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