blob: 6636a36a2d2098f922542ac15f14998d56d62a64 [file] [log] [blame]
/* Copyright (c) 2020, Google Inc.
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
// This file is generated from
// ./ > curve25519_tables.h
static const fe d = {{
#if defined(OPENSSL_64_BIT)
929955233495203, 466365720129213, 1662059464998953, 2033849074728123,
56195235, 13857412, 51736253, 6949390, 114729, 24766616, 60832955, 30306712,
48412415, 21499315
static const fe sqrtm1 = {{
#if defined(OPENSSL_64_BIT)
1718705420411056, 234908883556509, 2233514472574048, 2117202627021982,
34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654,
31548777, 326685, 11406482
static const fe d2 = {{
#if defined(OPENSSL_64_BIT)
1859910466990425, 932731440258426, 1072319116312658, 1815898335770999,
45281625, 27714825, 36363642, 13898781, 229458, 15978800, 54557047,
27058993, 29715967, 9444199
#if defined(OPENSSL_SMALL)
// This block of code replaces the standard base-point table with a much smaller
// one. The standard table is 30,720 bytes while this one is just 960.
// This table contains 15 pairs of group elements, (x, y), where each field
// element is serialised with |fe_tobytes|. If |i| is the index of the group
// element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
// is the most significant bit). The value of the group element is then:
// (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator.
static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
// k25519Precomp[i][j] = (j+1)*256^i*B
const uint8_t k25519Precomp[32][8][3][32] = {
{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0xe, 0x8c,
0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48,
0xb, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x7},
{0x3e, 0x91, 0x40, 0xd7, 0x5, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40,
0xd1, 0x5, 0x9f, 0x39, 0xfd, 0x9, 0x8a, 0x8f, 0x68, 0x34, 0x84,
0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44},
{0x68, 0xaa, 0x7a, 0x87, 0x5, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa,
0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d,
0x1b, 0x5a, 0xa8, 0x65, 0xc, 0x9f, 0x68, 0x7b, 0x11, 0x6f},
{0xd7, 0x71, 0x3c, 0x93, 0xfc, 0xe7, 0x24, 0x92, 0xb5, 0xf5, 0xf,
0x7a, 0x96, 0x9d, 0x46, 0x9f, 0x2, 0x7, 0xd6, 0xe1, 0x65, 0x9a,
0xa6, 0x5a, 0x2e, 0x2e, 0x7d, 0xa8, 0x3f, 0x6, 0xc, 0x59},
{0xa8, 0xd5, 0xb4, 0x42, 0x60, 0xa5, 0x99, 0x8a, 0xf6, 0xac, 0x60,
0x4e, 0xc, 0x81, 0x2b, 0x8f, 0xaa, 0x37, 0x6e, 0xb1, 0x6b, 0x23,
0x9e, 0xe0, 0x55, 0x25, 0xc9, 0x69, 0xa6, 0x95, 0xb5, 0x6b},
{0x5f, 0x7a, 0x9b, 0xa5, 0xb3, 0xa8, 0xfa, 0x43, 0x78, 0xcf, 0x9a,
0x5d, 0xdd, 0x6b, 0xc1, 0x36, 0x31, 0x6a, 0x3d, 0xb, 0x84, 0xa0,
0xf, 0x50, 0x73, 0xb, 0xa5, 0x3e, 0xb1, 0xf5, 0x1a, 0x70},
{0x30, 0x97, 0xee, 0x4c, 0xa8, 0xb0, 0x25, 0xaf, 0x8a, 0x4b, 0x86,
0xe8, 0x30, 0x84, 0x5a, 0x2, 0x32, 0x67, 0x1, 0x9f, 0x2, 0x50,
0x1b, 0xc1, 0xf4, 0xf8, 0x80, 0x9a, 0x1b, 0x4e, 0x16, 0x7a},
{0x65, 0xd2, 0xfc, 0xa4, 0xe8, 0x1f, 0x61, 0x56, 0x7d, 0xba, 0xc1,
0xe5, 0xfd, 0x53, 0xd3, 0x3b, 0xbd, 0xd6, 0x4b, 0x21, 0x1a, 0xf3,
0x31, 0x81, 0x62, 0xda, 0x5b, 0x55, 0x87, 0x15, 0xb9, 0x2a},
{0x89, 0xd8, 0xd0, 0xd, 0x3f, 0x93, 0xae, 0x14, 0x62, 0xda, 0x35,
0x1c, 0x22, 0x23, 0x94, 0x58, 0x4c, 0xdb, 0xf2, 0x8c, 0x45, 0xe5,
0x70, 0xd1, 0xc6, 0xb4, 0xb9, 0x12, 0xaf, 0x26, 0x28, 0x5a},
{0x9f, 0x9, 0xfc, 0x8e, 0xb9, 0x51, 0x73, 0x28, 0x38, 0x25, 0xfd,
0x7d, 0xf4, 0xc6, 0x65, 0x67, 0x65, 0x92, 0xa, 0xfb, 0x3d, 0x8d,
0x34, 0xca, 0x27, 0x87, 0xe5, 0x21, 0x3, 0x91, 0xe, 0x68},
{0xbf, 0x18, 0x68, 0x5, 0xa, 0x5, 0xfe, 0x95, 0xa9, 0xfa, 0x60,
0x56, 0x71, 0x89, 0x7e, 0x32, 0x73, 0x50, 0xa0, 0x6, 0xcd, 0xe3,
0xe8, 0xc3, 0x9a, 0xa4, 0x45, 0x74, 0x4c, 0x3f, 0x93, 0x27},
{0x9, 0xff, 0x76, 0xc4, 0xe9, 0xfb, 0x13, 0x5a, 0x72, 0xc1, 0x5c,
0x7b, 0x45, 0x39, 0x9e, 0x6e, 0x94, 0x44, 0x2b, 0x10, 0xf9, 0xdc,
0xdb, 0x5d, 0x2b, 0x3e, 0x55, 0x63, 0xbf, 0xc, 0x9d, 0x7f},
{0x33, 0xbb, 0xa5, 0x8, 0x44, 0xbc, 0x12, 0xa2, 0x2, 0xed, 0x5e,
0xc7, 0xc3, 0x48, 0x50, 0x8d, 0x44, 0xec, 0xbf, 0x5a, 0xc, 0xeb,
0x1b, 0xdd, 0xeb, 0x6, 0xe2, 0x46, 0xf1, 0xcc, 0x45, 0x29},
{0xba, 0xd6, 0x47, 0xa4, 0xc3, 0x82, 0x91, 0x7f, 0xb7, 0x29, 0x27,
0x4b, 0xd1, 0x14, 0x0, 0xd5, 0x87, 0xa0, 0x64, 0xb8, 0x1c, 0xf1,
0x3c, 0xe3, 0xf3, 0x55, 0x1b, 0xeb, 0x73, 0x7e, 0x4a, 0x15},
{0x85, 0x82, 0x2a, 0x81, 0xf1, 0xdb, 0xbb, 0xbc, 0xfc, 0xd1, 0xbd,
0xd0, 0x7, 0x8, 0xe, 0x27, 0x2d, 0xa7, 0xbd, 0x1b, 0xb, 0x67,
0x1b, 0xb4, 0x9a, 0xb6, 0x3b, 0x6b, 0x69, 0xbe, 0xaa, 0x43},
{0x31, 0x71, 0x15, 0x77, 0xeb, 0xee, 0xc, 0x3a, 0x88, 0xaf, 0xc8,
0x0, 0x89, 0x15, 0x27, 0x9b, 0x36, 0xa7, 0x59, 0xda, 0x68, 0xb6,
0x65, 0x80, 0xbd, 0x38, 0xcc, 0xa2, 0xb6, 0x7b, 0xe5, 0x51},
{0xa4, 0x8c, 0x7d, 0x7b, 0xb6, 0x6, 0x98, 0x49, 0x39, 0x27, 0xd2,
0x27, 0x84, 0xe2, 0x5b, 0x57, 0xb9, 0x53, 0x45, 0x20, 0xe7, 0x5c,
0x8, 0xbb, 0x84, 0x78, 0x41, 0xae, 0x41, 0x4c, 0xb6, 0x38},
{0x71, 0x4b, 0xea, 0x2, 0x67, 0x32, 0xac, 0x85, 0x1, 0xbb, 0xa1,
0x41, 0x3, 0xe0, 0x70, 0xbe, 0x44, 0xc1, 0x3b, 0x8, 0x4b, 0xa2,
0xe4, 0x53, 0xe3, 0x61, 0xd, 0x9f, 0x1a, 0xe9, 0xb8, 0x10},
{0xbf, 0xa3, 0x4e, 0x94, 0xd0, 0x5c, 0x1a, 0x6b, 0xd2, 0xc0, 0x9d,
0xb3, 0x3a, 0x35, 0x70, 0x74, 0x49, 0x2e, 0x54, 0x28, 0x82, 0x52,
0xb2, 0x71, 0x7e, 0x92, 0x3c, 0x28, 0x69, 0xea, 0x1b, 0x46},
{0xb1, 0x21, 0x32, 0xaa, 0x9a, 0x2c, 0x6f, 0xba, 0xa7, 0x23, 0xba,
0x3b, 0x53, 0x21, 0xa0, 0x6c, 0x3a, 0x2c, 0x19, 0x92, 0x4f, 0x76,
0xea, 0x9d, 0xe0, 0x17, 0x53, 0x2e, 0x5d, 0xdd, 0x6e, 0x1d},
{0xa2, 0xb3, 0xb8, 0x1, 0xc8, 0x6d, 0x83, 0xf1, 0x9a, 0xa4, 0x3e,
0x5, 0x47, 0x5f, 0x3, 0xb3, 0xf3, 0xad, 0x77, 0x58, 0xba, 0x41,
0x9c, 0x52, 0xa7, 0x90, 0xf, 0x6a, 0x1c, 0xbb, 0x9f, 0x7a},
{0x8f, 0x3e, 0xdd, 0x4, 0x66, 0x59, 0xb7, 0x59, 0x2c, 0x70, 0x88,
0xe2, 0x77, 0x3, 0xb3, 0x6c, 0x23, 0xc3, 0xd9, 0x5e, 0x66, 0x9c,
0x33, 0xb1, 0x2f, 0xe5, 0xbc, 0x61, 0x60, 0xe7, 0x15, 0x9},
{0xd9, 0x34, 0x92, 0xf3, 0xed, 0x5d, 0xa7, 0xe2, 0xf9, 0x58, 0xb5,
0xe1, 0x80, 0x76, 0x3d, 0x96, 0xfb, 0x23, 0x3c, 0x6e, 0xac, 0x41,
0x27, 0x2c, 0xc3, 0x1, 0xe, 0x32, 0xa1, 0x24, 0x90, 0x3a},
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