1 /* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */ 2 3 #include "uECC.h" 4 5 // NULL 6 #include "stddef.h" 7 8 // suppress MSVC C4244: conversion from uECC_word_t to int 9 #ifdef _MSC_VER 10 #pragma warning( disable : 4244 ) 11 #endif 12 13 #ifndef uECC_PLATFORM 14 #if __AVR__ 15 #define uECC_PLATFORM uECC_avr 16 #elif defined(__thumb2__) || defined(_M_ARMT) /* I think MSVC only supports Thumb-2 targets */ 17 #define uECC_PLATFORM uECC_arm_thumb2 18 #elif defined(__thumb__) 19 #define uECC_PLATFORM uECC_arm_thumb 20 #elif defined(__arm__) || defined(_M_ARM) 21 #define uECC_PLATFORM uECC_arm 22 #elif defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__I86__) 23 #define uECC_PLATFORM uECC_x86 24 #elif defined(__amd64__) || defined(_M_X64) 25 #define uECC_PLATFORM uECC_x86_64 26 #else 27 #define uECC_PLATFORM uECC_arch_other 28 #endif 29 #endif 30 31 #ifndef uECC_WORD_SIZE 32 #if uECC_PLATFORM == uECC_avr 33 #define uECC_WORD_SIZE 1 34 #elif (uECC_PLATFORM == uECC_x86_64) 35 #define uECC_WORD_SIZE 8 36 #else 37 #define uECC_WORD_SIZE 4 38 #endif 39 #endif 40 41 #if (uECC_CURVE == uECC_secp160r1 || uECC_CURVE == uECC_secp224r1) && (uECC_WORD_SIZE == 8) 42 #undef uECC_WORD_SIZE 43 #define uECC_WORD_SIZE 4 44 #if (uECC_PLATFORM == uECC_x86_64) 45 #undef uECC_PLATFORM 46 #define uECC_PLATFORM uECC_x86 47 #endif 48 #endif 49 50 #if (uECC_WORD_SIZE != 1) && (uECC_WORD_SIZE != 4) && (uECC_WORD_SIZE != 8) 51 #error "Unsupported value for uECC_WORD_SIZE" 52 #endif 53 54 #if (uECC_ASM && (uECC_PLATFORM == uECC_avr) && (uECC_WORD_SIZE != 1)) 55 #pragma message ("uECC_WORD_SIZE must be 1 when using AVR asm") 56 #undef uECC_WORD_SIZE 57 #define uECC_WORD_SIZE 1 58 #endif 59 60 #if (uECC_ASM && \ 61 (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb) && \ 62 (uECC_WORD_SIZE != 4)) 63 #pragma message ("uECC_WORD_SIZE must be 4 when using ARM asm") 64 #undef uECC_WORD_SIZE 65 #define uECC_WORD_SIZE 4 66 #endif 67 68 #if __STDC_VERSION__ >= 199901L 69 #define RESTRICT restrict 70 #else 71 #define RESTRICT 72 #endif 73 74 #if defined(__SIZEOF_INT128__) || ((__clang_major__ * 100 + __clang_minor__) >= 302) 75 #define SUPPORTS_INT128 1 76 #else 77 #define SUPPORTS_INT128 0 78 #endif 79 80 #define MAX_TRIES 64 81 82 #if (uECC_WORD_SIZE == 1) 83 84 typedef uint8_t uECC_word_t; 85 typedef uint16_t uECC_dword_t; 86 typedef uint8_t wordcount_t; 87 typedef int8_t swordcount_t; 88 typedef int16_t bitcount_t; 89 typedef int8_t cmpresult_t; 90 91 #define HIGH_BIT_SET 0x80 92 #define uECC_WORD_BITS 8 93 #define uECC_WORD_BITS_SHIFT 3 94 #define uECC_WORD_BITS_MASK 0x07 95 96 #define uECC_WORDS_1 20 97 #define uECC_WORDS_2 24 98 #define uECC_WORDS_3 32 99 #define uECC_WORDS_4 32 100 #define uECC_WORDS_5 28 101 102 #define uECC_N_WORDS_1 21 103 #define uECC_N_WORDS_2 24 104 #define uECC_N_WORDS_3 32 105 #define uECC_N_WORDS_4 32 106 #define uECC_N_WORDS_5 28 107 108 #define Curve_P_1 {0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, \ 109 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 110 0xFF, 0xFF, 0xFF, 0xFF} 111 #define Curve_P_2 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 112 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 113 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF} 114 #define Curve_P_3 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 115 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, \ 116 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \ 117 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF} 118 #define Curve_P_4 {0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, \ 119 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 120 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 121 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF} 122 #define Curve_P_5 {0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \ 123 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, \ 124 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 125 0xFF, 0xFF, 0xFF, 0xFF} 126 127 #define Curve_B_1 {0x45, 0xFA, 0x65, 0xC5, 0xAD, 0xD4, 0xD4, 0x81, \ 128 0x9F, 0xF8, 0xAC, 0x65, 0x8B, 0x7A, 0xBD, 0x54, \ 129 0xFC, 0xBE, 0x97, 0x1C} 130 #define Curve_B_2 {0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE, \ 131 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F, \ 132 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64} 133 #define Curve_B_3 {0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B, \ 134 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65, \ 135 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3, \ 136 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A} 137 #define Curve_B_4 {0x07, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \ 138 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \ 139 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \ 140 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00} 141 #define Curve_B_5 {0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27, \ 142 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50, \ 143 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C, \ 144 0x85, 0x0A, 0x05, 0xB4} 145 146 #define Curve_G_1 { \ 147 {0x82, 0xFC, 0xCB, 0x13, 0xB9, 0x8B, 0xC3, 0x68, \ 148 0x89, 0x69, 0x64, 0x46, 0x28, 0x73, 0xF5, 0x8E, \ 149 0x68, 0xB5, 0x96, 0x4A}, \ 150 {0x32, 0xFB, 0xC5, 0x7A, 0x37, 0x51, 0x23, 0x04, \ 151 0x12, 0xC9, 0xDC, 0x59, 0x7D, 0x94, 0x68, 0x31, \ 152 0x55, 0x28, 0xA6, 0x23}} 153 154 #define Curve_G_2 { \ 155 {0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4, \ 156 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C, \ 157 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18}, \ 158 {0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73, \ 159 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63, \ 160 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07}} 161 162 #define Curve_G_3 { \ 163 {0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4, \ 164 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77, \ 165 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8, \ 166 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B}, \ 167 {0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB, \ 168 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B, \ 169 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E, \ 170 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F}} 171 172 #define Curve_G_4 { \ 173 {0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59, \ 174 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02, \ 175 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55, \ 176 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79}, \ 177 {0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C, \ 178 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD, \ 179 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D, \ 180 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48}} 181 182 #define Curve_G_5 { \ 183 {0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34, \ 184 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A, \ 185 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B, \ 186 0xBD, 0x0C, 0x0E, 0xB7}, \ 187 {0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44, \ 188 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD, \ 189 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5, \ 190 0x88, 0x63, 0x37, 0xBD}} 191 192 #define Curve_N_1 {0x57, 0x22, 0x75, 0xCA, 0xD3, 0xAE, 0x27, 0xF9, \ 193 0xC8, 0xF4, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, \ 194 0x00, 0x00, 0x00, 0x00, 0x01} 195 #define Curve_N_2 {0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14, \ 196 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF, \ 197 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF} 198 #define Curve_N_3 {0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3, \ 199 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC, \ 200 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 201 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF} 202 #define Curve_N_4 {0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF, \ 203 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA, \ 204 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 205 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF} 206 #define Curve_N_5 {0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13, \ 207 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF, \ 208 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \ 209 0xFF, 0xFF, 0xFF, 0xFF} 210 211 #elif (uECC_WORD_SIZE == 4) 212 213 typedef uint32_t uECC_word_t; 214 typedef uint64_t uECC_dword_t; 215 typedef unsigned wordcount_t; 216 typedef int swordcount_t; 217 typedef int bitcount_t; 218 typedef int cmpresult_t; 219 220 #define HIGH_BIT_SET 0x80000000 221 #define uECC_WORD_BITS 32 222 #define uECC_WORD_BITS_SHIFT 5 223 #define uECC_WORD_BITS_MASK 0x01F 224 225 #define uECC_WORDS_1 5 226 #define uECC_WORDS_2 6 227 #define uECC_WORDS_3 8 228 #define uECC_WORDS_4 8 229 #define uECC_WORDS_5 7 230 231 #define uECC_N_WORDS_1 6 232 #define uECC_N_WORDS_2 6 233 #define uECC_N_WORDS_3 8 234 #define uECC_N_WORDS_4 8 235 #define uECC_N_WORDS_5 7 236 237 #define Curve_P_1 {0x7FFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} 238 #define Curve_P_2 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} 239 #define Curve_P_3 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, \ 240 0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF} 241 #define Curve_P_4 {0xFFFFFC2F, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, \ 242 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} 243 #define Curve_P_5 {0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFF, \ 244 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} 245 246 #define Curve_B_1 {0xC565FA45, 0x81D4D4AD, 0x65ACF89F, 0x54BD7A8B, 0x1C97BEFC} 247 #define Curve_B_2 {0xC146B9B1, 0xFEB8DEEC, 0x72243049, 0x0FA7E9AB, 0xE59C80E7, 0x64210519} 248 #define Curve_B_3 {0x27D2604B, 0x3BCE3C3E, 0xCC53B0F6, 0x651D06B0, \ 249 0x769886BC, 0xB3EBBD55, 0xAA3A93E7, 0x5AC635D8} 250 #define Curve_B_4 {0x00000007, 0x00000000, 0x00000000, 0x00000000, \ 251 0x00000000, 0x00000000, 0x00000000, 0x00000000} 252 #define Curve_B_5 {0x2355FFB4, 0x270B3943, 0xD7BFD8BA, 0x5044B0B7, \ 253 0xF5413256, 0x0C04B3AB, 0xB4050A85} 254 255 #define Curve_G_1 { \ 256 {0x13CBFC82, 0x68C38BB9, 0x46646989, 0x8EF57328, 0x4A96B568}, \ 257 {0x7AC5FB32, 0x04235137, 0x59DCC912, 0x3168947D, 0x23A62855}} 258 259 #define Curve_G_2 { \ 260 {0x82FF1012, 0xF4FF0AFD, 0x43A18800, 0x7CBF20EB, 0xB03090F6, 0x188DA80E}, \ 261 {0x1E794811, 0x73F977A1, 0x6B24CDD5, 0x631011ED, 0xFFC8DA78, 0x07192B95}} 262 263 #define Curve_G_3 { \ 264 {0xD898C296, 0xF4A13945, 0x2DEB33A0, 0x77037D81, \ 265 0x63A440F2, 0xF8BCE6E5, 0xE12C4247, 0x6B17D1F2}, \ 266 {0x37BF51F5, 0xCBB64068, 0x6B315ECE, 0x2BCE3357, \ 267 0x7C0F9E16, 0x8EE7EB4A, 0xFE1A7F9B, 0x4FE342E2}} 268 269 #define Curve_G_4 { \ 270 {0x16F81798, 0x59F2815B, 0x2DCE28D9, 0x029BFCDB, \ 271 0xCE870B07, 0x55A06295, 0xF9DCBBAC, 0x79BE667E}, \ 272 {0xFB10D4B8, 0x9C47D08F, 0xA6855419, 0xFD17B448, \ 273 0x0E1108A8, 0x5DA4FBFC, 0x26A3C465, 0x483ADA77}} 274 275 #define Curve_G_5 { \ 276 {0x115C1D21, 0x343280D6, 0x56C21122, 0x4A03C1D3, \ 277 0x321390B9, 0x6BB4BF7F, 0xB70E0CBD}, \ 278 {0x85007E34, 0x44D58199, 0x5A074764, 0xCD4375A0, \ 279 0x4C22DFE6, 0xB5F723FB, 0xBD376388}} 280 281 #define Curve_N_1 {0xCA752257, 0xF927AED3, 0x0001F4C8, 0x00000000, 0x00000000, 0x00000001} 282 #define Curve_N_2 {0xB4D22831, 0x146BC9B1, 0x99DEF836, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} 283 #define Curve_N_3 {0xFC632551, 0xF3B9CAC2, 0xA7179E84, 0xBCE6FAAD, \ 284 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF} 285 #define Curve_N_4 {0xD0364141, 0xBFD25E8C, 0xAF48A03B, 0xBAAEDCE6, \ 286 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} 287 #define Curve_N_5 {0x5C5C2A3D, 0x13DD2945, 0xE0B8F03E, 0xFFFF16A2, \ 288 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} 289 290 #elif (uECC_WORD_SIZE == 8) 291 292 typedef uint64_t uECC_word_t; 293 #if SUPPORTS_INT128 294 typedef unsigned __int128 uECC_dword_t; 295 #endif 296 typedef unsigned wordcount_t; 297 typedef int swordcount_t; 298 typedef int bitcount_t; 299 typedef int cmpresult_t; 300 301 #define HIGH_BIT_SET 0x8000000000000000ull 302 #define uECC_WORD_BITS 64 303 #define uECC_WORD_BITS_SHIFT 6 304 #define uECC_WORD_BITS_MASK 0x03F 305 306 #define uECC_WORDS_1 3 307 #define uECC_WORDS_2 3 308 #define uECC_WORDS_3 4 309 #define uECC_WORDS_4 4 310 #define uECC_WORDS_5 4 311 312 #define uECC_N_WORDS_1 3 313 #define uECC_N_WORDS_2 3 314 #define uECC_N_WORDS_3 4 315 #define uECC_N_WORDS_4 4 316 #define uECC_N_WORDS_5 4 317 318 #define Curve_P_1 {0xFFFFFFFF7FFFFFFFull, 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull} 319 #define Curve_P_2 {0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFEull, 0xFFFFFFFFFFFFFFFFull} 320 #define Curve_P_3 {0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \ 321 0x0000000000000000ull, 0xFFFFFFFF00000001ull} 322 #define Curve_P_4 {0xFFFFFFFEFFFFFC2Full, 0xFFFFFFFFFFFFFFFFull, \ 323 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFFull} 324 #define Curve_P_5 {0x0000000000000001ull, 0xFFFFFFFF00000000ull, \ 325 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull} 326 327 #define Curve_B_1 {0x81D4D4ADC565FA45ull, 0x54BD7A8B65ACF89Full, 0x000000001C97BEFCull} 328 #define Curve_B_2 {0xFEB8DEECC146B9B1ull, 0x0FA7E9AB72243049ull, 0x64210519E59C80E7ull} 329 #define Curve_B_3 {0x3BCE3C3E27D2604Bull, 0x651D06B0CC53B0F6ull, \ 330 0xB3EBBD55769886BCull, 0x5AC635D8AA3A93E7ull} 331 #define Curve_B_4 {0x0000000000000007ull, 0x0000000000000000ull, \ 332 0x0000000000000000ull, 0x0000000000000000ull} 333 #define Curve_B_5 {0x270B39432355FFB4ull, 0x5044B0B7D7BFD8BAull, \ 334 0x0C04B3ABF5413256ull, 0x00000000B4050A85ull} 335 336 #define Curve_G_1 { \ 337 {0x68C38BB913CBFC82ull, 0x8EF5732846646989ull, 0x000000004A96B568ull}, \ 338 {0x042351377AC5FB32ull, 0x3168947D59DCC912ull, 0x0000000023A62855ull}} 339 340 #define Curve_G_2 { \ 341 {0xF4FF0AFD82FF1012ull, 0x7CBF20EB43A18800ull, 0x188DA80EB03090F6ull}, \ 342 {0x73F977A11E794811ull, 0x631011ED6B24CDD5ull, 0x07192B95FFC8DA78ull}} 343 344 #define Curve_G_3 { \ 345 {0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, 0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull}, \ 346 {0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, 0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull}} 347 348 #define Curve_G_4 { \ 349 {0x59F2815B16F81798ull, 0x029BFCDB2DCE28D9ull, 0x55A06295CE870B07ull, 0x79BE667EF9DCBBACull}, \ 350 {0x9C47D08FFB10D4B8ull, 0xFD17B448A6855419ull, 0x5DA4FBFC0E1108A8ull, 0x483ADA7726A3C465ull}} 351 352 #define Curve_G_5 { \ 353 {0x343280D6115C1D21ull, 0x4A03C1D356C21122ull, 0x6BB4BF7F321390B9ull, 0x00000000B70E0CBDull}, \ 354 {0x44D5819985007E34ull, 0xCD4375A05A074764ull, 0xB5F723FB4C22DFE6ull, 0x00000000BD376388ull}} 355 356 #define Curve_N_1 {0xF927AED3CA752257ull, 0x000000000001F4C8ull, 0x0000000100000000ull} 357 #define Curve_N_2 {0x146BC9B1B4D22831ull, 0xFFFFFFFF99DEF836ull, 0xFFFFFFFFFFFFFFFFull} 358 #define Curve_N_3 {0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, \ 359 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull} 360 #define Curve_N_4 {0xBFD25E8CD0364141ull, 0xBAAEDCE6AF48A03Bull, \ 361 0xFFFFFFFFFFFFFFFEull, 0xFFFFFFFFFFFFFFFFull} 362 #define Curve_N_5 {0x13DD29455C5C2A3Dull, 0xFFFF16A2E0B8F03Eull, \ 363 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull} 364 365 #endif /* (uECC_WORD_SIZE == 8) */ 366 367 #define uECC_WORDS uECC_CONCAT(uECC_WORDS_, uECC_CURVE) 368 #define uECC_N_WORDS uECC_CONCAT(uECC_N_WORDS_, uECC_CURVE) 369 370 typedef struct EccPoint { 371 uECC_word_t x[uECC_WORDS]; 372 uECC_word_t y[uECC_WORDS]; 373 } EccPoint; 374 375 static const uECC_word_t curve_p[uECC_WORDS] = uECC_CONCAT(Curve_P_, uECC_CURVE); 376 // Global object `curve_b' is only referenced from function `curve_x_side', it should be defined within that functions block scope 377 static const EccPoint curve_G = uECC_CONCAT(Curve_G_, uECC_CURVE); 378 static const uECC_word_t curve_n[uECC_N_WORDS] = uECC_CONCAT(Curve_N_, uECC_CURVE); 379 380 static void vli_clear(uECC_word_t *vli); 381 static uECC_word_t vli_isZero(const uECC_word_t *vli); 382 static uECC_word_t vli_testBit(const uECC_word_t *vli, bitcount_t bit); 383 #ifdef ENABLE_MICRO_ECC_ECDSA 384 static bitcount_t vli_numBits(const uECC_word_t *vli, wordcount_t max_words); 385 #endif 386 static void vli_set(uECC_word_t *dest, const uECC_word_t *src); 387 static cmpresult_t vli_cmp(const uECC_word_t *left, const uECC_word_t *right); 388 #ifdef ENABLE_MICRO_ECC_ECDSA 389 static cmpresult_t vli_equal(const uECC_word_t *left, const uECC_word_t *right); 390 #endif 391 static void vli_rshift1(uECC_word_t *vli); 392 static uECC_word_t vli_add(uECC_word_t *result, 393 const uECC_word_t *left, 394 const uECC_word_t *right); 395 static uECC_word_t vli_sub(uECC_word_t *result, 396 const uECC_word_t *left, 397 const uECC_word_t *right); 398 static void vli_mult(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right); 399 static void vli_modAdd(uECC_word_t *result, 400 const uECC_word_t *left, 401 const uECC_word_t *right, 402 const uECC_word_t *mod); 403 static void vli_modSub(uECC_word_t *result, 404 const uECC_word_t *left, 405 const uECC_word_t *right, 406 const uECC_word_t *mod); 407 static void vli_mmod_fast(uECC_word_t *RESTRICT result, uECC_word_t *RESTRICT product); 408 static void vli_modMult_fast(uECC_word_t *result, 409 const uECC_word_t *left, 410 const uECC_word_t *right); 411 static void vli_modInv(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod); 412 #if uECC_SQUARE_FUNC 413 static void vli_square(uECC_word_t *result, const uECC_word_t *left); 414 static void vli_modSquare_fast(uECC_word_t *result, const uECC_word_t *left); 415 #endif 416 417 #if ((defined(_WIN32) || defined(_WIN64)) && !defined(uECC_NO_DEFAULT_RNG)) 418 /* Windows */ 419 420 #define WIN32_LEAN_AND_MEAN 421 #include <windows.h> 422 #include <wincrypt.h> 423 424 static int default_RNG(uint8_t *dest, unsigned size) { 425 HCRYPTPROV prov; 426 if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) { 427 return 0; 428 } 429 430 CryptGenRandom(prov, size, (BYTE *)dest); 431 CryptReleaseContext(prov, 0); 432 return 1; 433 } 434 435 #elif (defined(unix) || defined(__linux__) || defined(__unix__) || defined(__unix) || \ 436 (defined(__APPLE__) && defined(__MACH__)) || defined(uECC_POSIX)) && !defined(uECC_NO_DEFAULT_RNG) 437 438 /* Some POSIX-like system with /dev/urandom or /dev/random. */ 439 #include <sys/types.h> 440 #include <fcntl.h> 441 #include <unistd.h> 442 443 #ifndef O_CLOEXEC 444 #define O_CLOEXEC 0 445 #endif 446 447 static int default_RNG(uint8_t *dest, unsigned size) { 448 int fd = open("/dev/urandom", O_RDONLY | O_CLOEXEC); 449 if (fd == -1) { 450 fd = open("/dev/random", O_RDONLY | O_CLOEXEC); 451 if (fd == -1) { 452 return 0; 453 } 454 } 455 456 char *ptr = (char *)dest; 457 size_t left = size; 458 while (left > 0) { 459 ssize_t bytes_read = read(fd, ptr, left); 460 if (bytes_read <= 0) { // read failed 461 close(fd); 462 return 0; 463 } 464 left -= bytes_read; 465 ptr += bytes_read; 466 } 467 468 close(fd); 469 return 1; 470 } 471 472 #else /* Some other platform */ 473 474 static int default_RNG(uint8_t *dest, unsigned size) { 475 (void) dest; 476 (void) size; 477 return 0; 478 } 479 480 #endif 481 482 static uECC_RNG_Function g_rng_function = &default_RNG; 483 484 void uECC_set_rng(uECC_RNG_Function rng_function) { 485 g_rng_function = rng_function; 486 } 487 488 #ifdef __GNUC__ /* Only support GCC inline asm for now */ 489 #if (uECC_ASM && (uECC_PLATFORM == uECC_avr)) 490 #include "asm_avr.inc" 491 #endif 492 493 #if (uECC_ASM && (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb || \ 494 uECC_PLATFORM == uECC_arm_thumb2)) 495 #include "asm_arm.inc" 496 #endif 497 #endif 498 499 #if !asm_clear 500 static void vli_clear(uECC_word_t *vli) { 501 wordcount_t i; 502 for (i = 0; i < uECC_WORDS; ++i) { 503 vli[i] = 0; 504 } 505 } 506 #endif 507 508 /* Returns 1 if vli == 0, 0 otherwise. */ 509 #if !asm_isZero 510 static uECC_word_t vli_isZero(const uECC_word_t *vli) { 511 wordcount_t i; 512 for (i = 0; i < uECC_WORDS; ++i) { 513 if (vli[i]) { 514 return 0; 515 } 516 } 517 return 1; 518 } 519 #endif 520 521 /* Returns nonzero if bit 'bit' of vli is set. */ 522 #if !asm_testBit 523 static uECC_word_t vli_testBit(const uECC_word_t *vli, bitcount_t bit) { 524 return (vli[bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK))); 525 } 526 #endif 527 528 #ifdef ENABLE_MICO_ECC_ECDSA 529 530 /* Counts the number of words in vli. */ 531 #if !asm_numBits 532 static wordcount_t vli_numDigits(const uECC_word_t *vli, wordcount_t max_words) { 533 swordcount_t i; 534 /* Search from the end until we find a non-zero digit. 535 We do it in reverse because we expect that most digits will be nonzero. */ 536 for (i = max_words - 1; i >= 0 && vli[i] == 0; --i) { 537 } 538 539 return (i + 1); 540 } 541 542 /* Counts the number of bits required to represent vli. */ 543 static bitcount_t vli_numBits(const uECC_word_t *vli, wordcount_t max_words) { 544 uECC_word_t i; 545 uECC_word_t digit; 546 547 wordcount_t num_digits = vli_numDigits(vli, max_words); 548 if (num_digits == 0) { 549 return 0; 550 } 551 552 digit = vli[num_digits - 1]; 553 for (i = 0; digit; ++i) { 554 digit >>= 1; 555 } 556 557 return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i); 558 } 559 560 #endif /* ENABLE_MICO_ECC_ECDSA */ 561 562 #endif /* !asm_numBits */ 563 564 /* Sets dest = src. */ 565 #if !asm_set 566 static void vli_set(uECC_word_t *dest, const uECC_word_t *src) { 567 wordcount_t i; 568 for (i = 0; i < uECC_WORDS; ++i) { 569 dest[i] = src[i]; 570 } 571 } 572 #endif 573 574 /* Returns sign of left - right. */ 575 #if !asm_cmp 576 static cmpresult_t vli_cmp(const uECC_word_t *left, const uECC_word_t *right) { 577 swordcount_t i; 578 for (i = uECC_WORDS - 1; i >= 0; --i) { 579 if (left[i] > right[i]) { 580 return 1; 581 } else if (left[i] < right[i]) { 582 return -1; 583 } 584 } 585 return 0; 586 } 587 #endif 588 589 #ifdef ENABLE_MICRO_ECC_ECDSA 590 591 static cmpresult_t vli_equal(const uECC_word_t *left, const uECC_word_t *right) { 592 uECC_word_t result = 0; 593 swordcount_t i; 594 for (i = uECC_WORDS - 1; i >= 0; --i) { 595 result |= (left[i] ^ right[i]); 596 } 597 return (result == 0); 598 } 599 600 #endif 601 602 /* Computes vli = vli >> 1. */ 603 #if !asm_rshift1 604 static void vli_rshift1(uECC_word_t *vli) { 605 uECC_word_t *end = vli; 606 uECC_word_t carry = 0; 607 uECC_word_t *vli_ = vli; 608 609 vli_ += uECC_WORDS; 610 while (vli_-- > end) { 611 uECC_word_t temp = *vli_; 612 *vli_ = (temp >> 1) | carry; 613 carry = temp << (uECC_WORD_BITS - 1); 614 } 615 } 616 #endif 617 618 /* Computes result = left + right, returning carry. Can modify in place. */ 619 #if !asm_add 620 static uECC_word_t vli_add(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 621 uECC_word_t carry = 0; 622 wordcount_t i; 623 for (i = 0; i < uECC_WORDS; ++i) { 624 uECC_word_t sum = left[i] + right[i] + carry; 625 if (sum != left[i]) { 626 carry = (sum < left[i]); 627 } 628 result[i] = sum; 629 } 630 return carry; 631 } 632 #endif 633 634 /* Computes result = left - right, returning borrow. Can modify in place. */ 635 #if !asm_sub 636 static uECC_word_t vli_sub(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 637 uECC_word_t borrow = 0; 638 wordcount_t i; 639 for (i = 0; i < uECC_WORDS; ++i) { 640 uECC_word_t diff = left[i] - right[i] - borrow; 641 if (diff != left[i]) { 642 borrow = (diff > left[i]); 643 } 644 result[i] = diff; 645 } 646 return borrow; 647 } 648 #endif 649 650 #if (!asm_mult || (uECC_SQUARE_FUNC && !asm_square) || uECC_CURVE == uECC_secp256k1) 651 static void muladd(uECC_word_t a, 652 uECC_word_t b, 653 uECC_word_t *r0, 654 uECC_word_t *r1, 655 uECC_word_t *r2) { 656 #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128 657 uint64_t a0 = a & 0xffffffffull; 658 uint64_t a1 = a >> 32; 659 uint64_t b0 = b & 0xffffffffull; 660 uint64_t b1 = b >> 32; 661 662 uint64_t i0 = a0 * b0; 663 uint64_t i1 = a0 * b1; 664 uint64_t i2 = a1 * b0; 665 uint64_t i3 = a1 * b1; 666 667 uint64_t p0, p1; 668 669 i2 += (i0 >> 32); 670 i2 += i1; 671 if (i2 < i1) { // overflow 672 i3 += 0x100000000ull; 673 } 674 675 p0 = (i0 & 0xffffffffull) | (i2 << 32); 676 p1 = i3 + (i2 >> 32); 677 678 *r0 += p0; 679 *r1 += (p1 + (*r0 < p0)); 680 *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0)); 681 #else 682 uECC_dword_t p = (uECC_dword_t)a * b; 683 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; 684 r01 += p; 685 *r2 += (r01 < p); 686 *r1 = r01 >> uECC_WORD_BITS; 687 *r0 = (uECC_word_t)r01; 688 #endif 689 } 690 #define muladd_exists 1 691 #endif 692 693 #if !asm_mult 694 static void vli_mult(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 695 uECC_word_t r0 = 0; 696 uECC_word_t r1 = 0; 697 uECC_word_t r2 = 0; 698 wordcount_t i, k; 699 700 /* Compute each digit of result in sequence, maintaining the carries. */ 701 for (k = 0; k < uECC_WORDS; ++k) { 702 for (i = 0; i <= k; ++i) { 703 muladd(left[i], right[k - i], &r0, &r1, &r2); 704 } 705 result[k] = r0; 706 r0 = r1; 707 r1 = r2; 708 r2 = 0; 709 } 710 for (k = uECC_WORDS; k < uECC_WORDS * 2 - 1; ++k) { 711 for (i = (k + 1) - uECC_WORDS; i < uECC_WORDS; ++i) { 712 muladd(left[i], right[k - i], &r0, &r1, &r2); 713 } 714 result[k] = r0; 715 r0 = r1; 716 r1 = r2; 717 r2 = 0; 718 } 719 result[uECC_WORDS * 2 - 1] = r0; 720 } 721 #endif 722 723 #if uECC_SQUARE_FUNC 724 725 #if !asm_square 726 static void mul2add(uECC_word_t a, 727 uECC_word_t b, 728 uECC_word_t *r0, 729 uECC_word_t *r1, 730 uECC_word_t *r2) { 731 #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128 732 uint64_t a0 = a & 0xffffffffull; 733 uint64_t a1 = a >> 32; 734 uint64_t b0 = b & 0xffffffffull; 735 uint64_t b1 = b >> 32; 736 737 uint64_t i0 = a0 * b0; 738 uint64_t i1 = a0 * b1; 739 uint64_t i2 = a1 * b0; 740 uint64_t i3 = a1 * b1; 741 742 uint64_t p0, p1; 743 744 i2 += (i0 >> 32); 745 i2 += i1; 746 if (i2 < i1) 747 { // overflow 748 i3 += 0x100000000ull; 749 } 750 751 p0 = (i0 & 0xffffffffull) | (i2 << 32); 752 p1 = i3 + (i2 >> 32); 753 754 *r2 += (p1 >> 63); 755 p1 = (p1 << 1) | (p0 >> 63); 756 p0 <<= 1; 757 758 *r0 += p0; 759 *r1 += (p1 + (*r0 < p0)); 760 *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0)); 761 #else 762 uECC_dword_t p = (uECC_dword_t)a * b; 763 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; 764 *r2 += (p >> (uECC_WORD_BITS * 2 - 1)); 765 p *= 2; 766 r01 += p; 767 *r2 += (r01 < p); 768 *r1 = r01 >> uECC_WORD_BITS; 769 *r0 = (uECC_word_t)r01; 770 #endif 771 } 772 773 static void vli_square(uECC_word_t *result, const uECC_word_t *left) { 774 uECC_word_t r0 = 0; 775 uECC_word_t r1 = 0; 776 uECC_word_t r2 = 0; 777 778 wordcount_t i, k; 779 780 for (k = 0; k < uECC_WORDS * 2 - 1; ++k) { 781 uECC_word_t min = (k < uECC_WORDS ? 0 : (k + 1) - uECC_WORDS); 782 for (i = min; i <= k && i <= k - i; ++i) { 783 if (i < k-i) { 784 mul2add(left[i], left[k - i], &r0, &r1, &r2); 785 } else { 786 muladd(left[i], left[k - i], &r0, &r1, &r2); 787 } 788 } 789 result[k] = r0; 790 r0 = r1; 791 r1 = r2; 792 r2 = 0; 793 } 794 795 result[uECC_WORDS * 2 - 1] = r0; 796 } 797 #endif 798 799 #else /* uECC_SQUARE_FUNC */ 800 801 #define vli_square(result, left, size) vli_mult((result), (left), (left), (size)) 802 803 #endif /* uECC_SQUARE_FUNC */ 804 805 806 /* Computes result = (left + right) % mod. 807 Assumes that left < mod and right < mod, and that result does not overlap mod. */ 808 #if !asm_modAdd 809 static void vli_modAdd(uECC_word_t *result, 810 const uECC_word_t *left, 811 const uECC_word_t *right, 812 const uECC_word_t *mod) { 813 uECC_word_t carry = vli_add(result, left, right); 814 if (carry || vli_cmp(result, mod) >= 0) { 815 /* result > mod (result = mod + remainder), so subtract mod to get remainder. */ 816 vli_sub(result, result, mod); 817 } 818 } 819 #endif 820 821 /* Computes result = (left - right) % mod. 822 Assumes that left < mod and right < mod, and that result does not overlap mod. */ 823 #if !asm_modSub 824 static void vli_modSub(uECC_word_t *result, 825 const uECC_word_t *left, 826 const uECC_word_t *right, 827 const uECC_word_t *mod) { 828 uECC_word_t l_borrow = vli_sub(result, left, right); 829 if (l_borrow) { 830 /* In this case, result == -diff == (max int) - diff. Since -x % d == d - x, 831 we can get the correct result from result + mod (with overflow). */ 832 vli_add(result, result, mod); 833 } 834 } 835 #endif 836 837 #if !asm_modSub_fast 838 #define vli_modSub_fast(result, left, right) vli_modSub((result), (left), (right), curve_p) 839 #endif 840 841 #if !asm_mmod_fast 842 843 #if (uECC_CURVE == uECC_secp160r1 || uECC_CURVE == uECC_secp256k1) 844 /* omega_mult() is defined farther below for the different curves / word sizes */ 845 static void omega_mult(uECC_word_t * RESTRICT result, const uECC_word_t * RESTRICT right); 846 847 /* Computes result = product % curve_p 848 see http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf page 354 849 850 Note that this only works if log2(omega) < log2(p) / 2 */ 851 static void vli_mmod_fast(uECC_word_t *RESTRICT result, uECC_word_t *RESTRICT product) { 852 uECC_word_t tmp[2 * uECC_WORDS]; 853 uECC_word_t carry; 854 855 vli_clear(tmp); 856 vli_clear(tmp + uECC_WORDS); 857 858 omega_mult(tmp, product + uECC_WORDS); /* (Rq, q) = q * c */ 859 860 carry = vli_add(result, product, tmp); /* (C, r) = r + q */ 861 vli_clear(product); 862 omega_mult(product, tmp + uECC_WORDS); /* Rq*c */ 863 carry += vli_add(result, result, product); /* (C1, r) = r + Rq*c */ 864 865 while (carry > 0) { 866 --carry; 867 vli_sub(result, result, curve_p); 868 } 869 if (vli_cmp(result, curve_p) > 0) { 870 vli_sub(result, result, curve_p); 871 } 872 } 873 874 #endif 875 876 #if uECC_CURVE == uECC_secp160r1 877 878 #if uECC_WORD_SIZE == 1 879 static void omega_mult(uint8_t * RESTRICT result, const uint8_t * RESTRICT right) { 880 uint8_t carry; 881 uint8_t i; 882 883 /* Multiply by (2^31 + 1). */ 884 vli_set(result + 4, right); /* 2^32 */ 885 vli_rshift1(result + 4); /* 2^31 */ 886 result[3] = right[0] << 7; /* get last bit from shift */ 887 888 carry = vli_add(result, result, right); /* 2^31 + 1 */ 889 for (i = uECC_WORDS; carry; ++i) { 890 uint16_t sum = (uint16_t)result[i] + carry; 891 result[i] = (uint8_t)sum; 892 carry = sum >> 8; 893 } 894 } 895 #elif uECC_WORD_SIZE == 4 896 static void omega_mult(uint32_t * RESTRICT result, const uint32_t * RESTRICT right) { 897 uint32_t carry; 898 unsigned i; 899 900 /* Multiply by (2^31 + 1). */ 901 vli_set(result + 1, right); /* 2^32 */ 902 vli_rshift1(result + 1); /* 2^31 */ 903 result[0] = right[0] << 31; /* get last bit from shift */ 904 905 carry = vli_add(result, result, right); /* 2^31 + 1 */ 906 for (i = uECC_WORDS; carry; ++i) { 907 uint64_t sum = (uint64_t)result[i] + carry; 908 result[i] = (uint32_t)sum; 909 carry = sum >> 32; 910 } 911 } 912 #endif /* uECC_WORD_SIZE */ 913 914 #elif uECC_CURVE == uECC_secp192r1 915 916 /* Computes result = product % curve_p. 917 See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf */ 918 #if uECC_WORD_SIZE == 1 919 static void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) { 920 uint8_t tmp[uECC_WORDS]; 921 uint8_t carry; 922 923 vli_set(result, product); 924 925 vli_set(tmp, &product[24]); 926 carry = vli_add(result, result, tmp); 927 928 tmp[0] = tmp[1] = tmp[2] = tmp[3] = tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0; 929 tmp[8] = product[24]; tmp[9] = product[25]; tmp[10] = product[26]; tmp[11] = product[27]; 930 tmp[12] = product[28]; tmp[13] = product[29]; tmp[14] = product[30]; tmp[15] = product[31]; 931 tmp[16] = product[32]; tmp[17] = product[33]; tmp[18] = product[34]; tmp[19] = product[35]; 932 tmp[20] = product[36]; tmp[21] = product[37]; tmp[22] = product[38]; tmp[23] = product[39]; 933 carry += vli_add(result, result, tmp); 934 935 tmp[0] = tmp[8] = product[40]; 936 tmp[1] = tmp[9] = product[41]; 937 tmp[2] = tmp[10] = product[42]; 938 tmp[3] = tmp[11] = product[43]; 939 tmp[4] = tmp[12] = product[44]; 940 tmp[5] = tmp[13] = product[45]; 941 tmp[6] = tmp[14] = product[46]; 942 tmp[7] = tmp[15] = product[47]; 943 tmp[16] = tmp[17] = tmp[18] = tmp[19] = tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 944 carry += vli_add(result, result, tmp); 945 946 while (carry || vli_cmp(curve_p, result) != 1) { 947 carry -= vli_sub(result, result, curve_p); 948 } 949 } 950 #elif uECC_WORD_SIZE == 4 951 static void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) { 952 uint32_t tmp[uECC_WORDS]; 953 int carry; 954 955 vli_set(result, product); 956 957 vli_set(tmp, &product[6]); 958 carry = vli_add(result, result, tmp); 959 960 tmp[0] = tmp[1] = 0; 961 tmp[2] = product[6]; 962 tmp[3] = product[7]; 963 tmp[4] = product[8]; 964 tmp[5] = product[9]; 965 carry += vli_add(result, result, tmp); 966 967 tmp[0] = tmp[2] = product[10]; 968 tmp[1] = tmp[3] = product[11]; 969 tmp[4] = tmp[5] = 0; 970 carry += vli_add(result, result, tmp); 971 972 while (carry || vli_cmp(curve_p, result) != 1) { 973 carry -= vli_sub(result, result, curve_p); 974 } 975 } 976 #else 977 static void vli_mmod_fast(uint64_t *RESTRICT result, uint64_t *RESTRICT product) { 978 uint64_t tmp[uECC_WORDS]; 979 int carry; 980 981 vli_set(result, product); 982 983 vli_set(tmp, &product[3]); 984 carry = vli_add(result, result, tmp); 985 986 tmp[0] = 0; 987 tmp[1] = product[3]; 988 tmp[2] = product[4]; 989 carry += vli_add(result, result, tmp); 990 991 tmp[0] = tmp[1] = product[5]; 992 tmp[2] = 0; 993 carry += vli_add(result, result, tmp); 994 995 while (carry || vli_cmp(curve_p, result) != 1) { 996 carry -= vli_sub(result, result, curve_p); 997 } 998 } 999 #endif /* uECC_WORD_SIZE */ 1000 1001 #elif uECC_CURVE == uECC_secp256r1 1002 1003 /* Computes result = product % curve_p 1004 from www.nsa.gov/ia/_files/nist-routines.pdf */ 1005 #if uECC_WORD_SIZE == 1 1006 static void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) { 1007 uint8_t tmp[uECC_BYTES]; 1008 int8_t carry; 1009 1010 /* t */ 1011 vli_set(result, product); 1012 1013 /* s1 */ 1014 tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0; 1015 tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0; 1016 tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0; 1017 tmp[12] = product[44]; tmp[13] = product[45]; tmp[14] = product[46]; tmp[15] = product[47]; 1018 tmp[16] = product[48]; tmp[17] = product[49]; tmp[18] = product[50]; tmp[19] = product[51]; 1019 tmp[20] = product[52]; tmp[21] = product[53]; tmp[22] = product[54]; tmp[23] = product[55]; 1020 tmp[24] = product[56]; tmp[25] = product[57]; tmp[26] = product[58]; tmp[27] = product[59]; 1021 tmp[28] = product[60]; tmp[29] = product[61]; tmp[30] = product[62]; tmp[31] = product[63]; 1022 carry = vli_add(tmp, tmp, tmp); 1023 carry += vli_add(result, result, tmp); 1024 1025 /* s2 */ 1026 tmp[12] = product[48]; tmp[13] = product[49]; tmp[14] = product[50]; tmp[15] = product[51]; 1027 tmp[16] = product[52]; tmp[17] = product[53]; tmp[18] = product[54]; tmp[19] = product[55]; 1028 tmp[20] = product[56]; tmp[21] = product[57]; tmp[22] = product[58]; tmp[23] = product[59]; 1029 tmp[24] = product[60]; tmp[25] = product[61]; tmp[26] = product[62]; tmp[27] = product[63]; 1030 tmp[28] = tmp[29] = tmp[30] = tmp[31] = 0; 1031 carry += vli_add(tmp, tmp, tmp); 1032 carry += vli_add(result, result, tmp); 1033 1034 /* s3 */ 1035 tmp[0] = product[32]; tmp[1] = product[33]; tmp[2] = product[34]; tmp[3] = product[35]; 1036 tmp[4] = product[36]; tmp[5] = product[37]; tmp[6] = product[38]; tmp[7] = product[39]; 1037 tmp[8] = product[40]; tmp[9] = product[41]; tmp[10] = product[42]; tmp[11] = product[43]; 1038 tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0; 1039 tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0; 1040 tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 1041 tmp[24] = product[56]; tmp[25] = product[57]; tmp[26] = product[58]; tmp[27] = product[59]; 1042 tmp[28] = product[60]; tmp[29] = product[61]; tmp[30] = product[62]; tmp[31] = product[63]; 1043 carry += vli_add(result, result, tmp); 1044 1045 /* s4 */ 1046 tmp[0] = product[36]; tmp[1] = product[37]; tmp[2] = product[38]; tmp[3] = product[39]; 1047 tmp[4] = product[40]; tmp[5] = product[41]; tmp[6] = product[42]; tmp[7] = product[43]; 1048 tmp[8] = product[44]; tmp[9] = product[45]; tmp[10] = product[46]; tmp[11] = product[47]; 1049 tmp[12] = product[52]; tmp[13] = product[53]; tmp[14] = product[54]; tmp[15] = product[55]; 1050 tmp[16] = product[56]; tmp[17] = product[57]; tmp[18] = product[58]; tmp[19] = product[59]; 1051 tmp[20] = product[60]; tmp[21] = product[61]; tmp[22] = product[62]; tmp[23] = product[63]; 1052 tmp[24] = product[52]; tmp[25] = product[53]; tmp[26] = product[54]; tmp[27] = product[55]; 1053 tmp[28] = product[32]; tmp[29] = product[33]; tmp[30] = product[34]; tmp[31] = product[35]; 1054 carry += vli_add(result, result, tmp); 1055 1056 /* d1 */ 1057 tmp[0] = product[44]; tmp[1] = product[45]; tmp[2] = product[46]; tmp[3] = product[47]; 1058 tmp[4] = product[48]; tmp[5] = product[49]; tmp[6] = product[50]; tmp[7] = product[51]; 1059 tmp[8] = product[52]; tmp[9] = product[53]; tmp[10] = product[54]; tmp[11] = product[55]; 1060 tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0; 1061 tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0; 1062 tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 1063 tmp[24] = product[32]; tmp[25] = product[33]; tmp[26] = product[34]; tmp[27] = product[35]; 1064 tmp[28] = product[40]; tmp[29] = product[41]; tmp[30] = product[42]; tmp[31] = product[43]; 1065 carry -= vli_sub(result, result, tmp); 1066 1067 /* d2 */ 1068 tmp[0] = product[48]; tmp[1] = product[49]; tmp[2] = product[50]; tmp[3] = product[51]; 1069 tmp[4] = product[52]; tmp[5] = product[53]; tmp[6] = product[54]; tmp[7] = product[55]; 1070 tmp[8] = product[56]; tmp[9] = product[57]; tmp[10] = product[58]; tmp[11] = product[59]; 1071 tmp[12] = product[60]; tmp[13] = product[61]; tmp[14] = product[62]; tmp[15] = product[63]; 1072 tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0; 1073 tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 1074 tmp[24] = product[36]; tmp[25] = product[37]; tmp[26] = product[38]; tmp[27] = product[39]; 1075 tmp[28] = product[44]; tmp[29] = product[45]; tmp[30] = product[46]; tmp[31] = product[47]; 1076 carry -= vli_sub(result, result, tmp); 1077 1078 /* d3 */ 1079 tmp[0] = product[52]; tmp[1] = product[53]; tmp[2] = product[54]; tmp[3] = product[55]; 1080 tmp[4] = product[56]; tmp[5] = product[57]; tmp[6] = product[58]; tmp[7] = product[59]; 1081 tmp[8] = product[60]; tmp[9] = product[61]; tmp[10] = product[62]; tmp[11] = product[63]; 1082 tmp[12] = product[32]; tmp[13] = product[33]; tmp[14] = product[34]; tmp[15] = product[35]; 1083 tmp[16] = product[36]; tmp[17] = product[37]; tmp[18] = product[38]; tmp[19] = product[39]; 1084 tmp[20] = product[40]; tmp[21] = product[41]; tmp[22] = product[42]; tmp[23] = product[43]; 1085 tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0; 1086 tmp[28] = product[48]; tmp[29] = product[49]; tmp[30] = product[50]; tmp[31] = product[51]; 1087 carry -= vli_sub(result, result, tmp); 1088 1089 /* d4 */ 1090 tmp[0] = product[56]; tmp[1] = product[57]; tmp[2] = product[58]; tmp[3] = product[59]; 1091 tmp[4] = product[60]; tmp[5] = product[61]; tmp[6] = product[62]; tmp[7] = product[63]; 1092 tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0; 1093 tmp[12] = product[36]; tmp[13] = product[37]; tmp[14] = product[38]; tmp[15] = product[39]; 1094 tmp[16] = product[40]; tmp[17] = product[41]; tmp[18] = product[42]; tmp[19] = product[43]; 1095 tmp[20] = product[44]; tmp[21] = product[45]; tmp[22] = product[46]; tmp[23] = product[47]; 1096 tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0; 1097 tmp[28] = product[52]; tmp[29] = product[53]; tmp[30] = product[54]; tmp[31] = product[55]; 1098 carry -= vli_sub(result, result, tmp); 1099 1100 if (carry < 0) { 1101 do { 1102 carry += vli_add(result, result, curve_p); 1103 } while (carry < 0); 1104 } else { 1105 while (carry || vli_cmp(curve_p, result) != 1) { 1106 carry -= vli_sub(result, result, curve_p); 1107 } 1108 } 1109 } 1110 #elif uECC_WORD_SIZE == 4 1111 static void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) { 1112 uint32_t tmp[uECC_WORDS]; 1113 int carry; 1114 1115 /* t */ 1116 vli_set(result, product); 1117 1118 /* s1 */ 1119 tmp[0] = tmp[1] = tmp[2] = 0; 1120 tmp[3] = product[11]; 1121 tmp[4] = product[12]; 1122 tmp[5] = product[13]; 1123 tmp[6] = product[14]; 1124 tmp[7] = product[15]; 1125 carry = vli_add(tmp, tmp, tmp); 1126 carry += vli_add(result, result, tmp); 1127 1128 /* s2 */ 1129 tmp[3] = product[12]; 1130 tmp[4] = product[13]; 1131 tmp[5] = product[14]; 1132 tmp[6] = product[15]; 1133 tmp[7] = 0; 1134 carry += vli_add(tmp, tmp, tmp); 1135 carry += vli_add(result, result, tmp); 1136 1137 /* s3 */ 1138 tmp[0] = product[8]; 1139 tmp[1] = product[9]; 1140 tmp[2] = product[10]; 1141 tmp[3] = tmp[4] = tmp[5] = 0; 1142 tmp[6] = product[14]; 1143 tmp[7] = product[15]; 1144 carry += vli_add(result, result, tmp); 1145 1146 /* s4 */ 1147 tmp[0] = product[9]; 1148 tmp[1] = product[10]; 1149 tmp[2] = product[11]; 1150 tmp[3] = product[13]; 1151 tmp[4] = product[14]; 1152 tmp[5] = product[15]; 1153 tmp[6] = product[13]; 1154 tmp[7] = product[8]; 1155 carry += vli_add(result, result, tmp); 1156 1157 /* d1 */ 1158 tmp[0] = product[11]; 1159 tmp[1] = product[12]; 1160 tmp[2] = product[13]; 1161 tmp[3] = tmp[4] = tmp[5] = 0; 1162 tmp[6] = product[8]; 1163 tmp[7] = product[10]; 1164 carry -= vli_sub(result, result, tmp); 1165 1166 /* d2 */ 1167 tmp[0] = product[12]; 1168 tmp[1] = product[13]; 1169 tmp[2] = product[14]; 1170 tmp[3] = product[15]; 1171 tmp[4] = tmp[5] = 0; 1172 tmp[6] = product[9]; 1173 tmp[7] = product[11]; 1174 carry -= vli_sub(result, result, tmp); 1175 1176 /* d3 */ 1177 tmp[0] = product[13]; 1178 tmp[1] = product[14]; 1179 tmp[2] = product[15]; 1180 tmp[3] = product[8]; 1181 tmp[4] = product[9]; 1182 tmp[5] = product[10]; 1183 tmp[6] = 0; 1184 tmp[7] = product[12]; 1185 carry -= vli_sub(result, result, tmp); 1186 1187 /* d4 */ 1188 tmp[0] = product[14]; 1189 tmp[1] = product[15]; 1190 tmp[2] = 0; 1191 tmp[3] = product[9]; 1192 tmp[4] = product[10]; 1193 tmp[5] = product[11]; 1194 tmp[6] = 0; 1195 tmp[7] = product[13]; 1196 carry -= vli_sub(result, result, tmp); 1197 1198 if (carry < 0) { 1199 do { 1200 carry += vli_add(result, result, curve_p); 1201 } while (carry < 0); 1202 } else { 1203 while (carry || vli_cmp(curve_p, result) != 1) { 1204 carry -= vli_sub(result, result, curve_p); 1205 } 1206 } 1207 } 1208 #else 1209 static void vli_mmod_fast(uint64_t *RESTRICT result, uint64_t *RESTRICT product) { 1210 uint64_t tmp[uECC_WORDS]; 1211 int carry; 1212 1213 /* t */ 1214 vli_set(result, product); 1215 1216 /* s1 */ 1217 tmp[0] = 0; 1218 tmp[1] = product[5] & 0xffffffff00000000ull; 1219 tmp[2] = product[6]; 1220 tmp[3] = product[7]; 1221 carry = vli_add(tmp, tmp, tmp); 1222 carry += vli_add(result, result, tmp); 1223 1224 /* s2 */ 1225 tmp[1] = product[6] << 32; 1226 tmp[2] = (product[6] >> 32) | (product[7] << 32); 1227 tmp[3] = product[7] >> 32; 1228 carry += vli_add(tmp, tmp, tmp); 1229 carry += vli_add(result, result, tmp); 1230 1231 /* s3 */ 1232 tmp[0] = product[4]; 1233 tmp[1] = product[5] & 0xffffffff; 1234 tmp[2] = 0; 1235 tmp[3] = product[7]; 1236 carry += vli_add(result, result, tmp); 1237 1238 /* s4 */ 1239 tmp[0] = (product[4] >> 32) | (product[5] << 32); 1240 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull); 1241 tmp[2] = product[7]; 1242 tmp[3] = (product[6] >> 32) | (product[4] << 32); 1243 carry += vli_add(result, result, tmp); 1244 1245 /* d1 */ 1246 tmp[0] = (product[5] >> 32) | (product[6] << 32); 1247 tmp[1] = (product[6] >> 32); 1248 tmp[2] = 0; 1249 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32); 1250 carry -= vli_sub(result, result, tmp); 1251 1252 /* d2 */ 1253 tmp[0] = product[6]; 1254 tmp[1] = product[7]; 1255 tmp[2] = 0; 1256 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull); 1257 carry -= vli_sub(result, result, tmp); 1258 1259 /* d3 */ 1260 tmp[0] = (product[6] >> 32) | (product[7] << 32); 1261 tmp[1] = (product[7] >> 32) | (product[4] << 32); 1262 tmp[2] = (product[4] >> 32) | (product[5] << 32); 1263 tmp[3] = (product[6] << 32); 1264 carry -= vli_sub(result, result, tmp); 1265 1266 /* d4 */ 1267 tmp[0] = product[7]; 1268 tmp[1] = product[4] & 0xffffffff00000000ull; 1269 tmp[2] = product[5]; 1270 tmp[3] = product[6] & 0xffffffff00000000ull; 1271 carry -= vli_sub(result, result, tmp); 1272 1273 if (carry < 0) { 1274 do { 1275 carry += vli_add(result, result, curve_p); 1276 } while (carry < 0); 1277 } else { 1278 while (carry || vli_cmp(curve_p, result) != 1) { 1279 carry -= vli_sub(result, result, curve_p); 1280 } 1281 } 1282 } 1283 #endif /* uECC_WORD_SIZE */ 1284 1285 #elif uECC_CURVE == uECC_secp256k1 1286 1287 #if uECC_WORD_SIZE == 1 1288 static void omega_mult(uint8_t * RESTRICT result, const uint8_t * RESTRICT right) { 1289 /* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ 1290 uECC_word_t r0 = 0; 1291 uECC_word_t r1 = 0; 1292 uECC_word_t r2 = 0; 1293 wordcount_t k; 1294 1295 /* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ 1296 muladd(0xD1, right[0], &r0, &r1, &r2); 1297 result[0] = r0; 1298 r0 = r1; 1299 r1 = r2; 1300 /* r2 is still 0 */ 1301 1302 for (k = 1; k < uECC_WORDS; ++k) { 1303 muladd(0x03, right[k - 1], &r0, &r1, &r2); 1304 muladd(0xD1, right[k], &r0, &r1, &r2); 1305 result[k] = r0; 1306 r0 = r1; 1307 r1 = r2; 1308 r2 = 0; 1309 } 1310 muladd(0x03, right[uECC_WORDS - 1], &r0, &r1, &r2); 1311 result[uECC_WORDS] = r0; 1312 result[uECC_WORDS + 1] = r1; 1313 1314 result[4 + uECC_WORDS] = vli_add(result + 4, result + 4, right); /* add the 2^32 multiple */ 1315 } 1316 #elif uECC_WORD_SIZE == 4 1317 static void omega_mult(uint32_t * RESTRICT result, const uint32_t * RESTRICT right) { 1318 /* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ 1319 uint32_t carry = 0; 1320 wordcount_t k; 1321 1322 for (k = 0; k < uECC_WORDS; ++k) { 1323 uint64_t p = (uint64_t)0x3D1 * right[k] + carry; 1324 result[k] = (p & 0xffffffff); 1325 carry = p >> 32; 1326 } 1327 result[uECC_WORDS] = carry; 1328 1329 result[1 + uECC_WORDS] = vli_add(result + 1, result + 1, right); /* add the 2^32 multiple */ 1330 } 1331 #else 1332 static void omega_mult(uint64_t * RESTRICT result, const uint64_t * RESTRICT right) { 1333 uECC_word_t r0 = 0; 1334 uECC_word_t r1 = 0; 1335 uECC_word_t r2 = 0; 1336 wordcount_t k; 1337 1338 /* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ 1339 for (k = 0; k < uECC_WORDS; ++k) { 1340 muladd(0x1000003D1ull, right[k], &r0, &r1, &r2); 1341 result[k] = r0; 1342 r0 = r1; 1343 r1 = r2; 1344 r2 = 0; 1345 } 1346 result[uECC_WORDS] = r0; 1347 } 1348 #endif /* uECC_WORD_SIZE */ 1349 1350 #elif uECC_CURVE == uECC_secp224r1 1351 1352 /* Computes result = product % curve_p 1353 from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1354 #if uECC_WORD_SIZE == 1 1355 // TODO it may be faster to use the omega_mult method when fully asm optimized. 1356 void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) { 1357 uint8_t tmp[uECC_WORDS]; 1358 int8_t carry; 1359 1360 /* t */ 1361 vli_set(result, product); 1362 1363 /* s1 */ 1364 tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0; 1365 tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0; 1366 tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0; 1367 tmp[12] = product[28]; tmp[13] = product[29]; tmp[14] = product[30]; tmp[15] = product[31]; 1368 tmp[16] = product[32]; tmp[17] = product[33]; tmp[18] = product[34]; tmp[19] = product[35]; 1369 tmp[20] = product[36]; tmp[21] = product[37]; tmp[22] = product[38]; tmp[23] = product[39]; 1370 tmp[24] = product[40]; tmp[25] = product[41]; tmp[26] = product[42]; tmp[27] = product[43]; 1371 carry = vli_add(result, result, tmp); 1372 1373 /* s2 */ 1374 tmp[12] = product[44]; tmp[13] = product[45]; tmp[14] = product[46]; tmp[15] = product[47]; 1375 tmp[16] = product[48]; tmp[17] = product[49]; tmp[18] = product[50]; tmp[19] = product[51]; 1376 tmp[20] = product[52]; tmp[21] = product[53]; tmp[22] = product[54]; tmp[23] = product[55]; 1377 tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0; 1378 carry += vli_add(result, result, tmp); 1379 1380 /* d1 */ 1381 tmp[0] = product[28]; tmp[1] = product[29]; tmp[2] = product[30]; tmp[3] = product[31]; 1382 tmp[4] = product[32]; tmp[5] = product[33]; tmp[6] = product[34]; tmp[7] = product[35]; 1383 tmp[8] = product[36]; tmp[9] = product[37]; tmp[10] = product[38]; tmp[11] = product[39]; 1384 tmp[12] = product[40]; tmp[13] = product[41]; tmp[14] = product[42]; tmp[15] = product[43]; 1385 tmp[16] = product[44]; tmp[17] = product[45]; tmp[18] = product[46]; tmp[19] = product[47]; 1386 tmp[20] = product[48]; tmp[21] = product[49]; tmp[22] = product[50]; tmp[23] = product[51]; 1387 tmp[24] = product[52]; tmp[25] = product[53]; tmp[26] = product[54]; tmp[27] = product[55]; 1388 carry -= vli_sub(result, result, tmp); 1389 1390 /* d2 */ 1391 tmp[0] = product[44]; tmp[1] = product[45]; tmp[2] = product[46]; tmp[3] = product[47]; 1392 tmp[4] = product[48]; tmp[5] = product[49]; tmp[6] = product[50]; tmp[7] = product[51]; 1393 tmp[8] = product[52]; tmp[9] = product[53]; tmp[10] = product[54]; tmp[11] = product[55]; 1394 tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0; 1395 tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0; 1396 tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 1397 tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0; 1398 carry -= vli_sub(result, result, tmp); 1399 1400 if (carry < 0) { 1401 do { 1402 carry += vli_add(result, result, curve_p); 1403 } while (carry < 0); 1404 } else { 1405 while (carry || vli_cmp(curve_p, result) != 1) { 1406 carry -= vli_sub(result, result, curve_p); 1407 } 1408 } 1409 } 1410 #elif uECC_WORD_SIZE == 4 1411 void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) 1412 { 1413 uint32_t tmp[uECC_WORDS]; 1414 int carry; 1415 1416 /* t */ 1417 vli_set(result, product); 1418 1419 /* s1 */ 1420 tmp[0] = tmp[1] = tmp[2] = 0; 1421 tmp[3] = product[7]; 1422 tmp[4] = product[8]; 1423 tmp[5] = product[9]; 1424 tmp[6] = product[10]; 1425 carry = vli_add(result, result, tmp); 1426 1427 /* s2 */ 1428 tmp[3] = product[11]; 1429 tmp[4] = product[12]; 1430 tmp[5] = product[13]; 1431 tmp[6] = 0; 1432 carry += vli_add(result, result, tmp); 1433 1434 /* d1 */ 1435 tmp[0] = product[7]; 1436 tmp[1] = product[8]; 1437 tmp[2] = product[9]; 1438 tmp[3] = product[10]; 1439 tmp[4] = product[11]; 1440 tmp[5] = product[12]; 1441 tmp[6] = product[13]; 1442 carry -= vli_sub(result, result, tmp); 1443 1444 /* d2 */ 1445 tmp[0] = product[11]; 1446 tmp[1] = product[12]; 1447 tmp[2] = product[13]; 1448 tmp[3] = tmp[4] = tmp[5] = tmp[6] = 0; 1449 carry -= vli_sub(result, result, tmp); 1450 1451 if (carry < 0) { 1452 do { 1453 carry += vli_add(result, result, curve_p); 1454 } while (carry < 0); 1455 } else { 1456 while (carry || vli_cmp(curve_p, result) != 1) { 1457 carry -= vli_sub(result, result, curve_p); 1458 } 1459 } 1460 } 1461 #endif /* uECC_WORD_SIZE */ 1462 1463 #endif /* uECC_CURVE */ 1464 #endif /* !asm_mmod_fast */ 1465 1466 /* Computes result = (left * right) % curve_p. */ 1467 static void vli_modMult_fast(uECC_word_t *result, 1468 const uECC_word_t *left, 1469 const uECC_word_t *right) { 1470 uECC_word_t product[2 * uECC_WORDS]; 1471 vli_mult(product, left, right); 1472 vli_mmod_fast(result, product); 1473 } 1474 1475 #if uECC_SQUARE_FUNC 1476 1477 /* Computes result = left^2 % curve_p. */ 1478 static void vli_modSquare_fast(uECC_word_t *result, const uECC_word_t *left) { 1479 uECC_word_t product[2 * uECC_WORDS]; 1480 vli_square(product, left); 1481 vli_mmod_fast(result, product); 1482 } 1483 1484 #else /* uECC_SQUARE_FUNC */ 1485 1486 #define vli_modSquare_fast(result, left) vli_modMult_fast((result), (left), (left)) 1487 1488 #endif /* uECC_SQUARE_FUNC */ 1489 1490 1491 #define EVEN(vli) (!(vli[0] & 1)) 1492 /* Computes result = (1 / input) % mod. All VLIs are the same size. 1493 See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" 1494 labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf */ 1495 #if !asm_modInv 1496 static void vli_modInv(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod) { 1497 uECC_word_t a[uECC_WORDS], b[uECC_WORDS], u[uECC_WORDS], v[uECC_WORDS]; 1498 uECC_word_t carry; 1499 cmpresult_t cmpResult; 1500 1501 if (vli_isZero(input)) { 1502 vli_clear(result); 1503 return; 1504 } 1505 1506 vli_set(a, input); 1507 vli_set(b, mod); 1508 vli_clear(u); 1509 u[0] = 1; 1510 vli_clear(v); 1511 while ((cmpResult = vli_cmp(a, b)) != 0) { 1512 carry = 0; 1513 if (EVEN(a)) { 1514 vli_rshift1(a); 1515 if (!EVEN(u)) { 1516 carry = vli_add(u, u, mod); 1517 } 1518 vli_rshift1(u); 1519 if (carry) { 1520 u[uECC_WORDS - 1] |= HIGH_BIT_SET; 1521 } 1522 } else if (EVEN(b)) { 1523 vli_rshift1(b); 1524 if (!EVEN(v)) { 1525 carry = vli_add(v, v, mod); 1526 } 1527 vli_rshift1(v); 1528 if (carry) { 1529 v[uECC_WORDS - 1] |= HIGH_BIT_SET; 1530 } 1531 } else if (cmpResult > 0) { 1532 vli_sub(a, a, b); 1533 vli_rshift1(a); 1534 if (vli_cmp(u, v) < 0) { 1535 vli_add(u, u, mod); 1536 } 1537 vli_sub(u, u, v); 1538 if (!EVEN(u)) { 1539 carry = vli_add(u, u, mod); 1540 } 1541 vli_rshift1(u); 1542 if (carry) { 1543 u[uECC_WORDS - 1] |= HIGH_BIT_SET; 1544 } 1545 } else { 1546 vli_sub(b, b, a); 1547 vli_rshift1(b); 1548 if (vli_cmp(v, u) < 0) { 1549 vli_add(v, v, mod); 1550 } 1551 vli_sub(v, v, u); 1552 if (!EVEN(v)) { 1553 carry = vli_add(v, v, mod); 1554 } 1555 vli_rshift1(v); 1556 if (carry) { 1557 v[uECC_WORDS - 1] |= HIGH_BIT_SET; 1558 } 1559 } 1560 } 1561 vli_set(result, u); 1562 } 1563 #endif /* !asm_modInv */ 1564 1565 /* ------ Point operations ------ */ 1566 1567 /* Returns 1 if 'point' is the point at infinity, 0 otherwise. */ 1568 static cmpresult_t EccPoint_isZero(const EccPoint *point) { 1569 return (vli_isZero(point->x) && vli_isZero(point->y)); 1570 } 1571 1572 /* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates. 1573 From eprint.iacr.org/2011/338.pdf 1574 */ 1575 1576 /* Double in place */ 1577 #if (uECC_CURVE == uECC_secp256k1) 1578 static void EccPoint_double_jacobian(uECC_word_t * RESTRICT X1, 1579 uECC_word_t * RESTRICT Y1, 1580 uECC_word_t * RESTRICT Z1) { 1581 /* t1 = X, t2 = Y, t3 = Z */ 1582 uECC_word_t t4[uECC_WORDS]; 1583 uECC_word_t t5[uECC_WORDS]; 1584 1585 if (vli_isZero(Z1)) { 1586 return; 1587 } 1588 1589 vli_modSquare_fast(t5, Y1); /* t5 = y1^2 */ 1590 vli_modMult_fast(t4, X1, t5); /* t4 = x1*y1^2 = A */ 1591 vli_modSquare_fast(X1, X1); /* t1 = x1^2 */ 1592 vli_modSquare_fast(t5, t5); /* t5 = y1^4 */ 1593 vli_modMult_fast(Z1, Y1, Z1); /* t3 = y1*z1 = z3 */ 1594 1595 vli_modAdd(Y1, X1, X1, curve_p); /* t2 = 2*x1^2 */ 1596 vli_modAdd(Y1, Y1, X1, curve_p); /* t2 = 3*x1^2 */ 1597 if (vli_testBit(Y1, 0)) { 1598 uECC_word_t carry = vli_add(Y1, Y1, curve_p); 1599 vli_rshift1(Y1); 1600 Y1[uECC_WORDS - 1] |= carry << (uECC_WORD_BITS - 1); 1601 } else { 1602 vli_rshift1(Y1); 1603 } 1604 /* t2 = 3/2*(x1^2) = B */ 1605 1606 vli_modSquare_fast(X1, Y1); /* t1 = B^2 */ 1607 vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - A */ 1608 vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - 2A = x3 */ 1609 1610 vli_modSub(t4, t4, X1, curve_p); /* t4 = A - x3 */ 1611 vli_modMult_fast(Y1, Y1, t4); /* t2 = B * (A - x3) */ 1612 vli_modSub(Y1, Y1, t5, curve_p); /* t2 = B * (A - x3) - y1^4 = y3 */ 1613 } 1614 #else 1615 static void EccPoint_double_jacobian(uECC_word_t * RESTRICT X1, 1616 uECC_word_t * RESTRICT Y1, 1617 uECC_word_t * RESTRICT Z1) { 1618 /* t1 = X, t2 = Y, t3 = Z */ 1619 uECC_word_t t4[uECC_WORDS]; 1620 uECC_word_t t5[uECC_WORDS]; 1621 1622 if (vli_isZero(Z1)) { 1623 return; 1624 } 1625 1626 vli_modSquare_fast(t4, Y1); /* t4 = y1^2 */ 1627 vli_modMult_fast(t5, X1, t4); /* t5 = x1*y1^2 = A */ 1628 vli_modSquare_fast(t4, t4); /* t4 = y1^4 */ 1629 vli_modMult_fast(Y1, Y1, Z1); /* t2 = y1*z1 = z3 */ 1630 vli_modSquare_fast(Z1, Z1); /* t3 = z1^2 */ 1631 1632 vli_modAdd(X1, X1, Z1, curve_p); /* t1 = x1 + z1^2 */ 1633 vli_modAdd(Z1, Z1, Z1, curve_p); /* t3 = 2*z1^2 */ 1634 vli_modSub_fast(Z1, X1, Z1); /* t3 = x1 - z1^2 */ 1635 vli_modMult_fast(X1, X1, Z1); /* t1 = x1^2 - z1^4 */ 1636 1637 vli_modAdd(Z1, X1, X1, curve_p); /* t3 = 2*(x1^2 - z1^4) */ 1638 vli_modAdd(X1, X1, Z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */ 1639 if (vli_testBit(X1, 0)) { 1640 uECC_word_t l_carry = vli_add(X1, X1, curve_p); 1641 vli_rshift1(X1); 1642 X1[uECC_WORDS - 1] |= l_carry << (uECC_WORD_BITS - 1); 1643 } else { 1644 vli_rshift1(X1); 1645 } 1646 /* t1 = 3/2*(x1^2 - z1^4) = B */ 1647 1648 vli_modSquare_fast(Z1, X1); /* t3 = B^2 */ 1649 vli_modSub_fast(Z1, Z1, t5); /* t3 = B^2 - A */ 1650 vli_modSub_fast(Z1, Z1, t5); /* t3 = B^2 - 2A = x3 */ 1651 vli_modSub_fast(t5, t5, Z1); /* t5 = A - x3 */ 1652 vli_modMult_fast(X1, X1, t5); /* t1 = B * (A - x3) */ 1653 vli_modSub_fast(t4, X1, t4); /* t4 = B * (A - x3) - y1^4 = y3 */ 1654 1655 vli_set(X1, Z1); 1656 vli_set(Z1, Y1); 1657 vli_set(Y1, t4); 1658 } 1659 #endif 1660 1661 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ 1662 static void apply_z(uECC_word_t * RESTRICT X1, 1663 uECC_word_t * RESTRICT Y1, 1664 const uECC_word_t * RESTRICT Z) { 1665 uECC_word_t t1[uECC_WORDS]; 1666 1667 vli_modSquare_fast(t1, Z); /* z^2 */ 1668 vli_modMult_fast(X1, X1, t1); /* x1 * z^2 */ 1669 vli_modMult_fast(t1, t1, Z); /* z^3 */ 1670 vli_modMult_fast(Y1, Y1, t1); /* y1 * z^3 */ 1671 } 1672 1673 /* P = (x1, y1) => 2P, (x2, y2) => P' */ 1674 static void XYcZ_initial_double(uECC_word_t * RESTRICT X1, 1675 uECC_word_t * RESTRICT Y1, 1676 uECC_word_t * RESTRICT X2, 1677 uECC_word_t * RESTRICT Y2, 1678 const uECC_word_t * RESTRICT initial_Z) { 1679 uECC_word_t z[uECC_WORDS]; 1680 if (initial_Z) { 1681 vli_set(z, initial_Z); 1682 } else { 1683 vli_clear(z); 1684 z[0] = 1; 1685 } 1686 1687 vli_set(X2, X1); 1688 vli_set(Y2, Y1); 1689 1690 apply_z(X1, Y1, z); 1691 EccPoint_double_jacobian(X1, Y1, z); 1692 apply_z(X2, Y2, z); 1693 } 1694 1695 /* Input P = (x1, y1, Z), Q = (x2, y2, Z) 1696 Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) 1697 or P => P', Q => P + Q 1698 */ 1699 static void XYcZ_add(uECC_word_t * RESTRICT X1, 1700 uECC_word_t * RESTRICT Y1, 1701 uECC_word_t * RESTRICT X2, 1702 uECC_word_t * RESTRICT Y2) { 1703 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 1704 uECC_word_t t5[uECC_WORDS]; 1705 1706 vli_modSub_fast(t5, X2, X1); /* t5 = x2 - x1 */ 1707 vli_modSquare_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */ 1708 vli_modMult_fast(X1, X1, t5); /* t1 = x1*A = B */ 1709 vli_modMult_fast(X2, X2, t5); /* t3 = x2*A = C */ 1710 vli_modSub_fast(Y2, Y2, Y1); /* t4 = y2 - y1 */ 1711 vli_modSquare_fast(t5, Y2); /* t5 = (y2 - y1)^2 = D */ 1712 1713 vli_modSub_fast(t5, t5, X1); /* t5 = D - B */ 1714 vli_modSub_fast(t5, t5, X2); /* t5 = D - B - C = x3 */ 1715 vli_modSub_fast(X2, X2, X1); /* t3 = C - B */ 1716 vli_modMult_fast(Y1, Y1, X2); /* t2 = y1*(C - B) */ 1717 vli_modSub_fast(X2, X1, t5); /* t3 = B - x3 */ 1718 vli_modMult_fast(Y2, Y2, X2); /* t4 = (y2 - y1)*(B - x3) */ 1719 vli_modSub_fast(Y2, Y2, Y1); /* t4 = y3 */ 1720 1721 vli_set(X2, t5); 1722 } 1723 1724 /* Input P = (x1, y1, Z), Q = (x2, y2, Z) 1725 Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) 1726 or P => P - Q, Q => P + Q 1727 */ 1728 static void XYcZ_addC(uECC_word_t * RESTRICT X1, 1729 uECC_word_t * RESTRICT Y1, 1730 uECC_word_t * RESTRICT X2, 1731 uECC_word_t * RESTRICT Y2) { 1732 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 1733 uECC_word_t t5[uECC_WORDS]; 1734 uECC_word_t t6[uECC_WORDS]; 1735 uECC_word_t t7[uECC_WORDS]; 1736 1737 vli_modSub_fast(t5, X2, X1); /* t5 = x2 - x1 */ 1738 vli_modSquare_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */ 1739 vli_modMult_fast(X1, X1, t5); /* t1 = x1*A = B */ 1740 vli_modMult_fast(X2, X2, t5); /* t3 = x2*A = C */ 1741 vli_modAdd(t5, Y2, Y1, curve_p); /* t5 = y2 + y1 */ 1742 vli_modSub_fast(Y2, Y2, Y1); /* t4 = y2 - y1 */ 1743 1744 vli_modSub_fast(t6, X2, X1); /* t6 = C - B */ 1745 vli_modMult_fast(Y1, Y1, t6); /* t2 = y1 * (C - B) = E */ 1746 vli_modAdd(t6, X1, X2, curve_p); /* t6 = B + C */ 1747 vli_modSquare_fast(X2, Y2); /* t3 = (y2 - y1)^2 = D */ 1748 vli_modSub_fast(X2, X2, t6); /* t3 = D - (B + C) = x3 */ 1749 1750 vli_modSub_fast(t7, X1, X2); /* t7 = B - x3 */ 1751 vli_modMult_fast(Y2, Y2, t7); /* t4 = (y2 - y1)*(B - x3) */ 1752 vli_modSub_fast(Y2, Y2, Y1); /* t4 = (y2 - y1)*(B - x3) - E = y3 */ 1753 1754 vli_modSquare_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */ 1755 vli_modSub_fast(t7, t7, t6); /* t7 = F - (B + C) = x3' */ 1756 vli_modSub_fast(t6, t7, X1); /* t6 = x3' - B */ 1757 vli_modMult_fast(t6, t6, t5); /* t6 = (y2 + y1)*(x3' - B) */ 1758 vli_modSub_fast(Y1, t6, Y1); /* t2 = (y2 + y1)*(x3' - B) - E = y3' */ 1759 1760 vli_set(X1, t7); 1761 } 1762 1763 static void EccPoint_mult(EccPoint * RESTRICT result, 1764 const EccPoint * RESTRICT point, 1765 const uECC_word_t * RESTRICT scalar, 1766 const uECC_word_t * RESTRICT initialZ, 1767 bitcount_t numBits) { 1768 /* R0 and R1 */ 1769 uECC_word_t Rx[2][uECC_WORDS]; 1770 uECC_word_t Ry[2][uECC_WORDS]; 1771 uECC_word_t z[uECC_WORDS]; 1772 bitcount_t i; 1773 uECC_word_t nb; 1774 1775 vli_set(Rx[1], point->x); 1776 vli_set(Ry[1], point->y); 1777 1778 XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initialZ); 1779 1780 for (i = numBits - 2; i > 0; --i) { 1781 nb = !vli_testBit(scalar, i); 1782 XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb]); 1783 XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb]); 1784 } 1785 1786 nb = !vli_testBit(scalar, 0); 1787 XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb]); 1788 1789 /* Find final 1/Z value. */ 1790 vli_modSub_fast(z, Rx[1], Rx[0]); /* X1 - X0 */ 1791 vli_modMult_fast(z, z, Ry[1 - nb]); /* Yb * (X1 - X0) */ 1792 vli_modMult_fast(z, z, point->x); /* xP * Yb * (X1 - X0) */ 1793 vli_modInv(z, z, curve_p); /* 1 / (xP * Yb * (X1 - X0)) */ 1794 vli_modMult_fast(z, z, point->y); /* yP / (xP * Yb * (X1 - X0)) */ 1795 vli_modMult_fast(z, z, Rx[1 - nb]); /* Xb * yP / (xP * Yb * (X1 - X0)) */ 1796 /* End 1/Z calculation */ 1797 1798 XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb]); 1799 apply_z(Rx[0], Ry[0], z); 1800 1801 vli_set(result->x, Rx[0]); 1802 vli_set(result->y, Ry[0]); 1803 } 1804 1805 static int EccPoint_compute_public_key(EccPoint *result, uECC_word_t *private) { 1806 uECC_word_t tmp1[uECC_WORDS]; 1807 uECC_word_t tmp2[uECC_WORDS]; 1808 uECC_word_t *p2[2] = {tmp1, tmp2}; 1809 uECC_word_t carry; 1810 1811 /* Make sure the private key is in the range [1, n-1]. */ 1812 if (vli_isZero(private)) { 1813 return 0; 1814 } 1815 1816 #if (uECC_CURVE == uECC_secp160r1) 1817 // Don't regularize the bitcount for secp160r1, since it would have a larger performance 1818 // impact (about 2% slower on average) and requires the vli_xxx_n functions, leading to 1819 // a significant increase in code size. 1820 1821 EccPoint_mult(result, &curve_G, private, NULL, vli_numBits(private, uECC_WORDS)); 1822 #else 1823 if (vli_cmp(curve_n, private) != 1) { 1824 return 0; 1825 } 1826 1827 // Regularize the bitcount for the private key so that attackers cannot use a side channel 1828 // attack to learn the number of leading zeros. 1829 carry = vli_add(tmp1, private, curve_n); 1830 vli_add(tmp2, tmp1, curve_n); 1831 EccPoint_mult(result, &curve_G, p2[!carry], NULL, (uECC_BYTES * 8) + 1); 1832 #endif 1833 1834 if (EccPoint_isZero(result)) { 1835 return 0; 1836 } 1837 return 1; 1838 } 1839 1840 #ifdef ENABLE_MICRO_ECC_COMPRESSION 1841 1842 #if uECC_CURVE == uECC_secp224r1 1843 1844 /* Routine 3.2.4 RS; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1845 static void mod_sqrt_secp224r1_rs(uECC_word_t *d1, 1846 uECC_word_t *e1, 1847 uECC_word_t *f1, 1848 const uECC_word_t *d0, 1849 const uECC_word_t *e0, 1850 const uECC_word_t *f0) { 1851 uECC_word_t t[uECC_WORDS]; 1852 1853 vli_modSquare_fast(t, d0); /* t <-- d0 ^ 2 */ 1854 vli_modMult_fast(e1, d0, e0); /* e1 <-- d0 * e0 */ 1855 vli_modAdd(d1, t, f0, curve_p); /* d1 <-- t + f0 */ 1856 vli_modAdd(e1, e1, e1, curve_p); /* e1 <-- e1 + e1 */ 1857 vli_modMult_fast(f1, t, f0); /* f1 <-- t * f0 */ 1858 vli_modAdd(f1, f1, f1, curve_p); /* f1 <-- f1 + f1 */ 1859 vli_modAdd(f1, f1, f1, curve_p); /* f1 <-- f1 + f1 */ 1860 } 1861 1862 /* Routine 3.2.5 RSS; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1863 static void mod_sqrt_secp224r1_rss(uECC_word_t *d1, 1864 uECC_word_t *e1, 1865 uECC_word_t *f1, 1866 const uECC_word_t *d0, 1867 const uECC_word_t *e0, 1868 const uECC_word_t *f0, 1869 const bitcount_t j) { 1870 bitcount_t i; 1871 1872 vli_set(d1, d0); /* d1 <-- d0 */ 1873 vli_set(e1, e0); /* e1 <-- e0 */ 1874 vli_set(f1, f0); /* f1 <-- f0 */ 1875 for (i = 1; i <= j; i++) { 1876 mod_sqrt_secp224r1_rs(d1, e1, f1, d1, e1, f1); /* RS (d1,e1,f1,d1,e1,f1) */ 1877 } 1878 } 1879 1880 /* Routine 3.2.6 RM; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1881 static void mod_sqrt_secp224r1_rm(uECC_word_t *d2, 1882 uECC_word_t *e2, 1883 uECC_word_t *f2, 1884 const uECC_word_t *c, 1885 const uECC_word_t *d0, 1886 const uECC_word_t *e0, 1887 const uECC_word_t *d1, 1888 const uECC_word_t *e1) { 1889 uECC_word_t t1[uECC_WORDS]; 1890 uECC_word_t t2[uECC_WORDS]; 1891 1892 vli_modMult_fast(t1, e0, e1); /* t1 <-- e0 * e1 */ 1893 vli_modMult_fast(t1, t1, c); /* t1 <-- t1 * c */ 1894 vli_modSub_fast(t1, curve_p, t1); /* t1 <-- p - t1 */ 1895 vli_modMult_fast(t2, d0, d1); /* t2 <-- d0 * d1 */ 1896 vli_modAdd(t2, t2, t1, curve_p); /* t2 <-- t2 + t1 */ 1897 vli_modMult_fast(t1, d0, e1); /* t1 <-- d0 * e1 */ 1898 vli_modMult_fast(e2, d1, e0); /* e2 <-- d1 * e0 */ 1899 vli_modAdd(e2, e2, t1, curve_p); /* e2 <-- e2 + t1 */ 1900 vli_modSquare_fast(f2, e2); /* f2 <-- e2^2 */ 1901 vli_modMult_fast(f2, f2, c); /* f2 <-- f2 * c */ 1902 vli_modSub_fast(f2, curve_p, f2); /* f2 <-- p - f2 */ 1903 vli_set(d2, t2); /* d2 <-- t2 */ 1904 } 1905 1906 /* Routine 3.2.7 RP; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1907 static void mod_sqrt_secp224r1_rp(uECC_word_t *d1, 1908 uECC_word_t *e1, 1909 uECC_word_t *f1, 1910 const uECC_word_t *c, 1911 const uECC_word_t *r) { 1912 wordcount_t i; 1913 wordcount_t pow2i = 1; 1914 uECC_word_t d0[uECC_WORDS]; 1915 uECC_word_t e0[uECC_WORDS] = {1}; /* e0 <-- 1 */ 1916 uECC_word_t f0[uECC_WORDS]; 1917 1918 vli_set(d0, r); /* d0 <-- r */ 1919 vli_modSub_fast(f0, curve_p, c); /* f0 <-- p - c */ 1920 for (i = 0; i <= 6; i++) { 1921 mod_sqrt_secp224r1_rss(d1, e1, f1, d0, e0, f0, pow2i); /* RSS (d1,e1,f1,d0,e0,f0,2^i) */ 1922 mod_sqrt_secp224r1_rm(d1, e1, f1, c, d1, e1, d0, e0); /* RM (d1,e1,f1,c,d1,e1,d0,e0) */ 1923 vli_set(d0, d1); /* d0 <-- d1 */ 1924 vli_set(e0, e1); /* e0 <-- e1 */ 1925 vli_set(f0, f1); /* f0 <-- f1 */ 1926 pow2i *= 2; 1927 } 1928 } 1929 1930 /* Compute a = sqrt(a) (mod curve_p). */ 1931 /* Routine 3.2.8 mp_mod_sqrt_224; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1932 static void mod_sqrt(uECC_word_t *a) { 1933 bitcount_t i; 1934 uECC_word_t e1[uECC_WORDS]; 1935 uECC_word_t f1[uECC_WORDS]; 1936 uECC_word_t d0[uECC_WORDS]; 1937 uECC_word_t e0[uECC_WORDS]; 1938 uECC_word_t f0[uECC_WORDS]; 1939 uECC_word_t d1[uECC_WORDS]; 1940 1941 // s = a; using constant instead of random value 1942 mod_sqrt_secp224r1_rp(d0, e0, f0, a, a); /* RP (d0, e0, f0, c, s) */ 1943 mod_sqrt_secp224r1_rs(d1, e1, f1, d0, e0, f0); /* RS (d1, e1, f1, d0, e0, f0) */ 1944 for (i = 1; i <= 95; i++) { 1945 vli_set(d0, d1); /* d0 <-- d1 */ 1946 vli_set(e0, e1); /* e0 <-- e1 */ 1947 vli_set(f0, f1); /* f0 <-- f1 */ 1948 mod_sqrt_secp224r1_rs(d1, e1, f1, d0, e0, f0); /* RS (d1, e1, f1, d0, e0, f0) */ 1949 if (vli_isZero(d1)) { /* if d1 == 0 */ 1950 break; 1951 } 1952 } 1953 vli_modInv(f1, e0, curve_p); /* f1 <-- 1 / e0 */ 1954 vli_modMult_fast(a, d0, f1); /* a <-- d0 / e0 */ 1955 } 1956 1957 #else /* uECC_CURVE */ 1958 1959 /* Compute a = sqrt(a) (mod curve_p). */ 1960 static void mod_sqrt(uECC_word_t *a) { 1961 bitcount_t i; 1962 uECC_word_t p1[uECC_WORDS] = {1}; 1963 uECC_word_t l_result[uECC_WORDS] = {1}; 1964 1965 /* Since curve_p == 3 (mod 4) for all supported curves, we can 1966 compute sqrt(a) = a^((curve_p + 1) / 4) (mod curve_p). */ 1967 vli_add(p1, curve_p, p1); /* p1 = curve_p + 1 */ 1968 for (i = vli_numBits(p1, uECC_WORDS) - 1; i > 1; --i) { 1969 vli_modSquare_fast(l_result, l_result); 1970 if (vli_testBit(p1, i)) { 1971 vli_modMult_fast(l_result, l_result, a); 1972 } 1973 } 1974 vli_set(a, l_result); 1975 } 1976 #endif /* uECC_CURVE */ 1977 1978 #endif /* ENABLE_MICRO_ECC_COMPRESSION */ 1979 1980 1981 #if uECC_WORD_SIZE == 1 1982 1983 static void vli_nativeToBytes(uint8_t * RESTRICT dest, const uint8_t * RESTRICT src) { 1984 uint8_t i; 1985 for (i = 0; i < uECC_BYTES; ++i) { 1986 dest[i] = src[(uECC_BYTES - 1) - i]; 1987 } 1988 } 1989 1990 #define vli_bytesToNative(dest, src) vli_nativeToBytes((dest), (src)) 1991 1992 #elif uECC_WORD_SIZE == 4 1993 1994 static void vli_nativeToBytes(uint8_t *bytes, const uint32_t *native) { 1995 unsigned i; 1996 for (i = 0; i < uECC_WORDS; ++i) { 1997 uint8_t *digit = bytes + 4 * (uECC_WORDS - 1 - i); 1998 digit[0] = native[i] >> 24; 1999 digit[1] = native[i] >> 16; 2000 digit[2] = native[i] >> 8; 2001 digit[3] = native[i]; 2002 } 2003 } 2004 2005 static void vli_bytesToNative(uint32_t *native, const uint8_t *bytes) { 2006 unsigned i; 2007 for (i = 0; i < uECC_WORDS; ++i) { 2008 const uint8_t *digit = bytes + 4 * (uECC_WORDS - 1 - i); 2009 native[i] = ((uint32_t)digit[0] << 24) | ((uint32_t)digit[1] << 16) | 2010 ((uint32_t)digit[2] << 8) | (uint32_t)digit[3]; 2011 } 2012 } 2013 2014 #else 2015 2016 static void vli_nativeToBytes(uint8_t *bytes, const uint64_t *native) { 2017 unsigned i; 2018 for (i = 0; i < uECC_WORDS; ++i) { 2019 uint8_t *digit = bytes + 8 * (uECC_WORDS - 1 - i); 2020 digit[0] = native[i] >> 56; 2021 digit[1] = native[i] >> 48; 2022 digit[2] = native[i] >> 40; 2023 digit[3] = native[i] >> 32; 2024 digit[4] = native[i] >> 24; 2025 digit[5] = native[i] >> 16; 2026 digit[6] = native[i] >> 8; 2027 digit[7] = native[i]; 2028 } 2029 } 2030 2031 static void vli_bytesToNative(uint64_t *native, const uint8_t *bytes) { 2032 unsigned i; 2033 for (i = 0; i < uECC_WORDS; ++i) { 2034 const uint8_t *digit = bytes + 8 * (uECC_WORDS - 1 - i); 2035 native[i] = ((uint64_t)digit[0] << 56) | ((uint64_t)digit[1] << 48) | 2036 ((uint64_t)digit[2] << 40) | ((uint64_t)digit[3] << 32) | 2037 ((uint64_t)digit[4] << 24) | ((uint64_t)digit[5] << 16) | 2038 ((uint64_t)digit[6] << 8) | (uint64_t)digit[7]; 2039 } 2040 } 2041 2042 #endif /* uECC_WORD_SIZE */ 2043 2044 int uECC_make_key(uint8_t public_key[uECC_BYTES*2], uint8_t private_key[uECC_BYTES]) { 2045 uECC_word_t private[uECC_WORDS]; 2046 EccPoint public; 2047 uECC_word_t tries; 2048 for (tries = 0; tries < MAX_TRIES; ++tries) { 2049 if (g_rng_function((uint8_t *)private, sizeof(private)) && 2050 EccPoint_compute_public_key(&public, private)) { 2051 vli_nativeToBytes(private_key, private); 2052 vli_nativeToBytes(public_key, public.x); 2053 vli_nativeToBytes(public_key + uECC_BYTES, public.y); 2054 return 1; 2055 } 2056 } 2057 return 0; 2058 } 2059 2060 int uECC_shared_secret(const uint8_t public_key[uECC_BYTES*2], 2061 const uint8_t private_key[uECC_BYTES], 2062 uint8_t secret[uECC_BYTES]) { 2063 EccPoint public; 2064 EccPoint product; 2065 uECC_word_t private[uECC_WORDS]; 2066 uECC_word_t tmp[uECC_WORDS]; 2067 uECC_word_t *p2[2] = {private, tmp}; 2068 uECC_word_t random[uECC_WORDS]; 2069 uECC_word_t *initial_Z = NULL; 2070 uECC_word_t tries; 2071 uECC_word_t carry; 2072 2073 // Try to get a random initial Z value to improve protection against side-channel 2074 // attacks. If the RNG fails every time (eg it was not defined), we continue so that 2075 // uECC_shared_secret() can still work without an RNG defined. 2076 for (tries = 0; tries < MAX_TRIES; ++tries) { 2077 if (g_rng_function((uint8_t *)random, sizeof(random)) && !vli_isZero(random)) { 2078 initial_Z = random; 2079 break; 2080 } 2081 } 2082 2083 vli_bytesToNative(private, private_key); 2084 vli_bytesToNative(public.x, public_key); 2085 vli_bytesToNative(public.y, public_key + uECC_BYTES); 2086 2087 #if (uECC_CURVE == uECC_secp160r1) 2088 // Don't regularize the bitcount for secp160r1. 2089 EccPoint_mult(&product, &public, private, initial_Z, vli_numBits(private, uECC_WORDS)); 2090 #else 2091 // Regularize the bitcount for the private key so that attackers cannot use a side channel 2092 // attack to learn the number of leading zeros. 2093 carry = vli_add(private, private, curve_n); 2094 vli_add(tmp, private, curve_n); 2095 EccPoint_mult(&product, &public, p2[!carry], initial_Z, (uECC_BYTES * 8) + 1); 2096 #endif 2097 2098 vli_nativeToBytes(secret, product.x); 2099 return !EccPoint_isZero(&product); 2100 } 2101 2102 #ifdef ENABLE_MICRO_ECC_COMPRESSION 2103 2104 void uECC_compress(const uint8_t public_key[uECC_BYTES*2], uint8_t compressed[uECC_BYTES+1]) { 2105 wordcount_t i; 2106 for (i = 0; i < uECC_BYTES; ++i) { 2107 compressed[i+1] = public_key[i]; 2108 } 2109 compressed[0] = 2 + (public_key[uECC_BYTES * 2 - 1] & 0x01); 2110 } 2111 2112 #endif 2113 2114 /* Computes result = x^3 + ax + b. result must not overlap x. */ 2115 static void curve_x_side(uECC_word_t * RESTRICT result, const uECC_word_t * RESTRICT x) { 2116 static const uECC_word_t curve_b[uECC_WORDS] = uECC_CONCAT(Curve_B_, uECC_CURVE); 2117 #if (uECC_CURVE == uECC_secp256k1) 2118 vli_modSquare_fast(result, x); /* r = x^2 */ 2119 vli_modMult_fast(result, result, x); /* r = x^3 */ 2120 vli_modAdd(result, result, curve_b, curve_p); /* r = x^3 + b */ 2121 #else 2122 uECC_word_t _3[uECC_WORDS] = {3}; /* -a = 3 */ 2123 2124 vli_modSquare_fast(result, x); /* r = x^2 */ 2125 vli_modSub_fast(result, result, _3); /* r = x^2 - 3 */ 2126 vli_modMult_fast(result, result, x); /* r = x^3 - 3x */ 2127 vli_modAdd(result, result, curve_b, curve_p); /* r = x^3 - 3x + b */ 2128 #endif 2129 } 2130 2131 #ifdef ENABLE_MICRO_ECC_COMPRESSION 2132 2133 void uECC_decompress(const uint8_t compressed[uECC_BYTES+1], uint8_t public_key[uECC_BYTES*2]) { 2134 EccPoint point; 2135 vli_bytesToNative(point.x, compressed + 1); 2136 curve_x_side(point.y, point.x); 2137 mod_sqrt(point.y); 2138 2139 if ((point.y[0] & 0x01) != (compressed[0] & 0x01)) { 2140 vli_sub(point.y, curve_p, point.y); 2141 } 2142 2143 vli_nativeToBytes(public_key, point.x); 2144 vli_nativeToBytes(public_key + uECC_BYTES, point.y); 2145 } 2146 2147 #endif /* ENABLE_MICRO_ECC_COMPRESSION */ 2148 2149 int uECC_valid_public_key(const uint8_t public_key[uECC_BYTES*2]) { 2150 uECC_word_t tmp1[uECC_WORDS]; 2151 uECC_word_t tmp2[uECC_WORDS]; 2152 EccPoint public; 2153 2154 vli_bytesToNative(public.x, public_key); 2155 vli_bytesToNative(public.y, public_key + uECC_BYTES); 2156 2157 // The point at infinity is invalid. 2158 if (EccPoint_isZero(&public)) { 2159 return 0; 2160 } 2161 2162 // x and y must be smaller than p. 2163 if (vli_cmp(curve_p, public.x) != 1 || vli_cmp(curve_p, public.y) != 1) { 2164 return 0; 2165 } 2166 2167 vli_modSquare_fast(tmp1, public.y); /* tmp1 = y^2 */ 2168 curve_x_side(tmp2, public.x); /* tmp2 = x^3 + ax + b */ 2169 2170 /* Make sure that y^2 == x^3 + ax + b */ 2171 return (vli_cmp(tmp1, tmp2) == 0); 2172 } 2173 2174 int uECC_compute_public_key(const uint8_t private_key[uECC_BYTES], 2175 uint8_t public_key[uECC_BYTES * 2]) { 2176 uECC_word_t private[uECC_WORDS]; 2177 EccPoint public; 2178 2179 vli_bytesToNative(private, private_key); 2180 2181 if (!EccPoint_compute_public_key(&public, private)) { 2182 return 0; 2183 } 2184 2185 vli_nativeToBytes(public_key, public.x); 2186 vli_nativeToBytes(public_key + uECC_BYTES, public.y); 2187 return 1; 2188 } 2189 2190 int uECC_bytes(void) { 2191 return uECC_BYTES; 2192 } 2193 2194 int uECC_curve(void) { 2195 return uECC_CURVE; 2196 } 2197 2198 /* -------- ECDSA code -------- */ 2199 2200 #ifdef ENABLE_MICRO_ECC_ECDSA 2201 2202 #if (uECC_CURVE == uECC_secp160r1) 2203 static void vli_clear_n(uECC_word_t *vli) { 2204 vli_clear(vli); 2205 vli[uECC_N_WORDS - 1] = 0; 2206 } 2207 2208 static uECC_word_t vli_isZero_n(const uECC_word_t *vli) { 2209 if (vli[uECC_N_WORDS - 1]) { 2210 return 0; 2211 } 2212 return vli_isZero(vli); 2213 } 2214 2215 static void vli_set_n(uECC_word_t *dest, const uECC_word_t *src) { 2216 vli_set(dest, src); 2217 dest[uECC_N_WORDS - 1] = src[uECC_N_WORDS - 1]; 2218 } 2219 2220 static cmpresult_t vli_cmp_n(const uECC_word_t *left, const uECC_word_t *right) { 2221 if (left[uECC_N_WORDS - 1] > right[uECC_N_WORDS - 1]) { 2222 return 1; 2223 } else if (left[uECC_N_WORDS - 1] < right[uECC_N_WORDS - 1]) { 2224 return -1; 2225 } 2226 return vli_cmp(left, right); 2227 } 2228 2229 static void vli_rshift1_n(uECC_word_t *vli) { 2230 vli_rshift1(vli); 2231 vli[uECC_N_WORDS - 2] |= vli[uECC_N_WORDS - 1] << (uECC_WORD_BITS - 1); 2232 vli[uECC_N_WORDS - 1] = vli[uECC_N_WORDS - 1] >> 1; 2233 } 2234 2235 static uECC_word_t vli_add_n(uECC_word_t *result, 2236 const uECC_word_t *left, 2237 const uECC_word_t *right) { 2238 uECC_word_t carry = vli_add(result, left, right); 2239 uECC_word_t sum = left[uECC_N_WORDS - 1] + right[uECC_N_WORDS - 1] + carry; 2240 if (sum != left[uECC_N_WORDS - 1]) { 2241 carry = (sum < left[uECC_N_WORDS - 1]); 2242 } 2243 result[uECC_N_WORDS - 1] = sum; 2244 return carry; 2245 } 2246 2247 static uECC_word_t vli_sub_n(uECC_word_t *result, 2248 const uECC_word_t *left, 2249 const uECC_word_t *right) { 2250 uECC_word_t borrow = vli_sub(result, left, right); 2251 uECC_word_t diff = left[uECC_N_WORDS - 1] - right[uECC_N_WORDS - 1] - borrow; 2252 if (diff != left[uECC_N_WORDS - 1]) { 2253 borrow = (diff > left[uECC_N_WORDS - 1]); 2254 } 2255 result[uECC_N_WORDS - 1] = diff; 2256 return borrow; 2257 } 2258 2259 #if !muladd_exists 2260 static void muladd(uECC_word_t a, 2261 uECC_word_t b, 2262 uECC_word_t *r0, 2263 uECC_word_t *r1, 2264 uECC_word_t *r2) { 2265 uECC_dword_t p = (uECC_dword_t)a * b; 2266 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; 2267 r01 += p; 2268 *r2 += (r01 < p); 2269 *r1 = r01 >> uECC_WORD_BITS; 2270 *r0 = (uECC_word_t)r01; 2271 } 2272 #define muladd_exists 1 2273 #endif 2274 2275 static void vli_mult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 2276 uECC_word_t r0 = 0; 2277 uECC_word_t r1 = 0; 2278 uECC_word_t r2 = 0; 2279 wordcount_t i, k; 2280 2281 for (k = 0; k < uECC_N_WORDS * 2 - 1; ++k) { 2282 wordcount_t min = (k < uECC_N_WORDS ? 0 : (k + 1) - uECC_N_WORDS); 2283 wordcount_t max = (k < uECC_N_WORDS ? k : uECC_N_WORDS - 1); 2284 for (i = min; i <= max; ++i) { 2285 muladd(left[i], right[k - i], &r0, &r1, &r2); 2286 } 2287 result[k] = r0; 2288 r0 = r1; 2289 r1 = r2; 2290 r2 = 0; 2291 } 2292 result[uECC_N_WORDS * 2 - 1] = r0; 2293 } 2294 2295 static void vli_modAdd_n(uECC_word_t *result, 2296 const uECC_word_t *left, 2297 const uECC_word_t *right, 2298 const uECC_word_t *mod) { 2299 uECC_word_t carry = vli_add_n(result, left, right); 2300 if (carry || vli_cmp_n(result, mod) >= 0) { 2301 vli_sub_n(result, result, mod); 2302 } 2303 } 2304 2305 static void vli_modInv_n(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod) { 2306 uECC_word_t a[uECC_N_WORDS], b[uECC_N_WORDS], u[uECC_N_WORDS], v[uECC_N_WORDS]; 2307 uECC_word_t carry; 2308 cmpresult_t cmpResult; 2309 2310 if (vli_isZero_n(input)) { 2311 vli_clear_n(result); 2312 return; 2313 } 2314 2315 vli_set_n(a, input); 2316 vli_set_n(b, mod); 2317 vli_clear_n(u); 2318 u[0] = 1; 2319 vli_clear_n(v); 2320 while ((cmpResult = vli_cmp_n(a, b)) != 0) { 2321 carry = 0; 2322 if (EVEN(a)) { 2323 vli_rshift1_n(a); 2324 if (!EVEN(u)) { 2325 carry = vli_add_n(u, u, mod); 2326 } 2327 vli_rshift1_n(u); 2328 if (carry) { 2329 u[uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2330 } 2331 } else if (EVEN(b)) { 2332 vli_rshift1_n(b); 2333 if (!EVEN(v)) { 2334 carry = vli_add_n(v, v, mod); 2335 } 2336 vli_rshift1_n(v); 2337 if (carry) { 2338 v[uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2339 } 2340 } else if (cmpResult > 0) { 2341 vli_sub_n(a, a, b); 2342 vli_rshift1_n(a); 2343 if (vli_cmp_n(u, v) < 0) { 2344 vli_add_n(u, u, mod); 2345 } 2346 vli_sub_n(u, u, v); 2347 if (!EVEN(u)) { 2348 carry = vli_add_n(u, u, mod); 2349 } 2350 vli_rshift1_n(u); 2351 if (carry) { 2352 u[uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2353 } 2354 } else { 2355 vli_sub_n(b, b, a); 2356 vli_rshift1_n(b); 2357 if (vli_cmp_n(v, u) < 0) { 2358 vli_add_n(v, v, mod); 2359 } 2360 vli_sub_n(v, v, u); 2361 if (!EVEN(v)) { 2362 carry = vli_add_n(v, v, mod); 2363 } 2364 vli_rshift1_n(v); 2365 if (carry) { 2366 v[uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2367 } 2368 } 2369 } 2370 vli_set_n(result, u); 2371 } 2372 2373 static void vli2_rshift1_n(uECC_word_t *vli) { 2374 vli_rshift1_n(vli); 2375 vli[uECC_N_WORDS - 1] |= vli[uECC_N_WORDS] << (uECC_WORD_BITS - 1); 2376 vli_rshift1_n(vli + uECC_N_WORDS); 2377 } 2378 2379 static uECC_word_t vli2_sub_n(uECC_word_t *result, 2380 const uECC_word_t *left, 2381 const uECC_word_t *right) { 2382 uECC_word_t borrow = 0; 2383 wordcount_t i; 2384 for (i = 0; i < uECC_N_WORDS * 2; ++i) { 2385 uECC_word_t diff = left[i] - right[i] - borrow; 2386 if (diff != left[i]) { 2387 borrow = (diff > left[i]); 2388 } 2389 result[i] = diff; 2390 } 2391 return borrow; 2392 } 2393 2394 /* Computes result = (left * right) % curve_n. */ 2395 static void vli_modMult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 2396 bitcount_t i; 2397 uECC_word_t product[2 * uECC_N_WORDS]; 2398 uECC_word_t modMultiple[2 * uECC_N_WORDS]; 2399 uECC_word_t tmp[2 * uECC_N_WORDS]; 2400 uECC_word_t *v[2] = {tmp, product}; 2401 uECC_word_t index = 1; 2402 2403 vli_mult_n(product, left, right); 2404 vli_clear_n(modMultiple); 2405 vli_set(modMultiple + uECC_N_WORDS + 1, curve_n); 2406 vli_rshift1(modMultiple + uECC_N_WORDS + 1); 2407 modMultiple[2 * uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2408 modMultiple[uECC_N_WORDS] = HIGH_BIT_SET; 2409 2410 for (i = 0; 2411 i <= ((((bitcount_t)uECC_N_WORDS) << uECC_WORD_BITS_SHIFT) + (uECC_WORD_BITS - 1)); 2412 ++i) { 2413 uECC_word_t borrow = vli2_sub_n(v[1 - index], v[index], modMultiple); 2414 index = !(index ^ borrow); /* Swap the index if there was no borrow */ 2415 vli2_rshift1_n(modMultiple); 2416 } 2417 vli_set_n(result, v[index]); 2418 } 2419 2420 #else 2421 2422 #define vli_cmp_n vli_cmp 2423 #define vli_modInv_n vli_modInv 2424 #define vli_modAdd_n vli_modAdd 2425 2426 static void vli2_rshift1(uECC_word_t *vli) { 2427 vli_rshift1(vli); 2428 vli[uECC_WORDS - 1] |= vli[uECC_WORDS] << (uECC_WORD_BITS - 1); 2429 vli_rshift1(vli + uECC_WORDS); 2430 } 2431 2432 static uECC_word_t vli2_sub(uECC_word_t *result, 2433 const uECC_word_t *left, 2434 const uECC_word_t *right) { 2435 uECC_word_t borrow = 0; 2436 wordcount_t i; 2437 for (i = 0; i < uECC_WORDS * 2; ++i) { 2438 uECC_word_t diff = left[i] - right[i] - borrow; 2439 if (diff != left[i]) { 2440 borrow = (diff > left[i]); 2441 } 2442 result[i] = diff; 2443 } 2444 return borrow; 2445 } 2446 2447 /* Computes result = (left * right) % curve_n. */ 2448 static void vli_modMult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 2449 uECC_word_t product[2 * uECC_WORDS]; 2450 uECC_word_t modMultiple[2 * uECC_WORDS]; 2451 uECC_word_t tmp[2 * uECC_WORDS]; 2452 uECC_word_t *v[2] = {tmp, product}; 2453 bitcount_t i; 2454 uECC_word_t index = 1; 2455 2456 vli_mult(product, left, right); 2457 vli_set(modMultiple + uECC_WORDS, curve_n); /* works if curve_n has its highest bit set */ 2458 vli_clear(modMultiple); 2459 2460 for (i = 0; i <= uECC_BYTES * 8; ++i) { 2461 uECC_word_t borrow = vli2_sub(v[1 - index], v[index], modMultiple); 2462 index = !(index ^ borrow); /* Swap the index if there was no borrow */ 2463 vli2_rshift1(modMultiple); 2464 } 2465 vli_set(result, v[index]); 2466 } 2467 #endif /* (uECC_CURVE != uECC_secp160r1) */ 2468 2469 static int uECC_sign_with_k(const uint8_t private_key[uECC_BYTES], 2470 const uint8_t message_hash[uECC_BYTES], 2471 uECC_word_t k[uECC_N_WORDS], 2472 uint8_t signature[uECC_BYTES*2]) { 2473 uECC_word_t tmp[uECC_N_WORDS]; 2474 uECC_word_t s[uECC_N_WORDS]; 2475 uECC_word_t *k2[2] = {tmp, s}; 2476 EccPoint p; 2477 uECC_word_t carry; 2478 uECC_word_t tries; 2479 2480 /* Make sure 0 < k < curve_n */ 2481 if (vli_isZero(k) || vli_cmp_n(curve_n, k) != 1) { 2482 return 0; 2483 } 2484 2485 #if (uECC_CURVE == uECC_secp160r1) 2486 /* Make sure that we don't leak timing information about k. 2487 See http://eprint.iacr.org/2011/232.pdf */ 2488 vli_add_n(tmp, k, curve_n); 2489 carry = (tmp[uECC_WORDS] & 0x02); 2490 vli_add_n(s, tmp, curve_n); 2491 2492 /* p = k * G */ 2493 EccPoint_mult(&p, &curve_G, k2[!carry], NULL, (uECC_BYTES * 8) + 2); 2494 #else 2495 /* Make sure that we don't leak timing information about k. 2496 See http://eprint.iacr.org/2011/232.pdf */ 2497 carry = vli_add(tmp, k, curve_n); 2498 vli_add(s, tmp, curve_n); 2499 2500 /* p = k * G */ 2501 EccPoint_mult(&p, &curve_G, k2[!carry], NULL, (uECC_BYTES * 8) + 1); 2502 2503 /* r = x1 (mod n) */ 2504 if (vli_cmp(curve_n, p.x) != 1) { 2505 vli_sub(p.x, p.x, curve_n); 2506 } 2507 #endif 2508 if (vli_isZero(p.x)) { 2509 return 0; 2510 } 2511 2512 // Attempt to get a random number to prevent side channel analysis of k. 2513 // If the RNG fails every time (eg it was not defined), we continue so that 2514 // deterministic signing can still work (with reduced security) without 2515 // an RNG defined. 2516 carry = 0; // use to signal that the RNG succeeded at least once. 2517 for (tries = 0; tries < MAX_TRIES; ++tries) { 2518 if (!g_rng_function((uint8_t *)tmp, sizeof(tmp))) { 2519 continue; 2520 } 2521 carry = 1; 2522 if (!vli_isZero(tmp)) { 2523 break; 2524 } 2525 } 2526 if (!carry) { 2527 vli_clear(tmp); 2528 tmp[0] = 1; 2529 } 2530 2531 /* Prevent side channel analysis of vli_modInv() to determine 2532 bits of k / the private key by premultiplying by a random number */ 2533 vli_modMult_n(k, k, tmp); /* k' = rand * k */ 2534 vli_modInv_n(k, k, curve_n); /* k = 1 / k' */ 2535 vli_modMult_n(k, k, tmp); /* k = 1 / k */ 2536 2537 vli_nativeToBytes(signature, p.x); /* store r */ 2538 2539 tmp[uECC_N_WORDS - 1] = 0; 2540 vli_bytesToNative(tmp, private_key); /* tmp = d */ 2541 s[uECC_N_WORDS - 1] = 0; 2542 vli_set(s, p.x); 2543 vli_modMult_n(s, tmp, s); /* s = r*d */ 2544 2545 vli_bytesToNative(tmp, message_hash); 2546 vli_modAdd_n(s, tmp, s, curve_n); /* s = e + r*d */ 2547 vli_modMult_n(s, s, k); /* s = (e + r*d) / k */ 2548 #if (uECC_CURVE == uECC_secp160r1) 2549 if (s[uECC_N_WORDS - 1]) { 2550 return 0; 2551 } 2552 #endif 2553 vli_nativeToBytes(signature + uECC_BYTES, s); 2554 return 1; 2555 } 2556 2557 int uECC_sign(const uint8_t private_key[uECC_BYTES], 2558 const uint8_t message_hash[uECC_BYTES], 2559 uint8_t signature[uECC_BYTES*2]) { 2560 uECC_word_t k[uECC_N_WORDS]; 2561 uECC_word_t tries; 2562 2563 for (tries = 0; tries < MAX_TRIES; ++tries) { 2564 if(g_rng_function((uint8_t *)k, sizeof(k))) { 2565 #if (uECC_CURVE == uECC_secp160r1) 2566 k[uECC_WORDS] &= 0x01; 2567 #endif 2568 if (uECC_sign_with_k(private_key, message_hash, k, signature)) { 2569 return 1; 2570 } 2571 } 2572 } 2573 return 0; 2574 } 2575 2576 /* Compute an HMAC using K as a key (as in RFC 6979). Note that K is always 2577 the same size as the hash result size. */ 2578 static void HMAC_init(uECC_HashContext *hash_context, const uint8_t *K) { 2579 uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size; 2580 unsigned i; 2581 for (i = 0; i < hash_context->result_size; ++i) 2582 pad[i] = K[i] ^ 0x36; 2583 for (; i < hash_context->block_size; ++i) 2584 pad[i] = 0x36; 2585 2586 hash_context->init_hash(hash_context); 2587 hash_context->update_hash(hash_context, pad, hash_context->block_size); 2588 } 2589 2590 static void HMAC_update(uECC_HashContext *hash_context, 2591 const uint8_t *message, 2592 unsigned message_size) { 2593 hash_context->update_hash(hash_context, message, message_size); 2594 } 2595 2596 static void HMAC_finish(uECC_HashContext *hash_context, const uint8_t *K, uint8_t *result) { 2597 uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size; 2598 unsigned i; 2599 for (i = 0; i < hash_context->result_size; ++i) 2600 pad[i] = K[i] ^ 0x5c; 2601 for (; i < hash_context->block_size; ++i) 2602 pad[i] = 0x5c; 2603 2604 hash_context->finish_hash(hash_context, result); 2605 2606 hash_context->init_hash(hash_context); 2607 hash_context->update_hash(hash_context, pad, hash_context->block_size); 2608 hash_context->update_hash(hash_context, result, hash_context->result_size); 2609 hash_context->finish_hash(hash_context, result); 2610 } 2611 2612 /* V = HMAC_K(V) */ 2613 static void update_V(uECC_HashContext *hash_context, uint8_t *K, uint8_t *V) { 2614 HMAC_init(hash_context, K); 2615 HMAC_update(hash_context, V, hash_context->result_size); 2616 HMAC_finish(hash_context, K, V); 2617 } 2618 2619 /* Deterministic signing, similar to RFC 6979. Differences are: 2620 * We just use (truncated) H(m) directly rather than bits2octets(H(m)) 2621 (it is not reduced modulo curve_n). 2622 * We generate a value for k (aka T) directly rather than converting endianness. 2623 2624 Layout of hash_context->tmp: <K> | <V> | (1 byte overlapped 0x00 or 0x01) / <HMAC pad> */ 2625 int uECC_sign_deterministic(const uint8_t private_key[uECC_BYTES], 2626 const uint8_t message_hash[uECC_BYTES], 2627 uECC_HashContext *hash_context, 2628 uint8_t signature[uECC_BYTES*2]) { 2629 uint8_t *K = hash_context->tmp; 2630 uint8_t *V = K + hash_context->result_size; 2631 uECC_word_t tries; 2632 unsigned i; 2633 for (i = 0; i < hash_context->result_size; ++i) { 2634 V[i] = 0x01; 2635 K[i] = 0; 2636 } 2637 2638 // K = HMAC_K(V || 0x00 || int2octets(x) || h(m)) 2639 HMAC_init(hash_context, K); 2640 V[hash_context->result_size] = 0x00; 2641 HMAC_update(hash_context, V, hash_context->result_size + 1); 2642 HMAC_update(hash_context, private_key, uECC_BYTES); 2643 HMAC_update(hash_context, message_hash, uECC_BYTES); 2644 HMAC_finish(hash_context, K, K); 2645 2646 update_V(hash_context, K, V); 2647 2648 // K = HMAC_K(V || 0x01 || int2octets(x) || h(m)) 2649 HMAC_init(hash_context, K); 2650 V[hash_context->result_size] = 0x01; 2651 HMAC_update(hash_context, V, hash_context->result_size + 1); 2652 HMAC_update(hash_context, private_key, uECC_BYTES); 2653 HMAC_update(hash_context, message_hash, uECC_BYTES); 2654 HMAC_finish(hash_context, K, K); 2655 2656 update_V(hash_context, K, V); 2657 2658 for (tries = 0; tries < MAX_TRIES; ++tries) { 2659 uECC_word_t T[uECC_N_WORDS]; 2660 uint8_t *T_ptr = (uint8_t *)T; 2661 unsigned T_bytes = 0; 2662 while (T_bytes < sizeof(T)) { 2663 update_V(hash_context, K, V); 2664 for (i = 0; i < hash_context->result_size && T_bytes < sizeof(T); ++i, ++T_bytes) { 2665 T_ptr[T_bytes] = V[i]; 2666 } 2667 } 2668 #if (uECC_CURVE == uECC_secp160r1) 2669 T[uECC_WORDS] &= 0x01; 2670 #endif 2671 2672 if (uECC_sign_with_k(private_key, message_hash, T, signature)) { 2673 return 1; 2674 } 2675 2676 // K = HMAC_K(V || 0x00) 2677 HMAC_init(hash_context, K); 2678 V[hash_context->result_size] = 0x00; 2679 HMAC_update(hash_context, V, hash_context->result_size + 1); 2680 HMAC_finish(hash_context, K, K); 2681 2682 update_V(hash_context, K, V); 2683 } 2684 return 0; 2685 } 2686 2687 static bitcount_t smax(bitcount_t a, bitcount_t b) { 2688 return (a > b ? a : b); 2689 } 2690 2691 int uECC_verify(const uint8_t public_key[uECC_BYTES*2], 2692 const uint8_t hash[uECC_BYTES], 2693 const uint8_t signature[uECC_BYTES*2]) { 2694 uECC_word_t u1[uECC_N_WORDS], u2[uECC_N_WORDS]; 2695 uECC_word_t z[uECC_N_WORDS]; 2696 EccPoint public, sum; 2697 uECC_word_t rx[uECC_WORDS]; 2698 uECC_word_t ry[uECC_WORDS]; 2699 uECC_word_t tx[uECC_WORDS]; 2700 uECC_word_t ty[uECC_WORDS]; 2701 uECC_word_t tz[uECC_WORDS]; 2702 const EccPoint *points[4]; 2703 const EccPoint *point; 2704 bitcount_t numBits; 2705 bitcount_t i; 2706 uECC_word_t r[uECC_N_WORDS], s[uECC_N_WORDS]; 2707 r[uECC_N_WORDS - 1] = 0; 2708 s[uECC_N_WORDS - 1] = 0; 2709 2710 vli_bytesToNative(public.x, public_key); 2711 vli_bytesToNative(public.y, public_key + uECC_BYTES); 2712 vli_bytesToNative(r, signature); 2713 vli_bytesToNative(s, signature + uECC_BYTES); 2714 2715 if (vli_isZero(r) || vli_isZero(s)) { /* r, s must not be 0. */ 2716 return 0; 2717 } 2718 2719 #if (uECC_CURVE != uECC_secp160r1) 2720 if (vli_cmp(curve_n, r) != 1 || vli_cmp(curve_n, s) != 1) { /* r, s must be < n. */ 2721 return 0; 2722 } 2723 #endif 2724 2725 /* Calculate u1 and u2. */ 2726 vli_modInv_n(z, s, curve_n); /* Z = s^-1 */ 2727 u1[uECC_N_WORDS - 1] = 0; 2728 vli_bytesToNative(u1, hash); 2729 vli_modMult_n(u1, u1, z); /* u1 = e/s */ 2730 vli_modMult_n(u2, r, z); /* u2 = r/s */ 2731 2732 /* Calculate sum = G + Q. */ 2733 vli_set(sum.x, public.x); 2734 vli_set(sum.y, public.y); 2735 vli_set(tx, curve_G.x); 2736 vli_set(ty, curve_G.y); 2737 vli_modSub_fast(z, sum.x, tx); /* Z = x2 - x1 */ 2738 XYcZ_add(tx, ty, sum.x, sum.y); 2739 vli_modInv(z, z, curve_p); /* Z = 1/Z */ 2740 apply_z(sum.x, sum.y, z); 2741 2742 /* Use Shamir's trick to calculate u1*G + u2*Q */ 2743 points[0] = 0; 2744 points[1] = &curve_G; 2745 points[2] = &public; 2746 points[3] = ∑ 2747 numBits = smax(vli_numBits(u1, uECC_N_WORDS), vli_numBits(u2, uECC_N_WORDS)); 2748 2749 point = points[(!!vli_testBit(u1, numBits - 1)) | ((!!vli_testBit(u2, numBits - 1)) << 1)]; 2750 vli_set(rx, point->x); 2751 vli_set(ry, point->y); 2752 vli_clear(z); 2753 z[0] = 1; 2754 2755 for (i = numBits - 2; i >= 0; --i) { 2756 uECC_word_t index; 2757 EccPoint_double_jacobian(rx, ry, z); 2758 2759 index = (!!vli_testBit(u1, i)) | ((!!vli_testBit(u2, i)) << 1); 2760 point = points[index]; 2761 if (point) { 2762 vli_set(tx, point->x); 2763 vli_set(ty, point->y); 2764 apply_z(tx, ty, z); 2765 vli_modSub_fast(tz, rx, tx); /* Z = x2 - x1 */ 2766 XYcZ_add(tx, ty, rx, ry); 2767 vli_modMult_fast(z, z, tz); 2768 } 2769 } 2770 2771 vli_modInv(z, z, curve_p); /* Z = 1/Z */ 2772 apply_z(rx, ry, z); 2773 2774 /* v = x1 (mod n) */ 2775 #if (uECC_CURVE != uECC_secp160r1) 2776 if (vli_cmp(curve_n, rx) != 1) { 2777 vli_sub(rx, rx, curve_n); 2778 } 2779 #endif 2780 2781 /* Accept only if v == r. */ 2782 return vli_equal(rx, r); 2783 } 2784 2785 #endif 2786