/* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */ #include "uECC.h" #ifndef uECC_PLATFORM #if defined(__AVR__) && __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(__clang_major__) && defined(__clang_minor__) && (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 #include 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 #include #include #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 !defined(asm_clear) || !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 !defined(asm_isZero) || !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 !defined(asm_testBit) || !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 !defined(asm_numBits) || !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 !defined(asm_set) || !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 !defined(asm_cmp) || !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 !defined(asm_rshift1) || !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 !defined(asm_add) || !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 !defined(asm_sub) || !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 !defined(asm_modAdd) || !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 !defined(asm_modSub) || !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 !defined(asm_modSub_fast) || !asm_modSub_fast #define vli_modSub_fast(result, left, right) vli_modSub((result), (left), (right), curve_p) #endif #if !defined(asm_mmod_fast) || !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 !defined(asm_modInv) || !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) { #if (uECC_CURVE != uECC_secp160r1) uECC_word_t tmp1[uECC_WORDS]; uECC_word_t tmp2[uECC_WORDS]; uECC_word_t *p2[2] = {tmp1, tmp2}; uECC_word_t carry; #endif /* 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] = (uint8_t)(native[i] >> 24); digit[1] = (uint8_t)(native[i] >> 16); digit[2] = (uint8_t)(native[i] >> 8); digit[3] = (uint8_t)(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 random[uECC_WORDS]; uECC_word_t *initial_Z = 0; uECC_word_t tries; #if (uECC_CURVE != uECC_secp160r1) uECC_word_t tmp[uECC_WORDS]; uECC_word_t *p2[2] = {private, tmp}; uECC_word_t carry; #endif // 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 tmp[uECC_N_WORDS]; */ /* -Wunused-variable */ /* uECC_word_t s[uECC_N_WORDS]; */ /* -Wunused-variable */ /* uECC_word_t *k2[2] = {tmp, s}; */ /* -Wunused-variable */ /* EccPoint p; */ /* -Wunused-variable */ 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: | | (1 byte overlapped 0x00 or 0x01) / */ 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] = ∑ 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); }