,0x75ba95fc, 0x77622510,0x79fb732b, + 0xa53755c6,0x18905f76}, + {0xce95560a,0xddf25357, 0xba19e45c,0x8b4ab8e4, 0xdd21f325,0xd2e88688, + 0x25885d85,0x8571ff18}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x16a0d2bb,0x4f922fc5, 0x1a623499,0xd5cc16c, 0x57c62c8b,0x9241cf3a, + 0xfd1b667f,0x2f5e6961}, + {0xf5a01797,0x5c15c70b, 0x60956192,0x3d20b44d, 0x71fdb52,0x4911b37, + 0x8d6f0f7b,0xf648f916}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xe137bbbc,0x9e566847, 0x8a6a0bec,0xe434469e, 0x79d73463,0xb1c42761, + 0x133d0015,0x5abe0285}, + {0xc04c7dab,0x92aa837c, 0x43260c07,0x573d9f4c, 0x78e6cc37,0xc931562, + 0x6b6f7383,0x94bb725b}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xbfe20925,0x62a8c244, 0x8fdce867,0x91c19ac3, 0xdd387063,0x5a96a5d5, + 0x21d324f6,0x61d587d4}, + {0xa37173ea,0xe87673a2, 0x53778b65,0x23848008, 0x5bab43e,0x10f8441e, + 0x4621efbe,0xfa11fe12}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x2cb19ffd,0x1c891f2b, 0xb1923c23,0x1ba8d5b, 0x8ac5ca8e,0xb6d03d67, + 0x1f13bedc,0x586eb04c}, + {0x27e8ed09,0xc35c6e5, 0x1819ede2,0x1e81a33c, 0x56c652fa,0x278fd6c0, + 0x70864f11,0x19d5ac08}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xd2b533d5,0x62577734, 0xa1bdddc0,0x673b8af6, 0xa79ec293,0x577e7c9a, + 0xc3b266b1,0xbb6de651}, + {0xb65259b3,0xe7e9303a, 0xd03a7480,0xd6a0afd3, 0x9b3cfc27,0xc5ac83d1, + 0x5d18b99b,0x60b4619a}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x1ae5aa1c,0xbd6a38e1, 0x49e73658,0xb8b7652b, 0xee5f87ed,0xb130014, + 0xaeebffcd,0x9d0f27b2}, + {0x7a730a55,0xca924631, 0xddbbc83a,0x9c955b2f, 0xac019a71,0x7c1dfe0, + 0x356ec48d,0x244a566d}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xf4f8b16a,0x56f8410e, 0xc47b266a,0x97241afe, 0x6d9c87c1,0xa406b8e, + 0xcd42ab1b,0x803f3e02}, + {0x4dbec69,0x7f0309a8, 0x3bbad05f,0xa83b85f7, 0xad8e197f,0xc6097273, + 0x5067adc1,0xc097440e}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xc379ab34,0x846a56f2, 0x841df8d1,0xa8ee068b, 0x176c68ef,0x20314459, + 0x915f1f30,0xf1af32d5}, + {0x5d75bd50,0x99c37531, 0xf72f67bc,0x837cffba, 0x48d7723f,0x613a418, + 0xe2d41c8b,0x23d0f130}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xd5be5a2b,0xed93e225, 0x5934f3c6,0x6fe79983, 0x22626ffc,0x43140926, + 0x7990216a,0x50bbb4d9}, + {0xe57ec63e,0x378191c6, 0x181dcdb2,0x65422c40, 0x236e0f6,0x41a8099b, + 0x1fe49c3,0x2b100118}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x9b391593,0xfc68b5c5, 0x598270fc,0xc385f5a2, 0xd19adcbb,0x7144f3aa, + 0x83fbae0c,0xdd558999}, + {0x74b82ff4,0x93b88b8e, 0x71e734c9,0xd2e03c40, 0x43c0322a,0x9a7a9eaf, + 0x149d6041,0xe6e4c551}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x80ec21fe,0x5fe14bfe, 0xc255be82,0xf6ce116a, 0x2f4a5d67,0x98bc5a07, + 0xdb7e63af,0xfad27148}, + {0x29ab05b3,0x90c0b6ac, 0x4e251ae6,0x37a9a83c, 0xc2aade7d,0xa7dc875, + 0x9f0e1a84,0x77387de3}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xa56c0dd7,0x1e9ecc49, 0x46086c74,0xa5cffcd8, 0xf505aece,0x8f7a1408, + 0xbef0c47e,0xb37b85c0}, + {0xcc0e6a8f,0x3596b6e4, 0x6b388f23,0xfd6d4bbf, 0xc39cef4e,0xaba453fa, + 0xf9f628d5,0x9c135ac8}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x95c8f8be,0xa1c7294, 0x3bf362bf,0x2961c480, 0xdf63d4ac,0x9e418403, + 0x91ece900,0xc109f9cb}, + {0x58945705,0xc2d095d0, 0xddeb85c0,0xb9083d96, 0x7a40449b,0x84692b8d, + 0x2eee1ee1,0x9bc3344f}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x42913074,0xd5ae356, 0x48a542b1,0x55491b27, 0xb310732a,0x469ca665, + 0x5f1a4cc1,0x29591d52}, + {0xb84f983f,0xe76f5b6b, 0x9f5f84e1,0xbe7eef41, 0x80baa189,0x1200d496, + 0x18ef332c,0x6376551f}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}}, + {{{0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, + {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, + {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}}, + {{0x4147519a,0x20288602, 0x26b372f0,0xd0981eac, 0xa785ebc8,0xa9d4a7ca, + 0xdbdf58e9,0xd953c50d}, + {0xfd590f8f,0x9d6361cc, 0x44e6c917,0x72e9626b, 0x22eb64cf,0x7fd96110, + 0x9eb288f3,0x863ebb7e}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xb0e63d34,0x4fe7ee31, 0xa9e54fab,0xf4600572, 0xd5e7b5a4,0xc0493334, + 0x6d54831,0x8589fb92}, + {0x6583553a,0xaa70f5cc, 0xe25649e5,0x879094a, 0x10044652,0xcc904507, + 0x2541c4f,0xebb0696d}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x3b89da99,0xabbaa0c0, 0xb8284022,0xa6f2d79e, 0xb81c05e8,0x27847862, + 0x5e54d63,0x337a4b59}, + {0x21f7794a,0x3c67500d, 0x7d6d7f61,0x207005b7, 0x4cfd6e8,0xa5a3781, + 0xf4c2fbd6,0xd65e0d5}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x6d3549cf,0xd433e50f, 0xfacd665e,0x6f33696f, 0xce11fcb4,0x695bfdac, + 0xaf7c9860,0x810ee252}, + {0x7159bb2c,0x65450fe1, 0x758b357b,0xf7dfbebe, 0xd69fea72,0x2b057e74, + 0x92731745,0xd485717a}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xe83f7669,0xce1f69bb, 0x72877d6b,0x9f8ae82, 0x3244278d,0x9548ae54, + 0xe3c2c19c,0x207755de}, + {0x6fef1945,0x87bd61d9, 0xb12d28c3,0x18813cef, 0x72df64aa,0x9fbcd1d6, + 0x7154b00d,0x48dc5ee5}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xf49a3154,0xef0f469e, 0x6e2b2e9a,0x3e85a595, 0xaa924a9c,0x45aaec1e, + 0xa09e4719,0xaa12dfc8}, + {0x4df69f1d,0x26f27227, 0xa2ff5e73,0xe0e4c82c, 0xb7a9dd44,0xb9d8ce73, + 0xe48ca901,0x6c036e73}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xa47153f0,0xe1e421e1, 0x920418c9,0xb86c3b79, 0x705d7672,0x93bdce87, + 0xcab79a77,0xf25ae793}, + {0x6d869d0c,0x1f3194a3, 0x4986c264,0x9d55c882, 0x96e945e,0x49fb5ea3, + 0x13db0a3e,0x39b8e653}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x35d0b34a,0xe3417bc0, 0x8327c0a7,0x440b386b, 0xac0362d1,0x8fb7262d, + 0xe0cdf943,0x2c41114c}, + {0xad95a0b1,0x2ba5cef1, 0x67d54362,0xc09b37a8, 0x1e486c9,0x26d6cdd2, + 0x42ff9297,0x20477abf}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xbc0a67d2,0xf121b41, 0x444d248a,0x62d4760a, 0x659b4737,0xe044f1d, + 0x250bb4a8,0x8fde365}, + {0x848bf287,0xaceec3da, 0xd3369d6e,0xc2a62182, 0x92449482,0x3582dfdc, + 0x565d6cd7,0x2f7e2fd2}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x178a876b,0xa0122b5, 0x85104b4,0x51ff96ff, 0x14f29f76,0x50b31ab, + 0x5f87d4e6,0x84abb28b}, + {0x8270790a,0xd5ed439f, 0x85e3f46b,0x2d6cb59d, 0x6c1e2212,0x75f55c1b, + 0x17655640,0xe5436f67}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x9aeb596d,0xc2965ecc, 0x23c92b4,0x1ea03e7, 0x2e013961,0x4704b4b6, + 0x905ea367,0xca8fd3f}, + {0x551b2b61,0x92523a42, 0x390fcd06,0x1eb7a89c, 0x392a63e,0xe7f1d2be, + 0x4ddb0c33,0x96dca264}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x15339848,0x231c210e, 0x70778c8d,0xe87a28e8, 0x6956e170,0x9d1de661, + 0x2bb09c0b,0x4ac3c938}, + {0x6998987d,0x19be0551, 0xae09f4d6,0x8b2376c4, 0x1a3f933d,0x1de0b765, + 0xe39705f4,0x380d94c7}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x8c31c31d,0x3685954b, 0x5bf21a0c,0x68533d00, 0x75c79ec9,0xbd7626e, + 0x42c69d54,0xca177547}, + {0xf6d2dbb2,0xcc6edaff, 0x174a9d18,0xfd0d8cbd, 0xaa4578e8,0x875e8793, + 0x9cab2ce6,0xa976a713}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0xb43ea1db,0xce37ab11, 0x5259d292,0xa7ff1a9, 0x8f84f186,0x851b0221, + 0xdefaad13,0xa7222bea}, + {0x2b0a9144,0xa2ac78ec, 0xf2fa59c5,0x5a024051, 0x6147ce38,0x91d1eca5, + 0xbc2ac690,0xbe94d523}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, + {{0x79ec1a0f,0x2d8daefd, 0xceb39c97,0x3bbcd6fd, 0x58f61a95,0xf5575ffc, + 0xadf7b420,0xdbd986c4}, + {0x15f39eb7,0x81aa8814, 0xb98d976c,0x6ee2fcf5, 0xcf2f717d,0x5465475d, + 0x6860bbd0,0x8e24d3c4}, + {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}}}; +#endif + +// select_point selects the |idx|th point from a precomputation table and +// copies it to out. +static void select_point(const limb_t idx, size_t size, + const fe pre_comp[/*size*/][3], + fe out[3]) { + OPENSSL_memset(out, 0, sizeof(fe) * 3); + for (size_t i = 0; i < size; i++) { + limb_t mismatch = i ^ idx; + fe_cmovznz(out[0], mismatch, pre_comp[i][0], out[0]); + fe_cmovznz(out[1], mismatch, pre_comp[i][1], out[1]); + fe_cmovznz(out[2], mismatch, pre_comp[i][2], out[2]); + } +} + +// get_bit returns the |i|th bit in |in| +static char get_bit(const uint8_t *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 p_pre_comp, the scalar +// in p_scalar, if non-NULL. 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(fe x_out, fe y_out, fe z_out, + const uint8_t *p_scalar, const uint8_t *g_scalar, + const fe p_pre_comp[17][3]) { + // set nq to the point at infinity + fe nq[3] = {{0},{0},{0}}, ftmp, tmp[3]; + uint64_t bits; + uint8_t sign, digit; + + // Loop over both scalars msb-to-lsb, interleaving additions of multiples + // of the generator (two in each of the last 32 rounds) and additions of p + // (every 5th round). + + int skip = 1; // save two point operations in the first round + size_t i = p_scalar != NULL ? 255 : 31; + for (;;) { + // double + if (!skip) { + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + } + + // add multiples of the generator + if (g_scalar != NULL && i <= 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) { + point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, + tmp[0], tmp[1], tmp[2]); + } else { + fe_copy(nq[0], tmp[0]); + fe_copy(nq[1], tmp[1]); + fe_copy(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); + point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, tmp[0], + tmp[1], tmp[2]); + } + + // do other additions every 5 doublings + if (p_scalar != NULL && i % 5 == 0) { + bits = get_bit(p_scalar, i + 4) << 5; + bits |= get_bit(p_scalar, i + 3) << 4; + bits |= get_bit(p_scalar, i + 2) << 3; + bits |= get_bit(p_scalar, i + 1) << 2; + bits |= get_bit(p_scalar, i) << 1; + bits |= get_bit(p_scalar, 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, p_pre_comp, tmp); + fe_opp(ftmp, tmp[1]); // (X, -Y, Z) is the negative point. + fe_cmovznz(tmp[1], sign, tmp[1], ftmp); + + if (!skip) { + point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */, + tmp[0], tmp[1], tmp[2]); + } else { + fe_copy(nq[0], tmp[0]); + fe_copy(nq[1], tmp[1]); + fe_copy(nq[2], tmp[2]); + skip = 0; + } + } + + if (i == 0) { + break; + } + --i; + } + fe_copy(x_out, nq[0]); + fe_copy(y_out, nq[1]); + fe_copy(z_out, nq[2]); +} + +// OPENSSL EC_METHOD FUNCTIONS + +// Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = +// (X/Z^2, Y/Z^3). +static int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x_out, + BIGNUM *y_out, + BN_CTX *ctx) { + fe x, y, z1, z2; + + if (EC_POINT_is_at_infinity(group, point)) { + OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); + return 0; + } + if (!BN_to_fe(x, &point->X) || + !BN_to_fe(y, &point->Y) || + !BN_to_fe(z1, &point->Z)) { + return 0; + } + + fe_inv(z2, z1); + fe_sqr(z1, z2); + + if (x_out != NULL) { + fe_mul(x, x, z1); + fe_from_montgomery(x); + if (!fe_to_BN(x_out, x)) { + OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); + return 0; + } + } + + if (y_out != NULL) { + fe_mul(z1, z1, z2); + fe_mul(y, y, z1); + fe_from_montgomery(y); + if (!fe_to_BN(y_out, y)) { + OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); + return 0; + } + } + + return 1; +} + +static int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, + const EC_SCALAR *g_scalar, + const EC_POINT *p, + const EC_SCALAR *p_scalar, + BN_CTX *unused_ctx) { + fe p_pre_comp[17][3]; + fe x_out, y_out, z_out; + + if (p != NULL && p_scalar != NULL) { + // We treat NULL scalars as 0, and NULL points as points at infinity, i.e., + // they contribute nothing to the linear combination. + OPENSSL_memset(&p_pre_comp, 0, sizeof(p_pre_comp)); + // Precompute multiples. + if (!BN_to_fe(p_pre_comp[1][0], &p->X) || + !BN_to_fe(p_pre_comp[1][1], &p->Y) || + !BN_to_fe(p_pre_comp[1][2], &p->Z)) { + return 0; + } + for (size_t j = 2; j <= 16; ++j) { + if (j & 1) { + point_add(p_pre_comp[j][0], p_pre_comp[j][1], + p_pre_comp[j][2], p_pre_comp[1][0], + p_pre_comp[1][1], p_pre_comp[1][2], + 0, + p_pre_comp[j - 1][0], p_pre_comp[j - 1][1], + p_pre_comp[j - 1][2]); + } else { + point_double(p_pre_comp[j][0], p_pre_comp[j][1], + p_pre_comp[j][2], p_pre_comp[j / 2][0], + p_pre_comp[j / 2][1], p_pre_comp[j / 2][2]); + } + } + } + + batch_mul(x_out, y_out, z_out, + (p != NULL && p_scalar != NULL) ? p_scalar->bytes : NULL, + g_scalar != NULL ? g_scalar->bytes : NULL, + (const fe (*) [3])p_pre_comp); + + if (!fe_to_BN(&r->X, x_out) || + !fe_to_BN(&r->Y, y_out) || + !fe_to_BN(&r->Z, z_out)) { + OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); + return 0; + } + return 1; +} + +DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistp256_method) { + out->group_init = ec_GFp_mont_group_init; + out->group_finish = ec_GFp_mont_group_finish; + out->group_set_curve = ec_GFp_mont_group_set_curve; + out->point_get_affine_coordinates = + ec_GFp_nistp256_point_get_affine_coordinates; + out->mul = ec_GFp_nistp256_points_mul; +// The variable-time wNAF point multiplication uses fewer field operations than +// the constant-time implementation here, but the 64-bit field arithmetic in +// this file is much faster than the generic BIGNUM-based field arithmetic used +// by wNAF. For 32-bit, the wNAF code is overall ~60% faster on non-precomputed +// points, so we use it for public inputs. +#if defined(BORINGSSL_NISTP256_64BIT) + out->mul_public = ec_GFp_nistp256_points_mul; +#else + out->mul_public = ec_wNAF_mul; +#endif + out->field_mul = ec_GFp_mont_field_mul; + out->field_sqr = ec_GFp_mont_field_sqr; + out->field_encode = ec_GFp_mont_field_encode; + out->field_decode = ec_GFp_mont_field_decode; +}; + +#undef BORINGSSL_NISTP256_64BIT |