Google Git
Sign in
fuchsia / third_party / github.com / kmackay / micro-ecc / 2bc81fd84556f01768f37fa60e85f2187ac00c8a / . / uECC.c
blob: afd4578893ca52b7e466aa0e385ac83171e10d7d [file] [log] [blame]
/* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */
#include "uECC.h"
#ifndef uECC_PLATFORM
#if __AVR__
#define uECC_PLATFORM uECC_avr
#elif defined(__thumb2__) || defined(_M_ARMT) /* I think MSVC only supports Thumb-2 targets */
#define uECC_PLATFORM uECC_arm_thumb2
#elif defined(__thumb__)
#define uECC_PLATFORM uECC_arm_thumb
#elif defined(__arm__) || defined(_M_ARM)
#define uECC_PLATFORM uECC_arm
#elif defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__I86__)
#define uECC_PLATFORM uECC_x86
#elif defined(__amd64__) || defined(_M_X64)
#define uECC_PLATFORM uECC_x86_64
#else
#define uECC_PLATFORM uECC_arch_other
#endif
#endif
#ifndef uECC_WORD_SIZE
#if uECC_PLATFORM == uECC_avr
#define uECC_WORD_SIZE 1
#elif (uECC_PLATFORM == uECC_x86_64)
#define uECC_WORD_SIZE 8
#else
#define uECC_WORD_SIZE 4
#endif
#endif
#if (uECC_CURVE == uECC_secp160r1 || uECC_CURVE == uECC_secp224r1) && (uECC_WORD_SIZE == 8)
#undef uECC_WORD_SIZE
#define uECC_WORD_SIZE 4
#if (uECC_PLATFORM == uECC_x86_64)
#undef uECC_PLATFORM
#define uECC_PLATFORM uECC_x86
#endif
#endif
#if (uECC_WORD_SIZE != 1) && (uECC_WORD_SIZE != 4) && (uECC_WORD_SIZE != 8)
#error "Unsupported value for uECC_WORD_SIZE"
#endif
#if (uECC_ASM && (uECC_PLATFORM == uECC_avr) && (uECC_WORD_SIZE != 1))
#pragma message ("uECC_WORD_SIZE must be 1 when using AVR asm")
#undef uECC_WORD_SIZE
#define uECC_WORD_SIZE 1
#endif
#if (uECC_ASM && \
(uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb) && \
(uECC_WORD_SIZE != 4))
#pragma message ("uECC_WORD_SIZE must be 4 when using ARM asm")
#undef uECC_WORD_SIZE
#define uECC_WORD_SIZE 4
#endif
#if __STDC_VERSION__ >= 199901L
#define RESTRICT restrict
#else
#define RESTRICT
#endif
#if defined(__SIZEOF_INT128__) || ((__clang_major__ * 100 + __clang_minor__) >= 302)
#define SUPPORTS_INT128 1
#else
#define SUPPORTS_INT128 0
#endif
#define MAX_TRIES 64
#if (uECC_WORD_SIZE == 1)
typedef uint8_t uECC_word_t;
typedef uint16_t uECC_dword_t;
typedef uint8_t wordcount_t;
typedef int8_t swordcount_t;
typedef int16_t bitcount_t;
typedef int8_t cmpresult_t;
#define HIGH_BIT_SET 0x80
#define uECC_WORD_BITS 8
#define uECC_WORD_BITS_SHIFT 3
#define uECC_WORD_BITS_MASK 0x07
#define uECC_WORDS_1 20
#define uECC_WORDS_2 24
#define uECC_WORDS_3 32
#define uECC_WORDS_4 32
#define uECC_WORDS_5 28
#define uECC_N_WORDS_1 21
#define uECC_N_WORDS_2 24
#define uECC_N_WORDS_3 32
#define uECC_N_WORDS_4 32
#define uECC_N_WORDS_5 28
#define Curve_P_1 {0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF}
#define Curve_P_2 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF}
#define Curve_P_3 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, \
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF}
#define Curve_P_4 {0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF}
#define Curve_P_5 {0x01, 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}
#define Curve_B_1 {0x45, 0xFA, 0x65, 0xC5, 0xAD, 0xD4, 0xD4, 0x81, \
0x9F, 0xF8, 0xAC, 0x65, 0x8B, 0x7A, 0xBD, 0x54, \
0xFC, 0xBE, 0x97, 0x1C}
#define Curve_B_2 {0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE, \
0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F, \
0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64}
#define Curve_B_3 {0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B, \
0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65, \
0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3, \
0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A}
#define Curve_B_4 {0x07, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}
#define Curve_B_5 {0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27, \
0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50, \
0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C, \
0x85, 0x0A, 0x05, 0xB4}
#define Curve_G_1 { \
{0x82, 0xFC, 0xCB, 0x13, 0xB9, 0x8B, 0xC3, 0x68, \
0x89, 0x69, 0x64, 0x46, 0x28, 0x73, 0xF5, 0x8E, \
0x68, 0xB5, 0x96, 0x4A}, \
{0x32, 0xFB, 0xC5, 0x7A, 0x37, 0x51, 0x23, 0x04, \
0x12, 0xC9, 0xDC, 0x59, 0x7D, 0x94, 0x68, 0x31, \
0x55, 0x28, 0xA6, 0x23}}
#define Curve_G_2 { \
{0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4, \
0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C, \
0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18}, \
{0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73, \
0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63, \
0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07}}
#define Curve_G_3 { \
{0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4, \
0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77, \
0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8, \
0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B}, \
{0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB, \
0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B, \
0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E, \
0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F}}
#define Curve_G_4 { \
{0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59, \
0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02, \
0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55, \
0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79}, \
{0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C, \
0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD, \
0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D, \
0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48}}
#define Curve_G_5 { \
{0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34, \
0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A, \
0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B, \
0xBD, 0x0C, 0x0E, 0xB7}, \
{0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44, \
0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD, \
0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5, \
0x88, 0x63, 0x37, 0xBD}}
#define Curve_N_1 {0x57, 0x22, 0x75, 0xCA, 0xD3, 0xAE, 0x27, 0xF9, \
0xC8, 0xF4, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, \
0x00, 0x00, 0x00, 0x00, 0x01}
#define Curve_N_2 {0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14, \
0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF}
#define Curve_N_3 {0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3, \
0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF}
#define Curve_N_4 {0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF, \
0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA, \
0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF}
#define Curve_N_5 {0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13, \
0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF}
#elif (uECC_WORD_SIZE == 4)
typedef uint32_t uECC_word_t;
typedef uint64_t uECC_dword_t;
typedef unsigned wordcount_t;
typedef int swordcount_t;
typedef int bitcount_t;
typedef int cmpresult_t;
#define HIGH_BIT_SET 0x80000000
#define uECC_WORD_BITS 32
#define uECC_WORD_BITS_SHIFT 5
#define uECC_WORD_BITS_MASK 0x01F
#define uECC_WORDS_1 5
#define uECC_WORDS_2 6
#define uECC_WORDS_3 8
#define uECC_WORDS_4 8
#define uECC_WORDS_5 7
#define uECC_N_WORDS_1 6
#define uECC_N_WORDS_2 6
#define uECC_N_WORDS_3 8
#define uECC_N_WORDS_4 8
#define uECC_N_WORDS_5 7
#define Curve_P_1 {0x7FFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_P_2 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_P_3 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, \
0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF}
#define Curve_P_4 {0xFFFFFC2F, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, \
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_P_5 {0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFF, \
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_B_1 {0xC565FA45, 0x81D4D4AD, 0x65ACF89F, 0x54BD7A8B, 0x1C97BEFC}
#define Curve_B_2 {0xC146B9B1, 0xFEB8DEEC, 0x72243049, 0x0FA7E9AB, 0xE59C80E7, 0x64210519}
#define Curve_B_3 {0x27D2604B, 0x3BCE3C3E, 0xCC53B0F6, 0x651D06B0, \
0x769886BC, 0xB3EBBD55, 0xAA3A93E7, 0x5AC635D8}
#define Curve_B_4 {0x00000007, 0x00000000, 0x00000000, 0x00000000, \
0x00000000, 0x00000000, 0x00000000, 0x00000000}
#define Curve_B_5 {0x2355FFB4, 0x270B3943, 0xD7BFD8BA, 0x5044B0B7, \
0xF5413256, 0x0C04B3AB, 0xB4050A85}
#define Curve_G_1 { \
{0x13CBFC82, 0x68C38BB9, 0x46646989, 0x8EF57328, 0x4A96B568}, \
{0x7AC5FB32, 0x04235137, 0x59DCC912, 0x3168947D, 0x23A62855}}
#define Curve_G_2 { \
{0x82FF1012, 0xF4FF0AFD, 0x43A18800, 0x7CBF20EB, 0xB03090F6, 0x188DA80E}, \
{0x1E794811, 0x73F977A1, 0x6B24CDD5, 0x631011ED, 0xFFC8DA78, 0x07192B95}}
#define Curve_G_3 { \
{0xD898C296, 0xF4A13945, 0x2DEB33A0, 0x77037D81, \
0x63A440F2, 0xF8BCE6E5, 0xE12C4247, 0x6B17D1F2}, \
{0x37BF51F5, 0xCBB64068, 0x6B315ECE, 0x2BCE3357, \
0x7C0F9E16, 0x8EE7EB4A, 0xFE1A7F9B, 0x4FE342E2}}
#define Curve_G_4 { \
{0x16F81798, 0x59F2815B, 0x2DCE28D9, 0x029BFCDB, \
0xCE870B07, 0x55A06295, 0xF9DCBBAC, 0x79BE667E}, \
{0xFB10D4B8, 0x9C47D08F, 0xA6855419, 0xFD17B448, \
0x0E1108A8, 0x5DA4FBFC, 0x26A3C465, 0x483ADA77}}
#define Curve_G_5 { \
{0x115C1D21, 0x343280D6, 0x56C21122, 0x4A03C1D3, \
0x321390B9, 0x6BB4BF7F, 0xB70E0CBD}, \
{0x85007E34, 0x44D58199, 0x5A074764, 0xCD4375A0, \
0x4C22DFE6, 0xB5F723FB, 0xBD376388}}
#define Curve_N_1 {0xCA752257, 0xF927AED3, 0x0001F4C8, 0x00000000, 0x00000000, 0x00000001}
#define Curve_N_2 {0xB4D22831, 0x146BC9B1, 0x99DEF836, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_N_3 {0xFC632551, 0xF3B9CAC2, 0xA7179E84, 0xBCE6FAAD, \
0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF}
#define Curve_N_4 {0xD0364141, 0xBFD25E8C, 0xAF48A03B, 0xBAAEDCE6, \
0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_N_5 {0x5C5C2A3D, 0x13DD2945, 0xE0B8F03E, 0xFFFF16A2, \
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#elif (uECC_WORD_SIZE == 8)
typedef uint64_t uECC_word_t;
#if SUPPORTS_INT128
typedef unsigned __int128 uECC_dword_t;
#endif
typedef unsigned wordcount_t;
typedef int swordcount_t;
typedef int bitcount_t;
typedef int cmpresult_t;
#define HIGH_BIT_SET 0x8000000000000000ull
#define uECC_WORD_BITS 64
#define uECC_WORD_BITS_SHIFT 6
#define uECC_WORD_BITS_MASK 0x03F
#define uECC_WORDS_1 3
#define uECC_WORDS_2 3
#define uECC_WORDS_3 4
#define uECC_WORDS_4 4
#define uECC_WORDS_5 4
#define uECC_N_WORDS_1 3
#define uECC_N_WORDS_2 3
#define uECC_N_WORDS_3 4
#define uECC_N_WORDS_4 4
#define uECC_N_WORDS_5 4
#define Curve_P_1 {0xFFFFFFFF7FFFFFFFull, 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull}
#define Curve_P_2 {0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFEull, 0xFFFFFFFFFFFFFFFFull}
#define Curve_P_3 {0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \
0x0000000000000000ull, 0xFFFFFFFF00000001ull}
#define Curve_P_4 {0xFFFFFFFEFFFFFC2Full, 0xFFFFFFFFFFFFFFFFull, \
0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFFull}
#define Curve_P_5 {0x0000000000000001ull, 0xFFFFFFFF00000000ull, \
0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull}
#define Curve_B_1 {0x81D4D4ADC565FA45ull, 0x54BD7A8B65ACF89Full, 0x000000001C97BEFCull}
#define Curve_B_2 {0xFEB8DEECC146B9B1ull, 0x0FA7E9AB72243049ull, 0x64210519E59C80E7ull}
#define Curve_B_3 {0x3BCE3C3E27D2604Bull, 0x651D06B0CC53B0F6ull, \
0xB3EBBD55769886BCull, 0x5AC635D8AA3A93E7ull}
#define Curve_B_4 {0x0000000000000007ull, 0x0000000000000000ull, \
0x0000000000000000ull, 0x0000000000000000ull}
#define Curve_B_5 {0x270B39432355FFB4ull, 0x5044B0B7D7BFD8BAull, \
0x0C04B3ABF5413256ull, 0x00000000B4050A85ull}
#define Curve_G_1 { \
{0x68C38BB913CBFC82ull, 0x8EF5732846646989ull, 0x000000004A96B568ull}, \
{0x042351377AC5FB32ull, 0x3168947D59DCC912ull, 0x0000000023A62855ull}}
#define Curve_G_2 { \
{0xF4FF0AFD82FF1012ull, 0x7CBF20EB43A18800ull, 0x188DA80EB03090F6ull}, \
{0x73F977A11E794811ull, 0x631011ED6B24CDD5ull, 0x07192B95FFC8DA78ull}}
#define Curve_G_3 { \
{0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, 0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull}, \
{0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, 0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull}}
#define Curve_G_4 { \
{0x59F2815B16F81798ull, 0x029BFCDB2DCE28D9ull, 0x55A06295CE870B07ull, 0x79BE667EF9DCBBACull}, \
{0x9C47D08FFB10D4B8ull, 0xFD17B448A6855419ull, 0x5DA4FBFC0E1108A8ull, 0x483ADA7726A3C465ull}}
#define Curve_G_5 { \
{0x343280D6115C1D21ull, 0x4A03C1D356C21122ull, 0x6BB4BF7F321390B9ull, 0x00000000B70E0CBDull}, \
{0x44D5819985007E34ull, 0xCD4375A05A074764ull, 0xB5F723FB4C22DFE6ull, 0x00000000BD376388ull}}
#define Curve_N_1 {0xF927AED3CA752257ull, 0x000000000001F4C8ull, 0x0000000100000000ull}
#define Curve_N_2 {0x146BC9B1B4D22831ull, 0xFFFFFFFF99DEF836ull, 0xFFFFFFFFFFFFFFFFull}
#define Curve_N_3 {0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, \
0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull}
#define Curve_N_4 {0xBFD25E8CD0364141ull, 0xBAAEDCE6AF48A03Bull, \
0xFFFFFFFFFFFFFFFEull, 0xFFFFFFFFFFFFFFFFull}
#define Curve_N_5 {0x13DD29455C5C2A3Dull, 0xFFFF16A2E0B8F03Eull, \
0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull}
#endif /* (uECC_WORD_SIZE == 8) */
#define uECC_WORDS uECC_CONCAT(uECC_WORDS_, uECC_CURVE)
#define uECC_N_WORDS uECC_CONCAT(uECC_N_WORDS_, uECC_CURVE)
typedef struct EccPoint {
uECC_word_t x[uECC_WORDS];
uECC_word_t y[uECC_WORDS];
} EccPoint;
static const uECC_word_t curve_p[uECC_WORDS] = uECC_CONCAT(Curve_P_, uECC_CURVE);
static const uECC_word_t curve_b[uECC_WORDS] = uECC_CONCAT(Curve_B_, uECC_CURVE);
static const EccPoint curve_G = uECC_CONCAT(Curve_G_, uECC_CURVE);
static const uECC_word_t curve_n[uECC_N_WORDS] = uECC_CONCAT(Curve_N_, uECC_CURVE);
static void vli_clear(uECC_word_t *vli);
static uECC_word_t vli_isZero(const uECC_word_t *vli);
static uECC_word_t vli_testBit(const uECC_word_t *vli, bitcount_t bit);
static bitcount_t vli_numBits(const uECC_word_t *vli, wordcount_t max_words);
static void vli_set(uECC_word_t *dest, const uECC_word_t *src);
static cmpresult_t vli_cmp(const uECC_word_t *left, const uECC_word_t *right);
static cmpresult_t vli_equal(const uECC_word_t *left, const uECC_word_t *right);
static void vli_rshift1(uECC_word_t *vli);
static uECC_word_t vli_add(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right);
static uECC_word_t vli_sub(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right);
static void vli_mult(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right);
static void vli_modAdd(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
const uECC_word_t *mod);
static void vli_modSub(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
const uECC_word_t *mod);
static void vli_mmod_fast(uECC_word_t *RESTRICT result, uECC_word_t *RESTRICT product);
static void vli_modMult_fast(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right);
static void vli_modInv(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod);
#if uECC_SQUARE_FUNC
static void vli_square(uECC_word_t *result, const uECC_word_t *left);
static void vli_modSquare_fast(uECC_word_t *result, const uECC_word_t *left);
#endif
#if (defined(_WIN32) || defined(_WIN64))
/* Windows */
#define WIN32_LEAN_AND_MEAN
#include <windows.h>
#include <wincrypt.h>
static int default_RNG(uint8_t *dest, unsigned size) {
HCRYPTPROV prov;
if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) {
return 0;
}
CryptGenRandom(prov, size, (BYTE *)dest);
CryptReleaseContext(prov, 0);
return 1;
}
#elif defined(unix) || defined(__linux__) || defined(__unix__) || defined(__unix) || \
(defined(__APPLE__) && defined(__MACH__)) || defined(uECC_POSIX)
/* Some POSIX-like system with /dev/urandom or /dev/random. */
#include <sys/types.h>
#include <fcntl.h>
#include <unistd.h>
#ifndef O_CLOEXEC
#define O_CLOEXEC 0
#endif
static int default_RNG(uint8_t *dest, unsigned size) {
int fd = open("/dev/urandom", O_RDONLY | O_CLOEXEC);
if (fd == -1) {
fd = open("/dev/random", O_RDONLY | O_CLOEXEC);
if (fd == -1) {
return 0;
}
}
char *ptr = (char *)dest;
size_t left = size;
while (left > 0) {
ssize_t bytes_read = read(fd, ptr, left);
if (bytes_read <= 0) { // read failed
close(fd);
return 0;
}
left -= bytes_read;
ptr += bytes_read;
}
close(fd);
return 1;
}
#else /* Some other platform */
static int default_RNG(uint8_t *dest, unsigned size) {
return 0;
}
#endif
static uECC_RNG_Function g_rng_function = &default_RNG;
void uECC_set_rng(uECC_RNG_Function rng_function) {
g_rng_function = rng_function;
}
#ifdef __GNUC__ /* Only support GCC inline asm for now */
#if (uECC_ASM && (uECC_PLATFORM == uECC_avr))
#include "asm_avr.inc"
#endif
#if (uECC_ASM && (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb || \
uECC_PLATFORM == uECC_arm_thumb2))
#include "asm_arm.inc"
#endif
#endif
#if !asm_clear
static void vli_clear(uECC_word_t *vli) {
wordcount_t i;
for (i = 0; i < uECC_WORDS; ++i) {
vli[i] = 0;
}
}
#endif
/* Returns 1 if vli == 0, 0 otherwise. */
#if !asm_isZero
static uECC_word_t vli_isZero(const uECC_word_t *vli) {
wordcount_t i;
for (i = 0; i < uECC_WORDS; ++i) {
if (vli[i]) {
return 0;
}
}
return 1;
}
#endif
/* Returns nonzero if bit 'bit' of vli is set. */
#if !asm_testBit
static uECC_word_t vli_testBit(const uECC_word_t *vli, bitcount_t bit) {
return (vli[bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK)));
}
#endif
/* Counts the number of words in vli. */
#if !asm_numBits
static wordcount_t vli_numDigits(const uECC_word_t *vli, wordcount_t max_words) {
swordcount_t i;
/* Search from the end until we find a non-zero digit.
We do it in reverse because we expect that most digits will be nonzero. */
for (i = max_words - 1; i >= 0 && vli[i] == 0; --i) {
}
return (i + 1);
}
/* Counts the number of bits required to represent vli. */
static bitcount_t vli_numBits(const uECC_word_t *vli, wordcount_t max_words) {
uECC_word_t i;
uECC_word_t digit;
wordcount_t num_digits = vli_numDigits(vli, max_words);
if (num_digits == 0) {
return 0;
}
digit = vli[num_digits - 1];
for (i = 0; digit; ++i) {
digit >>= 1;
}
return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i);
}
#endif /* !asm_numBits */
/* Sets dest = src. */
#if !asm_set
static void vli_set(uECC_word_t *dest, const uECC_word_t *src) {
wordcount_t i;
for (i = 0; i < uECC_WORDS; ++i) {
dest[i] = src[i];
}
}
#endif
/* Returns sign of left - right. */
#if !asm_cmp
static cmpresult_t vli_cmp(const uECC_word_t *left, const uECC_word_t *right) {
swordcount_t i;
for (i = uECC_WORDS - 1; i >= 0; --i) {
if (left[i] > right[i]) {
return 1;
} else if (left[i] < right[i]) {
return -1;
}
}
return 0;
}
#endif
static cmpresult_t vli_equal(const uECC_word_t *left, const uECC_word_t *right) {
uECC_word_t result = 0;
swordcount_t i;
for (i = uECC_WORDS - 1; i >= 0; --i) {
result |= (left[i] ^ right[i]);
}
return (result == 0);
}
/* Computes vli = vli >> 1. */
#if !asm_rshift1
static void vli_rshift1(uECC_word_t *vli) {
uECC_word_t *end = vli;
uECC_word_t carry = 0;
vli += uECC_WORDS;
while (vli-- > end) {
uECC_word_t temp = *vli;
*vli = (temp >> 1) | carry;
carry = temp << (uECC_WORD_BITS - 1);
}
}
#endif
/* Computes result = left + right, returning carry. Can modify in place. */
#if !asm_add
static uECC_word_t vli_add(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
uECC_word_t carry = 0;
wordcount_t i;
for (i = 0; i < uECC_WORDS; ++i) {
uECC_word_t sum = left[i] + right[i] + carry;
if (sum != left[i]) {
carry = (sum < left[i]);
}
result[i] = sum;
}
return carry;
}
#endif
/* Computes result = left - right, returning borrow. Can modify in place. */
#if !asm_sub
static uECC_word_t vli_sub(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
uECC_word_t borrow = 0;
wordcount_t i;
for (i = 0; i < uECC_WORDS; ++i) {
uECC_word_t diff = left[i] - right[i] - borrow;
if (diff != left[i]) {
borrow = (diff > left[i]);
}
result[i] = diff;
}
return borrow;
}
#endif
#if (!asm_mult || (uECC_SQUARE_FUNC && !asm_square) || uECC_CURVE == uECC_secp256k1)
static void muladd(uECC_word_t a,
uECC_word_t b,
uECC_word_t *r0,
uECC_word_t *r1,
uECC_word_t *r2) {
#if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128
uint64_t a0 = a & 0xffffffffull;
uint64_t a1 = a >> 32;
uint64_t b0 = b & 0xffffffffull;
uint64_t b1 = b >> 32;
uint64_t i0 = a0 * b0;
uint64_t i1 = a0 * b1;
uint64_t i2 = a1 * b0;
uint64_t i3 = a1 * b1;
uint64_t p0, p1;
i2 += (i0 >> 32);
i2 += i1;
if (i2 < i1) { // overflow
i3 += 0x100000000ull;
}
p0 = (i0 & 0xffffffffull) | (i2 << 32);
p1 = i3 + (i2 >> 32);
*r0 += p0;
*r1 += (p1 + (*r0 < p0));
*r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0));
#else
uECC_dword_t p = (uECC_dword_t)a * b;
uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
r01 += p;
*r2 += (r01 < p);
*r1 = r01 >> uECC_WORD_BITS;
*r0 = (uECC_word_t)r01;
#endif
}
#define muladd_exists 1
#endif
#if !asm_mult
static void vli_mult(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t i, k;
/* Compute each digit of result in sequence, maintaining the carries. */
for (k = 0; k < uECC_WORDS; ++k) {
for (i = 0; i <= k; ++i) {
muladd(left[i], right[k - i], &r0, &r1, &r2);
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
for (k = uECC_WORDS; k < uECC_WORDS * 2 - 1; ++k) {
for (i = (k + 1) - uECC_WORDS; i < uECC_WORDS; ++i) {
muladd(left[i], right[k - i], &r0, &r1, &r2);
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
result[uECC_WORDS * 2 - 1] = r0;
}
#endif
#if uECC_SQUARE_FUNC
#if !asm_square
static void mul2add(uECC_word_t a,
uECC_word_t b,
uECC_word_t *r0,
uECC_word_t *r1,
uECC_word_t *r2) {
#if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128
uint64_t a0 = a & 0xffffffffull;
uint64_t a1 = a >> 32;
uint64_t b0 = b & 0xffffffffull;
uint64_t b1 = b >> 32;
uint64_t i0 = a0 * b0;
uint64_t i1 = a0 * b1;
uint64_t i2 = a1 * b0;
uint64_t i3 = a1 * b1;
uint64_t p0, p1;
i2 += (i0 >> 32);
i2 += i1;
if (i2 < i1)
{ // overflow
i3 += 0x100000000ull;
}
p0 = (i0 & 0xffffffffull) | (i2 << 32);
p1 = i3 + (i2 >> 32);
*r2 += (p1 >> 63);
p1 = (p1 << 1) | (p0 >> 63);
p0 <<= 1;
*r0 += p0;
*r1 += (p1 + (*r0 < p0));
*r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0));
#else
uECC_dword_t p = (uECC_dword_t)a * b;
uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
*r2 += (p >> (uECC_WORD_BITS * 2 - 1));
p *= 2;
r01 += p;
*r2 += (r01 < p);
*r1 = r01 >> uECC_WORD_BITS;
*r0 = (uECC_word_t)r01;
#endif
}
static void vli_square(uECC_word_t *result, const uECC_word_t *left) {
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t i, k;
for (k = 0; k < uECC_WORDS * 2 - 1; ++k) {
uECC_word_t min = (k < uECC_WORDS ? 0 : (k + 1) - uECC_WORDS);
for (i = min; i <= k && i <= k - i; ++i) {
if (i < k-i) {
mul2add(left[i], left[k - i], &r0, &r1, &r2);
} else {
muladd(left[i], left[k - i], &r0, &r1, &r2);
}
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
result[uECC_WORDS * 2 - 1] = r0;
}
#endif
#else /* uECC_SQUARE_FUNC */
#define vli_square(result, left, size) vli_mult((result), (left), (left), (size))
#endif /* uECC_SQUARE_FUNC */
/* Computes result = (left + right) % mod.
Assumes that left < mod and right < mod, and that result does not overlap mod. */
#if !asm_modAdd
static void vli_modAdd(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
const uECC_word_t *mod) {
uECC_word_t carry = vli_add(result, left, right);
if (carry || vli_cmp(result, mod) >= 0) {
/* result > mod (result = mod + remainder), so subtract mod to get remainder. */
vli_sub(result, result, mod);
}
}
#endif
/* Computes result = (left - right) % mod.
Assumes that left < mod and right < mod, and that result does not overlap mod. */
#if !asm_modSub
static void vli_modSub(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
const uECC_word_t *mod) {
uECC_word_t l_borrow = vli_sub(result, left, right);
if (l_borrow) {
/* In this case, result == -diff == (max int) - diff. Since -x % d == d - x,
we can get the correct result from result + mod (with overflow). */
vli_add(result, result, mod);
}
}
#endif
#if !asm_modSub_fast
#define vli_modSub_fast(result, left, right) vli_modSub((result), (left), (right), curve_p)
#endif
#if !asm_mmod_fast
#if (uECC_CURVE == uECC_secp160r1 || uECC_CURVE == uECC_secp256k1)
/* omega_mult() is defined farther below for the different curves / word sizes */
static void omega_mult(uECC_word_t * RESTRICT result, const uECC_word_t * RESTRICT right);
/* Computes result = product % curve_p
see http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf page 354
Note that this only works if log2(omega) < log2(p) / 2 */
static void vli_mmod_fast(uECC_word_t *RESTRICT result, uECC_word_t *RESTRICT product) {
uECC_word_t tmp[2 * uECC_WORDS];
uECC_word_t carry;
vli_clear(tmp);
vli_clear(tmp + uECC_WORDS);
omega_mult(tmp, product + uECC_WORDS); /* (Rq, q) = q * c */
carry = vli_add(result, product, tmp); /* (C, r) = r + q */
vli_clear(product);
omega_mult(product, tmp + uECC_WORDS); /* Rq*c */
carry += vli_add(result, result, product); /* (C1, r) = r + Rq*c */
while (carry > 0) {
--carry;
vli_sub(result, result, curve_p);
}
if (vli_cmp(result, curve_p) > 0) {
vli_sub(result, result, curve_p);
}
}
#endif
#if uECC_CURVE == uECC_secp160r1
#if uECC_WORD_SIZE == 1
static void omega_mult(uint8_t * RESTRICT result, const uint8_t * RESTRICT right) {
uint8_t carry;
uint8_t i;
/* Multiply by (2^31 + 1). */
vli_set(result + 4, right); /* 2^32 */
vli_rshift1(result + 4); /* 2^31 */
result[3] = right[0] << 7; /* get last bit from shift */
carry = vli_add(result, result, right); /* 2^31 + 1 */
for (i = uECC_WORDS; carry; ++i) {
uint16_t sum = (uint16_t)result[i] + carry;
result[i] = (uint8_t)sum;
carry = sum >> 8;
}
}
#elif uECC_WORD_SIZE == 4
static void omega_mult(uint32_t * RESTRICT result, const uint32_t * RESTRICT right) {
uint32_t carry;
unsigned i;
/* Multiply by (2^31 + 1). */
vli_set(result + 1, right); /* 2^32 */
vli_rshift1(result + 1); /* 2^31 */
result[0] = right[0] << 31; /* get last bit from shift */
carry = vli_add(result, result, right); /* 2^31 + 1 */
for (i = uECC_WORDS; carry; ++i) {
uint64_t sum = (uint64_t)result[i] + carry;
result[i] = (uint32_t)sum;
carry = sum >> 32;
}
}
#endif /* uECC_WORD_SIZE */
#elif uECC_CURVE == uECC_secp192r1
/* Computes result = product % curve_p.
See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf */
#if uECC_WORD_SIZE == 1
static void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) {
uint8_t tmp[uECC_WORDS];
uint8_t carry;
vli_set(result, product);
vli_set(tmp, &product[24]);
carry = vli_add(result, result, tmp);
tmp[0] = tmp[1] = tmp[2] = tmp[3] = tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0;
tmp[8] = product[24]; tmp[9] = product[25]; tmp[10] = product[26]; tmp[11] = product[27];
tmp[12] = product[28]; tmp[13] = product[29]; tmp[14] = product[30]; tmp[15] = product[31];
tmp[16] = product[32]; tmp[17] = product[33]; tmp[18] = product[34]; tmp[19] = product[35];
tmp[20] = product[36]; tmp[21] = product[37]; tmp[22] = product[38]; tmp[23] = product[39];
carry += vli_add(result, result, tmp);
tmp[0] = tmp[8] = product[40];
tmp[1] = tmp[9] = product[41];
tmp[2] = tmp[10] = product[42];
tmp[3] = tmp[11] = product[43];
tmp[4] = tmp[12] = product[44];
tmp[5] = tmp[13] = product[45];
tmp[6] = tmp[14] = product[46];
tmp[7] = tmp[15] = product[47];
tmp[16] = tmp[17] = tmp[18] = tmp[19] = tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
carry += vli_add(result, result, tmp);
while (carry || vli_cmp(curve_p, result) != 1) {
carry -= vli_sub(result, result, curve_p);
}
}
#elif uECC_WORD_SIZE == 4
static void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) {
uint32_t tmp[uECC_WORDS];
int carry;
vli_set(result, product);
vli_set(tmp, &product[6]);
carry = vli_add(result, result, tmp);
tmp[0] = tmp[1] = 0;
tmp[2] = product[6];
tmp[3] = product[7];
tmp[4] = product[8];
tmp[5] = product[9];
carry += vli_add(result, result, tmp);
tmp[0] = tmp[2] = product[10];
tmp[1] = tmp[3] = product[11];
tmp[4] = tmp[5] = 0;
carry += vli_add(result, result, tmp);
while (carry || vli_cmp(curve_p, result) != 1) {
carry -= vli_sub(result, result, curve_p);
}
}
#else
static void vli_mmod_fast(uint64_t *RESTRICT result, uint64_t *RESTRICT product) {
uint64_t tmp[uECC_WORDS];
int carry;
vli_set(result, product);
vli_set(tmp, &product[3]);
carry = vli_add(result, result, tmp);
tmp[0] = 0;
tmp[1] = product[3];
tmp[2] = product[4];
carry += vli_add(result, result, tmp);
tmp[0] = tmp[1] = product[5];
tmp[2] = 0;
carry += vli_add(result, result, tmp);
while (carry || vli_cmp(curve_p, result) != 1) {
carry -= vli_sub(result, result, curve_p);
}
}
#endif /* uECC_WORD_SIZE */
#elif uECC_CURVE == uECC_secp256r1
/* Computes result = product % curve_p
from http://www.nsa.gov/ia/_files/nist-routines.pdf */
#if uECC_WORD_SIZE == 1
static void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) {
uint8_t tmp[uECC_BYTES];
int8_t carry;
/* t */
vli_set(result, product);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0;
tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0;
tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0;
tmp[12] = product[44]; tmp[13] = product[45]; tmp[14] = product[46]; tmp[15] = product[47];
tmp[16] = product[48]; tmp[17] = product[49]; tmp[18] = product[50]; tmp[19] = product[51];
tmp[20] = product[52]; tmp[21] = product[53]; tmp[22] = product[54]; tmp[23] = product[55];
tmp[24] = product[56]; tmp[25] = product[57]; tmp[26] = product[58]; tmp[27] = product[59];
tmp[28] = product[60]; tmp[29] = product[61]; tmp[30] = product[62]; tmp[31] = product[63];
carry = vli_add(tmp, tmp, tmp);
carry += vli_add(result, result, tmp);
/* s2 */
tmp[12] = product[48]; tmp[13] = product[49]; tmp[14] = product[50]; tmp[15] = product[51];
tmp[16] = product[52]; tmp[17] = product[53]; tmp[18] = product[54]; tmp[19] = product[55];
tmp[20] = product[56]; tmp[21] = product[57]; tmp[22] = product[58]; tmp[23] = product[59];
tmp[24] = product[60]; tmp[25] = product[61]; tmp[26] = product[62]; tmp[27] = product[63];
tmp[28] = tmp[29] = tmp[30] = tmp[31] = 0;
carry += vli_add(tmp, tmp, tmp);
carry += vli_add(result, result, tmp);
/* s3 */
tmp[0] = product[32]; tmp[1] = product[33]; tmp[2] = product[34]; tmp[3] = product[35];
tmp[4] = product[36]; tmp[5] = product[37]; tmp[6] = product[38]; tmp[7] = product[39];
tmp[8] = product[40]; tmp[9] = product[41]; tmp[10] = product[42]; tmp[11] = product[43];
tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0;
tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
tmp[24] = product[56]; tmp[25] = product[57]; tmp[26] = product[58]; tmp[27] = product[59];
tmp[28] = product[60]; tmp[29] = product[61]; tmp[30] = product[62]; tmp[31] = product[63];
carry += vli_add(result, result, tmp);
/* s4 */
tmp[0] = product[36]; tmp[1] = product[37]; tmp[2] = product[38]; tmp[3] = product[39];
tmp[4] = product[40]; tmp[5] = product[41]; tmp[6] = product[42]; tmp[7] = product[43];
tmp[8] = product[44]; tmp[9] = product[45]; tmp[10] = product[46]; tmp[11] = product[47];
tmp[12] = product[52]; tmp[13] = product[53]; tmp[14] = product[54]; tmp[15] = product[55];
tmp[16] = product[56]; tmp[17] = product[57]; tmp[18] = product[58]; tmp[19] = product[59];
tmp[20] = product[60]; tmp[21] = product[61]; tmp[22] = product[62]; tmp[23] = product[63];
tmp[24] = product[52]; tmp[25] = product[53]; tmp[26] = product[54]; tmp[27] = product[55];
tmp[28] = product[32]; tmp[29] = product[33]; tmp[30] = product[34]; tmp[31] = product[35];
carry += vli_add(result, result, tmp);
/* d1 */
tmp[0] = product[44]; tmp[1] = product[45]; tmp[2] = product[46]; tmp[3] = product[47];
tmp[4] = product[48]; tmp[5] = product[49]; tmp[6] = product[50]; tmp[7] = product[51];
tmp[8] = product[52]; tmp[9] = product[53]; tmp[10] = product[54]; tmp[11] = product[55];
tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0;
tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
tmp[24] = product[32]; tmp[25] = product[33]; tmp[26] = product[34]; tmp[27] = product[35];
tmp[28] = product[40]; tmp[29] = product[41]; tmp[30] = product[42]; tmp[31] = product[43];
carry -= vli_sub(result, result, tmp);
/* d2 */
tmp[0] = product[48]; tmp[1] = product[49]; tmp[2] = product[50]; tmp[3] = product[51];
tmp[4] = product[52]; tmp[5] = product[53]; tmp[6] = product[54]; tmp[7] = product[55];
tmp[8] = product[56]; tmp[9] = product[57]; tmp[10] = product[58]; tmp[11] = product[59];
tmp[12] = product[60]; tmp[13] = product[61]; tmp[14] = product[62]; tmp[15] = product[63];
tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
tmp[24] = product[36]; tmp[25] = product[37]; tmp[26] = product[38]; tmp[27] = product[39];
tmp[28] = product[44]; tmp[29] = product[45]; tmp[30] = product[46]; tmp[31] = product[47];
carry -= vli_sub(result, result, tmp);
/* d3 */
tmp[0] = product[52]; tmp[1] = product[53]; tmp[2] = product[54]; tmp[3] = product[55];
tmp[4] = product[56]; tmp[5] = product[57]; tmp[6] = product[58]; tmp[7] = product[59];
tmp[8] = product[60]; tmp[9] = product[61]; tmp[10] = product[62]; tmp[11] = product[63];
tmp[12] = product[32]; tmp[13] = product[33]; tmp[14] = product[34]; tmp[15] = product[35];
tmp[16] = product[36]; tmp[17] = product[37]; tmp[18] = product[38]; tmp[19] = product[39];
tmp[20] = product[40]; tmp[21] = product[41]; tmp[22] = product[42]; tmp[23] = product[43];
tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
tmp[28] = product[48]; tmp[29] = product[49]; tmp[30] = product[50]; tmp[31] = product[51];
carry -= vli_sub(result, result, tmp);
/* d4 */
tmp[0] = product[56]; tmp[1] = product[57]; tmp[2] = product[58]; tmp[3] = product[59];
tmp[4] = product[60]; tmp[5] = product[61]; tmp[6] = product[62]; tmp[7] = product[63];
tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0;
tmp[12] = product[36]; tmp[13] = product[37]; tmp[14] = product[38]; tmp[15] = product[39];
tmp[16] = product[40]; tmp[17] = product[41]; tmp[18] = product[42]; tmp[19] = product[43];
tmp[20] = product[44]; tmp[21] = product[45]; tmp[22] = product[46]; tmp[23] = product[47];
tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
tmp[28] = product[52]; tmp[29] = product[53]; tmp[30] = product[54]; tmp[31] = product[55];
carry -= vli_sub(result, result, tmp);
if (carry < 0) {
do {
carry += vli_add(result, result, curve_p);
} while (carry < 0);
} else {
while (carry || vli_cmp(curve_p, result) != 1) {
carry -= vli_sub(result, result, curve_p);
}
}
}
#elif uECC_WORD_SIZE == 4
static void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) {
uint32_t tmp[uECC_WORDS];
int carry;
/* t */
vli_set(result, product);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = 0;
tmp[3] = product[11];
tmp[4] = product[12];
tmp[5] = product[13];
tmp[6] = product[14];
tmp[7] = product[15];
carry = vli_add(tmp, tmp, tmp);
carry += vli_add(result, result, tmp);
/* s2 */
tmp[3] = product[12];
tmp[4] = product[13];
tmp[5] = product[14];
tmp[6] = product[15];
tmp[7] = 0;
carry += vli_add(tmp, tmp, tmp);
carry += vli_add(result, result, tmp);
/* s3 */
tmp[0] = product[8];
tmp[1] = product[9];
tmp[2] = product[10];
tmp[3] = tmp[4] = tmp[5] = 0;
tmp[6] = product[14];
tmp[7] = product[15];
carry += vli_add(result, result, tmp);
/* s4 */
tmp[0] = product[9];
tmp[1] = product[10];
tmp[2] = product[11];
tmp[3] = product[13];
tmp[4] = product[14];
tmp[5] = product[15];
tmp[6] = product[13];
tmp[7] = product[8];
carry += vli_add(result, result, tmp);
/* d1 */
tmp[0] = product[11];
tmp[1] = product[12];
tmp[2] = product[13];
tmp[3] = tmp[4] = tmp[5] = 0;
tmp[6] = product[8];
tmp[7] = product[10];
carry -= vli_sub(result, result, tmp);
/* d2 */
tmp[0] = product[12];
tmp[1] = product[13];
tmp[2] = product[14];
tmp[3] = product[15];
tmp[4] = tmp[5] = 0;
tmp[6] = product[9];
tmp[7] = product[11];
carry -= vli_sub(result, result, tmp);
/* d3 */
tmp[0] = product[13];
tmp[1] = product[14];
tmp[2] = product[15];
tmp[3] = product[8];
tmp[4] = product[9];
tmp[5] = product[10];
tmp[6] = 0;
tmp[7] = product[12];
carry -= vli_sub(result, result, tmp);
/* d4 */
tmp[0] = product[14];
tmp[1] = product[15];
tmp[2] = 0;
tmp[3] = product[9];
tmp[4] = product[10];
tmp[5] = product[11];
tmp[6] = 0;
tmp[7] = product[13];
carry -= vli_sub(result, result, tmp);
if (carry < 0) {
do {
carry += vli_add(result, result, curve_p);
} while (carry < 0);
} else {
while (carry || vli_cmp(curve_p, result) != 1) {
carry -= vli_sub(result, result, curve_p);
}
}
}
#else
static void vli_mmod_fast(uint64_t *RESTRICT result, uint64_t *RESTRICT product) {
uint64_t tmp[uECC_WORDS];
int carry;
/* t */
vli_set(result, product);
/* s1 */
tmp[0] = 0;
tmp[1] = product[5] & 0xffffffff00000000ull;
tmp[2] = product[6];
tmp[3] = product[7];
carry = vli_add(tmp, tmp, tmp);
carry += vli_add(result, result, tmp);
/* s2 */
tmp[1] = product[6] << 32;
tmp[2] = (product[6] >> 32) | (product[7] << 32);
tmp[3] = product[7] >> 32;
carry += vli_add(tmp, tmp, tmp);
carry += vli_add(result, result, tmp);
/* s3 */
tmp[0] = product[4];
tmp[1] = product[5] & 0xffffffff;
tmp[2] = 0;
tmp[3] = product[7];
carry += vli_add(result, result, tmp);
/* s4 */
tmp[0] = (product[4] >> 32) | (product[5] << 32);
tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
tmp[2] = product[7];
tmp[3] = (product[6] >> 32) | (product[4] << 32);
carry += vli_add(result, result, tmp);
/* d1 */
tmp[0] = (product[5] >> 32) | (product[6] << 32);
tmp[1] = (product[6] >> 32);
tmp[2] = 0;
tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
carry -= vli_sub(result, result, tmp);
/* d2 */
tmp[0] = product[6];
tmp[1] = product[7];
tmp[2] = 0;
tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
carry -= vli_sub(result, result, tmp);
/* d3 */
tmp[0] = (product[6] >> 32) | (product[7] << 32);
tmp[1] = (product[7] >> 32) | (product[4] << 32);
tmp[2] = (product[4] >> 32) | (product[5] << 32);
tmp[3] = (product[6] << 32);
carry -= vli_sub(result, result, tmp);
/* d4 */
tmp[0] = product[7];
tmp[1] = product[4] & 0xffffffff00000000ull;
tmp[2] = product[5];
tmp[3] = product[6] & 0xffffffff00000000ull;
carry -= vli_sub(result, result, tmp);
if (carry < 0) {
do {
carry += vli_add(result, result, curve_p);
} while (carry < 0);
} else {
while (carry || vli_cmp(curve_p, result) != 1) {
carry -= vli_sub(result, result, curve_p);
}
}
}
#endif /* uECC_WORD_SIZE */
#elif uECC_CURVE == uECC_secp256k1
#if uECC_WORD_SIZE == 1
static void omega_mult(uint8_t * RESTRICT result, const uint8_t * RESTRICT right) {
/* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t k;
/* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
muladd(0xD1, right[0], &r0, &r1, &r2);
result[0] = r0;
r0 = r1;
r1 = r2;
/* r2 is still 0 */
for (k = 1; k < uECC_WORDS; ++k) {
muladd(0x03, right[k - 1], &r0, &r1, &r2);
muladd(0xD1, right[k], &r0, &r1, &r2);
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
muladd(0x03, right[uECC_WORDS - 1], &r0, &r1, &r2);
result[uECC_WORDS] = r0;
result[uECC_WORDS + 1] = r1;
result[4 + uECC_WORDS] = vli_add(result + 4, result + 4, right); /* add the 2^32 multiple */
}
#elif uECC_WORD_SIZE == 4
static void omega_mult(uint32_t * RESTRICT result, const uint32_t * RESTRICT right) {
/* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
uint32_t carry = 0;
wordcount_t k;
for (k = 0; k < uECC_WORDS; ++k) {
uint64_t p = (uint64_t)0x3D1 * right[k] + carry;
result[k] = (p & 0xffffffff);
carry = p >> 32;
}
result[uECC_WORDS] = carry;
result[1 + uECC_WORDS] = vli_add(result + 1, result + 1, right); /* add the 2^32 multiple */
}
#else
static void omega_mult(uint64_t * RESTRICT result, const uint64_t * RESTRICT right) {
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t k;
/* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
for (k = 0; k < uECC_WORDS; ++k) {
muladd(0x1000003D1ull, right[k], &r0, &r1, &r2);
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
result[uECC_WORDS] = r0;
}
#endif /* uECC_WORD_SIZE */
#elif uECC_CURVE == uECC_secp224r1
/* Computes result = product % curve_p
from http://www.nsa.gov/ia/_files/nist-routines.pdf */
#if uECC_WORD_SIZE == 1
// TODO it may be faster to use the omega_mult method when fully asm optimized.
void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) {
uint8_t tmp[uECC_WORDS];
int8_t carry;
/* t */
vli_set(result, product);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0;
tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0;
tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0;
tmp[12] = product[28]; tmp[13] = product[29]; tmp[14] = product[30]; tmp[15] = product[31];
tmp[16] = product[32]; tmp[17] = product[33]; tmp[18] = product[34]; tmp[19] = product[35];
tmp[20] = product[36]; tmp[21] = product[37]; tmp[22] = product[38]; tmp[23] = product[39];
tmp[24] = product[40]; tmp[25] = product[41]; tmp[26] = product[42]; tmp[27] = product[43];
carry = vli_add(result, result, tmp);
/* s2 */
tmp[12] = product[44]; tmp[13] = product[45]; tmp[14] = product[46]; tmp[15] = product[47];
tmp[16] = product[48]; tmp[17] = product[49]; tmp[18] = product[50]; tmp[19] = product[51];
tmp[20] = product[52]; tmp[21] = product[53]; tmp[22] = product[54]; tmp[23] = product[55];
tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
carry += vli_add(result, result, tmp);
/* d1 */
tmp[0] = product[28]; tmp[1] = product[29]; tmp[2] = product[30]; tmp[3] = product[31];
tmp[4] = product[32]; tmp[5] = product[33]; tmp[6] = product[34]; tmp[7] = product[35];
tmp[8] = product[36]; tmp[9] = product[37]; tmp[10] = product[38]; tmp[11] = product[39];
tmp[12] = product[40]; tmp[13] = product[41]; tmp[14] = product[42]; tmp[15] = product[43];
tmp[16] = product[44]; tmp[17] = product[45]; tmp[18] = product[46]; tmp[19] = product[47];
tmp[20] = product[48]; tmp[21] = product[49]; tmp[22] = product[50]; tmp[23] = product[51];
tmp[24] = product[52]; tmp[25] = product[53]; tmp[26] = product[54]; tmp[27] = product[55];
carry -= vli_sub(result, result, tmp);
/* d2 */
tmp[0] = product[44]; tmp[1] = product[45]; tmp[2] = product[46]; tmp[3] = product[47];
tmp[4] = product[48]; tmp[5] = product[49]; tmp[6] = product[50]; tmp[7] = product[51];
tmp[8] = product[52]; tmp[9] = product[53]; tmp[10] = product[54]; tmp[11] = product[55];
tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0;
tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
carry -= vli_sub(result, result, tmp);
if (carry < 0) {
do {
carry += vli_add(result, result, curve_p);
} while (carry < 0);
} else {
while (carry || vli_cmp(curve_p, result) != 1) {
carry -= vli_sub(result, result, curve_p);
}
}
}
#elif uECC_WORD_SIZE == 4
void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product)
{
uint32_t tmp[uECC_WORDS];
int carry;
/* t */
vli_set(result, product);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = 0;
tmp[3] = product[7];
tmp[4] = product[8];
tmp[5] = product[9];
tmp[6] = product[10];
carry = vli_add(result, result, tmp);
/* s2 */
tmp[3] = product[11];
tmp[4] = product[12];
tmp[5] = product[13];
tmp[6] = 0;
carry += vli_add(result, result, tmp);
/* d1 */
tmp[0] = product[7];
tmp[1] = product[8];
tmp[2] = product[9];
tmp[3] = product[10];
tmp[4] = product[11];
tmp[5] = product[12];
tmp[6] = product[13];
carry -= vli_sub(result, result, tmp);
/* d2 */
tmp[0] = product[11];
tmp[1] = product[12];
tmp[2] = product[13];
tmp[3] = tmp[4] = tmp[5] = tmp[6] = 0;
carry -= vli_sub(result, result, tmp);
if (carry < 0) {
do {
carry += vli_add(result, result, curve_p);
} while (carry < 0);
} else {
while (carry || vli_cmp(curve_p, result) != 1) {
carry -= vli_sub(result, result, curve_p);
}
}
}
#endif /* uECC_WORD_SIZE */
#endif /* uECC_CURVE */
#endif /* !asm_mmod_fast */
/* Computes result = (left * right) % curve_p. */
static void vli_modMult_fast(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right) {
uECC_word_t product[2 * uECC_WORDS];
vli_mult(product, left, right);
vli_mmod_fast(result, product);
}
#if uECC_SQUARE_FUNC
/* Computes result = left^2 % curve_p. */
static void vli_modSquare_fast(uECC_word_t *result, const uECC_word_t *left) {
uECC_word_t product[2 * uECC_WORDS];
vli_square(product, left);
vli_mmod_fast(result, product);
}
#else /* uECC_SQUARE_FUNC */
#define vli_modSquare_fast(result, left) vli_modMult_fast((result), (left), (left))
#endif /* uECC_SQUARE_FUNC */
#define EVEN(vli) (!(vli[0] & 1))
/* Computes result = (1 / input) % mod. All VLIs are the same size.
See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf */
#if !asm_modInv
static void vli_modInv(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod) {
uECC_word_t a[uECC_WORDS], b[uECC_WORDS], u[uECC_WORDS], v[uECC_WORDS];
uECC_word_t carry;
cmpresult_t cmpResult;
if (vli_isZero(input)) {
vli_clear(result);
return;
}
vli_set(a, input);
vli_set(b, mod);
vli_clear(u);
u[0] = 1;
vli_clear(v);
while ((cmpResult = vli_cmp(a, b)) != 0) {
carry = 0;
if (EVEN(a)) {
vli_rshift1(a);
if (!EVEN(u)) {
carry = vli_add(u, u, mod);
}
vli_rshift1(u);
if (carry) {
u[uECC_WORDS - 1] |= HIGH_BIT_SET;
}
} else if (EVEN(b)) {
vli_rshift1(b);
if (!EVEN(v)) {
carry = vli_add(v, v, mod);
}
vli_rshift1(v);
if (carry) {
v[uECC_WORDS - 1] |= HIGH_BIT_SET;
}
} else if (cmpResult > 0) {
vli_sub(a, a, b);
vli_rshift1(a);
if (vli_cmp(u, v) < 0) {
vli_add(u, u, mod);
}
vli_sub(u, u, v);
if (!EVEN(u)) {
carry = vli_add(u, u, mod);
}
vli_rshift1(u);
if (carry) {
u[uECC_WORDS - 1] |= HIGH_BIT_SET;
}
} else {
vli_sub(b, b, a);
vli_rshift1(b);
if (vli_cmp(v, u) < 0) {
vli_add(v, v, mod);
}
vli_sub(v, v, u);
if (!EVEN(v)) {
carry = vli_add(v, v, mod);
}
vli_rshift1(v);
if (carry) {
v[uECC_WORDS - 1] |= HIGH_BIT_SET;
}
}
}
vli_set(result, u);
}
#endif /* !asm_modInv */
/* ------ Point operations ------ */
/* Returns 1 if 'point' is the point at infinity, 0 otherwise. */
static cmpresult_t EccPoint_isZero(const EccPoint *point) {
return (vli_isZero(point->x) && vli_isZero(point->y));
}
/* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates.
From http://eprint.iacr.org/2011/338.pdf
*/
/* Double in place */
#if (uECC_CURVE == uECC_secp256k1)
static void EccPoint_double_jacobian(uECC_word_t * RESTRICT X1,
uECC_word_t * RESTRICT Y1,
uECC_word_t * RESTRICT Z1) {
/* t1 = X, t2 = Y, t3 = Z */
uECC_word_t t4[uECC_WORDS];
uECC_word_t t5[uECC_WORDS];
if (vli_isZero(Z1)) {
return;
}
vli_modSquare_fast(t5, Y1); /* t5 = y1^2 */
vli_modMult_fast(t4, X1, t5); /* t4 = x1*y1^2 = A */
vli_modSquare_fast(X1, X1); /* t1 = x1^2 */
vli_modSquare_fast(t5, t5); /* t5 = y1^4 */
vli_modMult_fast(Z1, Y1, Z1); /* t3 = y1*z1 = z3 */
vli_modAdd(Y1, X1, X1, curve_p); /* t2 = 2*x1^2 */
vli_modAdd(Y1, Y1, X1, curve_p); /* t2 = 3*x1^2 */
if (vli_testBit(Y1, 0)) {
uECC_word_t carry = vli_add(Y1, Y1, curve_p);
vli_rshift1(Y1);
Y1[uECC_WORDS - 1] |= carry << (uECC_WORD_BITS - 1);
} else {
vli_rshift1(Y1);
}
/* t2 = 3/2*(x1^2) = B */
vli_modSquare_fast(X1, Y1); /* t1 = B^2 */
vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - A */
vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - 2A = x3 */
vli_modSub(t4, t4, X1, curve_p); /* t4 = A - x3 */
vli_modMult_fast(Y1, Y1, t4); /* t2 = B * (A - x3) */
vli_modSub(Y1, Y1, t5, curve_p); /* t2 = B * (A - x3) - y1^4 = y3 */
}
#else
static void EccPoint_double_jacobian(uECC_word_t * RESTRICT X1,
uECC_word_t * RESTRICT Y1,
uECC_word_t * RESTRICT Z1) {
/* t1 = X, t2 = Y, t3 = Z */
uECC_word_t t4[uECC_WORDS];
uECC_word_t t5[uECC_WORDS];
if (vli_isZero(Z1)) {
return;
}
vli_modSquare_fast(t4, Y1); /* t4 = y1^2 */
vli_modMult_fast(t5, X1, t4); /* t5 = x1*y1^2 = A */
vli_modSquare_fast(t4, t4); /* t4 = y1^4 */
vli_modMult_fast(Y1, Y1, Z1); /* t2 = y1*z1 = z3 */
vli_modSquare_fast(Z1, Z1); /* t3 = z1^2 */
vli_modAdd(X1, X1, Z1, curve_p); /* t1 = x1 + z1^2 */
vli_modAdd(Z1, Z1, Z1, curve_p); /* t3 = 2*z1^2 */
vli_modSub_fast(Z1, X1, Z1); /* t3 = x1 - z1^2 */
vli_modMult_fast(X1, X1, Z1); /* t1 = x1^2 - z1^4 */
vli_modAdd(Z1, X1, X1, curve_p); /* t3 = 2*(x1^2 - z1^4) */
vli_modAdd(X1, X1, Z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */
if (vli_testBit(X1, 0)) {
uECC_word_t l_carry = vli_add(X1, X1, curve_p);
vli_rshift1(X1);
X1[uECC_WORDS - 1] |= l_carry << (uECC_WORD_BITS - 1);
} else {
vli_rshift1(X1);
}
/* t1 = 3/2*(x1^2 - z1^4) = B */
vli_modSquare_fast(Z1, X1); /* t3 = B^2 */
vli_modSub_fast(Z1, Z1, t5); /* t3 = B^2 - A */
vli_modSub_fast(Z1, Z1, t5); /* t3 = B^2 - 2A = x3 */
vli_modSub_fast(t5, t5, Z1); /* t5 = A - x3 */
vli_modMult_fast(X1, X1, t5); /* t1 = B * (A - x3) */
vli_modSub_fast(t4, X1, t4); /* t4 = B * (A - x3) - y1^4 = y3 */
vli_set(X1, Z1);
vli_set(Z1, Y1);
vli_set(Y1, t4);
}
#endif
/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
static void apply_z(uECC_word_t * RESTRICT X1,
uECC_word_t * RESTRICT Y1,
const uECC_word_t * RESTRICT Z) {
uECC_word_t t1[uECC_WORDS];
vli_modSquare_fast(t1, Z); /* z^2 */
vli_modMult_fast(X1, X1, t1); /* x1 * z^2 */
vli_modMult_fast(t1, t1, Z); /* z^3 */
vli_modMult_fast(Y1, Y1, t1); /* y1 * z^3 */
}
/* P = (x1, y1) => 2P, (x2, y2) => P' */
static void XYcZ_initial_double(uECC_word_t * RESTRICT X1,
uECC_word_t * RESTRICT Y1,
uECC_word_t * RESTRICT X2,
uECC_word_t * RESTRICT Y2,
const uECC_word_t * RESTRICT initial_Z) {
uECC_word_t z[uECC_WORDS];
if (initial_Z) {
vli_set(z, initial_Z);
} else {
vli_clear(z);
z[0] = 1;
}
vli_set(X2, X1);
vli_set(Y2, Y1);
apply_z(X1, Y1, z);
EccPoint_double_jacobian(X1, Y1, z);
apply_z(X2, Y2, z);
}
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
or P => P', Q => P + Q
*/
static void XYcZ_add(uECC_word_t * RESTRICT X1,
uECC_word_t * RESTRICT Y1,
uECC_word_t * RESTRICT X2,
uECC_word_t * RESTRICT Y2) {
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
uECC_word_t t5[uECC_WORDS];
vli_modSub_fast(t5, X2, X1); /* t5 = x2 - x1 */
vli_modSquare_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */
vli_modMult_fast(X1, X1, t5); /* t1 = x1*A = B */
vli_modMult_fast(X2, X2, t5); /* t3 = x2*A = C */
vli_modSub_fast(Y2, Y2, Y1); /* t4 = y2 - y1 */
vli_modSquare_fast(t5, Y2); /* t5 = (y2 - y1)^2 = D */
vli_modSub_fast(t5, t5, X1); /* t5 = D - B */
vli_modSub_fast(t5, t5, X2); /* t5 = D - B - C = x3 */
vli_modSub_fast(X2, X2, X1); /* t3 = C - B */
vli_modMult_fast(Y1, Y1, X2); /* t2 = y1*(C - B) */
vli_modSub_fast(X2, X1, t5); /* t3 = B - x3 */
vli_modMult_fast(Y2, Y2, X2); /* t4 = (y2 - y1)*(B - x3) */
vli_modSub_fast(Y2, Y2, Y1); /* t4 = y3 */
vli_set(X2, t5);
}
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
or P => P - Q, Q => P + Q
*/
static void XYcZ_addC(uECC_word_t * RESTRICT X1,
uECC_word_t * RESTRICT Y1,
uECC_word_t * RESTRICT X2,
uECC_word_t * RESTRICT Y2) {
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
uECC_word_t t5[uECC_WORDS];
uECC_word_t t6[uECC_WORDS];
uECC_word_t t7[uECC_WORDS];
vli_modSub_fast(t5, X2, X1); /* t5 = x2 - x1 */
vli_modSquare_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */
vli_modMult_fast(X1, X1, t5); /* t1 = x1*A = B */
vli_modMult_fast(X2, X2, t5); /* t3 = x2*A = C */
vli_modAdd(t5, Y2, Y1, curve_p); /* t5 = y2 + y1 */
vli_modSub_fast(Y2, Y2, Y1); /* t4 = y2 - y1 */
vli_modSub_fast(t6, X2, X1); /* t6 = C - B */
vli_modMult_fast(Y1, Y1, t6); /* t2 = y1 * (C - B) = E */
vli_modAdd(t6, X1, X2, curve_p); /* t6 = B + C */
vli_modSquare_fast(X2, Y2); /* t3 = (y2 - y1)^2 = D */
vli_modSub_fast(X2, X2, t6); /* t3 = D - (B + C) = x3 */
vli_modSub_fast(t7, X1, X2); /* t7 = B - x3 */
vli_modMult_fast(Y2, Y2, t7); /* t4 = (y2 - y1)*(B - x3) */
vli_modSub_fast(Y2, Y2, Y1); /* t4 = (y2 - y1)*(B - x3) - E = y3 */
vli_modSquare_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */
vli_modSub_fast(t7, t7, t6); /* t7 = F - (B + C) = x3' */
vli_modSub_fast(t6, t7, X1); /* t6 = x3' - B */
vli_modMult_fast(t6, t6, t5); /* t6 = (y2 + y1)*(x3' - B) */
vli_modSub_fast(Y1, t6, Y1); /* t2 = (y2 + y1)*(x3' - B) - E = y3' */
vli_set(X1, t7);
}
static void EccPoint_mult(EccPoint * RESTRICT result,
const EccPoint * RESTRICT point,
const uECC_word_t * RESTRICT scalar,
const uECC_word_t * RESTRICT initialZ,
bitcount_t numBits) {
/* R0 and R1 */
uECC_word_t Rx[2][uECC_WORDS];
uECC_word_t Ry[2][uECC_WORDS];
uECC_word_t z[uECC_WORDS];
bitcount_t i;
uECC_word_t nb;
vli_set(Rx[1], point->x);
vli_set(Ry[1], point->y);
XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initialZ);
for (i = numBits - 2; i > 0; --i) {
nb = !vli_testBit(scalar, i);
XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb]);
XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb]);
}
nb = !vli_testBit(scalar, 0);
XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb]);
/* Find final 1/Z value. */
vli_modSub_fast(z, Rx[1], Rx[0]); /* X1 - X0 */
vli_modMult_fast(z, z, Ry[1 - nb]); /* Yb * (X1 - X0) */
vli_modMult_fast(z, z, point->x); /* xP * Yb * (X1 - X0) */
vli_modInv(z, z, curve_p); /* 1 / (xP * Yb * (X1 - X0)) */
vli_modMult_fast(z, z, point->y); /* yP / (xP * Yb * (X1 - X0)) */
vli_modMult_fast(z, z, Rx[1 - nb]); /* Xb * yP / (xP * Yb * (X1 - X0)) */
/* End 1/Z calculation */
XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb]);
apply_z(Rx[0], Ry[0], z);
vli_set(result->x, Rx[0]);
vli_set(result->y, Ry[0]);
}
static int EccPoint_compute_public_key(EccPoint *result, uECC_word_t *private) {
uECC_word_t tmp1[uECC_WORDS];
uECC_word_t tmp2[uECC_WORDS];
uECC_word_t *p2[2] = {tmp1, tmp2};
uECC_word_t carry;
/* Make sure the private key is in the range [1, n-1]. */
if (vli_isZero(private)) {
return 0;
}
#if (uECC_CURVE == uECC_secp160r1)
// Don't regularize the bitcount for secp160r1, since it would have a larger performance
// impact (about 2% slower on average) and requires the vli_xxx_n functions, leading to
// a significant increase in code size.
EccPoint_mult(result, &curve_G, private, 0, vli_numBits(private, uECC_WORDS));
#else
if (vli_cmp(curve_n, private) != 1) {
return 0;
}
// Regularize the bitcount for the private key so that attackers cannot use a side channel
// attack to learn the number of leading zeros.
carry = vli_add(tmp1, private, curve_n);
vli_add(tmp2, tmp1, curve_n);
EccPoint_mult(result, &curve_G, p2[!carry], 0, (uECC_BYTES * 8) + 1);
#endif
if (EccPoint_isZero(result)) {
return 0;
}
return 1;
}
#if uECC_CURVE == uECC_secp224r1
/* Routine 3.2.4 RS; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1_rs(uECC_word_t *d1,
uECC_word_t *e1,
uECC_word_t *f1,
const uECC_word_t *d0,
const uECC_word_t *e0,
const uECC_word_t *f0) {
uECC_word_t t[uECC_WORDS];
vli_modSquare_fast(t, d0); /* t <-- d0 ^ 2 */
vli_modMult_fast(e1, d0, e0); /* e1 <-- d0 * e0 */
vli_modAdd(d1, t, f0, curve_p); /* d1 <-- t + f0 */
vli_modAdd(e1, e1, e1, curve_p); /* e1 <-- e1 + e1 */
vli_modMult_fast(f1, t, f0); /* f1 <-- t * f0 */
vli_modAdd(f1, f1, f1, curve_p); /* f1 <-- f1 + f1 */
vli_modAdd(f1, f1, f1, curve_p); /* f1 <-- f1 + f1 */
}
/* Routine 3.2.5 RSS; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1_rss(uECC_word_t *d1,
uECC_word_t *e1,
uECC_word_t *f1,
const uECC_word_t *d0,
const uECC_word_t *e0,
const uECC_word_t *f0,
const bitcount_t j) {
bitcount_t i;
vli_set(d1, d0); /* d1 <-- d0 */
vli_set(e1, e0); /* e1 <-- e0 */
vli_set(f1, f0); /* f1 <-- f0 */
for (i = 1; i <= j; i++) {
mod_sqrt_secp224r1_rs(d1, e1, f1, d1, e1, f1); /* RS (d1,e1,f1,d1,e1,f1) */
}
}
/* Routine 3.2.6 RM; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1_rm(uECC_word_t *d2,
uECC_word_t *e2,
uECC_word_t *f2,
const uECC_word_t *c,
const uECC_word_t *d0,
const uECC_word_t *e0,
const uECC_word_t *d1,
const uECC_word_t *e1) {
uECC_word_t t1[uECC_WORDS];
uECC_word_t t2[uECC_WORDS];
vli_modMult_fast(t1, e0, e1); /* t1 <-- e0 * e1 */
vli_modMult_fast(t1, t1, c); /* t1 <-- t1 * c */
vli_modSub_fast(t1, curve_p, t1); /* t1 <-- p - t1 */
vli_modMult_fast(t2, d0, d1); /* t2 <-- d0 * d1 */
vli_modAdd(t2, t2, t1, curve_p); /* t2 <-- t2 + t1 */
vli_modMult_fast(t1, d0, e1); /* t1 <-- d0 * e1 */
vli_modMult_fast(e2, d1, e0); /* e2 <-- d1 * e0 */
vli_modAdd(e2, e2, t1, curve_p); /* e2 <-- e2 + t1 */
vli_modSquare_fast(f2, e2); /* f2 <-- e2^2 */
vli_modMult_fast(f2, f2, c); /* f2 <-- f2 * c */
vli_modSub_fast(f2, curve_p, f2); /* f2 <-- p - f2 */
vli_set(d2, t2); /* d2 <-- t2 */
}
/* Routine 3.2.7 RP; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1_rp(uECC_word_t *d1,
uECC_word_t *e1,
uECC_word_t *f1,
const uECC_word_t *c,
const uECC_word_t *r) {
wordcount_t i;
wordcount_t pow2i = 1;
uECC_word_t d0[uECC_WORDS];
uECC_word_t e0[uECC_WORDS] = {1}; /* e0 <-- 1 */
uECC_word_t f0[uECC_WORDS];
vli_set(d0, r); /* d0 <-- r */
vli_modSub_fast(f0, curve_p, c); /* f0 <-- p - c */
for (i = 0; i <= 6; i++) {
mod_sqrt_secp224r1_rss(d1, e1, f1, d0, e0, f0, pow2i); /* RSS (d1,e1,f1,d0,e0,f0,2^i) */
mod_sqrt_secp224r1_rm(d1, e1, f1, c, d1, e1, d0, e0); /* RM (d1,e1,f1,c,d1,e1,d0,e0) */
vli_set(d0, d1); /* d0 <-- d1 */
vli_set(e0, e1); /* e0 <-- e1 */
vli_set(f0, f1); /* f0 <-- f1 */
pow2i *= 2;
}
}
/* Compute a = sqrt(a) (mod curve_p). */
/* Routine 3.2.8 mp_mod_sqrt_224; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt(uECC_word_t *a) {
bitcount_t i;
uECC_word_t e1[uECC_WORDS];
uECC_word_t f1[uECC_WORDS];
uECC_word_t d0[uECC_WORDS];
uECC_word_t e0[uECC_WORDS];
uECC_word_t f0[uECC_WORDS];
uECC_word_t d1[uECC_WORDS];
// s = a; using constant instead of random value
mod_sqrt_secp224r1_rp(d0, e0, f0, a, a); /* RP (d0, e0, f0, c, s) */
mod_sqrt_secp224r1_rs(d1, e1, f1, d0, e0, f0); /* RS (d1, e1, f1, d0, e0, f0) */
for (i = 1; i <= 95; i++) {
vli_set(d0, d1); /* d0 <-- d1 */
vli_set(e0, e1); /* e0 <-- e1 */
vli_set(f0, f1); /* f0 <-- f1 */
mod_sqrt_secp224r1_rs(d1, e1, f1, d0, e0, f0); /* RS (d1, e1, f1, d0, e0, f0) */
if (vli_isZero(d1)) { /* if d1 == 0 */
break;
}
}
vli_modInv(f1, e0, curve_p); /* f1 <-- 1 / e0 */
vli_modMult_fast(a, d0, f1); /* a <-- d0 / e0 */
}
#else /* uECC_CURVE */
/* Compute a = sqrt(a) (mod curve_p). */
static void mod_sqrt(uECC_word_t *a) {
bitcount_t i;
uECC_word_t p1[uECC_WORDS] = {1};
uECC_word_t l_result[uECC_WORDS] = {1};
/* Since curve_p == 3 (mod 4) for all supported curves, we can
compute sqrt(a) = a^((curve_p + 1) / 4) (mod curve_p). */
vli_add(p1, curve_p, p1); /* p1 = curve_p + 1 */
for (i = vli_numBits(p1, uECC_WORDS) - 1; i > 1; --i) {
vli_modSquare_fast(l_result, l_result);
if (vli_testBit(p1, i)) {
vli_modMult_fast(l_result, l_result, a);
}
}
vli_set(a, l_result);
}
#endif /* uECC_CURVE */
#if uECC_WORD_SIZE == 1
static void vli_nativeToBytes(uint8_t * RESTRICT dest, const uint8_t * RESTRICT src) {
uint8_t i;
for (i = 0; i < uECC_BYTES; ++i) {
dest[i] = src[(uECC_BYTES - 1) - i];
}
}
#define vli_bytesToNative(dest, src) vli_nativeToBytes((dest), (src))
#elif uECC_WORD_SIZE == 4
static void vli_nativeToBytes(uint8_t *bytes, const uint32_t *native) {
unsigned i;
for (i = 0; i < uECC_WORDS; ++i) {
uint8_t *digit = bytes + 4 * (uECC_WORDS - 1 - i);
digit[0] = native[i] >> 24;
digit[1] = native[i] >> 16;
digit[2] = native[i] >> 8;
digit[3] = native[i];
}
}
static void vli_bytesToNative(uint32_t *native, const uint8_t *bytes) {
unsigned i;
for (i = 0; i < uECC_WORDS; ++i) {
const uint8_t *digit = bytes + 4 * (uECC_WORDS - 1 - i);
native[i] = ((uint32_t)digit[0] << 24) | ((uint32_t)digit[1] << 16) |
((uint32_t)digit[2] << 8) | (uint32_t)digit[3];
}
}
#else
static void vli_nativeToBytes(uint8_t *bytes, const uint64_t *native) {
unsigned i;
for (i = 0; i < uECC_WORDS; ++i) {
uint8_t *digit = bytes + 8 * (uECC_WORDS - 1 - i);
digit[0] = native[i] >> 56;
digit[1] = native[i] >> 48;
digit[2] = native[i] >> 40;
digit[3] = native[i] >> 32;
digit[4] = native[i] >> 24;
digit[5] = native[i] >> 16;
digit[6] = native[i] >> 8;
digit[7] = native[i];
}
}
static void vli_bytesToNative(uint64_t *native, const uint8_t *bytes) {
unsigned i;
for (i = 0; i < uECC_WORDS; ++i) {
const uint8_t *digit = bytes + 8 * (uECC_WORDS - 1 - i);
native[i] = ((uint64_t)digit[0] << 56) | ((uint64_t)digit[1] << 48) |
((uint64_t)digit[2] << 40) | ((uint64_t)digit[3] << 32) |
((uint64_t)digit[4] << 24) | ((uint64_t)digit[5] << 16) |
((uint64_t)digit[6] << 8) | (uint64_t)digit[7];
}
}
#endif /* uECC_WORD_SIZE */
int uECC_make_key(uint8_t public_key[uECC_BYTES*2], uint8_t private_key[uECC_BYTES]) {
uECC_word_t private[uECC_WORDS];
EccPoint public;
uECC_word_t tries;
for (tries = 0; tries < MAX_TRIES; ++tries) {
if (g_rng_function((uint8_t *)private, sizeof(private)) &&
EccPoint_compute_public_key(&public, private)) {
vli_nativeToBytes(private_key, private);
vli_nativeToBytes(public_key, public.x);
vli_nativeToBytes(public_key + uECC_BYTES, public.y);
return 1;
}
}
return 0;
}
int uECC_shared_secret(const uint8_t public_key[uECC_BYTES*2],
const uint8_t private_key[uECC_BYTES],
uint8_t secret[uECC_BYTES]) {
EccPoint public;
EccPoint product;
uECC_word_t private[uECC_WORDS];
uECC_word_t tmp[uECC_WORDS];
uECC_word_t *p2[2] = {private, tmp};
uECC_word_t random[uECC_WORDS];
uECC_word_t *initial_Z = 0;
uECC_word_t tries;
uECC_word_t carry;
// Try to get a random initial Z value to improve protection against side-channel
// attacks. If the RNG fails every time (eg it was not defined), we continue so that
// uECC_shared_secret() can still work without an RNG defined.
for (tries = 0; tries < MAX_TRIES; ++tries) {
if (g_rng_function((uint8_t *)random, sizeof(random)) && !vli_isZero(random)) {
initial_Z = random;
break;
}
}
vli_bytesToNative(private, private_key);
vli_bytesToNative(public.x, public_key);
vli_bytesToNative(public.y, public_key + uECC_BYTES);
#if (uECC_CURVE == uECC_secp160r1)
// Don't regularize the bitcount for secp160r1.
EccPoint_mult(&product, &public, private, initial_Z, vli_numBits(private, uECC_WORDS));
#else
// Regularize the bitcount for the private key so that attackers cannot use a side channel
// attack to learn the number of leading zeros.
carry = vli_add(private, private, curve_n);
vli_add(tmp, private, curve_n);
EccPoint_mult(&product, &public, p2[!carry], initial_Z, (uECC_BYTES * 8) + 1);
#endif
vli_nativeToBytes(secret, product.x);
return !EccPoint_isZero(&product);
}
void uECC_compress(const uint8_t public_key[uECC_BYTES*2], uint8_t compressed[uECC_BYTES+1]) {
wordcount_t i;
for (i = 0; i < uECC_BYTES; ++i) {
compressed[i+1] = public_key[i];
}
compressed[0] = 2 + (public_key[uECC_BYTES * 2 - 1] & 0x01);
}
/* Computes result = x^3 + ax + b. result must not overlap x. */
static void curve_x_side(uECC_word_t * RESTRICT result, const uECC_word_t * RESTRICT x) {
#if (uECC_CURVE == uECC_secp256k1)
vli_modSquare_fast(result, x); /* r = x^2 */
vli_modMult_fast(result, result, x); /* r = x^3 */
vli_modAdd(result, result, curve_b, curve_p); /* r = x^3 + b */
#else
uECC_word_t _3[uECC_WORDS] = {3}; /* -a = 3 */
vli_modSquare_fast(result, x); /* r = x^2 */
vli_modSub_fast(result, result, _3); /* r = x^2 - 3 */
vli_modMult_fast(result, result, x); /* r = x^3 - 3x */
vli_modAdd(result, result, curve_b, curve_p); /* r = x^3 - 3x + b */
#endif
}
void uECC_decompress(const uint8_t compressed[uECC_BYTES+1], uint8_t public_key[uECC_BYTES*2]) {
EccPoint point;
vli_bytesToNative(point.x, compressed + 1);
curve_x_side(point.y, point.x);
mod_sqrt(point.y);
if ((point.y[0] & 0x01) != (compressed[0] & 0x01)) {
vli_sub(point.y, curve_p, point.y);
}
vli_nativeToBytes(public_key, point.x);
vli_nativeToBytes(public_key + uECC_BYTES, point.y);
}
int uECC_valid_public_key(const uint8_t public_key[uECC_BYTES*2]) {
uECC_word_t tmp1[uECC_WORDS];
uECC_word_t tmp2[uECC_WORDS];
EccPoint public;
vli_bytesToNative(public.x, public_key);
vli_bytesToNative(public.y, public_key + uECC_BYTES);
// The point at infinity is invalid.
if (EccPoint_isZero(&public)) {
return 0;
}
// x and y must be smaller than p.
if (vli_cmp(curve_p, public.x) != 1 || vli_cmp(curve_p, public.y) != 1) {
return 0;
}
vli_modSquare_fast(tmp1, public.y); /* tmp1 = y^2 */
curve_x_side(tmp2, public.x); /* tmp2 = x^3 + ax + b */
/* Make sure that y^2 == x^3 + ax + b */
return (vli_cmp(tmp1, tmp2) == 0);
}
int uECC_compute_public_key(const uint8_t private_key[uECC_BYTES],
uint8_t public_key[uECC_BYTES * 2]) {
uECC_word_t private[uECC_WORDS];
EccPoint public;
vli_bytesToNative(private, private_key);
if (!EccPoint_compute_public_key(&public, private)) {
return 0;
}
vli_nativeToBytes(public_key, public.x);
vli_nativeToBytes(public_key + uECC_BYTES, public.y);
return 1;
}
int uECC_bytes(void) {
return uECC_BYTES;
}
int uECC_curve(void) {
return uECC_CURVE;
}
/* -------- ECDSA code -------- */
#if (uECC_CURVE == uECC_secp160r1)
static void vli_clear_n(uECC_word_t *vli) {
vli_clear(vli);
vli[uECC_N_WORDS - 1] = 0;
}
static uECC_word_t vli_isZero_n(const uECC_word_t *vli) {
if (vli[uECC_N_WORDS - 1]) {
return 0;
}
return vli_isZero(vli);
}
static void vli_set_n(uECC_word_t *dest, const uECC_word_t *src) {
vli_set(dest, src);
dest[uECC_N_WORDS - 1] = src[uECC_N_WORDS - 1];
}
static cmpresult_t vli_cmp_n(const uECC_word_t *left, const uECC_word_t *right) {
if (left[uECC_N_WORDS - 1] > right[uECC_N_WORDS - 1]) {
return 1;
} else if (left[uECC_N_WORDS - 1] < right[uECC_N_WORDS - 1]) {
return -1;
}
return vli_cmp(left, right);
}
static void vli_rshift1_n(uECC_word_t *vli) {
vli_rshift1(vli);
vli[uECC_N_WORDS - 2] |= vli[uECC_N_WORDS - 1] << (uECC_WORD_BITS - 1);
vli[uECC_N_WORDS - 1] = vli[uECC_N_WORDS - 1] >> 1;
}
static uECC_word_t vli_add_n(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right) {
uECC_word_t carry = vli_add(result, left, right);
uECC_word_t sum = left[uECC_N_WORDS - 1] + right[uECC_N_WORDS - 1] + carry;
if (sum != left[uECC_N_WORDS - 1]) {
carry = (sum < left[uECC_N_WORDS - 1]);
}
result[uECC_N_WORDS - 1] = sum;
return carry;
}
static uECC_word_t vli_sub_n(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right) {
uECC_word_t borrow = vli_sub(result, left, right);
uECC_word_t diff = left[uECC_N_WORDS - 1] - right[uECC_N_WORDS - 1] - borrow;
if (diff != left[uECC_N_WORDS - 1]) {
borrow = (diff > left[uECC_N_WORDS - 1]);
}
result[uECC_N_WORDS - 1] = diff;
return borrow;
}
#if !muladd_exists
static void muladd(uECC_word_t a,
uECC_word_t b,
uECC_word_t *r0,
uECC_word_t *r1,
uECC_word_t *r2) {
uECC_dword_t p = (uECC_dword_t)a * b;
uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
r01 += p;
*r2 += (r01 < p);
*r1 = r01 >> uECC_WORD_BITS;
*r0 = (uECC_word_t)r01;
}
#define muladd_exists 1
#endif
static void vli_mult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t i, k;
for (k = 0; k < uECC_N_WORDS * 2 - 1; ++k) {
wordcount_t min = (k < uECC_N_WORDS ? 0 : (k + 1) - uECC_N_WORDS);
wordcount_t max = (k < uECC_N_WORDS ? k : uECC_N_WORDS - 1);
for (i = min; i <= max; ++i) {
muladd(left[i], right[k - i], &r0, &r1, &r2);
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
result[uECC_N_WORDS * 2 - 1] = r0;
}
static void vli_modAdd_n(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
const uECC_word_t *mod) {
uECC_word_t carry = vli_add_n(result, left, right);
if (carry || vli_cmp_n(result, mod) >= 0) {
vli_sub_n(result, result, mod);
}
}
static void vli_modInv_n(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod) {
uECC_word_t a[uECC_N_WORDS], b[uECC_N_WORDS], u[uECC_N_WORDS], v[uECC_N_WORDS];
uECC_word_t carry;
cmpresult_t cmpResult;
if (vli_isZero_n(input)) {
vli_clear_n(result);
return;
}
vli_set_n(a, input);
vli_set_n(b, mod);
vli_clear_n(u);
u[0] = 1;
vli_clear_n(v);
while ((cmpResult = vli_cmp_n(a, b)) != 0) {
carry = 0;
if (EVEN(a)) {
vli_rshift1_n(a);
if (!EVEN(u)) {
carry = vli_add_n(u, u, mod);
}
vli_rshift1_n(u);
if (carry) {
u[uECC_N_WORDS - 1] |= HIGH_BIT_SET;
}
} else if (EVEN(b)) {
vli_rshift1_n(b);
if (!EVEN(v)) {
carry = vli_add_n(v, v, mod);
}
vli_rshift1_n(v);
if (carry) {
v[uECC_N_WORDS - 1] |= HIGH_BIT_SET;
}
} else if (cmpResult > 0) {
vli_sub_n(a, a, b);
vli_rshift1_n(a);
if (vli_cmp_n(u, v) < 0) {
vli_add_n(u, u, mod);
}
vli_sub_n(u, u, v);
if (!EVEN(u)) {
carry = vli_add_n(u, u, mod);
}
vli_rshift1_n(u);
if (carry) {
u[uECC_N_WORDS - 1] |= HIGH_BIT_SET;
}
} else {
vli_sub_n(b, b, a);
vli_rshift1_n(b);
if (vli_cmp_n(v, u) < 0) {
vli_add_n(v, v, mod);
}
vli_sub_n(v, v, u);
if (!EVEN(v)) {
carry = vli_add_n(v, v, mod);
}
vli_rshift1_n(v);
if (carry) {
v[uECC_N_WORDS - 1] |= HIGH_BIT_SET;
}
}
}
vli_set_n(result, u);
}
static void vli2_rshift1_n(uECC_word_t *vli) {
vli_rshift1_n(vli);
vli[uECC_N_WORDS - 1] |= vli[uECC_N_WORDS] << (uECC_WORD_BITS - 1);
vli_rshift1_n(vli + uECC_N_WORDS);
}
static uECC_word_t vli2_sub_n(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right) {
uECC_word_t borrow = 0;
wordcount_t i;
for (i = 0; i < uECC_N_WORDS * 2; ++i) {
uECC_word_t diff = left[i] - right[i] - borrow;
if (diff != left[i]) {
borrow = (diff > left[i]);
}
result[i] = diff;
}
return borrow;
}
/* Computes result = (left * right) % curve_n. */
static void vli_modMult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
bitcount_t i;
uECC_word_t product[2 * uECC_N_WORDS];
uECC_word_t modMultiple[2 * uECC_N_WORDS];
uECC_word_t tmp[2 * uECC_N_WORDS];
uECC_word_t *v[2] = {tmp, product};
uECC_word_t index = 1;
vli_mult_n(product, left, right);
vli_clear_n(modMultiple);
vli_set(modMultiple + uECC_N_WORDS + 1, curve_n);
vli_rshift1(modMultiple + uECC_N_WORDS + 1);
modMultiple[2 * uECC_N_WORDS - 1] |= HIGH_BIT_SET;
modMultiple[uECC_N_WORDS] = HIGH_BIT_SET;
for (i = 0;
i <= ((((bitcount_t)uECC_N_WORDS) << uECC_WORD_BITS_SHIFT) + (uECC_WORD_BITS - 1));
++i) {
uECC_word_t borrow = vli2_sub_n(v[1 - index], v[index], modMultiple);
index = !(index ^ borrow); /* Swap the index if there was no borrow */
vli2_rshift1_n(modMultiple);
}
vli_set_n(result, v[index]);
}
#else
#define vli_cmp_n vli_cmp
#define vli_modInv_n vli_modInv
#define vli_modAdd_n vli_modAdd
static void vli2_rshift1(uECC_word_t *vli) {
vli_rshift1(vli);
vli[uECC_WORDS - 1] |= vli[uECC_WORDS] << (uECC_WORD_BITS - 1);
vli_rshift1(vli + uECC_WORDS);
}
static uECC_word_t vli2_sub(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right) {
uECC_word_t borrow = 0;
wordcount_t i;
for (i = 0; i < uECC_WORDS * 2; ++i) {
uECC_word_t diff = left[i] - right[i] - borrow;
if (diff != left[i]) {
borrow = (diff > left[i]);
}
result[i] = diff;
}
return borrow;
}
/* Computes result = (left * right) % curve_n. */
static void vli_modMult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
uECC_word_t product[2 * uECC_WORDS];
uECC_word_t modMultiple[2 * uECC_WORDS];
uECC_word_t tmp[2 * uECC_WORDS];
uECC_word_t *v[2] = {tmp, product};
bitcount_t i;
uECC_word_t index = 1;
vli_mult(product, left, right);
vli_set(modMultiple + uECC_WORDS, curve_n); /* works if curve_n has its highest bit set */
vli_clear(modMultiple);
for (i = 0; i <= uECC_BYTES * 8; ++i) {
uECC_word_t borrow = vli2_sub(v[1 - index], v[index], modMultiple);
index = !(index ^ borrow); /* Swap the index if there was no borrow */
vli2_rshift1(modMultiple);
}
vli_set(result, v[index]);
}
#endif /* (uECC_CURVE != uECC_secp160r1) */
static int uECC_sign_with_k(const uint8_t private_key[uECC_BYTES],
const uint8_t message_hash[uECC_BYTES],
uECC_word_t k[uECC_N_WORDS],
uint8_t signature[uECC_BYTES*2]) {
uECC_word_t tmp[uECC_N_WORDS];
uECC_word_t s[uECC_N_WORDS];
uECC_word_t *k2[2] = {tmp, s};
EccPoint p;
uECC_word_t carry;
uECC_word_t tries;
/* Make sure 0 < k < curve_n */
if (vli_isZero(k) || vli_cmp_n(curve_n, k) != 1) {
return 0;
}
#if (uECC_CURVE == uECC_secp160r1)
/* Make sure that we don't leak timing information about k.
See http://eprint.iacr.org/2011/232.pdf */
vli_add_n(tmp, k, curve_n);
carry = (tmp[uECC_WORDS] & 0x02);
vli_add_n(s, tmp, curve_n);
/* p = k * G */
EccPoint_mult(&p, &curve_G, k2[!carry], 0, (uECC_BYTES * 8) + 2);
#else
/* Make sure that we don't leak timing information about k.
See http://eprint.iacr.org/2011/232.pdf */
carry = vli_add(tmp, k, curve_n);
vli_add(s, tmp, curve_n);
/* p = k * G */
EccPoint_mult(&p, &curve_G, k2[!carry], 0, (uECC_BYTES * 8) + 1);
/* r = x1 (mod n) */
if (vli_cmp(curve_n, p.x) != 1) {
vli_sub(p.x, p.x, curve_n);
}
#endif
if (vli_isZero(p.x)) {
return 0;
}
// Attempt to get a random number to prevent side channel analysis of k.
// If the RNG fails every time (eg it was not defined), we continue so that
// deterministic signing can still work (with reduced security) without
// an RNG defined.
carry = 0; // use to signal that the RNG succeeded at least once.
for (tries = 0; tries < MAX_TRIES; ++tries) {
if (!g_rng_function((uint8_t *)tmp, sizeof(tmp))) {
continue;
}
carry = 1;
if (!vli_isZero(tmp)) {
break;
}
}
if (!carry) {
vli_clear(tmp);
tmp[0] = 1;
}
/* Prevent side channel analysis of vli_modInv() to determine
bits of k / the private key by premultiplying by a random number */
vli_modMult_n(k, k, tmp); /* k' = rand * k */
vli_modInv_n(k, k, curve_n); /* k = 1 / k' */
vli_modMult_n(k, k, tmp); /* k = 1 / k */
vli_nativeToBytes(signature, p.x); /* store r */
tmp[uECC_N_WORDS - 1] = 0;
vli_bytesToNative(tmp, private_key); /* tmp = d */
s[uECC_N_WORDS - 1] = 0;
vli_set(s, p.x);
vli_modMult_n(s, tmp, s); /* s = r*d */
vli_bytesToNative(tmp, message_hash);
vli_modAdd_n(s, tmp, s, curve_n); /* s = e + r*d */
vli_modMult_n(s, s, k); /* s = (e + r*d) / k */
#if (uECC_CURVE == uECC_secp160r1)
if (s[uECC_N_WORDS - 1]) {
return 0;
}
#endif
vli_nativeToBytes(signature + uECC_BYTES, s);
return 1;
}
int uECC_sign(const uint8_t private_key[uECC_BYTES],
const uint8_t message_hash[uECC_BYTES],
uint8_t signature[uECC_BYTES*2]) {
uECC_word_t k[uECC_N_WORDS];
uECC_word_t tries;
for (tries = 0; tries < MAX_TRIES; ++tries) {
if(g_rng_function((uint8_t *)k, sizeof(k))) {
#if (uECC_CURVE == uECC_secp160r1)
k[uECC_WORDS] &= 0x01;
#endif
if (uECC_sign_with_k(private_key, message_hash, k, signature)) {
return 1;
}
}
}
return 0;
}
/* Compute an HMAC using K as a key (as in RFC 6979). Note that K is always
the same size as the hash result size. */
static void HMAC_init(uECC_HashContext *hash_context, const uint8_t *K) {
uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size;
unsigned i;
for (i = 0; i < hash_context->result_size; ++i)
pad[i] = K[i] ^ 0x36;
for (; i < hash_context->block_size; ++i)
pad[i] = 0x36;
hash_context->init_hash(hash_context);
hash_context->update_hash(hash_context, pad, hash_context->block_size);
}
static void HMAC_update(uECC_HashContext *hash_context,
const uint8_t *message,
unsigned message_size) {
hash_context->update_hash(hash_context, message, message_size);
}
static void HMAC_finish(uECC_HashContext *hash_context, const uint8_t *K, uint8_t *result) {
uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size;
unsigned i;
for (i = 0; i < hash_context->result_size; ++i)
pad[i] = K[i] ^ 0x5c;
for (; i < hash_context->block_size; ++i)
pad[i] = 0x5c;
hash_context->finish_hash(hash_context, result);
hash_context->init_hash(hash_context);
hash_context->update_hash(hash_context, pad, hash_context->block_size);
hash_context->update_hash(hash_context, result, hash_context->result_size);
hash_context->finish_hash(hash_context, result);
}
/* V = HMAC_K(V) */
static void update_V(uECC_HashContext *hash_context, uint8_t *K, uint8_t *V) {
HMAC_init(hash_context, K);
HMAC_update(hash_context, V, hash_context->result_size);
HMAC_finish(hash_context, K, V);
}
/* Deterministic signing, similar to RFC 6979. Differences are:
* We just use (truncated) H(m) directly rather than bits2octets(H(m))
(it is not reduced modulo curve_n).
* We generate a value for k (aka T) directly rather than converting endianness.
Layout of hash_context->tmp: <K> | <V> | (1 byte overlapped 0x00 or 0x01) / <HMAC pad> */
int uECC_sign_deterministic(const uint8_t private_key[uECC_BYTES],
const uint8_t message_hash[uECC_BYTES],
uECC_HashContext *hash_context,
uint8_t signature[uECC_BYTES*2]) {
uint8_t *K = hash_context->tmp;
uint8_t *V = K + hash_context->result_size;
uECC_word_t tries;
unsigned i;
for (i = 0; i < hash_context->result_size; ++i) {
V[i] = 0x01;
K[i] = 0;
}
// K = HMAC_K(V || 0x00 || int2octets(x) || h(m))
HMAC_init(hash_context, K);
V[hash_context->result_size] = 0x00;
HMAC_update(hash_context, V, hash_context->result_size + 1);
HMAC_update(hash_context, private_key, uECC_BYTES);
HMAC_update(hash_context, message_hash, uECC_BYTES);
HMAC_finish(hash_context, K, K);
update_V(hash_context, K, V);
// K = HMAC_K(V || 0x01 || int2octets(x) || h(m))
HMAC_init(hash_context, K);
V[hash_context->result_size] = 0x01;
HMAC_update(hash_context, V, hash_context->result_size + 1);
HMAC_update(hash_context, private_key, uECC_BYTES);
HMAC_update(hash_context, message_hash, uECC_BYTES);
HMAC_finish(hash_context, K, K);
update_V(hash_context, K, V);
for (tries = 0; tries < MAX_TRIES; ++tries) {
uECC_word_t T[uECC_N_WORDS];
uint8_t *T_ptr = (uint8_t *)T;
unsigned T_bytes = 0;
while (T_bytes < sizeof(T)) {
update_V(hash_context, K, V);
for (i = 0; i < hash_context->result_size && T_bytes < sizeof(T); ++i, ++T_bytes) {
T_ptr[T_bytes] = V[i];
}
}
#if (uECC_CURVE == uECC_secp160r1)
T[uECC_WORDS] &= 0x01;
#endif
if (uECC_sign_with_k(private_key, message_hash, T, signature)) {
return 1;
}
// K = HMAC_K(V || 0x00)
HMAC_init(hash_context, K);
V[hash_context->result_size] = 0x00;
HMAC_update(hash_context, V, hash_context->result_size + 1);
HMAC_finish(hash_context, K, K);
update_V(hash_context, K, V);
}
return 0;
}
static bitcount_t smax(bitcount_t a, bitcount_t b) {
return (a > b ? a : b);
}
int uECC_verify(const uint8_t public_key[uECC_BYTES*2],
const uint8_t hash[uECC_BYTES],
const uint8_t signature[uECC_BYTES*2]) {
uECC_word_t u1[uECC_N_WORDS], u2[uECC_N_WORDS];
uECC_word_t z[uECC_N_WORDS];
EccPoint public, sum;
uECC_word_t rx[uECC_WORDS];
uECC_word_t ry[uECC_WORDS];
uECC_word_t tx[uECC_WORDS];
uECC_word_t ty[uECC_WORDS];
uECC_word_t tz[uECC_WORDS];
const EccPoint *points[4];
const EccPoint *point;
bitcount_t numBits;
bitcount_t i;
uECC_word_t r[uECC_N_WORDS], s[uECC_N_WORDS];
r[uECC_N_WORDS - 1] = 0;
s[uECC_N_WORDS - 1] = 0;
vli_bytesToNative(public.x, public_key);
vli_bytesToNative(public.y, public_key + uECC_BYTES);
vli_bytesToNative(r, signature);
vli_bytesToNative(s, signature + uECC_BYTES);
if (vli_isZero(r) || vli_isZero(s)) { /* r, s must not be 0. */
return 0;
}
#if (uECC_CURVE != uECC_secp160r1)
if (vli_cmp(curve_n, r) != 1 || vli_cmp(curve_n, s) != 1) { /* r, s must be < n. */
return 0;
}
#endif
/* Calculate u1 and u2. */
vli_modInv_n(z, s, curve_n); /* Z = s^-1 */
u1[uECC_N_WORDS - 1] = 0;
vli_bytesToNative(u1, hash);
vli_modMult_n(u1, u1, z); /* u1 = e/s */
vli_modMult_n(u2, r, z); /* u2 = r/s */
/* Calculate sum = G + Q. */
vli_set(sum.x, public.x);
vli_set(sum.y, public.y);
vli_set(tx, curve_G.x);
vli_set(ty, curve_G.y);
vli_modSub_fast(z, sum.x, tx); /* Z = x2 - x1 */
XYcZ_add(tx, ty, sum.x, sum.y);
vli_modInv(z, z, curve_p); /* Z = 1/Z */
apply_z(sum.x, sum.y, z);
/* Use Shamir's trick to calculate u1*G + u2*Q */
points[0] = 0;
points[1] = &curve_G;
points[2] = &public;
points[3] = &sum;
numBits = smax(vli_numBits(u1, uECC_N_WORDS), vli_numBits(u2, uECC_N_WORDS));
point = points[(!!vli_testBit(u1, numBits - 1)) | ((!!vli_testBit(u2, numBits - 1)) << 1)];
vli_set(rx, point->x);
vli_set(ry, point->y);
vli_clear(z);
z[0] = 1;
for (i = numBits - 2; i >= 0; --i) {
uECC_word_t index;
EccPoint_double_jacobian(rx, ry, z);
index = (!!vli_testBit(u1, i)) | ((!!vli_testBit(u2, i)) << 1);
point = points[index];
if (point) {
vli_set(tx, point->x);
vli_set(ty, point->y);
apply_z(tx, ty, z);
vli_modSub_fast(tz, rx, tx); /* Z = x2 - x1 */
XYcZ_add(tx, ty, rx, ry);
vli_modMult_fast(z, z, tz);
}
}
vli_modInv(z, z, curve_p); /* Z = 1/Z */
apply_z(rx, ry, z);
/* v = x1 (mod n) */
#if (uECC_CURVE != uECC_secp160r1)
if (vli_cmp(curve_n, rx) != 1) {
vli_sub(rx, rx, curve_n);
}
#endif
/* Accept only if v == r. */
return vli_equal(rx, r);
}