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