/* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */ #ifdef USE_BSD_ECC_LIB #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_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 16 #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_N_WORDS_1 21 #define uECC_N_WORDS_2 24 #define uECC_N_WORDS_3 32 #define uECC_N_WORDS_4 32 #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_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_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_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} #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_N_WORDS_1 6 #define uECC_N_WORDS_2 6 #define uECC_N_WORDS_3 8 #define uECC_N_WORDS_4 8 #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_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_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_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} #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_N_WORDS_1 3 #define uECC_N_WORDS_2 3 #define uECC_N_WORDS_3 4 #define uECC_N_WORDS_4 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_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_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 { \ {0x59F2815B16F81798, 0x029BFCDB2DCE28D9, 0x55A06295CE870B07, 0x79BE667EF9DCBBAC}, \ {0x9C47D08FFB10D4B8, 0xFD17B448A6855419, 0x5DA4FBFC0E1108A8, 0x483ADA7726A3C465}} #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 {0xBFD25E8CD0364141, 0xBAAEDCE6AF48A03B, 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF} #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 uECC_word_t curve_p[uECC_WORDS] = uECC_CONCAT(Curve_P_, uECC_CURVE); static uECC_word_t curve_b[uECC_WORDS] = uECC_CONCAT(Curve_B_, uECC_CURVE); static EccPoint curve_G = uECC_CONCAT(Curve_G_, uECC_CURVE); static uECC_word_t curve_n[uECC_N_WORDS] = uECC_CONCAT(Curve_N_, uECC_CURVE); static void vli_clear( uECC_word_t * p_vli ); static uECC_word_t vli_isZero( const uECC_word_t * p_vli ); static uECC_word_t vli_testBit( const uECC_word_t * p_vli, bitcount_t p_bit ); static bitcount_t vli_numBits( const uECC_word_t * p_vli, wordcount_t p_maxWords ); static void vli_set( uECC_word_t * p_dest, const uECC_word_t * p_src ); static cmpresult_t vli_cmp( uECC_word_t * p_left, uECC_word_t * p_right ); static cmpresult_t vli_equal( uECC_word_t * p_left, uECC_word_t * p_right ); static void vli_rshift1( uECC_word_t * p_vli ); static uECC_word_t vli_add( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ); static uECC_word_t vli_sub( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ); static void vli_mult( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ); static void vli_modAdd( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right, uECC_word_t * p_mod ); static void vli_modSub( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right, uECC_word_t * p_mod ); static void vli_mmod_fast( uECC_word_t * RESTRICT p_result, uECC_word_t * RESTRICT p_product ); static void vli_modMult_fast( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ); static void vli_modInv( uECC_word_t * p_result, uECC_word_t * p_input, uECC_word_t * p_mod ); #if uECC_SQUARE_FUNC static void vli_square( uECC_word_t * p_result, uECC_word_t * p_left ); static void vli_modSquare_fast( uECC_word_t * p_result, uECC_word_t * p_left ); #endif #if (defined(_WIN32) || defined(_WIN64)) /* Windows */ #define WIN32_LEAN_AND_MEAN #include #include static int default_RNG( uint8_t * p_dest, unsigned p_size ) { HCRYPTPROV l_prov; if (!CryptAcquireContext (&l_prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) { return 0; } CryptGenRandom(l_prov, p_size, (BYTE *) p_dest); CryptReleaseContext(l_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 * p_dest, unsigned p_size ) { int l_fd = open("/dev/urandom", O_RDONLY | O_CLOEXEC); if (l_fd == -1) { l_fd = open("/dev/random", O_RDONLY | O_CLOEXEC); if (l_fd == -1) { return 0; } } char *l_ptr = (char *)p_dest; size_t l_left = p_size; while (l_left > 0) { int l_read = read(l_fd, l_ptr, l_left); if (l_read <= 0) { // read failed close(l_fd); return 0; } l_left -= l_read; l_ptr += l_read; } close(l_fd); return 1; } #else /* Some other platform */ static int default_RNG( uint8_t * p_dest, unsigned p_size ) { return 0; } #endif static uECC_RNG_Function g_rng = &default_RNG; void uECC_set_rng( uECC_RNG_Function p_rng ) { g_rng = p_rng; } #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)) /* Skipping inclusion of optimized assembly code fror now - RVCT doesn't like it */ //#include "asm_arm.inc" #endif #endif #if !asm_clear static void vli_clear( uECC_word_t * p_vli ) { wordcount_t i; for (i = 0; i < uECC_WORDS; ++i) { p_vli[i] = 0; } } #endif /* Returns 1 if p_vli == 0, 0 otherwise. */ #if !asm_isZero static uECC_word_t vli_isZero( const uECC_word_t * p_vli ) { wordcount_t i; for (i = 0; i < uECC_WORDS; ++i) { if (p_vli[i]) { return 0; } } return 1; } #endif /* Returns nonzero if bit p_bit of p_vli is set. */ #if !asm_testBit static uECC_word_t vli_testBit( const uECC_word_t * p_vli, bitcount_t p_bit ) { return (p_vli[p_bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t) 1 << (p_bit & uECC_WORD_BITS_MASK))); } #endif /* Counts the number of words in p_vli. */ #if !asm_numBits static wordcount_t vli_numDigits( const uECC_word_t * p_vli, wordcount_t p_maxWords ) { 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 = p_maxWords - 1; i >= 0 && p_vli[i] == 0; --i) { } return ((wordcount_t)(i + 1)); } /* Counts the number of bits required to represent p_vli. */ static bitcount_t vli_numBits( const uECC_word_t * p_vli, wordcount_t p_maxWords ) { uECC_word_t i; uECC_word_t l_digit; wordcount_t l_numDigits = vli_numDigits(p_vli, p_maxWords); if (l_numDigits == 0) { return 0; } l_digit = p_vli[l_numDigits - 1]; for (i = 0; l_digit; ++i) { l_digit >>= 1; } return (((bitcount_t) (l_numDigits - 1) << uECC_WORD_BITS_SHIFT) + i); } #endif /* !asm_numBits */ /* Sets p_dest = p_src. */ #if !asm_set static void vli_set( uECC_word_t * p_dest, const uECC_word_t * p_src ) { wordcount_t i; for (i = 0; i < uECC_WORDS; ++i) { p_dest[i] = p_src[i]; } } #endif /* Returns sign of p_left - p_right. */ #if !asm_cmp static cmpresult_t vli_cmp( uECC_word_t * p_left, uECC_word_t * p_right ) { swordcount_t i; for (i = uECC_WORDS - 1; i >= 0; --i) { if (p_left[i] > p_right[i]) { return 1; } else if (p_left[i] < p_right[i]) { return -1; } } return 0; } #endif static cmpresult_t vli_equal( uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_result = 0; swordcount_t i; for (i = uECC_WORDS - 1; i >= 0; --i) { l_result |= (p_left[i] ^ p_right[i]); } return (l_result == 0); } /* Computes p_vli = p_vli >> 1. */ #if !asm_rshift1 static void vli_rshift1( uECC_word_t * p_vli ) { uECC_word_t *l_end = p_vli; uECC_word_t l_carry = 0; p_vli += uECC_WORDS; while (p_vli-- > l_end) { uECC_word_t l_temp = *p_vli; *p_vli = (l_temp >> 1) | l_carry; l_carry = l_temp << (uECC_WORD_BITS - 1); } } #endif /* Computes p_result = p_left + p_right, returning carry. Can modify in place. */ #if !asm_add static uECC_word_t vli_add( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_carry = 0; wordcount_t i; for (i = 0; i < uECC_WORDS; ++i) { uECC_word_t l_sum = p_left[i] + p_right[i] + l_carry; if (l_sum != p_left[i]) { l_carry = (l_sum < p_left[i]); } p_result[i] = l_sum; } return l_carry; } #endif /* Computes p_result = p_left - p_right, returning borrow. Can modify in place. */ #if !asm_sub static uECC_word_t vli_sub( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_borrow = 0; wordcount_t i; for (i = 0; i < uECC_WORDS; ++i) { uECC_word_t l_diff = p_left[i] - p_right[i] - l_borrow; if (l_diff != p_left[i]) { l_borrow = (l_diff > p_left[i]); } p_result[i] = l_diff; } return l_borrow; } #endif #if (!asm_mult || !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 * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t r0 = 0; uECC_word_t r1 = 0; uECC_word_t r2 = 0; wordcount_t i, k; /* Compute each digit of p_result in sequence, maintaining the carries. */ for (k = 0; k < uECC_WORDS; ++k) { for (i = 0; i <= k; ++i) { muladd(p_left[i], p_right[k - i], &r0, &r1, &r2); } p_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(p_left[i], p_right[k - i], &r0, &r1, &r2); } p_result[k] = r0; r0 = r1; r1 = r2; r2 = 0; } p_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 * p_result, uECC_word_t * p_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 l_min = (k < uECC_WORDS ? 0 : (k + 1) - uECC_WORDS); for (i = l_min; i <= k && i <= k - i; ++i) { if (i < k - i) { mul2add(p_left[i], p_left[k - i], &r0, &r1, &r2); } else { muladd(p_left[i], p_left[k - i], &r0, &r1, &r2); } } p_result[k] = r0; r0 = r1; r1 = r2; r2 = 0; } p_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 p_result = (p_left + p_right) % p_mod. Assumes that p_left < p_mod and p_right < p_mod, p_result != p_mod. */ #if !asm_modAdd static void vli_modAdd( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right, uECC_word_t * p_mod ) { uECC_word_t l_carry = vli_add(p_result, p_left, p_right); if (l_carry || vli_cmp(p_result, p_mod) >= 0) { /* p_result > p_mod (p_result = p_mod + remainder), so subtract p_mod to get remainder. */ vli_sub(p_result, p_result, p_mod); } } #endif /* Computes p_result = (p_left - p_right) % p_mod. Assumes that p_left < p_mod and p_right < p_mod, p_result != p_mod. */ #if !asm_modSub static void vli_modSub( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right, uECC_word_t * p_mod ) { uECC_word_t l_borrow = vli_sub(p_result, p_left, p_right); if (l_borrow) { /* In this case, p_result == -diff == (max int) - diff. Since -x % d == d - x, we can get the correct result from p_result + p_mod (with overflow). */ vli_add(p_result, p_result, p_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 p_result, uECC_word_t * RESTRICT p_right ); /* Computes p_result = p_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 p_result, uECC_word_t * RESTRICT p_product ) { uECC_word_t l_tmp[2 * uECC_WORDS]; uECC_word_t l_carry; vli_clear(l_tmp); vli_clear(l_tmp + uECC_WORDS); omega_mult(l_tmp, p_product + uECC_WORDS); /* (Rq, q) = q * c */ l_carry = vli_add(p_result, p_product, l_tmp); /* (C, r) = r + q */ vli_clear(p_product); omega_mult(p_product, l_tmp + uECC_WORDS); /* Rq*c */ l_carry += vli_add(p_result, p_result, p_product); /* (C1, r) = r + Rq*c */ while (l_carry > 0) { --l_carry; vli_sub(p_result, p_result, curve_p); } if (vli_cmp(p_result, curve_p) > 0) { vli_sub(p_result, p_result, curve_p); } } #endif #if uECC_CURVE == uECC_secp160r1 #if uECC_WORD_SIZE == 1 static void omega_mult( uint8_t * RESTRICT p_result, uint8_t * RESTRICT p_right ) { uint8_t l_carry; uint8_t i; /* Multiply by (2^31 + 1). */ vli_set(p_result + 4, p_right); /* 2^32 */ vli_rshift1(p_result + 4); /* 2^31 */ p_result[3] = p_right[0] << 7; /* get last bit from shift */ l_carry = vli_add(p_result, p_result, p_right); /* 2^31 + 1 */ for (i = uECC_WORDS; l_carry; ++i) { uint16_t l_sum = (uint16_t) p_result[i] + l_carry; p_result[i] = (uint8_t) l_sum; l_carry = l_sum >> 8; } } #elif uECC_WORD_SIZE == 4 static void omega_mult( uint32_t * RESTRICT p_result, uint32_t * RESTRICT p_right ) { uint32_t l_carry; unsigned i; /* Multiply by (2^31 + 1). */ vli_set(p_result + 1, p_right); /* 2^32 */ vli_rshift1(p_result + 1); /* 2^31 */ p_result[0] = p_right[0] << 31; /* get last bit from shift */ l_carry = vli_add(p_result, p_result, p_right); /* 2^31 + 1 */ for (i = uECC_WORDS; l_carry; ++i) { uint64_t l_sum = (uint64_t) p_result[i] + l_carry; p_result[i] = (uint32_t) l_sum; l_carry = l_sum >> 32; } } #endif /* uECC_WORD_SIZE */ #elif uECC_CURVE == uECC_secp192r1 /* Computes p_result = p_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 p_result, uint8_t * RESTRICT p_product ) { uint8_t l_tmp[uECC_WORDS]; uint8_t l_carry; vli_set(p_result, p_product); vli_set(l_tmp, &p_product[24]); l_carry = vli_add(p_result, p_result, l_tmp); l_tmp[0] = l_tmp[1] = l_tmp[2] = l_tmp[3] = l_tmp[4] = l_tmp[5] = l_tmp[6] = l_tmp[7] = 0; l_tmp[8] = p_product[24]; l_tmp[9] = p_product[25]; l_tmp[10] = p_product[26]; l_tmp[11] = p_product[27]; l_tmp[12] = p_product[28]; l_tmp[13] = p_product[29]; l_tmp[14] = p_product[30]; l_tmp[15] = p_product[31]; l_tmp[16] = p_product[32]; l_tmp[17] = p_product[33]; l_tmp[18] = p_product[34]; l_tmp[19] = p_product[35]; l_tmp[20] = p_product[36]; l_tmp[21] = p_product[37]; l_tmp[22] = p_product[38]; l_tmp[23] = p_product[39]; l_carry += vli_add(p_result, p_result, l_tmp); l_tmp[0] = l_tmp[8] = p_product[40]; l_tmp[1] = l_tmp[9] = p_product[41]; l_tmp[2] = l_tmp[10] = p_product[42]; l_tmp[3] = l_tmp[11] = p_product[43]; l_tmp[4] = l_tmp[12] = p_product[44]; l_tmp[5] = l_tmp[13] = p_product[45]; l_tmp[6] = l_tmp[14] = p_product[46]; l_tmp[7] = l_tmp[15] = p_product[47]; l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0; l_carry += vli_add(p_result, p_result, l_tmp); while (l_carry || vli_cmp(curve_p, p_result) != 1) { l_carry -= vli_sub(p_result, p_result, curve_p); } } #elif uECC_WORD_SIZE == 4 static void vli_mmod_fast( uint32_t * RESTRICT p_result, uint32_t * RESTRICT p_product ) { uint32_t l_tmp[uECC_WORDS]; int l_carry; vli_set(p_result, p_product); vli_set(l_tmp, &p_product[6]); l_carry = vli_add(p_result, p_result, l_tmp); l_tmp[0] = l_tmp[1] = 0; l_tmp[2] = p_product[6]; l_tmp[3] = p_product[7]; l_tmp[4] = p_product[8]; l_tmp[5] = p_product[9]; l_carry += vli_add(p_result, p_result, l_tmp); l_tmp[0] = l_tmp[2] = p_product[10]; l_tmp[1] = l_tmp[3] = p_product[11]; l_tmp[4] = l_tmp[5] = 0; l_carry += vli_add(p_result, p_result, l_tmp); while (l_carry || vli_cmp(curve_p, p_result) != 1) { l_carry -= vli_sub(p_result, p_result, curve_p); } } #else static void vli_mmod_fast( uint64_t * RESTRICT p_result, uint64_t * RESTRICT p_product ) { uint64_t l_tmp[uECC_WORDS]; int l_carry; vli_set(p_result, p_product); vli_set(l_tmp, &p_product[3]); l_carry = vli_add(p_result, p_result, l_tmp); l_tmp[0] = 0; l_tmp[1] = p_product[3]; l_tmp[2] = p_product[4]; l_carry += vli_add(p_result, p_result, l_tmp); l_tmp[0] = l_tmp[1] = p_product[5]; l_tmp[2] = 0; l_carry += vli_add(p_result, p_result, l_tmp); while (l_carry || vli_cmp(curve_p, p_result) != 1) { l_carry -= vli_sub(p_result, p_result, curve_p); } } #endif /* uECC_WORD_SIZE */ #elif uECC_CURVE == uECC_secp256r1 /* Computes p_result = p_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 p_result, uint8_t * RESTRICT p_product ) { uint8_t l_tmp[uECC_BYTES]; int8_t l_carry; /* t */ vli_set(p_result, p_product); /* s1 */ l_tmp[0] = l_tmp[1] = l_tmp[2] = l_tmp[3] = 0; l_tmp[4] = l_tmp[5] = l_tmp[6] = l_tmp[7] = 0; l_tmp[8] = l_tmp[9] = l_tmp[10] = l_tmp[11] = 0; l_tmp[12] = p_product[44]; l_tmp[13] = p_product[45]; l_tmp[14] = p_product[46]; l_tmp[15] = p_product[47]; l_tmp[16] = p_product[48]; l_tmp[17] = p_product[49]; l_tmp[18] = p_product[50]; l_tmp[19] = p_product[51]; l_tmp[20] = p_product[52]; l_tmp[21] = p_product[53]; l_tmp[22] = p_product[54]; l_tmp[23] = p_product[55]; l_tmp[24] = p_product[56]; l_tmp[25] = p_product[57]; l_tmp[26] = p_product[58]; l_tmp[27] = p_product[59]; l_tmp[28] = p_product[60]; l_tmp[29] = p_product[61]; l_tmp[30] = p_product[62]; l_tmp[31] = p_product[63]; l_carry = vli_add(l_tmp, l_tmp, l_tmp); l_carry += vli_add(p_result, p_result, l_tmp); /* s2 */ l_tmp[12] = p_product[48]; l_tmp[13] = p_product[49]; l_tmp[14] = p_product[50]; l_tmp[15] = p_product[51]; l_tmp[16] = p_product[52]; l_tmp[17] = p_product[53]; l_tmp[18] = p_product[54]; l_tmp[19] = p_product[55]; l_tmp[20] = p_product[56]; l_tmp[21] = p_product[57]; l_tmp[22] = p_product[58]; l_tmp[23] = p_product[59]; l_tmp[24] = p_product[60]; l_tmp[25] = p_product[61]; l_tmp[26] = p_product[62]; l_tmp[27] = p_product[63]; l_tmp[28] = l_tmp[29] = l_tmp[30] = l_tmp[31] = 0; l_carry += vli_add(l_tmp, l_tmp, l_tmp); l_carry += vli_add(p_result, p_result, l_tmp); /* s3 */ l_tmp[0] = p_product[32]; l_tmp[1] = p_product[33]; l_tmp[2] = p_product[34]; l_tmp[3] = p_product[35]; l_tmp[4] = p_product[36]; l_tmp[5] = p_product[37]; l_tmp[6] = p_product[38]; l_tmp[7] = p_product[39]; l_tmp[8] = p_product[40]; l_tmp[9] = p_product[41]; l_tmp[10] = p_product[42]; l_tmp[11] = p_product[43]; l_tmp[12] = l_tmp[13] = l_tmp[14] = l_tmp[15] = 0; l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0; l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0; l_tmp[24] = p_product[56]; l_tmp[25] = p_product[57]; l_tmp[26] = p_product[58]; l_tmp[27] = p_product[59]; l_tmp[28] = p_product[60]; l_tmp[29] = p_product[61]; l_tmp[30] = p_product[62]; l_tmp[31] = p_product[63]; l_carry += vli_add(p_result, p_result, l_tmp); /* s4 */ l_tmp[0] = p_product[36]; l_tmp[1] = p_product[37]; l_tmp[2] = p_product[38]; l_tmp[3] = p_product[39]; l_tmp[4] = p_product[40]; l_tmp[5] = p_product[41]; l_tmp[6] = p_product[42]; l_tmp[7] = p_product[43]; l_tmp[8] = p_product[44]; l_tmp[9] = p_product[45]; l_tmp[10] = p_product[46]; l_tmp[11] = p_product[47]; l_tmp[12] = p_product[52]; l_tmp[13] = p_product[53]; l_tmp[14] = p_product[54]; l_tmp[15] = p_product[55]; l_tmp[16] = p_product[56]; l_tmp[17] = p_product[57]; l_tmp[18] = p_product[58]; l_tmp[19] = p_product[59]; l_tmp[20] = p_product[60]; l_tmp[21] = p_product[61]; l_tmp[22] = p_product[62]; l_tmp[23] = p_product[63]; l_tmp[24] = p_product[52]; l_tmp[25] = p_product[53]; l_tmp[26] = p_product[54]; l_tmp[27] = p_product[55]; l_tmp[28] = p_product[32]; l_tmp[29] = p_product[33]; l_tmp[30] = p_product[34]; l_tmp[31] = p_product[35]; l_carry += vli_add(p_result, p_result, l_tmp); /* d1 */ l_tmp[0] = p_product[44]; l_tmp[1] = p_product[45]; l_tmp[2] = p_product[46]; l_tmp[3] = p_product[47]; l_tmp[4] = p_product[48]; l_tmp[5] = p_product[49]; l_tmp[6] = p_product[50]; l_tmp[7] = p_product[51]; l_tmp[8] = p_product[52]; l_tmp[9] = p_product[53]; l_tmp[10] = p_product[54]; l_tmp[11] = p_product[55]; l_tmp[12] = l_tmp[13] = l_tmp[14] = l_tmp[15] = 0; l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0; l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0; l_tmp[24] = p_product[32]; l_tmp[25] = p_product[33]; l_tmp[26] = p_product[34]; l_tmp[27] = p_product[35]; l_tmp[28] = p_product[40]; l_tmp[29] = p_product[41]; l_tmp[30] = p_product[42]; l_tmp[31] = p_product[43]; l_carry -= vli_sub(p_result, p_result, l_tmp); /* d2 */ l_tmp[0] = p_product[48]; l_tmp[1] = p_product[49]; l_tmp[2] = p_product[50]; l_tmp[3] = p_product[51]; l_tmp[4] = p_product[52]; l_tmp[5] = p_product[53]; l_tmp[6] = p_product[54]; l_tmp[7] = p_product[55]; l_tmp[8] = p_product[56]; l_tmp[9] = p_product[57]; l_tmp[10] = p_product[58]; l_tmp[11] = p_product[59]; l_tmp[12] = p_product[60]; l_tmp[13] = p_product[61]; l_tmp[14] = p_product[62]; l_tmp[15] = p_product[63]; l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0; l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0; l_tmp[24] = p_product[36]; l_tmp[25] = p_product[37]; l_tmp[26] = p_product[38]; l_tmp[27] = p_product[39]; l_tmp[28] = p_product[44]; l_tmp[29] = p_product[45]; l_tmp[30] = p_product[46]; l_tmp[31] = p_product[47]; l_carry -= vli_sub(p_result, p_result, l_tmp); /* d3 */ l_tmp[0] = p_product[52]; l_tmp[1] = p_product[53]; l_tmp[2] = p_product[54]; l_tmp[3] = p_product[55]; l_tmp[4] = p_product[56]; l_tmp[5] = p_product[57]; l_tmp[6] = p_product[58]; l_tmp[7] = p_product[59]; l_tmp[8] = p_product[60]; l_tmp[9] = p_product[61]; l_tmp[10] = p_product[62]; l_tmp[11] = p_product[63]; l_tmp[12] = p_product[32]; l_tmp[13] = p_product[33]; l_tmp[14] = p_product[34]; l_tmp[15] = p_product[35]; l_tmp[16] = p_product[36]; l_tmp[17] = p_product[37]; l_tmp[18] = p_product[38]; l_tmp[19] = p_product[39]; l_tmp[20] = p_product[40]; l_tmp[21] = p_product[41]; l_tmp[22] = p_product[42]; l_tmp[23] = p_product[43]; l_tmp[24] = l_tmp[25] = l_tmp[26] = l_tmp[27] = 0; l_tmp[28] = p_product[48]; l_tmp[29] = p_product[49]; l_tmp[30] = p_product[50]; l_tmp[31] = p_product[51]; l_carry -= vli_sub(p_result, p_result, l_tmp); /* d4 */ l_tmp[0] = p_product[56]; l_tmp[1] = p_product[57]; l_tmp[2] = p_product[58]; l_tmp[3] = p_product[59]; l_tmp[4] = p_product[60]; l_tmp[5] = p_product[61]; l_tmp[6] = p_product[62]; l_tmp[7] = p_product[63]; l_tmp[8] = l_tmp[9] = l_tmp[10] = l_tmp[11] = 0; l_tmp[12] = p_product[36]; l_tmp[13] = p_product[37]; l_tmp[14] = p_product[38]; l_tmp[15] = p_product[39]; l_tmp[16] = p_product[40]; l_tmp[17] = p_product[41]; l_tmp[18] = p_product[42]; l_tmp[19] = p_product[43]; l_tmp[20] = p_product[44]; l_tmp[21] = p_product[45]; l_tmp[22] = p_product[46]; l_tmp[23] = p_product[47]; l_tmp[24] = l_tmp[25] = l_tmp[26] = l_tmp[27] = 0; l_tmp[28] = p_product[52]; l_tmp[29] = p_product[53]; l_tmp[30] = p_product[54]; l_tmp[31] = p_product[55]; l_carry -= vli_sub(p_result, p_result, l_tmp); if (l_carry < 0) { do { l_carry += vli_add(p_result, p_result, curve_p); } while (l_carry < 0); } else { while (l_carry || vli_cmp(curve_p, p_result) != 1) { l_carry -= vli_sub(p_result, p_result, curve_p); } } } #elif uECC_WORD_SIZE == 4 static void vli_mmod_fast( uint32_t * RESTRICT p_result, uint32_t * RESTRICT p_product ) { uint32_t l_tmp[uECC_WORDS]; int l_carry; /* t */ vli_set(p_result, p_product); /* s1 */ l_tmp[0] = l_tmp[1] = l_tmp[2] = 0; l_tmp[3] = p_product[11]; l_tmp[4] = p_product[12]; l_tmp[5] = p_product[13]; l_tmp[6] = p_product[14]; l_tmp[7] = p_product[15]; l_carry = vli_add(l_tmp, l_tmp, l_tmp); l_carry += vli_add(p_result, p_result, l_tmp); /* s2 */ l_tmp[3] = p_product[12]; l_tmp[4] = p_product[13]; l_tmp[5] = p_product[14]; l_tmp[6] = p_product[15]; l_tmp[7] = 0; l_carry += vli_add(l_tmp, l_tmp, l_tmp); l_carry += vli_add(p_result, p_result, l_tmp); /* s3 */ l_tmp[0] = p_product[8]; l_tmp[1] = p_product[9]; l_tmp[2] = p_product[10]; l_tmp[3] = l_tmp[4] = l_tmp[5] = 0; l_tmp[6] = p_product[14]; l_tmp[7] = p_product[15]; l_carry += vli_add(p_result, p_result, l_tmp); /* s4 */ l_tmp[0] = p_product[9]; l_tmp[1] = p_product[10]; l_tmp[2] = p_product[11]; l_tmp[3] = p_product[13]; l_tmp[4] = p_product[14]; l_tmp[5] = p_product[15]; l_tmp[6] = p_product[13]; l_tmp[7] = p_product[8]; l_carry += vli_add(p_result, p_result, l_tmp); /* d1 */ l_tmp[0] = p_product[11]; l_tmp[1] = p_product[12]; l_tmp[2] = p_product[13]; l_tmp[3] = l_tmp[4] = l_tmp[5] = 0; l_tmp[6] = p_product[8]; l_tmp[7] = p_product[10]; l_carry -= vli_sub(p_result, p_result, l_tmp); /* d2 */ l_tmp[0] = p_product[12]; l_tmp[1] = p_product[13]; l_tmp[2] = p_product[14]; l_tmp[3] = p_product[15]; l_tmp[4] = l_tmp[5] = 0; l_tmp[6] = p_product[9]; l_tmp[7] = p_product[11]; l_carry -= vli_sub(p_result, p_result, l_tmp); /* d3 */ l_tmp[0] = p_product[13]; l_tmp[1] = p_product[14]; l_tmp[2] = p_product[15]; l_tmp[3] = p_product[8]; l_tmp[4] = p_product[9]; l_tmp[5] = p_product[10]; l_tmp[6] = 0; l_tmp[7] = p_product[12]; l_carry -= vli_sub(p_result, p_result, l_tmp); /* d4 */ l_tmp[0] = p_product[14]; l_tmp[1] = p_product[15]; l_tmp[2] = 0; l_tmp[3] = p_product[9]; l_tmp[4] = p_product[10]; l_tmp[5] = p_product[11]; l_tmp[6] = 0; l_tmp[7] = p_product[13]; l_carry -= vli_sub(p_result, p_result, l_tmp); if (l_carry < 0) { do { l_carry += vli_add(p_result, p_result, curve_p); } while (l_carry < 0); } else { while (l_carry || vli_cmp(curve_p, p_result) != 1) { l_carry -= vli_sub(p_result, p_result, curve_p); } } } #else static void vli_mmod_fast( uint64_t * RESTRICT p_result, uint64_t * RESTRICT p_product ) { uint64_t l_tmp[uECC_WORDS]; int l_carry; /* t */ vli_set(p_result, p_product); /* s1 */ l_tmp[0] = 0; l_tmp[1] = p_product[5] & 0xffffffff00000000ull; l_tmp[2] = p_product[6]; l_tmp[3] = p_product[7]; l_carry = vli_add(l_tmp, l_tmp, l_tmp); l_carry += vli_add(p_result, p_result, l_tmp); /* s2 */ l_tmp[1] = p_product[6] << 32; l_tmp[2] = (p_product[6] >> 32) | (p_product[7] << 32); l_tmp[3] = p_product[7] >> 32; l_carry += vli_add(l_tmp, l_tmp, l_tmp); l_carry += vli_add(p_result, p_result, l_tmp); /* s3 */ l_tmp[0] = p_product[4]; l_tmp[1] = p_product[5] & 0xffffffff; l_tmp[2] = 0; l_tmp[3] = p_product[7]; l_carry += vli_add(p_result, p_result, l_tmp); /* s4 */ l_tmp[0] = (p_product[4] >> 32) | (p_product[5] << 32); l_tmp[1] = (p_product[5] >> 32) | (p_product[6] & 0xffffffff00000000ull); l_tmp[2] = p_product[7]; l_tmp[3] = (p_product[6] >> 32) | (p_product[4] << 32); l_carry += vli_add(p_result, p_result, l_tmp); /* d1 */ l_tmp[0] = (p_product[5] >> 32) | (p_product[6] << 32); l_tmp[1] = (p_product[6] >> 32); l_tmp[2] = 0; l_tmp[3] = (p_product[4] & 0xffffffff) | (p_product[5] << 32); l_carry -= vli_sub(p_result, p_result, l_tmp); /* d2 */ l_tmp[0] = p_product[6]; l_tmp[1] = p_product[7]; l_tmp[2] = 0; l_tmp[3] = (p_product[4] >> 32) | (p_product[5] & 0xffffffff00000000ull); l_carry -= vli_sub(p_result, p_result, l_tmp); /* d3 */ l_tmp[0] = (p_product[6] >> 32) | (p_product[7] << 32); l_tmp[1] = (p_product[7] >> 32) | (p_product[4] << 32); l_tmp[2] = (p_product[4] >> 32) | (p_product[5] << 32); l_tmp[3] = (p_product[6] << 32); l_carry -= vli_sub(p_result, p_result, l_tmp); /* d4 */ l_tmp[0] = p_product[7]; l_tmp[1] = p_product[4] & 0xffffffff00000000ull; l_tmp[2] = p_product[5]; l_tmp[3] = p_product[6] & 0xffffffff00000000ull; l_carry -= vli_sub(p_result, p_result, l_tmp); if (l_carry < 0) { do { l_carry += vli_add(p_result, p_result, curve_p); } while (l_carry < 0); } else { while (l_carry || vli_cmp(curve_p, p_result) != 1) { l_carry -= vli_sub(p_result, p_result, curve_p); } } } #endif /* uECC_WORD_SIZE */ #elif uECC_CURVE == uECC_secp256k1 #if uECC_WORD_SIZE == 1 static void omega_mult( uint8_t * RESTRICT p_result, uint8_t * RESTRICT p_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, p_right[0], &r0, &r1, &r2); p_result[0] = r0; r0 = r1; r1 = r2; /* r2 is still 0 */ for (k = 1; k < uECC_WORDS; ++k) { muladd(0x03, p_right[k - 1], &r0, &r1, &r2); muladd(0xD1, p_right[k], &r0, &r1, &r2); p_result[k] = r0; r0 = r1; r1 = r2; r2 = 0; } muladd(0x03, p_right[uECC_WORDS - 1], &r0, &r1, &r2); p_result[uECC_WORDS] = r0; p_result[uECC_WORDS + 1] = r1; p_result[4 + uECC_WORDS] = vli_add(p_result + 4, p_result + 4, p_right); /* add the 2^32 multiple */ } #elif uECC_WORD_SIZE == 4 static void omega_mult( uint32_t * RESTRICT p_result, uint32_t * RESTRICT p_right ) { /* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ uint32_t l_carry = 0; wordcount_t k; for (k = 0; k < uECC_WORDS; ++k) { uint64_t p = (uint64_t) 0x3D1 * p_right[k] + l_carry; p_result[k] = (p & 0xffffffff); l_carry = p >> 32; } p_result[uECC_WORDS] = l_carry; p_result[1 + uECC_WORDS] = vli_add(p_result + 1, p_result + 1, p_right); /* add the 2^32 multiple */ } #else static void omega_mult( uint64_t * RESTRICT p_result, uint64_t * RESTRICT p_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, p_right[k], &r0, &r1, &r2); p_result[k] = r0; r0 = r1; r1 = r2; r2 = 0; } p_result[uECC_WORDS] = r0; } #endif /* uECC_WORD_SIZE */ #endif /* uECC_CURVE */ #endif /* !asm_mmod_fast */ /* Computes p_result = (p_left * p_right) % curve_p. */ static void vli_modMult_fast( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_product[2 * uECC_WORDS]; vli_mult(l_product, p_left, p_right); vli_mmod_fast(p_result, l_product); } #if uECC_SQUARE_FUNC /* Computes p_result = p_left^2 % curve_p. */ static void vli_modSquare_fast( uECC_word_t * p_result, uECC_word_t * p_left ) { uECC_word_t l_product[2 * uECC_WORDS]; vli_square(l_product, p_left); vli_mmod_fast(p_result, l_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 p_result = (1 / p_input) % p_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 * p_result, uECC_word_t * p_input, uECC_word_t * p_mod ) { uECC_word_t a[uECC_WORDS], b[uECC_WORDS], u[uECC_WORDS], v[uECC_WORDS]; uECC_word_t l_carry; cmpresult_t l_cmpResult; if (vli_isZero(p_input)) { vli_clear(p_result); return; } vli_set(a, p_input); vli_set(b, p_mod); vli_clear(u); u[0] = 1; vli_clear(v); while ((l_cmpResult = vli_cmp(a, b)) != 0) { l_carry = 0; if (EVEN(a)) { vli_rshift1(a); if (!EVEN(u)) { l_carry = vli_add(u, u, p_mod); } vli_rshift1(u); if (l_carry) { u[uECC_WORDS - 1] |= HIGH_BIT_SET; } } else if (EVEN(b)) { vli_rshift1(b); if (!EVEN(v)) { l_carry = vli_add(v, v, p_mod); } vli_rshift1(v); if (l_carry) { v[uECC_WORDS - 1] |= HIGH_BIT_SET; } } else if (l_cmpResult > 0) { vli_sub(a, a, b); vli_rshift1(a); if (vli_cmp(u, v) < 0) { vli_add(u, u, p_mod); } vli_sub(u, u, v); if (!EVEN(u)) { l_carry = vli_add(u, u, p_mod); } vli_rshift1(u); if (l_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, p_mod); } vli_sub(v, v, u); if (!EVEN(v)) { l_carry = vli_add(v, v, p_mod); } vli_rshift1(v); if (l_carry) { v[uECC_WORDS - 1] |= HIGH_BIT_SET; } } } vli_set(p_result, u); } #endif /* !asm_modInv */ /* ------ Point operations ------ */ /* Returns 1 if p_point is the point at infinity, 0 otherwise. */ static cmpresult_t EccPoint_isZero( EccPoint * p_point ) { return (vli_isZero(p_point->x) && vli_isZero(p_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 l_carry = vli_add(Y1, Y1, curve_p); vli_rshift1(Y1); Y1[uECC_WORDS - 1] |= l_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, 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 p_initialZ ) { uECC_word_t z[uECC_WORDS]; vli_set(X2, X1); vli_set(Y2, Y1); vli_clear(z); z[0] = 1; if (p_initialZ) { vli_set(z, p_initialZ); } 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); /* t4 = 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) */ vli_modAdd(t6, X1, X2, curve_p); /* t6 = B + C */ vli_modSquare_fast(X2, Y2); /* t3 = (y2 - y1)^2 */ vli_modSub_fast(X2, X2, t6); /* t3 = 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 = y3 */ vli_modSquare_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */ vli_modSub_fast(t7, t7, t6); /* t7 = 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 = y3' */ vli_set(X1, t7); } static void EccPoint_mult( EccPoint * RESTRICT p_result, EccPoint * RESTRICT p_point, const uECC_word_t * RESTRICT p_scalar, const uECC_word_t * RESTRICT p_initialZ, bitcount_t p_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], p_point->x); vli_set(Ry[1], p_point->y); XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], p_initialZ); for (i = p_numBits - 2; i > 0; --i) { nb = !vli_testBit(p_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(p_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, p_point->x); /* xP * Yb * (X1 - X0) */ vli_modInv(z, z, curve_p); /* 1 / (xP * Yb * (X1 - X0)) */ vli_modMult_fast(z, z, p_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(p_result->x, Rx[0]); vli_set(p_result->y, Ry[0]); } /* 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); } #if uECC_WORD_SIZE == 1 static void vli_nativeToBytes( uint8_t * RESTRICT p_dest, const uint8_t * RESTRICT p_src ) { uint8_t i; for (i = 0; i < uECC_BYTES; ++i) { p_dest[i] = p_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 * p_bytes, const uint32_t * p_native ) { unsigned i; for (i = 0; i < uECC_WORDS; ++i) { uint8_t *p_digit = p_bytes + 4 * (uECC_WORDS - 1 - i); p_digit[0] = p_native[i] >> 24; p_digit[1] = p_native[i] >> 16; p_digit[2] = p_native[i] >> 8; p_digit[3] = p_native[i]; } } static void vli_bytesToNative( uint32_t * p_native, const uint8_t * p_bytes ) { unsigned i; for (i = 0; i < uECC_WORDS; ++i) { const uint8_t *p_digit = p_bytes + 4 * (uECC_WORDS - 1 - i); p_native[i] = ((uint32_t) p_digit[0] << 24) | ((uint32_t) p_digit[1] << 16) | ((uint32_t) p_digit[2] << 8) | (uint32_t) p_digit[3]; } } #else static void vli_nativeToBytes( uint8_t * p_bytes, const uint64_t * p_native ) { unsigned i; for (i = 0; i < uECC_WORDS; ++i) { uint8_t *p_digit = p_bytes + 8 * (uECC_WORDS - 1 - i); p_digit[0] = p_native[i] >> 56; p_digit[1] = p_native[i] >> 48; p_digit[2] = p_native[i] >> 40; p_digit[3] = p_native[i] >> 32; p_digit[4] = p_native[i] >> 24; p_digit[5] = p_native[i] >> 16; p_digit[6] = p_native[i] >> 8; p_digit[7] = p_native[i]; } } static void vli_bytesToNative( uint64_t * p_native, const uint8_t * p_bytes ) { unsigned i; for (i = 0; i < uECC_WORDS; ++i) { const uint8_t *p_digit = p_bytes + 8 * (uECC_WORDS - 1 - i); p_native[i] = ((uint64_t) p_digit[0] << 56) | ((uint64_t) p_digit[1] << 48) | ((uint64_t) p_digit[2] << 40) | ((uint64_t) p_digit[3] << 32) | ((uint64_t) p_digit[4] << 24) | ((uint64_t) p_digit[5] << 16) | ((uint64_t) p_digit[6] << 8) | (uint64_t) p_digit[7]; } } #endif /* uECC_WORD_SIZE */ int uECC_make_key( uint8_t p_publicKey[uECC_BYTES * 2], uint8_t p_privateKey[uECC_BYTES] ) { EccPoint l_public; uECC_word_t l_private[uECC_WORDS]; uECC_word_t l_tries = 0; do { repeat: if (!g_rng((uint8_t *) l_private, sizeof(l_private)) || (l_tries++ >= MAX_TRIES)) { return 0; } if (vli_isZero(l_private)) { goto repeat; } /* Make sure the private key is in the range [1, n-1]. */ #if uECC_CURVE != uECC_secp160r1 if (vli_cmp(curve_n, l_private) != 1) { goto repeat; } #endif EccPoint_mult(&l_public, &curve_G, l_private, 0, vli_numBits(l_private, uECC_WORDS)); } while (EccPoint_isZero(&l_public)); vli_nativeToBytes(p_privateKey, l_private); vli_nativeToBytes(p_publicKey, l_public.x); vli_nativeToBytes(p_publicKey + uECC_BYTES, l_public.y); return 1; } int uECC_shared_secret( const uint8_t p_publicKey[uECC_BYTES * 2], const uint8_t p_privateKey[uECC_BYTES], uint8_t p_secret[uECC_BYTES], uint32_t l_random[uECC_WORDS] ) { EccPoint l_public; uECC_word_t l_private[uECC_WORDS]; vli_bytesToNative(l_private, p_privateKey); vli_bytesToNative(l_public.x, p_publicKey); vli_bytesToNative(l_public.y, p_publicKey + uECC_BYTES); EccPoint l_product; EccPoint_mult(&l_product, &l_public, l_private, (vli_isZero(l_random) ? 0 : l_random), vli_numBits(l_private, uECC_WORDS)); vli_nativeToBytes(p_secret, l_product.x); return !EccPoint_isZero(&l_product); } void uECC_compress( const uint8_t p_publicKey[uECC_BYTES * 2], uint8_t p_compressed[uECC_BYTES + 1] ) { wordcount_t i; for (i = 0; i < uECC_BYTES; ++i) { p_compressed[i + 1] = p_publicKey[i]; } p_compressed[0] = 2 + (p_publicKey[uECC_BYTES * 2 - 1] & 0x01); } void uECC_decompress( const uint8_t p_compressed[uECC_BYTES + 1], uint8_t p_publicKey[uECC_BYTES * 2] ) { EccPoint l_point; vli_bytesToNative(l_point.x, p_compressed + 1); #if (uECC_CURVE == uECC_secp256k1) vli_modSquare_fast(l_point.y, l_point.x); /* r = x^2 */ vli_modMult_fast(l_point.y, l_point.y, l_point.x); /* r = x^3 */ vli_modAdd(l_point.y, l_point.y, curve_b, curve_p); /* r = x^3 + b */ #else uECC_word_t _3[uECC_WORDS] = { 3 }; /* -a = 3 */ vli_modSquare_fast(l_point.y, l_point.x); /* y = x^2 */ vli_modSub_fast(l_point.y, l_point.y, _3); /* y = x^2 - 3 */ vli_modMult_fast(l_point.y, l_point.y, l_point.x); /* y = x^3 - 3x */ vli_modAdd(l_point.y, l_point.y, curve_b, curve_p); /* y = x^3 - 3x + b */ #endif mod_sqrt(l_point.y); if ((l_point.y[0] & 0x01) != (p_compressed[0] & 0x01)) { vli_sub(l_point.y, curve_p, l_point.y); } vli_nativeToBytes(p_publicKey, l_point.x); vli_nativeToBytes(p_publicKey + uECC_BYTES, l_point.y); } /* -------- ECDSA code -------- */ #if (uECC_CURVE == uECC_secp160r1) static void vli_clear_n( uECC_word_t * p_vli ) { vli_clear(p_vli); p_vli[uECC_N_WORDS - 1] = 0; } static uECC_word_t vli_isZero_n( const uECC_word_t * p_vli ) { if (p_vli[uECC_N_WORDS - 1]) { return 0; } return vli_isZero(p_vli); } static void vli_set_n( uECC_word_t * p_dest, const uECC_word_t * p_src ) { vli_set(p_dest, p_src); p_dest[uECC_N_WORDS - 1] = p_src[uECC_N_WORDS - 1]; } static cmpresult_t vli_cmp_n( uECC_word_t * p_left, uECC_word_t * p_right ) { if (p_left[uECC_N_WORDS - 1] > p_right[uECC_N_WORDS - 1]) { return 1; } else if (p_left[uECC_N_WORDS - 1] < p_right[uECC_N_WORDS - 1]) { return -1; } return vli_cmp(p_left, p_right); } static void vli_rshift1_n( uECC_word_t * p_vli ) { vli_rshift1(p_vli); p_vli[uECC_N_WORDS - 2] |= p_vli[uECC_N_WORDS - 1] << (uECC_WORD_BITS - 1); p_vli[uECC_N_WORDS - 1] = p_vli[uECC_N_WORDS - 1] >> 1; } static uECC_word_t vli_add_n( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_carry = vli_add(p_result, p_left, p_right); uECC_word_t l_sum = p_left[uECC_N_WORDS - 1] + p_right[uECC_N_WORDS - 1] + l_carry; if (l_sum != p_left[uECC_N_WORDS - 1]) { l_carry = (l_sum < p_left[uECC_N_WORDS - 1]); } p_result[uECC_N_WORDS - 1] = l_sum; return l_carry; } static uECC_word_t vli_sub_n( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_borrow = vli_sub(p_result, p_left, p_right); uECC_word_t l_diff = p_left[uECC_N_WORDS - 1] - p_right[uECC_N_WORDS - 1] - l_borrow; if (l_diff != p_left[uECC_N_WORDS - 1]) { l_borrow = (l_diff > p_left[uECC_N_WORDS - 1]); } p_result[uECC_N_WORDS - 1] = l_diff; return l_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 * p_result, uECC_word_t * p_left, uECC_word_t * p_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 l_min = (k < uECC_N_WORDS ? 0 : (k + 1) - uECC_N_WORDS); wordcount_t l_max = (k < uECC_N_WORDS ? k : uECC_N_WORDS - 1); for (i = l_min; i <= l_max; ++i) { muladd(p_left[i], p_right[k - i], &r0, &r1, &r2); } p_result[k] = r0; r0 = r1; r1 = r2; r2 = 0; } p_result[uECC_N_WORDS * 2 - 1] = r0; } static void vli_modAdd_n( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right, uECC_word_t * p_mod ) { uECC_word_t l_carry = vli_add_n(p_result, p_left, p_right); if (l_carry || vli_cmp_n(p_result, p_mod) >= 0) { vli_sub_n(p_result, p_result, p_mod); } } static void vli_modInv_n( uECC_word_t * p_result, uECC_word_t * p_input, uECC_word_t * p_mod ) { uECC_word_t a[uECC_N_WORDS], b[uECC_N_WORDS], u[uECC_N_WORDS], v[uECC_N_WORDS]; uECC_word_t l_carry; cmpresult_t l_cmpResult; if (vli_isZero_n(p_input)) { vli_clear_n(p_result); return; } vli_set_n(a, p_input); vli_set_n(b, p_mod); vli_clear_n(u); u[0] = 1; vli_clear_n(v); while ((l_cmpResult = vli_cmp_n(a, b)) != 0) { l_carry = 0; if (EVEN(a)) { vli_rshift1_n(a); if (!EVEN(u)) l_carry = vli_add_n(u, u, p_mod); vli_rshift1_n(u); if (l_carry) u[uECC_N_WORDS - 1] |= HIGH_BIT_SET; } else if (EVEN(b)) { vli_rshift1_n(b); if (!EVEN(v)) l_carry = vli_add_n(v, v, p_mod); vli_rshift1_n(v); if (l_carry) v[uECC_N_WORDS - 1] |= HIGH_BIT_SET; } else if (l_cmpResult > 0) { vli_sub_n(a, a, b); vli_rshift1_n(a); if (vli_cmp_n(u, v) < 0) vli_add_n(u, u, p_mod); vli_sub_n(u, u, v); if (!EVEN(u)) l_carry = vli_add_n(u, u, p_mod); vli_rshift1_n(u); if (l_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, p_mod); vli_sub_n(v, v, u); if (!EVEN(v)) l_carry = vli_add_n(v, v, p_mod); vli_rshift1_n(v); if (l_carry) v[uECC_N_WORDS - 1] |= HIGH_BIT_SET; } } vli_set_n(p_result, u); } static void vli2_rshift1_n( uECC_word_t * p_vli ) { vli_rshift1_n(p_vli); p_vli[uECC_N_WORDS - 1] |= p_vli[uECC_N_WORDS] << (uECC_WORD_BITS - 1); vli_rshift1_n(p_vli + uECC_N_WORDS); } static uECC_word_t vli2_sub_n( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_borrow = 0; wordcount_t i; for (i = 0; i < uECC_N_WORDS * 2; ++i) { uECC_word_t l_diff = p_left[i] - p_right[i] - l_borrow; if (l_diff != p_left[i]) { l_borrow = (l_diff > p_left[i]); } p_result[i] = l_diff; } return l_borrow; } /* Computes p_result = (p_left * p_right) % curve_n. */ static void vli_modMult_n( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_product[2 * uECC_N_WORDS]; uECC_word_t l_modMultiple[2 * uECC_N_WORDS]; uECC_word_t l_tmp[2 * uECC_N_WORDS]; uECC_word_t *v[2] = { l_tmp, l_product }; vli_mult_n(l_product, p_left, p_right); vli_clear_n(l_modMultiple); vli_set(l_modMultiple + uECC_N_WORDS + 1, curve_n); vli_rshift1(l_modMultiple + uECC_N_WORDS + 1); l_modMultiple[2 * uECC_N_WORDS - 1] |= HIGH_BIT_SET; l_modMultiple[uECC_N_WORDS] = HIGH_BIT_SET; bitcount_t i; uECC_word_t l_index = 1; for (i = 0; i <= ((((bitcount_t) uECC_N_WORDS) << uECC_WORD_BITS_SHIFT) + (uECC_WORD_BITS - 1)); ++i) { uECC_word_t l_borrow = vli2_sub_n(v[1 - l_index], v[l_index], l_modMultiple); l_index = !(l_index ^ l_borrow); /* Swap the index if there was no borrow */ vli2_rshift1_n(l_modMultiple); } vli_set_n(p_result, v[l_index]); } #else #define vli_modInv_n vli_modInv #define vli_modAdd_n vli_modAdd static void vli2_rshift1( uECC_word_t * p_vli ) { vli_rshift1(p_vli); p_vli[uECC_WORDS - 1] |= p_vli[uECC_WORDS] << (uECC_WORD_BITS - 1); vli_rshift1(p_vli + uECC_WORDS); } static uECC_word_t vli2_sub( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_borrow = 0; wordcount_t i; for (i = 0; i < uECC_WORDS * 2; ++i) { uECC_word_t l_diff = p_left[i] - p_right[i] - l_borrow; if (l_diff != p_left[i]) { l_borrow = (l_diff > p_left[i]); } p_result[i] = l_diff; } return l_borrow; } /* Computes p_result = (p_left * p_right) % curve_n. */ static void vli_modMult_n( uECC_word_t * p_result, uECC_word_t * p_left, uECC_word_t * p_right ) { uECC_word_t l_product[2 * uECC_WORDS]; uECC_word_t l_modMultiple[2 * uECC_WORDS]; uECC_word_t l_tmp[2 * uECC_WORDS]; uECC_word_t *v[2] = { l_tmp, l_product }; vli_mult(l_product, p_left, p_right); vli_set(l_modMultiple + uECC_WORDS, curve_n); /* works if curve_n has its highest bit set */ vli_clear(l_modMultiple); bitcount_t i; uECC_word_t l_index = 1; for (i = 0; i <= uECC_BYTES * 8; ++i) { uECC_word_t l_borrow = vli2_sub(v[1 - l_index], v[l_index], l_modMultiple); l_index = !(l_index ^ l_borrow); /* Swap the index if there was no borrow */ vli2_rshift1(l_modMultiple); } vli_set(p_result, v[l_index]); } #endif /* (uECC_CURVE != uECC_secp160r1) */ int uECC_sign( const uint8_t p_privateKey[uECC_BYTES], const uint8_t p_hash[uECC_BYTES], uint8_t p_signature[uECC_BYTES * 2] ) { uECC_word_t k[uECC_N_WORDS]; uECC_word_t l_tmp[uECC_N_WORDS]; uECC_word_t s[uECC_N_WORDS]; uECC_word_t *k2[2] = { l_tmp, s }; EccPoint p; uECC_word_t l_tries = 0; do { repeat: if (!g_rng((uint8_t *) k, sizeof(k)) || (l_tries++ >= MAX_TRIES)) { return 0; } if (vli_isZero(k)) { goto repeat; } #if (uECC_CURVE == uECC_secp160r1) k[uECC_WORDS] &= 0x01; if (vli_cmp_n(curve_n, k) != 1) { goto repeat; } /* make sure that we don't leak timing information about k. See http://eprint.iacr.org/2011/232.pdf */ vli_add_n(l_tmp, k, curve_n); uECC_word_t l_carry = (l_tmp[uECC_WORDS] & 0x02); vli_add_n(s, l_tmp, curve_n); /* p = k * G */ EccPoint_mult(&p, &curve_G, k2[!l_carry], 0, (uECC_BYTES * 8) + 2); #else if (vli_cmp(curve_n, k) != 1) { goto repeat; } /* make sure that we don't leak timing information about k. See http://eprint.iacr.org/2011/232.pdf */ uECC_word_t l_carry = vli_add(l_tmp, k, curve_n); vli_add(s, l_tmp, curve_n); /* p = k * G */ EccPoint_mult(&p, &curve_G, k2[!l_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 } while (vli_isZero(p.x)); l_tries = 0; do { if (!g_rng((uint8_t *) l_tmp, sizeof(l_tmp)) || (l_tries++ >= MAX_TRIES)) { return 0; } } while (vli_isZero(l_tmp)); /* 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, l_tmp); /* k' = rand * k */ vli_modInv_n(k, k, curve_n); /* k = 1 / k' */ vli_modMult_n(k, k, l_tmp); /* k = 1 / k */ vli_nativeToBytes(p_signature, p.x); /* store r */ l_tmp[uECC_N_WORDS - 1] = 0; vli_bytesToNative(l_tmp, p_privateKey); /* tmp = d */ s[uECC_N_WORDS - 1] = 0; vli_set(s, p.x); vli_modMult_n(s, l_tmp, s); /* s = r*d */ vli_bytesToNative(l_tmp, p_hash); vli_modAdd_n(s, l_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]) { goto repeat; } #endif vli_nativeToBytes(p_signature + uECC_BYTES, s); return 1; } static bitcount_t smax( bitcount_t a, bitcount_t b ) { return (a > b ? a : b); } int uECC_verify( const uint8_t p_publicKey[uECC_BYTES * 2], const uint8_t p_hash[uECC_BYTES], const uint8_t p_signature[uECC_BYTES * 2] ) { uECC_word_t u1[uECC_N_WORDS], u2[uECC_N_WORDS]; uECC_word_t z[uECC_N_WORDS]; EccPoint l_public, l_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]; 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(l_public.x, p_publicKey); vli_bytesToNative(l_public.y, p_publicKey + uECC_BYTES); vli_bytesToNative(r, p_signature); vli_bytesToNative(s, p_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, p_hash); vli_modMult_n(u1, u1, z); /* u1 = e/s */ vli_modMult_n(u2, r, z); /* u2 = r/s */ /* Calculate l_sum = G + Q. */ vli_set(l_sum.x, l_public.x); vli_set(l_sum.y, l_public.y); vli_set(tx, curve_G.x); vli_set(ty, curve_G.y); vli_modSub_fast(z, l_sum.x, tx); /* Z = x2 - x1 */ XYcZ_add(tx, ty, l_sum.x, l_sum.y); vli_modInv(z, z, curve_p); /* Z = 1/Z */ apply_z(l_sum.x, l_sum.y, z); /* Use Shamir's trick to calculate u1*G + u2*Q */ EccPoint *l_points[4] = { 0, &curve_G, &l_public, &l_sum }; bitcount_t l_numBits = smax(vli_numBits(u1, uECC_N_WORDS), vli_numBits(u2, uECC_N_WORDS)); EccPoint *l_point = l_points[(! !vli_testBit(u1, l_numBits - 1)) | ((! !vli_testBit(u2, l_numBits - 1)) << 1)]; vli_set(rx, l_point->x); vli_set(ry, l_point->y); vli_clear(z); z[0] = 1; bitcount_t i; for (i = l_numBits - 2; i >= 0; --i) { EccPoint_double_jacobian(rx, ry, z); uECC_word_t l_index = (! !vli_testBit(u1, i)) | ((! !vli_testBit(u2, i)) << 1); l_point = l_points[l_index]; if (l_point) { vli_set(tx, l_point->x); vli_set(ty, l_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); } int uECC_bytes( ) { return uECC_BYTES; } int uECC_curve( ) { return uECC_CURVE; } #endif /* USE_BSD_ECC_LIB */