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 (void) dest; 471 (void) size; 472 return 0; 473 } 474 475 #endif 476 477 static uECC_RNG_Function g_rng_function = &default_RNG; 478 479 void uECC_set_rng(uECC_RNG_Function rng_function) { 480 g_rng_function = rng_function; 481 } 482 483 #ifdef __GNUC__ /* Only support GCC inline asm for now */ 484 #if (uECC_ASM && (uECC_PLATFORM == uECC_avr)) 485 #include "asm_avr.inc" 486 #endif 487 488 #if (uECC_ASM && (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb || \ 489 uECC_PLATFORM == uECC_arm_thumb2)) 490 #include "asm_arm.inc" 491 #endif 492 #endif 493 494 #if !asm_clear 495 static void vli_clear(uECC_word_t *vli) { 496 wordcount_t i; 497 for (i = 0; i < uECC_WORDS; ++i) { 498 vli[i] = 0; 499 } 500 } 501 #endif 502 503 /* Returns 1 if vli == 0, 0 otherwise. */ 504 #if !asm_isZero 505 static uECC_word_t vli_isZero(const uECC_word_t *vli) { 506 wordcount_t i; 507 for (i = 0; i < uECC_WORDS; ++i) { 508 if (vli[i]) { 509 return 0; 510 } 511 } 512 return 1; 513 } 514 #endif 515 516 /* Returns nonzero if bit 'bit' of vli is set. */ 517 #if !asm_testBit 518 static uECC_word_t vli_testBit(const uECC_word_t *vli, bitcount_t bit) { 519 return (vli[bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK))); 520 } 521 #endif 522 523 #ifdef ENABLE_MICO_ECC_ECDSA 524 525 /* Counts the number of words in vli. */ 526 #if !asm_numBits 527 static wordcount_t vli_numDigits(const uECC_word_t *vli, wordcount_t max_words) { 528 swordcount_t i; 529 /* Search from the end until we find a non-zero digit. 530 We do it in reverse because we expect that most digits will be nonzero. */ 531 for (i = max_words - 1; i >= 0 && vli[i] == 0; --i) { 532 } 533 534 return (i + 1); 535 } 536 537 /* Counts the number of bits required to represent vli. */ 538 static bitcount_t vli_numBits(const uECC_word_t *vli, wordcount_t max_words) { 539 uECC_word_t i; 540 uECC_word_t digit; 541 542 wordcount_t num_digits = vli_numDigits(vli, max_words); 543 if (num_digits == 0) { 544 return 0; 545 } 546 547 digit = vli[num_digits - 1]; 548 for (i = 0; digit; ++i) { 549 digit >>= 1; 550 } 551 552 return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i); 553 } 554 555 #endif /* ENABLE_MICO_ECC_ECDSA */ 556 557 #endif /* !asm_numBits */ 558 559 /* Sets dest = src. */ 560 #if !asm_set 561 static void vli_set(uECC_word_t *dest, const uECC_word_t *src) { 562 wordcount_t i; 563 for (i = 0; i < uECC_WORDS; ++i) { 564 dest[i] = src[i]; 565 } 566 } 567 #endif 568 569 /* Returns sign of left - right. */ 570 #if !asm_cmp 571 static cmpresult_t vli_cmp(const uECC_word_t *left, const uECC_word_t *right) { 572 swordcount_t i; 573 for (i = uECC_WORDS - 1; i >= 0; --i) { 574 if (left[i] > right[i]) { 575 return 1; 576 } else if (left[i] < right[i]) { 577 return -1; 578 } 579 } 580 return 0; 581 } 582 #endif 583 584 #ifdef ENABLE_MICRO_ECC_ECDSA 585 586 static cmpresult_t vli_equal(const uECC_word_t *left, const uECC_word_t *right) { 587 uECC_word_t result = 0; 588 swordcount_t i; 589 for (i = uECC_WORDS - 1; i >= 0; --i) { 590 result |= (left[i] ^ right[i]); 591 } 592 return (result == 0); 593 } 594 595 #endif 596 597 /* Computes vli = vli >> 1. */ 598 #if !asm_rshift1 599 static void vli_rshift1(uECC_word_t *vli) { 600 uECC_word_t *end = vli; 601 uECC_word_t carry = 0; 602 uECC_word_t *vli_ = vli; 603 604 vli_ += uECC_WORDS; 605 while (vli_-- > end) { 606 uECC_word_t temp = *vli_; 607 *vli_ = (temp >> 1) | carry; 608 carry = temp << (uECC_WORD_BITS - 1); 609 } 610 } 611 #endif 612 613 /* Computes result = left + right, returning carry. Can modify in place. */ 614 #if !asm_add 615 static uECC_word_t vli_add(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 616 uECC_word_t carry = 0; 617 wordcount_t i; 618 for (i = 0; i < uECC_WORDS; ++i) { 619 uECC_word_t sum = left[i] + right[i] + carry; 620 if (sum != left[i]) { 621 carry = (sum < left[i]); 622 } 623 result[i] = sum; 624 } 625 return carry; 626 } 627 #endif 628 629 /* Computes result = left - right, returning borrow. Can modify in place. */ 630 #if !asm_sub 631 static uECC_word_t vli_sub(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 632 uECC_word_t borrow = 0; 633 wordcount_t i; 634 for (i = 0; i < uECC_WORDS; ++i) { 635 uECC_word_t diff = left[i] - right[i] - borrow; 636 if (diff != left[i]) { 637 borrow = (diff > left[i]); 638 } 639 result[i] = diff; 640 } 641 return borrow; 642 } 643 #endif 644 645 #if (!asm_mult || (uECC_SQUARE_FUNC && !asm_square) || uECC_CURVE == uECC_secp256k1) 646 static void muladd(uECC_word_t a, 647 uECC_word_t b, 648 uECC_word_t *r0, 649 uECC_word_t *r1, 650 uECC_word_t *r2) { 651 #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128 652 uint64_t a0 = a & 0xffffffffull; 653 uint64_t a1 = a >> 32; 654 uint64_t b0 = b & 0xffffffffull; 655 uint64_t b1 = b >> 32; 656 657 uint64_t i0 = a0 * b0; 658 uint64_t i1 = a0 * b1; 659 uint64_t i2 = a1 * b0; 660 uint64_t i3 = a1 * b1; 661 662 uint64_t p0, p1; 663 664 i2 += (i0 >> 32); 665 i2 += i1; 666 if (i2 < i1) { // overflow 667 i3 += 0x100000000ull; 668 } 669 670 p0 = (i0 & 0xffffffffull) | (i2 << 32); 671 p1 = i3 + (i2 >> 32); 672 673 *r0 += p0; 674 *r1 += (p1 + (*r0 < p0)); 675 *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0)); 676 #else 677 uECC_dword_t p = (uECC_dword_t)a * b; 678 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; 679 r01 += p; 680 *r2 += (r01 < p); 681 *r1 = r01 >> uECC_WORD_BITS; 682 *r0 = (uECC_word_t)r01; 683 #endif 684 } 685 #define muladd_exists 1 686 #endif 687 688 #if !asm_mult 689 static void vli_mult(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 690 uECC_word_t r0 = 0; 691 uECC_word_t r1 = 0; 692 uECC_word_t r2 = 0; 693 wordcount_t i, k; 694 695 /* Compute each digit of result in sequence, maintaining the carries. */ 696 for (k = 0; k < uECC_WORDS; ++k) { 697 for (i = 0; i <= k; ++i) { 698 muladd(left[i], right[k - i], &r0, &r1, &r2); 699 } 700 result[k] = r0; 701 r0 = r1; 702 r1 = r2; 703 r2 = 0; 704 } 705 for (k = uECC_WORDS; k < uECC_WORDS * 2 - 1; ++k) { 706 for (i = (k + 1) - uECC_WORDS; i < uECC_WORDS; ++i) { 707 muladd(left[i], right[k - i], &r0, &r1, &r2); 708 } 709 result[k] = r0; 710 r0 = r1; 711 r1 = r2; 712 r2 = 0; 713 } 714 result[uECC_WORDS * 2 - 1] = r0; 715 } 716 #endif 717 718 #if uECC_SQUARE_FUNC 719 720 #if !asm_square 721 static void mul2add(uECC_word_t a, 722 uECC_word_t b, 723 uECC_word_t *r0, 724 uECC_word_t *r1, 725 uECC_word_t *r2) { 726 #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128 727 uint64_t a0 = a & 0xffffffffull; 728 uint64_t a1 = a >> 32; 729 uint64_t b0 = b & 0xffffffffull; 730 uint64_t b1 = b >> 32; 731 732 uint64_t i0 = a0 * b0; 733 uint64_t i1 = a0 * b1; 734 uint64_t i2 = a1 * b0; 735 uint64_t i3 = a1 * b1; 736 737 uint64_t p0, p1; 738 739 i2 += (i0 >> 32); 740 i2 += i1; 741 if (i2 < i1) 742 { // overflow 743 i3 += 0x100000000ull; 744 } 745 746 p0 = (i0 & 0xffffffffull) | (i2 << 32); 747 p1 = i3 + (i2 >> 32); 748 749 *r2 += (p1 >> 63); 750 p1 = (p1 << 1) | (p0 >> 63); 751 p0 <<= 1; 752 753 *r0 += p0; 754 *r1 += (p1 + (*r0 < p0)); 755 *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0)); 756 #else 757 uECC_dword_t p = (uECC_dword_t)a * b; 758 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; 759 *r2 += (p >> (uECC_WORD_BITS * 2 - 1)); 760 p *= 2; 761 r01 += p; 762 *r2 += (r01 < p); 763 *r1 = r01 >> uECC_WORD_BITS; 764 *r0 = (uECC_word_t)r01; 765 #endif 766 } 767 768 static void vli_square(uECC_word_t *result, const uECC_word_t *left) { 769 uECC_word_t r0 = 0; 770 uECC_word_t r1 = 0; 771 uECC_word_t r2 = 0; 772 773 wordcount_t i, k; 774 775 for (k = 0; k < uECC_WORDS * 2 - 1; ++k) { 776 uECC_word_t min = (k < uECC_WORDS ? 0 : (k + 1) - uECC_WORDS); 777 for (i = min; i <= k && i <= k - i; ++i) { 778 if (i < k-i) { 779 mul2add(left[i], left[k - i], &r0, &r1, &r2); 780 } else { 781 muladd(left[i], left[k - i], &r0, &r1, &r2); 782 } 783 } 784 result[k] = r0; 785 r0 = r1; 786 r1 = r2; 787 r2 = 0; 788 } 789 790 result[uECC_WORDS * 2 - 1] = r0; 791 } 792 #endif 793 794 #else /* uECC_SQUARE_FUNC */ 795 796 #define vli_square(result, left, size) vli_mult((result), (left), (left), (size)) 797 798 #endif /* uECC_SQUARE_FUNC */ 799 800 801 /* Computes result = (left + right) % mod. 802 Assumes that left < mod and right < mod, and that result does not overlap mod. */ 803 #if !asm_modAdd 804 static void vli_modAdd(uECC_word_t *result, 805 const uECC_word_t *left, 806 const uECC_word_t *right, 807 const uECC_word_t *mod) { 808 uECC_word_t carry = vli_add(result, left, right); 809 if (carry || vli_cmp(result, mod) >= 0) { 810 /* result > mod (result = mod + remainder), so subtract mod to get remainder. */ 811 vli_sub(result, result, mod); 812 } 813 } 814 #endif 815 816 /* Computes result = (left - right) % mod. 817 Assumes that left < mod and right < mod, and that result does not overlap mod. */ 818 #if !asm_modSub 819 static void vli_modSub(uECC_word_t *result, 820 const uECC_word_t *left, 821 const uECC_word_t *right, 822 const uECC_word_t *mod) { 823 uECC_word_t l_borrow = vli_sub(result, left, right); 824 if (l_borrow) { 825 /* In this case, result == -diff == (max int) - diff. Since -x % d == d - x, 826 we can get the correct result from result + mod (with overflow). */ 827 vli_add(result, result, mod); 828 } 829 } 830 #endif 831 832 #if !asm_modSub_fast 833 #define vli_modSub_fast(result, left, right) vli_modSub((result), (left), (right), curve_p) 834 #endif 835 836 #if !asm_mmod_fast 837 838 #if (uECC_CURVE == uECC_secp160r1 || uECC_CURVE == uECC_secp256k1) 839 /* omega_mult() is defined farther below for the different curves / word sizes */ 840 static void omega_mult(uECC_word_t * RESTRICT result, const uECC_word_t * RESTRICT right); 841 842 /* Computes result = product % curve_p 843 see http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf page 354 844 845 Note that this only works if log2(omega) < log2(p) / 2 */ 846 static void vli_mmod_fast(uECC_word_t *RESTRICT result, uECC_word_t *RESTRICT product) { 847 uECC_word_t tmp[2 * uECC_WORDS]; 848 uECC_word_t carry; 849 850 vli_clear(tmp); 851 vli_clear(tmp + uECC_WORDS); 852 853 omega_mult(tmp, product + uECC_WORDS); /* (Rq, q) = q * c */ 854 855 carry = vli_add(result, product, tmp); /* (C, r) = r + q */ 856 vli_clear(product); 857 omega_mult(product, tmp + uECC_WORDS); /* Rq*c */ 858 carry += vli_add(result, result, product); /* (C1, r) = r + Rq*c */ 859 860 while (carry > 0) { 861 --carry; 862 vli_sub(result, result, curve_p); 863 } 864 if (vli_cmp(result, curve_p) > 0) { 865 vli_sub(result, result, curve_p); 866 } 867 } 868 869 #endif 870 871 #if uECC_CURVE == uECC_secp160r1 872 873 #if uECC_WORD_SIZE == 1 874 static void omega_mult(uint8_t * RESTRICT result, const uint8_t * RESTRICT right) { 875 uint8_t carry; 876 uint8_t i; 877 878 /* Multiply by (2^31 + 1). */ 879 vli_set(result + 4, right); /* 2^32 */ 880 vli_rshift1(result + 4); /* 2^31 */ 881 result[3] = right[0] << 7; /* get last bit from shift */ 882 883 carry = vli_add(result, result, right); /* 2^31 + 1 */ 884 for (i = uECC_WORDS; carry; ++i) { 885 uint16_t sum = (uint16_t)result[i] + carry; 886 result[i] = (uint8_t)sum; 887 carry = sum >> 8; 888 } 889 } 890 #elif uECC_WORD_SIZE == 4 891 static void omega_mult(uint32_t * RESTRICT result, const uint32_t * RESTRICT right) { 892 uint32_t carry; 893 unsigned i; 894 895 /* Multiply by (2^31 + 1). */ 896 vli_set(result + 1, right); /* 2^32 */ 897 vli_rshift1(result + 1); /* 2^31 */ 898 result[0] = right[0] << 31; /* get last bit from shift */ 899 900 carry = vli_add(result, result, right); /* 2^31 + 1 */ 901 for (i = uECC_WORDS; carry; ++i) { 902 uint64_t sum = (uint64_t)result[i] + carry; 903 result[i] = (uint32_t)sum; 904 carry = sum >> 32; 905 } 906 } 907 #endif /* uECC_WORD_SIZE */ 908 909 #elif uECC_CURVE == uECC_secp192r1 910 911 /* Computes result = product % curve_p. 912 See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf */ 913 #if uECC_WORD_SIZE == 1 914 static void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) { 915 uint8_t tmp[uECC_WORDS]; 916 uint8_t carry; 917 918 vli_set(result, product); 919 920 vli_set(tmp, &product[24]); 921 carry = vli_add(result, result, tmp); 922 923 tmp[0] = tmp[1] = tmp[2] = tmp[3] = tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0; 924 tmp[8] = product[24]; tmp[9] = product[25]; tmp[10] = product[26]; tmp[11] = product[27]; 925 tmp[12] = product[28]; tmp[13] = product[29]; tmp[14] = product[30]; tmp[15] = product[31]; 926 tmp[16] = product[32]; tmp[17] = product[33]; tmp[18] = product[34]; tmp[19] = product[35]; 927 tmp[20] = product[36]; tmp[21] = product[37]; tmp[22] = product[38]; tmp[23] = product[39]; 928 carry += vli_add(result, result, tmp); 929 930 tmp[0] = tmp[8] = product[40]; 931 tmp[1] = tmp[9] = product[41]; 932 tmp[2] = tmp[10] = product[42]; 933 tmp[3] = tmp[11] = product[43]; 934 tmp[4] = tmp[12] = product[44]; 935 tmp[5] = tmp[13] = product[45]; 936 tmp[6] = tmp[14] = product[46]; 937 tmp[7] = tmp[15] = product[47]; 938 tmp[16] = tmp[17] = tmp[18] = tmp[19] = tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 939 carry += vli_add(result, result, tmp); 940 941 while (carry || vli_cmp(curve_p, result) != 1) { 942 carry -= vli_sub(result, result, curve_p); 943 } 944 } 945 #elif uECC_WORD_SIZE == 4 946 static void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) { 947 uint32_t tmp[uECC_WORDS]; 948 int carry; 949 950 vli_set(result, product); 951 952 vli_set(tmp, &product[6]); 953 carry = vli_add(result, result, tmp); 954 955 tmp[0] = tmp[1] = 0; 956 tmp[2] = product[6]; 957 tmp[3] = product[7]; 958 tmp[4] = product[8]; 959 tmp[5] = product[9]; 960 carry += vli_add(result, result, tmp); 961 962 tmp[0] = tmp[2] = product[10]; 963 tmp[1] = tmp[3] = product[11]; 964 tmp[4] = tmp[5] = 0; 965 carry += vli_add(result, result, tmp); 966 967 while (carry || vli_cmp(curve_p, result) != 1) { 968 carry -= vli_sub(result, result, curve_p); 969 } 970 } 971 #else 972 static void vli_mmod_fast(uint64_t *RESTRICT result, uint64_t *RESTRICT product) { 973 uint64_t tmp[uECC_WORDS]; 974 int carry; 975 976 vli_set(result, product); 977 978 vli_set(tmp, &product[3]); 979 carry = vli_add(result, result, tmp); 980 981 tmp[0] = 0; 982 tmp[1] = product[3]; 983 tmp[2] = product[4]; 984 carry += vli_add(result, result, tmp); 985 986 tmp[0] = tmp[1] = product[5]; 987 tmp[2] = 0; 988 carry += vli_add(result, result, tmp); 989 990 while (carry || vli_cmp(curve_p, result) != 1) { 991 carry -= vli_sub(result, result, curve_p); 992 } 993 } 994 #endif /* uECC_WORD_SIZE */ 995 996 #elif uECC_CURVE == uECC_secp256r1 997 998 /* Computes result = product % curve_p 999 from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1000 #if uECC_WORD_SIZE == 1 1001 static void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) { 1002 uint8_t tmp[uECC_BYTES]; 1003 int8_t carry; 1004 1005 /* t */ 1006 vli_set(result, product); 1007 1008 /* s1 */ 1009 tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0; 1010 tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0; 1011 tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0; 1012 tmp[12] = product[44]; tmp[13] = product[45]; tmp[14] = product[46]; tmp[15] = product[47]; 1013 tmp[16] = product[48]; tmp[17] = product[49]; tmp[18] = product[50]; tmp[19] = product[51]; 1014 tmp[20] = product[52]; tmp[21] = product[53]; tmp[22] = product[54]; tmp[23] = product[55]; 1015 tmp[24] = product[56]; tmp[25] = product[57]; tmp[26] = product[58]; tmp[27] = product[59]; 1016 tmp[28] = product[60]; tmp[29] = product[61]; tmp[30] = product[62]; tmp[31] = product[63]; 1017 carry = vli_add(tmp, tmp, tmp); 1018 carry += vli_add(result, result, tmp); 1019 1020 /* s2 */ 1021 tmp[12] = product[48]; tmp[13] = product[49]; tmp[14] = product[50]; tmp[15] = product[51]; 1022 tmp[16] = product[52]; tmp[17] = product[53]; tmp[18] = product[54]; tmp[19] = product[55]; 1023 tmp[20] = product[56]; tmp[21] = product[57]; tmp[22] = product[58]; tmp[23] = product[59]; 1024 tmp[24] = product[60]; tmp[25] = product[61]; tmp[26] = product[62]; tmp[27] = product[63]; 1025 tmp[28] = tmp[29] = tmp[30] = tmp[31] = 0; 1026 carry += vli_add(tmp, tmp, tmp); 1027 carry += vli_add(result, result, tmp); 1028 1029 /* s3 */ 1030 tmp[0] = product[32]; tmp[1] = product[33]; tmp[2] = product[34]; tmp[3] = product[35]; 1031 tmp[4] = product[36]; tmp[5] = product[37]; tmp[6] = product[38]; tmp[7] = product[39]; 1032 tmp[8] = product[40]; tmp[9] = product[41]; tmp[10] = product[42]; tmp[11] = product[43]; 1033 tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0; 1034 tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0; 1035 tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 1036 tmp[24] = product[56]; tmp[25] = product[57]; tmp[26] = product[58]; tmp[27] = product[59]; 1037 tmp[28] = product[60]; tmp[29] = product[61]; tmp[30] = product[62]; tmp[31] = product[63]; 1038 carry += vli_add(result, result, tmp); 1039 1040 /* s4 */ 1041 tmp[0] = product[36]; tmp[1] = product[37]; tmp[2] = product[38]; tmp[3] = product[39]; 1042 tmp[4] = product[40]; tmp[5] = product[41]; tmp[6] = product[42]; tmp[7] = product[43]; 1043 tmp[8] = product[44]; tmp[9] = product[45]; tmp[10] = product[46]; tmp[11] = product[47]; 1044 tmp[12] = product[52]; tmp[13] = product[53]; tmp[14] = product[54]; tmp[15] = product[55]; 1045 tmp[16] = product[56]; tmp[17] = product[57]; tmp[18] = product[58]; tmp[19] = product[59]; 1046 tmp[20] = product[60]; tmp[21] = product[61]; tmp[22] = product[62]; tmp[23] = product[63]; 1047 tmp[24] = product[52]; tmp[25] = product[53]; tmp[26] = product[54]; tmp[27] = product[55]; 1048 tmp[28] = product[32]; tmp[29] = product[33]; tmp[30] = product[34]; tmp[31] = product[35]; 1049 carry += vli_add(result, result, tmp); 1050 1051 /* d1 */ 1052 tmp[0] = product[44]; tmp[1] = product[45]; tmp[2] = product[46]; tmp[3] = product[47]; 1053 tmp[4] = product[48]; tmp[5] = product[49]; tmp[6] = product[50]; tmp[7] = product[51]; 1054 tmp[8] = product[52]; tmp[9] = product[53]; tmp[10] = product[54]; tmp[11] = product[55]; 1055 tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0; 1056 tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0; 1057 tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 1058 tmp[24] = product[32]; tmp[25] = product[33]; tmp[26] = product[34]; tmp[27] = product[35]; 1059 tmp[28] = product[40]; tmp[29] = product[41]; tmp[30] = product[42]; tmp[31] = product[43]; 1060 carry -= vli_sub(result, result, tmp); 1061 1062 /* d2 */ 1063 tmp[0] = product[48]; tmp[1] = product[49]; tmp[2] = product[50]; tmp[3] = product[51]; 1064 tmp[4] = product[52]; tmp[5] = product[53]; tmp[6] = product[54]; tmp[7] = product[55]; 1065 tmp[8] = product[56]; tmp[9] = product[57]; tmp[10] = product[58]; tmp[11] = product[59]; 1066 tmp[12] = product[60]; tmp[13] = product[61]; tmp[14] = product[62]; tmp[15] = product[63]; 1067 tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0; 1068 tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 1069 tmp[24] = product[36]; tmp[25] = product[37]; tmp[26] = product[38]; tmp[27] = product[39]; 1070 tmp[28] = product[44]; tmp[29] = product[45]; tmp[30] = product[46]; tmp[31] = product[47]; 1071 carry -= vli_sub(result, result, tmp); 1072 1073 /* d3 */ 1074 tmp[0] = product[52]; tmp[1] = product[53]; tmp[2] = product[54]; tmp[3] = product[55]; 1075 tmp[4] = product[56]; tmp[5] = product[57]; tmp[6] = product[58]; tmp[7] = product[59]; 1076 tmp[8] = product[60]; tmp[9] = product[61]; tmp[10] = product[62]; tmp[11] = product[63]; 1077 tmp[12] = product[32]; tmp[13] = product[33]; tmp[14] = product[34]; tmp[15] = product[35]; 1078 tmp[16] = product[36]; tmp[17] = product[37]; tmp[18] = product[38]; tmp[19] = product[39]; 1079 tmp[20] = product[40]; tmp[21] = product[41]; tmp[22] = product[42]; tmp[23] = product[43]; 1080 tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0; 1081 tmp[28] = product[48]; tmp[29] = product[49]; tmp[30] = product[50]; tmp[31] = product[51]; 1082 carry -= vli_sub(result, result, tmp); 1083 1084 /* d4 */ 1085 tmp[0] = product[56]; tmp[1] = product[57]; tmp[2] = product[58]; tmp[3] = product[59]; 1086 tmp[4] = product[60]; tmp[5] = product[61]; tmp[6] = product[62]; tmp[7] = product[63]; 1087 tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0; 1088 tmp[12] = product[36]; tmp[13] = product[37]; tmp[14] = product[38]; tmp[15] = product[39]; 1089 tmp[16] = product[40]; tmp[17] = product[41]; tmp[18] = product[42]; tmp[19] = product[43]; 1090 tmp[20] = product[44]; tmp[21] = product[45]; tmp[22] = product[46]; tmp[23] = product[47]; 1091 tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0; 1092 tmp[28] = product[52]; tmp[29] = product[53]; tmp[30] = product[54]; tmp[31] = product[55]; 1093 carry -= vli_sub(result, result, tmp); 1094 1095 if (carry < 0) { 1096 do { 1097 carry += vli_add(result, result, curve_p); 1098 } while (carry < 0); 1099 } else { 1100 while (carry || vli_cmp(curve_p, result) != 1) { 1101 carry -= vli_sub(result, result, curve_p); 1102 } 1103 } 1104 } 1105 #elif uECC_WORD_SIZE == 4 1106 static void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) { 1107 uint32_t tmp[uECC_WORDS]; 1108 int carry; 1109 1110 /* t */ 1111 vli_set(result, product); 1112 1113 /* s1 */ 1114 tmp[0] = tmp[1] = tmp[2] = 0; 1115 tmp[3] = product[11]; 1116 tmp[4] = product[12]; 1117 tmp[5] = product[13]; 1118 tmp[6] = product[14]; 1119 tmp[7] = product[15]; 1120 carry = vli_add(tmp, tmp, tmp); 1121 carry += vli_add(result, result, tmp); 1122 1123 /* s2 */ 1124 tmp[3] = product[12]; 1125 tmp[4] = product[13]; 1126 tmp[5] = product[14]; 1127 tmp[6] = product[15]; 1128 tmp[7] = 0; 1129 carry += vli_add(tmp, tmp, tmp); 1130 carry += vli_add(result, result, tmp); 1131 1132 /* s3 */ 1133 tmp[0] = product[8]; 1134 tmp[1] = product[9]; 1135 tmp[2] = product[10]; 1136 tmp[3] = tmp[4] = tmp[5] = 0; 1137 tmp[6] = product[14]; 1138 tmp[7] = product[15]; 1139 carry += vli_add(result, result, tmp); 1140 1141 /* s4 */ 1142 tmp[0] = product[9]; 1143 tmp[1] = product[10]; 1144 tmp[2] = product[11]; 1145 tmp[3] = product[13]; 1146 tmp[4] = product[14]; 1147 tmp[5] = product[15]; 1148 tmp[6] = product[13]; 1149 tmp[7] = product[8]; 1150 carry += vli_add(result, result, tmp); 1151 1152 /* d1 */ 1153 tmp[0] = product[11]; 1154 tmp[1] = product[12]; 1155 tmp[2] = product[13]; 1156 tmp[3] = tmp[4] = tmp[5] = 0; 1157 tmp[6] = product[8]; 1158 tmp[7] = product[10]; 1159 carry -= vli_sub(result, result, tmp); 1160 1161 /* d2 */ 1162 tmp[0] = product[12]; 1163 tmp[1] = product[13]; 1164 tmp[2] = product[14]; 1165 tmp[3] = product[15]; 1166 tmp[4] = tmp[5] = 0; 1167 tmp[6] = product[9]; 1168 tmp[7] = product[11]; 1169 carry -= vli_sub(result, result, tmp); 1170 1171 /* d3 */ 1172 tmp[0] = product[13]; 1173 tmp[1] = product[14]; 1174 tmp[2] = product[15]; 1175 tmp[3] = product[8]; 1176 tmp[4] = product[9]; 1177 tmp[5] = product[10]; 1178 tmp[6] = 0; 1179 tmp[7] = product[12]; 1180 carry -= vli_sub(result, result, tmp); 1181 1182 /* d4 */ 1183 tmp[0] = product[14]; 1184 tmp[1] = product[15]; 1185 tmp[2] = 0; 1186 tmp[3] = product[9]; 1187 tmp[4] = product[10]; 1188 tmp[5] = product[11]; 1189 tmp[6] = 0; 1190 tmp[7] = product[13]; 1191 carry -= vli_sub(result, result, tmp); 1192 1193 if (carry < 0) { 1194 do { 1195 carry += vli_add(result, result, curve_p); 1196 } while (carry < 0); 1197 } else { 1198 while (carry || vli_cmp(curve_p, result) != 1) { 1199 carry -= vli_sub(result, result, curve_p); 1200 } 1201 } 1202 } 1203 #else 1204 static void vli_mmod_fast(uint64_t *RESTRICT result, uint64_t *RESTRICT product) { 1205 uint64_t tmp[uECC_WORDS]; 1206 int carry; 1207 1208 /* t */ 1209 vli_set(result, product); 1210 1211 /* s1 */ 1212 tmp[0] = 0; 1213 tmp[1] = product[5] & 0xffffffff00000000ull; 1214 tmp[2] = product[6]; 1215 tmp[3] = product[7]; 1216 carry = vli_add(tmp, tmp, tmp); 1217 carry += vli_add(result, result, tmp); 1218 1219 /* s2 */ 1220 tmp[1] = product[6] << 32; 1221 tmp[2] = (product[6] >> 32) | (product[7] << 32); 1222 tmp[3] = product[7] >> 32; 1223 carry += vli_add(tmp, tmp, tmp); 1224 carry += vli_add(result, result, tmp); 1225 1226 /* s3 */ 1227 tmp[0] = product[4]; 1228 tmp[1] = product[5] & 0xffffffff; 1229 tmp[2] = 0; 1230 tmp[3] = product[7]; 1231 carry += vli_add(result, result, tmp); 1232 1233 /* s4 */ 1234 tmp[0] = (product[4] >> 32) | (product[5] << 32); 1235 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull); 1236 tmp[2] = product[7]; 1237 tmp[3] = (product[6] >> 32) | (product[4] << 32); 1238 carry += vli_add(result, result, tmp); 1239 1240 /* d1 */ 1241 tmp[0] = (product[5] >> 32) | (product[6] << 32); 1242 tmp[1] = (product[6] >> 32); 1243 tmp[2] = 0; 1244 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32); 1245 carry -= vli_sub(result, result, tmp); 1246 1247 /* d2 */ 1248 tmp[0] = product[6]; 1249 tmp[1] = product[7]; 1250 tmp[2] = 0; 1251 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull); 1252 carry -= vli_sub(result, result, tmp); 1253 1254 /* d3 */ 1255 tmp[0] = (product[6] >> 32) | (product[7] << 32); 1256 tmp[1] = (product[7] >> 32) | (product[4] << 32); 1257 tmp[2] = (product[4] >> 32) | (product[5] << 32); 1258 tmp[3] = (product[6] << 32); 1259 carry -= vli_sub(result, result, tmp); 1260 1261 /* d4 */ 1262 tmp[0] = product[7]; 1263 tmp[1] = product[4] & 0xffffffff00000000ull; 1264 tmp[2] = product[5]; 1265 tmp[3] = product[6] & 0xffffffff00000000ull; 1266 carry -= vli_sub(result, result, tmp); 1267 1268 if (carry < 0) { 1269 do { 1270 carry += vli_add(result, result, curve_p); 1271 } while (carry < 0); 1272 } else { 1273 while (carry || vli_cmp(curve_p, result) != 1) { 1274 carry -= vli_sub(result, result, curve_p); 1275 } 1276 } 1277 } 1278 #endif /* uECC_WORD_SIZE */ 1279 1280 #elif uECC_CURVE == uECC_secp256k1 1281 1282 #if uECC_WORD_SIZE == 1 1283 static void omega_mult(uint8_t * RESTRICT result, const uint8_t * RESTRICT right) { 1284 /* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ 1285 uECC_word_t r0 = 0; 1286 uECC_word_t r1 = 0; 1287 uECC_word_t r2 = 0; 1288 wordcount_t k; 1289 1290 /* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ 1291 muladd(0xD1, right[0], &r0, &r1, &r2); 1292 result[0] = r0; 1293 r0 = r1; 1294 r1 = r2; 1295 /* r2 is still 0 */ 1296 1297 for (k = 1; k < uECC_WORDS; ++k) { 1298 muladd(0x03, right[k - 1], &r0, &r1, &r2); 1299 muladd(0xD1, right[k], &r0, &r1, &r2); 1300 result[k] = r0; 1301 r0 = r1; 1302 r1 = r2; 1303 r2 = 0; 1304 } 1305 muladd(0x03, right[uECC_WORDS - 1], &r0, &r1, &r2); 1306 result[uECC_WORDS] = r0; 1307 result[uECC_WORDS + 1] = r1; 1308 1309 result[4 + uECC_WORDS] = vli_add(result + 4, result + 4, right); /* add the 2^32 multiple */ 1310 } 1311 #elif uECC_WORD_SIZE == 4 1312 static void omega_mult(uint32_t * RESTRICT result, const uint32_t * RESTRICT right) { 1313 /* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ 1314 uint32_t carry = 0; 1315 wordcount_t k; 1316 1317 for (k = 0; k < uECC_WORDS; ++k) { 1318 uint64_t p = (uint64_t)0x3D1 * right[k] + carry; 1319 result[k] = (p & 0xffffffff); 1320 carry = p >> 32; 1321 } 1322 result[uECC_WORDS] = carry; 1323 1324 result[1 + uECC_WORDS] = vli_add(result + 1, result + 1, right); /* add the 2^32 multiple */ 1325 } 1326 #else 1327 static void omega_mult(uint64_t * RESTRICT result, const uint64_t * RESTRICT right) { 1328 uECC_word_t r0 = 0; 1329 uECC_word_t r1 = 0; 1330 uECC_word_t r2 = 0; 1331 wordcount_t k; 1332 1333 /* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */ 1334 for (k = 0; k < uECC_WORDS; ++k) { 1335 muladd(0x1000003D1ull, right[k], &r0, &r1, &r2); 1336 result[k] = r0; 1337 r0 = r1; 1338 r1 = r2; 1339 r2 = 0; 1340 } 1341 result[uECC_WORDS] = r0; 1342 } 1343 #endif /* uECC_WORD_SIZE */ 1344 1345 #elif uECC_CURVE == uECC_secp224r1 1346 1347 /* Computes result = product % curve_p 1348 from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1349 #if uECC_WORD_SIZE == 1 1350 // TODO it may be faster to use the omega_mult method when fully asm optimized. 1351 void vli_mmod_fast(uint8_t *RESTRICT result, uint8_t *RESTRICT product) { 1352 uint8_t tmp[uECC_WORDS]; 1353 int8_t carry; 1354 1355 /* t */ 1356 vli_set(result, product); 1357 1358 /* s1 */ 1359 tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0; 1360 tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0; 1361 tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0; 1362 tmp[12] = product[28]; tmp[13] = product[29]; tmp[14] = product[30]; tmp[15] = product[31]; 1363 tmp[16] = product[32]; tmp[17] = product[33]; tmp[18] = product[34]; tmp[19] = product[35]; 1364 tmp[20] = product[36]; tmp[21] = product[37]; tmp[22] = product[38]; tmp[23] = product[39]; 1365 tmp[24] = product[40]; tmp[25] = product[41]; tmp[26] = product[42]; tmp[27] = product[43]; 1366 carry = vli_add(result, result, tmp); 1367 1368 /* s2 */ 1369 tmp[12] = product[44]; tmp[13] = product[45]; tmp[14] = product[46]; tmp[15] = product[47]; 1370 tmp[16] = product[48]; tmp[17] = product[49]; tmp[18] = product[50]; tmp[19] = product[51]; 1371 tmp[20] = product[52]; tmp[21] = product[53]; tmp[22] = product[54]; tmp[23] = product[55]; 1372 tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0; 1373 carry += vli_add(result, result, tmp); 1374 1375 /* d1 */ 1376 tmp[0] = product[28]; tmp[1] = product[29]; tmp[2] = product[30]; tmp[3] = product[31]; 1377 tmp[4] = product[32]; tmp[5] = product[33]; tmp[6] = product[34]; tmp[7] = product[35]; 1378 tmp[8] = product[36]; tmp[9] = product[37]; tmp[10] = product[38]; tmp[11] = product[39]; 1379 tmp[12] = product[40]; tmp[13] = product[41]; tmp[14] = product[42]; tmp[15] = product[43]; 1380 tmp[16] = product[44]; tmp[17] = product[45]; tmp[18] = product[46]; tmp[19] = product[47]; 1381 tmp[20] = product[48]; tmp[21] = product[49]; tmp[22] = product[50]; tmp[23] = product[51]; 1382 tmp[24] = product[52]; tmp[25] = product[53]; tmp[26] = product[54]; tmp[27] = product[55]; 1383 carry -= vli_sub(result, result, tmp); 1384 1385 /* d2 */ 1386 tmp[0] = product[44]; tmp[1] = product[45]; tmp[2] = product[46]; tmp[3] = product[47]; 1387 tmp[4] = product[48]; tmp[5] = product[49]; tmp[6] = product[50]; tmp[7] = product[51]; 1388 tmp[8] = product[52]; tmp[9] = product[53]; tmp[10] = product[54]; tmp[11] = product[55]; 1389 tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0; 1390 tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0; 1391 tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0; 1392 tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0; 1393 carry -= vli_sub(result, result, tmp); 1394 1395 if (carry < 0) { 1396 do { 1397 carry += vli_add(result, result, curve_p); 1398 } while (carry < 0); 1399 } else { 1400 while (carry || vli_cmp(curve_p, result) != 1) { 1401 carry -= vli_sub(result, result, curve_p); 1402 } 1403 } 1404 } 1405 #elif uECC_WORD_SIZE == 4 1406 void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) 1407 { 1408 uint32_t tmp[uECC_WORDS]; 1409 int carry; 1410 1411 /* t */ 1412 vli_set(result, product); 1413 1414 /* s1 */ 1415 tmp[0] = tmp[1] = tmp[2] = 0; 1416 tmp[3] = product[7]; 1417 tmp[4] = product[8]; 1418 tmp[5] = product[9]; 1419 tmp[6] = product[10]; 1420 carry = vli_add(result, result, tmp); 1421 1422 /* s2 */ 1423 tmp[3] = product[11]; 1424 tmp[4] = product[12]; 1425 tmp[5] = product[13]; 1426 tmp[6] = 0; 1427 carry += vli_add(result, result, tmp); 1428 1429 /* d1 */ 1430 tmp[0] = product[7]; 1431 tmp[1] = product[8]; 1432 tmp[2] = product[9]; 1433 tmp[3] = product[10]; 1434 tmp[4] = product[11]; 1435 tmp[5] = product[12]; 1436 tmp[6] = product[13]; 1437 carry -= vli_sub(result, result, tmp); 1438 1439 /* d2 */ 1440 tmp[0] = product[11]; 1441 tmp[1] = product[12]; 1442 tmp[2] = product[13]; 1443 tmp[3] = tmp[4] = tmp[5] = tmp[6] = 0; 1444 carry -= vli_sub(result, result, tmp); 1445 1446 if (carry < 0) { 1447 do { 1448 carry += vli_add(result, result, curve_p); 1449 } while (carry < 0); 1450 } else { 1451 while (carry || vli_cmp(curve_p, result) != 1) { 1452 carry -= vli_sub(result, result, curve_p); 1453 } 1454 } 1455 } 1456 #endif /* uECC_WORD_SIZE */ 1457 1458 #endif /* uECC_CURVE */ 1459 #endif /* !asm_mmod_fast */ 1460 1461 /* Computes result = (left * right) % curve_p. */ 1462 static void vli_modMult_fast(uECC_word_t *result, 1463 const uECC_word_t *left, 1464 const uECC_word_t *right) { 1465 uECC_word_t product[2 * uECC_WORDS]; 1466 vli_mult(product, left, right); 1467 vli_mmod_fast(result, product); 1468 } 1469 1470 #if uECC_SQUARE_FUNC 1471 1472 /* Computes result = left^2 % curve_p. */ 1473 static void vli_modSquare_fast(uECC_word_t *result, const uECC_word_t *left) { 1474 uECC_word_t product[2 * uECC_WORDS]; 1475 vli_square(product, left); 1476 vli_mmod_fast(result, product); 1477 } 1478 1479 #else /* uECC_SQUARE_FUNC */ 1480 1481 #define vli_modSquare_fast(result, left) vli_modMult_fast((result), (left), (left)) 1482 1483 #endif /* uECC_SQUARE_FUNC */ 1484 1485 1486 #define EVEN(vli) (!(vli[0] & 1)) 1487 /* Computes result = (1 / input) % mod. All VLIs are the same size. 1488 See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" 1489 https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf */ 1490 #if !asm_modInv 1491 static void vli_modInv(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod) { 1492 uECC_word_t a[uECC_WORDS], b[uECC_WORDS], u[uECC_WORDS], v[uECC_WORDS]; 1493 uECC_word_t carry; 1494 cmpresult_t cmpResult; 1495 1496 if (vli_isZero(input)) { 1497 vli_clear(result); 1498 return; 1499 } 1500 1501 vli_set(a, input); 1502 vli_set(b, mod); 1503 vli_clear(u); 1504 u[0] = 1; 1505 vli_clear(v); 1506 while ((cmpResult = vli_cmp(a, b)) != 0) { 1507 carry = 0; 1508 if (EVEN(a)) { 1509 vli_rshift1(a); 1510 if (!EVEN(u)) { 1511 carry = vli_add(u, u, mod); 1512 } 1513 vli_rshift1(u); 1514 if (carry) { 1515 u[uECC_WORDS - 1] |= HIGH_BIT_SET; 1516 } 1517 } else if (EVEN(b)) { 1518 vli_rshift1(b); 1519 if (!EVEN(v)) { 1520 carry = vli_add(v, v, mod); 1521 } 1522 vli_rshift1(v); 1523 if (carry) { 1524 v[uECC_WORDS - 1] |= HIGH_BIT_SET; 1525 } 1526 } else if (cmpResult > 0) { 1527 vli_sub(a, a, b); 1528 vli_rshift1(a); 1529 if (vli_cmp(u, v) < 0) { 1530 vli_add(u, u, mod); 1531 } 1532 vli_sub(u, u, v); 1533 if (!EVEN(u)) { 1534 carry = vli_add(u, u, mod); 1535 } 1536 vli_rshift1(u); 1537 if (carry) { 1538 u[uECC_WORDS - 1] |= HIGH_BIT_SET; 1539 } 1540 } else { 1541 vli_sub(b, b, a); 1542 vli_rshift1(b); 1543 if (vli_cmp(v, u) < 0) { 1544 vli_add(v, v, mod); 1545 } 1546 vli_sub(v, v, u); 1547 if (!EVEN(v)) { 1548 carry = vli_add(v, v, mod); 1549 } 1550 vli_rshift1(v); 1551 if (carry) { 1552 v[uECC_WORDS - 1] |= HIGH_BIT_SET; 1553 } 1554 } 1555 } 1556 vli_set(result, u); 1557 } 1558 #endif /* !asm_modInv */ 1559 1560 /* ------ Point operations ------ */ 1561 1562 /* Returns 1 if 'point' is the point at infinity, 0 otherwise. */ 1563 static cmpresult_t EccPoint_isZero(const EccPoint *point) { 1564 return (vli_isZero(point->x) && vli_isZero(point->y)); 1565 } 1566 1567 /* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates. 1568 From http://eprint.iacr.org/2011/338.pdf 1569 */ 1570 1571 /* Double in place */ 1572 #if (uECC_CURVE == uECC_secp256k1) 1573 static void EccPoint_double_jacobian(uECC_word_t * RESTRICT X1, 1574 uECC_word_t * RESTRICT Y1, 1575 uECC_word_t * RESTRICT Z1) { 1576 /* t1 = X, t2 = Y, t3 = Z */ 1577 uECC_word_t t4[uECC_WORDS]; 1578 uECC_word_t t5[uECC_WORDS]; 1579 1580 if (vli_isZero(Z1)) { 1581 return; 1582 } 1583 1584 vli_modSquare_fast(t5, Y1); /* t5 = y1^2 */ 1585 vli_modMult_fast(t4, X1, t5); /* t4 = x1*y1^2 = A */ 1586 vli_modSquare_fast(X1, X1); /* t1 = x1^2 */ 1587 vli_modSquare_fast(t5, t5); /* t5 = y1^4 */ 1588 vli_modMult_fast(Z1, Y1, Z1); /* t3 = y1*z1 = z3 */ 1589 1590 vli_modAdd(Y1, X1, X1, curve_p); /* t2 = 2*x1^2 */ 1591 vli_modAdd(Y1, Y1, X1, curve_p); /* t2 = 3*x1^2 */ 1592 if (vli_testBit(Y1, 0)) { 1593 uECC_word_t carry = vli_add(Y1, Y1, curve_p); 1594 vli_rshift1(Y1); 1595 Y1[uECC_WORDS - 1] |= carry << (uECC_WORD_BITS - 1); 1596 } else { 1597 vli_rshift1(Y1); 1598 } 1599 /* t2 = 3/2*(x1^2) = B */ 1600 1601 vli_modSquare_fast(X1, Y1); /* t1 = B^2 */ 1602 vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - A */ 1603 vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - 2A = x3 */ 1604 1605 vli_modSub(t4, t4, X1, curve_p); /* t4 = A - x3 */ 1606 vli_modMult_fast(Y1, Y1, t4); /* t2 = B * (A - x3) */ 1607 vli_modSub(Y1, Y1, t5, curve_p); /* t2 = B * (A - x3) - y1^4 = y3 */ 1608 } 1609 #else 1610 static void EccPoint_double_jacobian(uECC_word_t * RESTRICT X1, 1611 uECC_word_t * RESTRICT Y1, 1612 uECC_word_t * RESTRICT Z1) { 1613 /* t1 = X, t2 = Y, t3 = Z */ 1614 uECC_word_t t4[uECC_WORDS]; 1615 uECC_word_t t5[uECC_WORDS]; 1616 1617 if (vli_isZero(Z1)) { 1618 return; 1619 } 1620 1621 vli_modSquare_fast(t4, Y1); /* t4 = y1^2 */ 1622 vli_modMult_fast(t5, X1, t4); /* t5 = x1*y1^2 = A */ 1623 vli_modSquare_fast(t4, t4); /* t4 = y1^4 */ 1624 vli_modMult_fast(Y1, Y1, Z1); /* t2 = y1*z1 = z3 */ 1625 vli_modSquare_fast(Z1, Z1); /* t3 = z1^2 */ 1626 1627 vli_modAdd(X1, X1, Z1, curve_p); /* t1 = x1 + z1^2 */ 1628 vli_modAdd(Z1, Z1, Z1, curve_p); /* t3 = 2*z1^2 */ 1629 vli_modSub_fast(Z1, X1, Z1); /* t3 = x1 - z1^2 */ 1630 vli_modMult_fast(X1, X1, Z1); /* t1 = x1^2 - z1^4 */ 1631 1632 vli_modAdd(Z1, X1, X1, curve_p); /* t3 = 2*(x1^2 - z1^4) */ 1633 vli_modAdd(X1, X1, Z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */ 1634 if (vli_testBit(X1, 0)) { 1635 uECC_word_t l_carry = vli_add(X1, X1, curve_p); 1636 vli_rshift1(X1); 1637 X1[uECC_WORDS - 1] |= l_carry << (uECC_WORD_BITS - 1); 1638 } else { 1639 vli_rshift1(X1); 1640 } 1641 /* t1 = 3/2*(x1^2 - z1^4) = B */ 1642 1643 vli_modSquare_fast(Z1, X1); /* t3 = B^2 */ 1644 vli_modSub_fast(Z1, Z1, t5); /* t3 = B^2 - A */ 1645 vli_modSub_fast(Z1, Z1, t5); /* t3 = B^2 - 2A = x3 */ 1646 vli_modSub_fast(t5, t5, Z1); /* t5 = A - x3 */ 1647 vli_modMult_fast(X1, X1, t5); /* t1 = B * (A - x3) */ 1648 vli_modSub_fast(t4, X1, t4); /* t4 = B * (A - x3) - y1^4 = y3 */ 1649 1650 vli_set(X1, Z1); 1651 vli_set(Z1, Y1); 1652 vli_set(Y1, t4); 1653 } 1654 #endif 1655 1656 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ 1657 static void apply_z(uECC_word_t * RESTRICT X1, 1658 uECC_word_t * RESTRICT Y1, 1659 const uECC_word_t * RESTRICT Z) { 1660 uECC_word_t t1[uECC_WORDS]; 1661 1662 vli_modSquare_fast(t1, Z); /* z^2 */ 1663 vli_modMult_fast(X1, X1, t1); /* x1 * z^2 */ 1664 vli_modMult_fast(t1, t1, Z); /* z^3 */ 1665 vli_modMult_fast(Y1, Y1, t1); /* y1 * z^3 */ 1666 } 1667 1668 /* P = (x1, y1) => 2P, (x2, y2) => P' */ 1669 static void XYcZ_initial_double(uECC_word_t * RESTRICT X1, 1670 uECC_word_t * RESTRICT Y1, 1671 uECC_word_t * RESTRICT X2, 1672 uECC_word_t * RESTRICT Y2, 1673 const uECC_word_t * RESTRICT initial_Z) { 1674 uECC_word_t z[uECC_WORDS]; 1675 if (initial_Z) { 1676 vli_set(z, initial_Z); 1677 } else { 1678 vli_clear(z); 1679 z[0] = 1; 1680 } 1681 1682 vli_set(X2, X1); 1683 vli_set(Y2, Y1); 1684 1685 apply_z(X1, Y1, z); 1686 EccPoint_double_jacobian(X1, Y1, z); 1687 apply_z(X2, Y2, z); 1688 } 1689 1690 /* Input P = (x1, y1, Z), Q = (x2, y2, Z) 1691 Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) 1692 or P => P', Q => P + Q 1693 */ 1694 static void XYcZ_add(uECC_word_t * RESTRICT X1, 1695 uECC_word_t * RESTRICT Y1, 1696 uECC_word_t * RESTRICT X2, 1697 uECC_word_t * RESTRICT Y2) { 1698 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 1699 uECC_word_t t5[uECC_WORDS]; 1700 1701 vli_modSub_fast(t5, X2, X1); /* t5 = x2 - x1 */ 1702 vli_modSquare_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */ 1703 vli_modMult_fast(X1, X1, t5); /* t1 = x1*A = B */ 1704 vli_modMult_fast(X2, X2, t5); /* t3 = x2*A = C */ 1705 vli_modSub_fast(Y2, Y2, Y1); /* t4 = y2 - y1 */ 1706 vli_modSquare_fast(t5, Y2); /* t5 = (y2 - y1)^2 = D */ 1707 1708 vli_modSub_fast(t5, t5, X1); /* t5 = D - B */ 1709 vli_modSub_fast(t5, t5, X2); /* t5 = D - B - C = x3 */ 1710 vli_modSub_fast(X2, X2, X1); /* t3 = C - B */ 1711 vli_modMult_fast(Y1, Y1, X2); /* t2 = y1*(C - B) */ 1712 vli_modSub_fast(X2, X1, t5); /* t3 = B - x3 */ 1713 vli_modMult_fast(Y2, Y2, X2); /* t4 = (y2 - y1)*(B - x3) */ 1714 vli_modSub_fast(Y2, Y2, Y1); /* t4 = y3 */ 1715 1716 vli_set(X2, t5); 1717 } 1718 1719 /* Input P = (x1, y1, Z), Q = (x2, y2, Z) 1720 Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) 1721 or P => P - Q, Q => P + Q 1722 */ 1723 static void XYcZ_addC(uECC_word_t * RESTRICT X1, 1724 uECC_word_t * RESTRICT Y1, 1725 uECC_word_t * RESTRICT X2, 1726 uECC_word_t * RESTRICT Y2) { 1727 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 1728 uECC_word_t t5[uECC_WORDS]; 1729 uECC_word_t t6[uECC_WORDS]; 1730 uECC_word_t t7[uECC_WORDS]; 1731 1732 vli_modSub_fast(t5, X2, X1); /* t5 = x2 - x1 */ 1733 vli_modSquare_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */ 1734 vli_modMult_fast(X1, X1, t5); /* t1 = x1*A = B */ 1735 vli_modMult_fast(X2, X2, t5); /* t3 = x2*A = C */ 1736 vli_modAdd(t5, Y2, Y1, curve_p); /* t5 = y2 + y1 */ 1737 vli_modSub_fast(Y2, Y2, Y1); /* t4 = y2 - y1 */ 1738 1739 vli_modSub_fast(t6, X2, X1); /* t6 = C - B */ 1740 vli_modMult_fast(Y1, Y1, t6); /* t2 = y1 * (C - B) = E */ 1741 vli_modAdd(t6, X1, X2, curve_p); /* t6 = B + C */ 1742 vli_modSquare_fast(X2, Y2); /* t3 = (y2 - y1)^2 = D */ 1743 vli_modSub_fast(X2, X2, t6); /* t3 = D - (B + C) = x3 */ 1744 1745 vli_modSub_fast(t7, X1, X2); /* t7 = B - x3 */ 1746 vli_modMult_fast(Y2, Y2, t7); /* t4 = (y2 - y1)*(B - x3) */ 1747 vli_modSub_fast(Y2, Y2, Y1); /* t4 = (y2 - y1)*(B - x3) - E = y3 */ 1748 1749 vli_modSquare_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */ 1750 vli_modSub_fast(t7, t7, t6); /* t7 = F - (B + C) = x3' */ 1751 vli_modSub_fast(t6, t7, X1); /* t6 = x3' - B */ 1752 vli_modMult_fast(t6, t6, t5); /* t6 = (y2 + y1)*(x3' - B) */ 1753 vli_modSub_fast(Y1, t6, Y1); /* t2 = (y2 + y1)*(x3' - B) - E = y3' */ 1754 1755 vli_set(X1, t7); 1756 } 1757 1758 static void EccPoint_mult(EccPoint * RESTRICT result, 1759 const EccPoint * RESTRICT point, 1760 const uECC_word_t * RESTRICT scalar, 1761 const uECC_word_t * RESTRICT initialZ, 1762 bitcount_t numBits) { 1763 /* R0 and R1 */ 1764 uECC_word_t Rx[2][uECC_WORDS]; 1765 uECC_word_t Ry[2][uECC_WORDS]; 1766 uECC_word_t z[uECC_WORDS]; 1767 bitcount_t i; 1768 uECC_word_t nb; 1769 1770 vli_set(Rx[1], point->x); 1771 vli_set(Ry[1], point->y); 1772 1773 XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initialZ); 1774 1775 for (i = numBits - 2; i > 0; --i) { 1776 nb = !vli_testBit(scalar, i); 1777 XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb]); 1778 XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb]); 1779 } 1780 1781 nb = !vli_testBit(scalar, 0); 1782 XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb]); 1783 1784 /* Find final 1/Z value. */ 1785 vli_modSub_fast(z, Rx[1], Rx[0]); /* X1 - X0 */ 1786 vli_modMult_fast(z, z, Ry[1 - nb]); /* Yb * (X1 - X0) */ 1787 vli_modMult_fast(z, z, point->x); /* xP * Yb * (X1 - X0) */ 1788 vli_modInv(z, z, curve_p); /* 1 / (xP * Yb * (X1 - X0)) */ 1789 vli_modMult_fast(z, z, point->y); /* yP / (xP * Yb * (X1 - X0)) */ 1790 vli_modMult_fast(z, z, Rx[1 - nb]); /* Xb * yP / (xP * Yb * (X1 - X0)) */ 1791 /* End 1/Z calculation */ 1792 1793 XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb]); 1794 apply_z(Rx[0], Ry[0], z); 1795 1796 vli_set(result->x, Rx[0]); 1797 vli_set(result->y, Ry[0]); 1798 } 1799 1800 static int EccPoint_compute_public_key(EccPoint *result, uECC_word_t *private) { 1801 uECC_word_t tmp1[uECC_WORDS]; 1802 uECC_word_t tmp2[uECC_WORDS]; 1803 uECC_word_t *p2[2] = {tmp1, tmp2}; 1804 uECC_word_t carry; 1805 1806 /* Make sure the private key is in the range [1, n-1]. */ 1807 if (vli_isZero(private)) { 1808 return 0; 1809 } 1810 1811 #if (uECC_CURVE == uECC_secp160r1) 1812 // Don't regularize the bitcount for secp160r1, since it would have a larger performance 1813 // impact (about 2% slower on average) and requires the vli_xxx_n functions, leading to 1814 // a significant increase in code size. 1815 1816 EccPoint_mult(result, &curve_G, private, NULL, vli_numBits(private, uECC_WORDS)); 1817 #else 1818 if (vli_cmp(curve_n, private) != 1) { 1819 return 0; 1820 } 1821 1822 // Regularize the bitcount for the private key so that attackers cannot use a side channel 1823 // attack to learn the number of leading zeros. 1824 carry = vli_add(tmp1, private, curve_n); 1825 vli_add(tmp2, tmp1, curve_n); 1826 EccPoint_mult(result, &curve_G, p2[!carry], NULL, (uECC_BYTES * 8) + 1); 1827 #endif 1828 1829 if (EccPoint_isZero(result)) { 1830 return 0; 1831 } 1832 return 1; 1833 } 1834 1835 #ifdef ENABLE_MICRO_ECC_COMPRESSION 1836 1837 #if uECC_CURVE == uECC_secp224r1 1838 1839 /* Routine 3.2.4 RS; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1840 static void mod_sqrt_secp224r1_rs(uECC_word_t *d1, 1841 uECC_word_t *e1, 1842 uECC_word_t *f1, 1843 const uECC_word_t *d0, 1844 const uECC_word_t *e0, 1845 const uECC_word_t *f0) { 1846 uECC_word_t t[uECC_WORDS]; 1847 1848 vli_modSquare_fast(t, d0); /* t <-- d0 ^ 2 */ 1849 vli_modMult_fast(e1, d0, e0); /* e1 <-- d0 * e0 */ 1850 vli_modAdd(d1, t, f0, curve_p); /* d1 <-- t + f0 */ 1851 vli_modAdd(e1, e1, e1, curve_p); /* e1 <-- e1 + e1 */ 1852 vli_modMult_fast(f1, t, f0); /* f1 <-- t * f0 */ 1853 vli_modAdd(f1, f1, f1, curve_p); /* f1 <-- f1 + f1 */ 1854 vli_modAdd(f1, f1, f1, curve_p); /* f1 <-- f1 + f1 */ 1855 } 1856 1857 /* Routine 3.2.5 RSS; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1858 static void mod_sqrt_secp224r1_rss(uECC_word_t *d1, 1859 uECC_word_t *e1, 1860 uECC_word_t *f1, 1861 const uECC_word_t *d0, 1862 const uECC_word_t *e0, 1863 const uECC_word_t *f0, 1864 const bitcount_t j) { 1865 bitcount_t i; 1866 1867 vli_set(d1, d0); /* d1 <-- d0 */ 1868 vli_set(e1, e0); /* e1 <-- e0 */ 1869 vli_set(f1, f0); /* f1 <-- f0 */ 1870 for (i = 1; i <= j; i++) { 1871 mod_sqrt_secp224r1_rs(d1, e1, f1, d1, e1, f1); /* RS (d1,e1,f1,d1,e1,f1) */ 1872 } 1873 } 1874 1875 /* Routine 3.2.6 RM; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1876 static void mod_sqrt_secp224r1_rm(uECC_word_t *d2, 1877 uECC_word_t *e2, 1878 uECC_word_t *f2, 1879 const uECC_word_t *c, 1880 const uECC_word_t *d0, 1881 const uECC_word_t *e0, 1882 const uECC_word_t *d1, 1883 const uECC_word_t *e1) { 1884 uECC_word_t t1[uECC_WORDS]; 1885 uECC_word_t t2[uECC_WORDS]; 1886 1887 vli_modMult_fast(t1, e0, e1); /* t1 <-- e0 * e1 */ 1888 vli_modMult_fast(t1, t1, c); /* t1 <-- t1 * c */ 1889 vli_modSub_fast(t1, curve_p, t1); /* t1 <-- p - t1 */ 1890 vli_modMult_fast(t2, d0, d1); /* t2 <-- d0 * d1 */ 1891 vli_modAdd(t2, t2, t1, curve_p); /* t2 <-- t2 + t1 */ 1892 vli_modMult_fast(t1, d0, e1); /* t1 <-- d0 * e1 */ 1893 vli_modMult_fast(e2, d1, e0); /* e2 <-- d1 * e0 */ 1894 vli_modAdd(e2, e2, t1, curve_p); /* e2 <-- e2 + t1 */ 1895 vli_modSquare_fast(f2, e2); /* f2 <-- e2^2 */ 1896 vli_modMult_fast(f2, f2, c); /* f2 <-- f2 * c */ 1897 vli_modSub_fast(f2, curve_p, f2); /* f2 <-- p - f2 */ 1898 vli_set(d2, t2); /* d2 <-- t2 */ 1899 } 1900 1901 /* Routine 3.2.7 RP; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1902 static void mod_sqrt_secp224r1_rp(uECC_word_t *d1, 1903 uECC_word_t *e1, 1904 uECC_word_t *f1, 1905 const uECC_word_t *c, 1906 const uECC_word_t *r) { 1907 wordcount_t i; 1908 wordcount_t pow2i = 1; 1909 uECC_word_t d0[uECC_WORDS]; 1910 uECC_word_t e0[uECC_WORDS] = {1}; /* e0 <-- 1 */ 1911 uECC_word_t f0[uECC_WORDS]; 1912 1913 vli_set(d0, r); /* d0 <-- r */ 1914 vli_modSub_fast(f0, curve_p, c); /* f0 <-- p - c */ 1915 for (i = 0; i <= 6; i++) { 1916 mod_sqrt_secp224r1_rss(d1, e1, f1, d0, e0, f0, pow2i); /* RSS (d1,e1,f1,d0,e0,f0,2^i) */ 1917 mod_sqrt_secp224r1_rm(d1, e1, f1, c, d1, e1, d0, e0); /* RM (d1,e1,f1,c,d1,e1,d0,e0) */ 1918 vli_set(d0, d1); /* d0 <-- d1 */ 1919 vli_set(e0, e1); /* e0 <-- e1 */ 1920 vli_set(f0, f1); /* f0 <-- f1 */ 1921 pow2i *= 2; 1922 } 1923 } 1924 1925 /* Compute a = sqrt(a) (mod curve_p). */ 1926 /* Routine 3.2.8 mp_mod_sqrt_224; from http://www.nsa.gov/ia/_files/nist-routines.pdf */ 1927 static void mod_sqrt(uECC_word_t *a) { 1928 bitcount_t i; 1929 uECC_word_t e1[uECC_WORDS]; 1930 uECC_word_t f1[uECC_WORDS]; 1931 uECC_word_t d0[uECC_WORDS]; 1932 uECC_word_t e0[uECC_WORDS]; 1933 uECC_word_t f0[uECC_WORDS]; 1934 uECC_word_t d1[uECC_WORDS]; 1935 1936 // s = a; using constant instead of random value 1937 mod_sqrt_secp224r1_rp(d0, e0, f0, a, a); /* RP (d0, e0, f0, c, s) */ 1938 mod_sqrt_secp224r1_rs(d1, e1, f1, d0, e0, f0); /* RS (d1, e1, f1, d0, e0, f0) */ 1939 for (i = 1; i <= 95; i++) { 1940 vli_set(d0, d1); /* d0 <-- d1 */ 1941 vli_set(e0, e1); /* e0 <-- e1 */ 1942 vli_set(f0, f1); /* f0 <-- f1 */ 1943 mod_sqrt_secp224r1_rs(d1, e1, f1, d0, e0, f0); /* RS (d1, e1, f1, d0, e0, f0) */ 1944 if (vli_isZero(d1)) { /* if d1 == 0 */ 1945 break; 1946 } 1947 } 1948 vli_modInv(f1, e0, curve_p); /* f1 <-- 1 / e0 */ 1949 vli_modMult_fast(a, d0, f1); /* a <-- d0 / e0 */ 1950 } 1951 1952 #else /* uECC_CURVE */ 1953 1954 /* Compute a = sqrt(a) (mod curve_p). */ 1955 static void mod_sqrt(uECC_word_t *a) { 1956 bitcount_t i; 1957 uECC_word_t p1[uECC_WORDS] = {1}; 1958 uECC_word_t l_result[uECC_WORDS] = {1}; 1959 1960 /* Since curve_p == 3 (mod 4) for all supported curves, we can 1961 compute sqrt(a) = a^((curve_p + 1) / 4) (mod curve_p). */ 1962 vli_add(p1, curve_p, p1); /* p1 = curve_p + 1 */ 1963 for (i = vli_numBits(p1, uECC_WORDS) - 1; i > 1; --i) { 1964 vli_modSquare_fast(l_result, l_result); 1965 if (vli_testBit(p1, i)) { 1966 vli_modMult_fast(l_result, l_result, a); 1967 } 1968 } 1969 vli_set(a, l_result); 1970 } 1971 #endif /* uECC_CURVE */ 1972 1973 #endif /* ENABLE_MICRO_ECC_COMPRESSION */ 1974 1975 1976 #if uECC_WORD_SIZE == 1 1977 1978 static void vli_nativeToBytes(uint8_t * RESTRICT dest, const uint8_t * RESTRICT src) { 1979 uint8_t i; 1980 for (i = 0; i < uECC_BYTES; ++i) { 1981 dest[i] = src[(uECC_BYTES - 1) - i]; 1982 } 1983 } 1984 1985 #define vli_bytesToNative(dest, src) vli_nativeToBytes((dest), (src)) 1986 1987 #elif uECC_WORD_SIZE == 4 1988 1989 static void vli_nativeToBytes(uint8_t *bytes, const uint32_t *native) { 1990 unsigned i; 1991 for (i = 0; i < uECC_WORDS; ++i) { 1992 uint8_t *digit = bytes + 4 * (uECC_WORDS - 1 - i); 1993 digit[0] = native[i] >> 24; 1994 digit[1] = native[i] >> 16; 1995 digit[2] = native[i] >> 8; 1996 digit[3] = native[i]; 1997 } 1998 } 1999 2000 static void vli_bytesToNative(uint32_t *native, const uint8_t *bytes) { 2001 unsigned i; 2002 for (i = 0; i < uECC_WORDS; ++i) { 2003 const uint8_t *digit = bytes + 4 * (uECC_WORDS - 1 - i); 2004 native[i] = ((uint32_t)digit[0] << 24) | ((uint32_t)digit[1] << 16) | 2005 ((uint32_t)digit[2] << 8) | (uint32_t)digit[3]; 2006 } 2007 } 2008 2009 #else 2010 2011 static void vli_nativeToBytes(uint8_t *bytes, const uint64_t *native) { 2012 unsigned i; 2013 for (i = 0; i < uECC_WORDS; ++i) { 2014 uint8_t *digit = bytes + 8 * (uECC_WORDS - 1 - i); 2015 digit[0] = native[i] >> 56; 2016 digit[1] = native[i] >> 48; 2017 digit[2] = native[i] >> 40; 2018 digit[3] = native[i] >> 32; 2019 digit[4] = native[i] >> 24; 2020 digit[5] = native[i] >> 16; 2021 digit[6] = native[i] >> 8; 2022 digit[7] = native[i]; 2023 } 2024 } 2025 2026 static void vli_bytesToNative(uint64_t *native, const uint8_t *bytes) { 2027 unsigned i; 2028 for (i = 0; i < uECC_WORDS; ++i) { 2029 const uint8_t *digit = bytes + 8 * (uECC_WORDS - 1 - i); 2030 native[i] = ((uint64_t)digit[0] << 56) | ((uint64_t)digit[1] << 48) | 2031 ((uint64_t)digit[2] << 40) | ((uint64_t)digit[3] << 32) | 2032 ((uint64_t)digit[4] << 24) | ((uint64_t)digit[5] << 16) | 2033 ((uint64_t)digit[6] << 8) | (uint64_t)digit[7]; 2034 } 2035 } 2036 2037 #endif /* uECC_WORD_SIZE */ 2038 2039 int uECC_make_key(uint8_t public_key[uECC_BYTES*2], uint8_t private_key[uECC_BYTES]) { 2040 uECC_word_t private[uECC_WORDS]; 2041 EccPoint public; 2042 uECC_word_t tries; 2043 for (tries = 0; tries < MAX_TRIES; ++tries) { 2044 if (g_rng_function((uint8_t *)private, sizeof(private)) && 2045 EccPoint_compute_public_key(&public, private)) { 2046 vli_nativeToBytes(private_key, private); 2047 vli_nativeToBytes(public_key, public.x); 2048 vli_nativeToBytes(public_key + uECC_BYTES, public.y); 2049 return 1; 2050 } 2051 } 2052 return 0; 2053 } 2054 2055 int uECC_shared_secret(const uint8_t public_key[uECC_BYTES*2], 2056 const uint8_t private_key[uECC_BYTES], 2057 uint8_t secret[uECC_BYTES]) { 2058 EccPoint public; 2059 EccPoint product; 2060 uECC_word_t private[uECC_WORDS]; 2061 uECC_word_t tmp[uECC_WORDS]; 2062 uECC_word_t *p2[2] = {private, tmp}; 2063 uECC_word_t random[uECC_WORDS]; 2064 uECC_word_t *initial_Z = NULL; 2065 uECC_word_t tries; 2066 uECC_word_t carry; 2067 2068 // Try to get a random initial Z value to improve protection against side-channel 2069 // attacks. If the RNG fails every time (eg it was not defined), we continue so that 2070 // uECC_shared_secret() can still work without an RNG defined. 2071 for (tries = 0; tries < MAX_TRIES; ++tries) { 2072 if (g_rng_function((uint8_t *)random, sizeof(random)) && !vli_isZero(random)) { 2073 initial_Z = random; 2074 break; 2075 } 2076 } 2077 2078 vli_bytesToNative(private, private_key); 2079 vli_bytesToNative(public.x, public_key); 2080 vli_bytesToNative(public.y, public_key + uECC_BYTES); 2081 2082 #if (uECC_CURVE == uECC_secp160r1) 2083 // Don't regularize the bitcount for secp160r1. 2084 EccPoint_mult(&product, &public, private, initial_Z, vli_numBits(private, uECC_WORDS)); 2085 #else 2086 // Regularize the bitcount for the private key so that attackers cannot use a side channel 2087 // attack to learn the number of leading zeros. 2088 carry = vli_add(private, private, curve_n); 2089 vli_add(tmp, private, curve_n); 2090 EccPoint_mult(&product, &public, p2[!carry], initial_Z, (uECC_BYTES * 8) + 1); 2091 #endif 2092 2093 vli_nativeToBytes(secret, product.x); 2094 return !EccPoint_isZero(&product); 2095 } 2096 2097 #ifdef ENABLE_MICRO_ECC_COMPRESSION 2098 2099 void uECC_compress(const uint8_t public_key[uECC_BYTES*2], uint8_t compressed[uECC_BYTES+1]) { 2100 wordcount_t i; 2101 for (i = 0; i < uECC_BYTES; ++i) { 2102 compressed[i+1] = public_key[i]; 2103 } 2104 compressed[0] = 2 + (public_key[uECC_BYTES * 2 - 1] & 0x01); 2105 } 2106 2107 #endif 2108 2109 /* Computes result = x^3 + ax + b. result must not overlap x. */ 2110 static void curve_x_side(uECC_word_t * RESTRICT result, const uECC_word_t * RESTRICT x) { 2111 static const uECC_word_t curve_b[uECC_WORDS] = uECC_CONCAT(Curve_B_, uECC_CURVE); 2112 #if (uECC_CURVE == uECC_secp256k1) 2113 vli_modSquare_fast(result, x); /* r = x^2 */ 2114 vli_modMult_fast(result, result, x); /* r = x^3 */ 2115 vli_modAdd(result, result, curve_b, curve_p); /* r = x^3 + b */ 2116 #else 2117 uECC_word_t _3[uECC_WORDS] = {3}; /* -a = 3 */ 2118 2119 vli_modSquare_fast(result, x); /* r = x^2 */ 2120 vli_modSub_fast(result, result, _3); /* r = x^2 - 3 */ 2121 vli_modMult_fast(result, result, x); /* r = x^3 - 3x */ 2122 vli_modAdd(result, result, curve_b, curve_p); /* r = x^3 - 3x + b */ 2123 #endif 2124 } 2125 2126 #ifdef ENABLE_MICRO_ECC_COMPRESSION 2127 2128 void uECC_decompress(const uint8_t compressed[uECC_BYTES+1], uint8_t public_key[uECC_BYTES*2]) { 2129 EccPoint point; 2130 vli_bytesToNative(point.x, compressed + 1); 2131 curve_x_side(point.y, point.x); 2132 mod_sqrt(point.y); 2133 2134 if ((point.y[0] & 0x01) != (compressed[0] & 0x01)) { 2135 vli_sub(point.y, curve_p, point.y); 2136 } 2137 2138 vli_nativeToBytes(public_key, point.x); 2139 vli_nativeToBytes(public_key + uECC_BYTES, point.y); 2140 } 2141 2142 #endif /* ENABLE_MICRO_ECC_COMPRESSION */ 2143 2144 int uECC_valid_public_key(const uint8_t public_key[uECC_BYTES*2]) { 2145 uECC_word_t tmp1[uECC_WORDS]; 2146 uECC_word_t tmp2[uECC_WORDS]; 2147 EccPoint public; 2148 2149 vli_bytesToNative(public.x, public_key); 2150 vli_bytesToNative(public.y, public_key + uECC_BYTES); 2151 2152 // The point at infinity is invalid. 2153 if (EccPoint_isZero(&public)) { 2154 return 0; 2155 } 2156 2157 // x and y must be smaller than p. 2158 if (vli_cmp(curve_p, public.x) != 1 || vli_cmp(curve_p, public.y) != 1) { 2159 return 0; 2160 } 2161 2162 vli_modSquare_fast(tmp1, public.y); /* tmp1 = y^2 */ 2163 curve_x_side(tmp2, public.x); /* tmp2 = x^3 + ax + b */ 2164 2165 /* Make sure that y^2 == x^3 + ax + b */ 2166 return (vli_cmp(tmp1, tmp2) == 0); 2167 } 2168 2169 int uECC_compute_public_key(const uint8_t private_key[uECC_BYTES], 2170 uint8_t public_key[uECC_BYTES * 2]) { 2171 uECC_word_t private[uECC_WORDS]; 2172 EccPoint public; 2173 2174 vli_bytesToNative(private, private_key); 2175 2176 if (!EccPoint_compute_public_key(&public, private)) { 2177 return 0; 2178 } 2179 2180 vli_nativeToBytes(public_key, public.x); 2181 vli_nativeToBytes(public_key + uECC_BYTES, public.y); 2182 return 1; 2183 } 2184 2185 int uECC_bytes(void) { 2186 return uECC_BYTES; 2187 } 2188 2189 int uECC_curve(void) { 2190 return uECC_CURVE; 2191 } 2192 2193 /* -------- ECDSA code -------- */ 2194 2195 #ifdef ENABLE_MICRO_ECC_ECDSA 2196 2197 #if (uECC_CURVE == uECC_secp160r1) 2198 static void vli_clear_n(uECC_word_t *vli) { 2199 vli_clear(vli); 2200 vli[uECC_N_WORDS - 1] = 0; 2201 } 2202 2203 static uECC_word_t vli_isZero_n(const uECC_word_t *vli) { 2204 if (vli[uECC_N_WORDS - 1]) { 2205 return 0; 2206 } 2207 return vli_isZero(vli); 2208 } 2209 2210 static void vli_set_n(uECC_word_t *dest, const uECC_word_t *src) { 2211 vli_set(dest, src); 2212 dest[uECC_N_WORDS - 1] = src[uECC_N_WORDS - 1]; 2213 } 2214 2215 static cmpresult_t vli_cmp_n(const uECC_word_t *left, const uECC_word_t *right) { 2216 if (left[uECC_N_WORDS - 1] > right[uECC_N_WORDS - 1]) { 2217 return 1; 2218 } else if (left[uECC_N_WORDS - 1] < right[uECC_N_WORDS - 1]) { 2219 return -1; 2220 } 2221 return vli_cmp(left, right); 2222 } 2223 2224 static void vli_rshift1_n(uECC_word_t *vli) { 2225 vli_rshift1(vli); 2226 vli[uECC_N_WORDS - 2] |= vli[uECC_N_WORDS - 1] << (uECC_WORD_BITS - 1); 2227 vli[uECC_N_WORDS - 1] = vli[uECC_N_WORDS - 1] >> 1; 2228 } 2229 2230 static uECC_word_t vli_add_n(uECC_word_t *result, 2231 const uECC_word_t *left, 2232 const uECC_word_t *right) { 2233 uECC_word_t carry = vli_add(result, left, right); 2234 uECC_word_t sum = left[uECC_N_WORDS - 1] + right[uECC_N_WORDS - 1] + carry; 2235 if (sum != left[uECC_N_WORDS - 1]) { 2236 carry = (sum < left[uECC_N_WORDS - 1]); 2237 } 2238 result[uECC_N_WORDS - 1] = sum; 2239 return carry; 2240 } 2241 2242 static uECC_word_t vli_sub_n(uECC_word_t *result, 2243 const uECC_word_t *left, 2244 const uECC_word_t *right) { 2245 uECC_word_t borrow = vli_sub(result, left, right); 2246 uECC_word_t diff = left[uECC_N_WORDS - 1] - right[uECC_N_WORDS - 1] - borrow; 2247 if (diff != left[uECC_N_WORDS - 1]) { 2248 borrow = (diff > left[uECC_N_WORDS - 1]); 2249 } 2250 result[uECC_N_WORDS - 1] = diff; 2251 return borrow; 2252 } 2253 2254 #if !muladd_exists 2255 static void muladd(uECC_word_t a, 2256 uECC_word_t b, 2257 uECC_word_t *r0, 2258 uECC_word_t *r1, 2259 uECC_word_t *r2) { 2260 uECC_dword_t p = (uECC_dword_t)a * b; 2261 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; 2262 r01 += p; 2263 *r2 += (r01 < p); 2264 *r1 = r01 >> uECC_WORD_BITS; 2265 *r0 = (uECC_word_t)r01; 2266 } 2267 #define muladd_exists 1 2268 #endif 2269 2270 static void vli_mult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 2271 uECC_word_t r0 = 0; 2272 uECC_word_t r1 = 0; 2273 uECC_word_t r2 = 0; 2274 wordcount_t i, k; 2275 2276 for (k = 0; k < uECC_N_WORDS * 2 - 1; ++k) { 2277 wordcount_t min = (k < uECC_N_WORDS ? 0 : (k + 1) - uECC_N_WORDS); 2278 wordcount_t max = (k < uECC_N_WORDS ? k : uECC_N_WORDS - 1); 2279 for (i = min; i <= max; ++i) { 2280 muladd(left[i], right[k - i], &r0, &r1, &r2); 2281 } 2282 result[k] = r0; 2283 r0 = r1; 2284 r1 = r2; 2285 r2 = 0; 2286 } 2287 result[uECC_N_WORDS * 2 - 1] = r0; 2288 } 2289 2290 static void vli_modAdd_n(uECC_word_t *result, 2291 const uECC_word_t *left, 2292 const uECC_word_t *right, 2293 const uECC_word_t *mod) { 2294 uECC_word_t carry = vli_add_n(result, left, right); 2295 if (carry || vli_cmp_n(result, mod) >= 0) { 2296 vli_sub_n(result, result, mod); 2297 } 2298 } 2299 2300 static void vli_modInv_n(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod) { 2301 uECC_word_t a[uECC_N_WORDS], b[uECC_N_WORDS], u[uECC_N_WORDS], v[uECC_N_WORDS]; 2302 uECC_word_t carry; 2303 cmpresult_t cmpResult; 2304 2305 if (vli_isZero_n(input)) { 2306 vli_clear_n(result); 2307 return; 2308 } 2309 2310 vli_set_n(a, input); 2311 vli_set_n(b, mod); 2312 vli_clear_n(u); 2313 u[0] = 1; 2314 vli_clear_n(v); 2315 while ((cmpResult = vli_cmp_n(a, b)) != 0) { 2316 carry = 0; 2317 if (EVEN(a)) { 2318 vli_rshift1_n(a); 2319 if (!EVEN(u)) { 2320 carry = vli_add_n(u, u, mod); 2321 } 2322 vli_rshift1_n(u); 2323 if (carry) { 2324 u[uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2325 } 2326 } else if (EVEN(b)) { 2327 vli_rshift1_n(b); 2328 if (!EVEN(v)) { 2329 carry = vli_add_n(v, v, mod); 2330 } 2331 vli_rshift1_n(v); 2332 if (carry) { 2333 v[uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2334 } 2335 } else if (cmpResult > 0) { 2336 vli_sub_n(a, a, b); 2337 vli_rshift1_n(a); 2338 if (vli_cmp_n(u, v) < 0) { 2339 vli_add_n(u, u, mod); 2340 } 2341 vli_sub_n(u, u, v); 2342 if (!EVEN(u)) { 2343 carry = vli_add_n(u, u, mod); 2344 } 2345 vli_rshift1_n(u); 2346 if (carry) { 2347 u[uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2348 } 2349 } else { 2350 vli_sub_n(b, b, a); 2351 vli_rshift1_n(b); 2352 if (vli_cmp_n(v, u) < 0) { 2353 vli_add_n(v, v, mod); 2354 } 2355 vli_sub_n(v, v, u); 2356 if (!EVEN(v)) { 2357 carry = vli_add_n(v, v, mod); 2358 } 2359 vli_rshift1_n(v); 2360 if (carry) { 2361 v[uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2362 } 2363 } 2364 } 2365 vli_set_n(result, u); 2366 } 2367 2368 static void vli2_rshift1_n(uECC_word_t *vli) { 2369 vli_rshift1_n(vli); 2370 vli[uECC_N_WORDS - 1] |= vli[uECC_N_WORDS] << (uECC_WORD_BITS - 1); 2371 vli_rshift1_n(vli + uECC_N_WORDS); 2372 } 2373 2374 static uECC_word_t vli2_sub_n(uECC_word_t *result, 2375 const uECC_word_t *left, 2376 const uECC_word_t *right) { 2377 uECC_word_t borrow = 0; 2378 wordcount_t i; 2379 for (i = 0; i < uECC_N_WORDS * 2; ++i) { 2380 uECC_word_t diff = left[i] - right[i] - borrow; 2381 if (diff != left[i]) { 2382 borrow = (diff > left[i]); 2383 } 2384 result[i] = diff; 2385 } 2386 return borrow; 2387 } 2388 2389 /* Computes result = (left * right) % curve_n. */ 2390 static void vli_modMult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 2391 bitcount_t i; 2392 uECC_word_t product[2 * uECC_N_WORDS]; 2393 uECC_word_t modMultiple[2 * uECC_N_WORDS]; 2394 uECC_word_t tmp[2 * uECC_N_WORDS]; 2395 uECC_word_t *v[2] = {tmp, product}; 2396 uECC_word_t index = 1; 2397 2398 vli_mult_n(product, left, right); 2399 vli_clear_n(modMultiple); 2400 vli_set(modMultiple + uECC_N_WORDS + 1, curve_n); 2401 vli_rshift1(modMultiple + uECC_N_WORDS + 1); 2402 modMultiple[2 * uECC_N_WORDS - 1] |= HIGH_BIT_SET; 2403 modMultiple[uECC_N_WORDS] = HIGH_BIT_SET; 2404 2405 for (i = 0; 2406 i <= ((((bitcount_t)uECC_N_WORDS) << uECC_WORD_BITS_SHIFT) + (uECC_WORD_BITS - 1)); 2407 ++i) { 2408 uECC_word_t borrow = vli2_sub_n(v[1 - index], v[index], modMultiple); 2409 index = !(index ^ borrow); /* Swap the index if there was no borrow */ 2410 vli2_rshift1_n(modMultiple); 2411 } 2412 vli_set_n(result, v[index]); 2413 } 2414 2415 #else 2416 2417 #define vli_cmp_n vli_cmp 2418 #define vli_modInv_n vli_modInv 2419 #define vli_modAdd_n vli_modAdd 2420 2421 static void vli2_rshift1(uECC_word_t *vli) { 2422 vli_rshift1(vli); 2423 vli[uECC_WORDS - 1] |= vli[uECC_WORDS] << (uECC_WORD_BITS - 1); 2424 vli_rshift1(vli + uECC_WORDS); 2425 } 2426 2427 static uECC_word_t vli2_sub(uECC_word_t *result, 2428 const uECC_word_t *left, 2429 const uECC_word_t *right) { 2430 uECC_word_t borrow = 0; 2431 wordcount_t i; 2432 for (i = 0; i < uECC_WORDS * 2; ++i) { 2433 uECC_word_t diff = left[i] - right[i] - borrow; 2434 if (diff != left[i]) { 2435 borrow = (diff > left[i]); 2436 } 2437 result[i] = diff; 2438 } 2439 return borrow; 2440 } 2441 2442 /* Computes result = (left * right) % curve_n. */ 2443 static void vli_modMult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) { 2444 uECC_word_t product[2 * uECC_WORDS]; 2445 uECC_word_t modMultiple[2 * uECC_WORDS]; 2446 uECC_word_t tmp[2 * uECC_WORDS]; 2447 uECC_word_t *v[2] = {tmp, product}; 2448 bitcount_t i; 2449 uECC_word_t index = 1; 2450 2451 vli_mult(product, left, right); 2452 vli_set(modMultiple + uECC_WORDS, curve_n); /* works if curve_n has its highest bit set */ 2453 vli_clear(modMultiple); 2454 2455 for (i = 0; i <= uECC_BYTES * 8; ++i) { 2456 uECC_word_t borrow = vli2_sub(v[1 - index], v[index], modMultiple); 2457 index = !(index ^ borrow); /* Swap the index if there was no borrow */ 2458 vli2_rshift1(modMultiple); 2459 } 2460 vli_set(result, v[index]); 2461 } 2462 #endif /* (uECC_CURVE != uECC_secp160r1) */ 2463 2464 static int uECC_sign_with_k(const uint8_t private_key[uECC_BYTES], 2465 const uint8_t message_hash[uECC_BYTES], 2466 uECC_word_t k[uECC_N_WORDS], 2467 uint8_t signature[uECC_BYTES*2]) { 2468 uECC_word_t tmp[uECC_N_WORDS]; 2469 uECC_word_t s[uECC_N_WORDS]; 2470 uECC_word_t *k2[2] = {tmp, s}; 2471 EccPoint p; 2472 uECC_word_t carry; 2473 uECC_word_t tries; 2474 2475 /* Make sure 0 < k < curve_n */ 2476 if (vli_isZero(k) || vli_cmp_n(curve_n, k) != 1) { 2477 return 0; 2478 } 2479 2480 #if (uECC_CURVE == uECC_secp160r1) 2481 /* Make sure that we don't leak timing information about k. 2482 See http://eprint.iacr.org/2011/232.pdf */ 2483 vli_add_n(tmp, k, curve_n); 2484 carry = (tmp[uECC_WORDS] & 0x02); 2485 vli_add_n(s, tmp, curve_n); 2486 2487 /* p = k * G */ 2488 EccPoint_mult(&p, &curve_G, k2[!carry], NULL, (uECC_BYTES * 8) + 2); 2489 #else 2490 /* Make sure that we don't leak timing information about k. 2491 See http://eprint.iacr.org/2011/232.pdf */ 2492 carry = vli_add(tmp, k, curve_n); 2493 vli_add(s, tmp, curve_n); 2494 2495 /* p = k * G */ 2496 EccPoint_mult(&p, &curve_G, k2[!carry], NULL, (uECC_BYTES * 8) + 1); 2497 2498 /* r = x1 (mod n) */ 2499 if (vli_cmp(curve_n, p.x) != 1) { 2500 vli_sub(p.x, p.x, curve_n); 2501 } 2502 #endif 2503 if (vli_isZero(p.x)) { 2504 return 0; 2505 } 2506 2507 // Attempt to get a random number to prevent side channel analysis of k. 2508 // If the RNG fails every time (eg it was not defined), we continue so that 2509 // deterministic signing can still work (with reduced security) without 2510 // an RNG defined. 2511 carry = 0; // use to signal that the RNG succeeded at least once. 2512 for (tries = 0; tries < MAX_TRIES; ++tries) { 2513 if (!g_rng_function((uint8_t *)tmp, sizeof(tmp))) { 2514 continue; 2515 } 2516 carry = 1; 2517 if (!vli_isZero(tmp)) { 2518 break; 2519 } 2520 } 2521 if (!carry) { 2522 vli_clear(tmp); 2523 tmp[0] = 1; 2524 } 2525 2526 /* Prevent side channel analysis of vli_modInv() to determine 2527 bits of k / the private key by premultiplying by a random number */ 2528 vli_modMult_n(k, k, tmp); /* k' = rand * k */ 2529 vli_modInv_n(k, k, curve_n); /* k = 1 / k' */ 2530 vli_modMult_n(k, k, tmp); /* k = 1 / k */ 2531 2532 vli_nativeToBytes(signature, p.x); /* store r */ 2533 2534 tmp[uECC_N_WORDS - 1] = 0; 2535 vli_bytesToNative(tmp, private_key); /* tmp = d */ 2536 s[uECC_N_WORDS - 1] = 0; 2537 vli_set(s, p.x); 2538 vli_modMult_n(s, tmp, s); /* s = r*d */ 2539 2540 vli_bytesToNative(tmp, message_hash); 2541 vli_modAdd_n(s, tmp, s, curve_n); /* s = e + r*d */ 2542 vli_modMult_n(s, s, k); /* s = (e + r*d) / k */ 2543 #if (uECC_CURVE == uECC_secp160r1) 2544 if (s[uECC_N_WORDS - 1]) { 2545 return 0; 2546 } 2547 #endif 2548 vli_nativeToBytes(signature + uECC_BYTES, s); 2549 return 1; 2550 } 2551 2552 int uECC_sign(const uint8_t private_key[uECC_BYTES], 2553 const uint8_t message_hash[uECC_BYTES], 2554 uint8_t signature[uECC_BYTES*2]) { 2555 uECC_word_t k[uECC_N_WORDS]; 2556 uECC_word_t tries; 2557 2558 for (tries = 0; tries < MAX_TRIES; ++tries) { 2559 if(g_rng_function((uint8_t *)k, sizeof(k))) { 2560 #if (uECC_CURVE == uECC_secp160r1) 2561 k[uECC_WORDS] &= 0x01; 2562 #endif 2563 if (uECC_sign_with_k(private_key, message_hash, k, signature)) { 2564 return 1; 2565 } 2566 } 2567 } 2568 return 0; 2569 } 2570 2571 /* Compute an HMAC using K as a key (as in RFC 6979). Note that K is always 2572 the same size as the hash result size. */ 2573 static void HMAC_init(uECC_HashContext *hash_context, const uint8_t *K) { 2574 uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size; 2575 unsigned i; 2576 for (i = 0; i < hash_context->result_size; ++i) 2577 pad[i] = K[i] ^ 0x36; 2578 for (; i < hash_context->block_size; ++i) 2579 pad[i] = 0x36; 2580 2581 hash_context->init_hash(hash_context); 2582 hash_context->update_hash(hash_context, pad, hash_context->block_size); 2583 } 2584 2585 static void HMAC_update(uECC_HashContext *hash_context, 2586 const uint8_t *message, 2587 unsigned message_size) { 2588 hash_context->update_hash(hash_context, message, message_size); 2589 } 2590 2591 static void HMAC_finish(uECC_HashContext *hash_context, const uint8_t *K, uint8_t *result) { 2592 uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size; 2593 unsigned i; 2594 for (i = 0; i < hash_context->result_size; ++i) 2595 pad[i] = K[i] ^ 0x5c; 2596 for (; i < hash_context->block_size; ++i) 2597 pad[i] = 0x5c; 2598 2599 hash_context->finish_hash(hash_context, result); 2600 2601 hash_context->init_hash(hash_context); 2602 hash_context->update_hash(hash_context, pad, hash_context->block_size); 2603 hash_context->update_hash(hash_context, result, hash_context->result_size); 2604 hash_context->finish_hash(hash_context, result); 2605 } 2606 2607 /* V = HMAC_K(V) */ 2608 static void update_V(uECC_HashContext *hash_context, uint8_t *K, uint8_t *V) { 2609 HMAC_init(hash_context, K); 2610 HMAC_update(hash_context, V, hash_context->result_size); 2611 HMAC_finish(hash_context, K, V); 2612 } 2613 2614 /* Deterministic signing, similar to RFC 6979. Differences are: 2615 * We just use (truncated) H(m) directly rather than bits2octets(H(m)) 2616 (it is not reduced modulo curve_n). 2617 * We generate a value for k (aka T) directly rather than converting endianness. 2618 2619 Layout of hash_context->tmp: <K> | <V> | (1 byte overlapped 0x00 or 0x01) / <HMAC pad> */ 2620 int uECC_sign_deterministic(const uint8_t private_key[uECC_BYTES], 2621 const uint8_t message_hash[uECC_BYTES], 2622 uECC_HashContext *hash_context, 2623 uint8_t signature[uECC_BYTES*2]) { 2624 uint8_t *K = hash_context->tmp; 2625 uint8_t *V = K + hash_context->result_size; 2626 uECC_word_t tries; 2627 unsigned i; 2628 for (i = 0; i < hash_context->result_size; ++i) { 2629 V[i] = 0x01; 2630 K[i] = 0; 2631 } 2632 2633 // K = HMAC_K(V || 0x00 || int2octets(x) || h(m)) 2634 HMAC_init(hash_context, K); 2635 V[hash_context->result_size] = 0x00; 2636 HMAC_update(hash_context, V, hash_context->result_size + 1); 2637 HMAC_update(hash_context, private_key, uECC_BYTES); 2638 HMAC_update(hash_context, message_hash, uECC_BYTES); 2639 HMAC_finish(hash_context, K, K); 2640 2641 update_V(hash_context, K, V); 2642 2643 // K = HMAC_K(V || 0x01 || int2octets(x) || h(m)) 2644 HMAC_init(hash_context, K); 2645 V[hash_context->result_size] = 0x01; 2646 HMAC_update(hash_context, V, hash_context->result_size + 1); 2647 HMAC_update(hash_context, private_key, uECC_BYTES); 2648 HMAC_update(hash_context, message_hash, uECC_BYTES); 2649 HMAC_finish(hash_context, K, K); 2650 2651 update_V(hash_context, K, V); 2652 2653 for (tries = 0; tries < MAX_TRIES; ++tries) { 2654 uECC_word_t T[uECC_N_WORDS]; 2655 uint8_t *T_ptr = (uint8_t *)T; 2656 unsigned T_bytes = 0; 2657 while (T_bytes < sizeof(T)) { 2658 update_V(hash_context, K, V); 2659 for (i = 0; i < hash_context->result_size && T_bytes < sizeof(T); ++i, ++T_bytes) { 2660 T_ptr[T_bytes] = V[i]; 2661 } 2662 } 2663 #if (uECC_CURVE == uECC_secp160r1) 2664 T[uECC_WORDS] &= 0x01; 2665 #endif 2666 2667 if (uECC_sign_with_k(private_key, message_hash, T, signature)) { 2668 return 1; 2669 } 2670 2671 // K = HMAC_K(V || 0x00) 2672 HMAC_init(hash_context, K); 2673 V[hash_context->result_size] = 0x00; 2674 HMAC_update(hash_context, V, hash_context->result_size + 1); 2675 HMAC_finish(hash_context, K, K); 2676 2677 update_V(hash_context, K, V); 2678 } 2679 return 0; 2680 } 2681 2682 static bitcount_t smax(bitcount_t a, bitcount_t b) { 2683 return (a > b ? a : b); 2684 } 2685 2686 int uECC_verify(const uint8_t public_key[uECC_BYTES*2], 2687 const uint8_t hash[uECC_BYTES], 2688 const uint8_t signature[uECC_BYTES*2]) { 2689 uECC_word_t u1[uECC_N_WORDS], u2[uECC_N_WORDS]; 2690 uECC_word_t z[uECC_N_WORDS]; 2691 EccPoint public, sum; 2692 uECC_word_t rx[uECC_WORDS]; 2693 uECC_word_t ry[uECC_WORDS]; 2694 uECC_word_t tx[uECC_WORDS]; 2695 uECC_word_t ty[uECC_WORDS]; 2696 uECC_word_t tz[uECC_WORDS]; 2697 const EccPoint *points[4]; 2698 const EccPoint *point; 2699 bitcount_t numBits; 2700 bitcount_t i; 2701 uECC_word_t r[uECC_N_WORDS], s[uECC_N_WORDS]; 2702 r[uECC_N_WORDS - 1] = 0; 2703 s[uECC_N_WORDS - 1] = 0; 2704 2705 vli_bytesToNative(public.x, public_key); 2706 vli_bytesToNative(public.y, public_key + uECC_BYTES); 2707 vli_bytesToNative(r, signature); 2708 vli_bytesToNative(s, signature + uECC_BYTES); 2709 2710 if (vli_isZero(r) || vli_isZero(s)) { /* r, s must not be 0. */ 2711 return 0; 2712 } 2713 2714 #if (uECC_CURVE != uECC_secp160r1) 2715 if (vli_cmp(curve_n, r) != 1 || vli_cmp(curve_n, s) != 1) { /* r, s must be < n. */ 2716 return 0; 2717 } 2718 #endif 2719 2720 /* Calculate u1 and u2. */ 2721 vli_modInv_n(z, s, curve_n); /* Z = s^-1 */ 2722 u1[uECC_N_WORDS - 1] = 0; 2723 vli_bytesToNative(u1, hash); 2724 vli_modMult_n(u1, u1, z); /* u1 = e/s */ 2725 vli_modMult_n(u2, r, z); /* u2 = r/s */ 2726 2727 /* Calculate sum = G + Q. */ 2728 vli_set(sum.x, public.x); 2729 vli_set(sum.y, public.y); 2730 vli_set(tx, curve_G.x); 2731 vli_set(ty, curve_G.y); 2732 vli_modSub_fast(z, sum.x, tx); /* Z = x2 - x1 */ 2733 XYcZ_add(tx, ty, sum.x, sum.y); 2734 vli_modInv(z, z, curve_p); /* Z = 1/Z */ 2735 apply_z(sum.x, sum.y, z); 2736 2737 /* Use Shamir's trick to calculate u1*G + u2*Q */ 2738 points[0] = 0; 2739 points[1] = &curve_G; 2740 points[2] = &public; 2741 points[3] = ∑ 2742 numBits = smax(vli_numBits(u1, uECC_N_WORDS), vli_numBits(u2, uECC_N_WORDS)); 2743 2744 point = points[(!!vli_testBit(u1, numBits - 1)) | ((!!vli_testBit(u2, numBits - 1)) << 1)]; 2745 vli_set(rx, point->x); 2746 vli_set(ry, point->y); 2747 vli_clear(z); 2748 z[0] = 1; 2749 2750 for (i = numBits - 2; i >= 0; --i) { 2751 uECC_word_t index; 2752 EccPoint_double_jacobian(rx, ry, z); 2753 2754 index = (!!vli_testBit(u1, i)) | ((!!vli_testBit(u2, i)) << 1); 2755 point = points[index]; 2756 if (point) { 2757 vli_set(tx, point->x); 2758 vli_set(ty, point->y); 2759 apply_z(tx, ty, z); 2760 vli_modSub_fast(tz, rx, tx); /* Z = x2 - x1 */ 2761 XYcZ_add(tx, ty, rx, ry); 2762 vli_modMult_fast(z, z, tz); 2763 } 2764 } 2765 2766 vli_modInv(z, z, curve_p); /* Z = 1/Z */ 2767 apply_z(rx, ry, z); 2768 2769 /* v = x1 (mod n) */ 2770 #if (uECC_CURVE != uECC_secp160r1) 2771 if (vli_cmp(curve_n, rx) != 1) { 2772 vli_sub(rx, rx, curve_n); 2773 } 2774 #endif 2775 2776 /* Accept only if v == r. */ 2777 return vli_equal(rx, r); 2778 } 2779 2780 #endif 2781