Kai Liu / uECC

micro-ECC for mbed, ported from GCC version from Github,

Dependents:   mbed_microECC Wallet_v1

uECC.cpp@0:b6fdeddc0bc9, 2017-09-07 (annotated)

Committer:
allankliu
Date:
Thu Sep 07 12:10:11 2017 +0000
Revision:
0:b6fdeddc0bc9
Init version, ported from GCC version of uECC of Github. Assembly optimization for thumb2 is disabled.

Who changed what in which revision?

UserRevisionLine numberNew contents of line
allankliu 0:b6fdeddc0bc9 1 /* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */
allankliu 0:b6fdeddc0bc9 2
allankliu 0:b6fdeddc0bc9 3 #include "uECC.h"
allankliu 0:b6fdeddc0bc9 4 #include "uECC_vli.h"
allankliu 0:b6fdeddc0bc9 5
allankliu 0:b6fdeddc0bc9 6 #ifndef uECC_RNG_MAX_TRIES
allankliu 0:b6fdeddc0bc9 7 #define uECC_RNG_MAX_TRIES 64
allankliu 0:b6fdeddc0bc9 8 #endif
allankliu 0:b6fdeddc0bc9 9
allankliu 0:b6fdeddc0bc9 10 #if uECC_ENABLE_VLI_API
allankliu 0:b6fdeddc0bc9 11 #define uECC_VLI_API
allankliu 0:b6fdeddc0bc9 12 #else
allankliu 0:b6fdeddc0bc9 13 #define uECC_VLI_API static
allankliu 0:b6fdeddc0bc9 14 #endif
allankliu 0:b6fdeddc0bc9 15
allankliu 0:b6fdeddc0bc9 16 #define CONCATX(a, ...) a ## __VA_ARGS__
allankliu 0:b6fdeddc0bc9 17 #define CONCAT(a, ...) CONCATX(a, __VA_ARGS__)
allankliu 0:b6fdeddc0bc9 18
allankliu 0:b6fdeddc0bc9 19 #define STRX(a) #a
allankliu 0:b6fdeddc0bc9 20 #define STR(a) STRX(a)
allankliu 0:b6fdeddc0bc9 21
allankliu 0:b6fdeddc0bc9 22 #define EVAL(...) EVAL1(EVAL1(EVAL1(EVAL1(__VA_ARGS__))))
allankliu 0:b6fdeddc0bc9 23 #define EVAL1(...) EVAL2(EVAL2(EVAL2(EVAL2(__VA_ARGS__))))
allankliu 0:b6fdeddc0bc9 24 #define EVAL2(...) EVAL3(EVAL3(EVAL3(EVAL3(__VA_ARGS__))))
allankliu 0:b6fdeddc0bc9 25 #define EVAL3(...) EVAL4(EVAL4(EVAL4(EVAL4(__VA_ARGS__))))
allankliu 0:b6fdeddc0bc9 26 #define EVAL4(...) __VA_ARGS__
allankliu 0:b6fdeddc0bc9 27
allankliu 0:b6fdeddc0bc9 28 #define DEC_1 0
allankliu 0:b6fdeddc0bc9 29 #define DEC_2 1
allankliu 0:b6fdeddc0bc9 30 #define DEC_3 2
allankliu 0:b6fdeddc0bc9 31 #define DEC_4 3
allankliu 0:b6fdeddc0bc9 32 #define DEC_5 4
allankliu 0:b6fdeddc0bc9 33 #define DEC_6 5
allankliu 0:b6fdeddc0bc9 34 #define DEC_7 6
allankliu 0:b6fdeddc0bc9 35 #define DEC_8 7
allankliu 0:b6fdeddc0bc9 36 #define DEC_9 8
allankliu 0:b6fdeddc0bc9 37 #define DEC_10 9
allankliu 0:b6fdeddc0bc9 38 #define DEC_11 10
allankliu 0:b6fdeddc0bc9 39 #define DEC_12 11
allankliu 0:b6fdeddc0bc9 40 #define DEC_13 12
allankliu 0:b6fdeddc0bc9 41 #define DEC_14 13
allankliu 0:b6fdeddc0bc9 42 #define DEC_15 14
allankliu 0:b6fdeddc0bc9 43 #define DEC_16 15
allankliu 0:b6fdeddc0bc9 44 #define DEC_17 16
allankliu 0:b6fdeddc0bc9 45 #define DEC_18 17
allankliu 0:b6fdeddc0bc9 46 #define DEC_19 18
allankliu 0:b6fdeddc0bc9 47 #define DEC_20 19
allankliu 0:b6fdeddc0bc9 48 #define DEC_21 20
allankliu 0:b6fdeddc0bc9 49 #define DEC_22 21
allankliu 0:b6fdeddc0bc9 50 #define DEC_23 22
allankliu 0:b6fdeddc0bc9 51 #define DEC_24 23
allankliu 0:b6fdeddc0bc9 52 #define DEC_25 24
allankliu 0:b6fdeddc0bc9 53 #define DEC_26 25
allankliu 0:b6fdeddc0bc9 54 #define DEC_27 26
allankliu 0:b6fdeddc0bc9 55 #define DEC_28 27
allankliu 0:b6fdeddc0bc9 56 #define DEC_29 28
allankliu 0:b6fdeddc0bc9 57 #define DEC_30 29
allankliu 0:b6fdeddc0bc9 58 #define DEC_31 30
allankliu 0:b6fdeddc0bc9 59 #define DEC_32 31
allankliu 0:b6fdeddc0bc9 60
allankliu 0:b6fdeddc0bc9 61 #define DEC(N) CONCAT(DEC_, N)
allankliu 0:b6fdeddc0bc9 62
allankliu 0:b6fdeddc0bc9 63 #define SECOND_ARG(_, val, ...) val
allankliu 0:b6fdeddc0bc9 64 #define SOME_CHECK_0 ~, 0
allankliu 0:b6fdeddc0bc9 65 #define GET_SECOND_ARG(...) SECOND_ARG(__VA_ARGS__, SOME,)
allankliu 0:b6fdeddc0bc9 66 #define SOME_OR_0(N) GET_SECOND_ARG(CONCAT(SOME_CHECK_, N))
allankliu 0:b6fdeddc0bc9 67
allankliu 0:b6fdeddc0bc9 68 #define EMPTY(...)
allankliu 0:b6fdeddc0bc9 69 #define DEFER(...) __VA_ARGS__ EMPTY()
allankliu 0:b6fdeddc0bc9 70
allankliu 0:b6fdeddc0bc9 71 #define REPEAT_NAME_0() REPEAT_0
allankliu 0:b6fdeddc0bc9 72 #define REPEAT_NAME_SOME() REPEAT_SOME
allankliu 0:b6fdeddc0bc9 73 #define REPEAT_0(...)
allankliu 0:b6fdeddc0bc9 74 #define REPEAT_SOME(N, stuff) DEFER(CONCAT(REPEAT_NAME_, SOME_OR_0(DEC(N))))()(DEC(N), stuff) stuff
allankliu 0:b6fdeddc0bc9 75 #define REPEAT(N, stuff) EVAL(REPEAT_SOME(N, stuff))
allankliu 0:b6fdeddc0bc9 76
allankliu 0:b6fdeddc0bc9 77 #define REPEATM_NAME_0() REPEATM_0
allankliu 0:b6fdeddc0bc9 78 #define REPEATM_NAME_SOME() REPEATM_SOME
allankliu 0:b6fdeddc0bc9 79 #define REPEATM_0(...)
allankliu 0:b6fdeddc0bc9 80 #define REPEATM_SOME(N, macro) macro(N) \
allankliu 0:b6fdeddc0bc9 81 DEFER(CONCAT(REPEATM_NAME_, SOME_OR_0(DEC(N))))()(DEC(N), macro)
allankliu 0:b6fdeddc0bc9 82 #define REPEATM(N, macro) EVAL(REPEATM_SOME(N, macro))
allankliu 0:b6fdeddc0bc9 83
allankliu 0:b6fdeddc0bc9 84 //#include "platform-specific.inc"
allankliu 0:b6fdeddc0bc9 85 #include "platform-specific.h"
allankliu 0:b6fdeddc0bc9 86
allankliu 0:b6fdeddc0bc9 87 #if (uECC_WORD_SIZE == 1)
allankliu 0:b6fdeddc0bc9 88 #if uECC_SUPPORTS_secp160r1
allankliu 0:b6fdeddc0bc9 89 #define uECC_MAX_WORDS 21 /* Due to the size of curve_n. */
allankliu 0:b6fdeddc0bc9 90 #endif
allankliu 0:b6fdeddc0bc9 91 #if uECC_SUPPORTS_secp192r1
allankliu 0:b6fdeddc0bc9 92 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 93 #define uECC_MAX_WORDS 24
allankliu 0:b6fdeddc0bc9 94 #endif
allankliu 0:b6fdeddc0bc9 95 #if uECC_SUPPORTS_secp224r1
allankliu 0:b6fdeddc0bc9 96 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 97 #define uECC_MAX_WORDS 28
allankliu 0:b6fdeddc0bc9 98 #endif
allankliu 0:b6fdeddc0bc9 99 #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1)
allankliu 0:b6fdeddc0bc9 100 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 101 #define uECC_MAX_WORDS 32
allankliu 0:b6fdeddc0bc9 102 #endif
allankliu 0:b6fdeddc0bc9 103 #elif (uECC_WORD_SIZE == 4)
allankliu 0:b6fdeddc0bc9 104 #if uECC_SUPPORTS_secp160r1
allankliu 0:b6fdeddc0bc9 105 #define uECC_MAX_WORDS 6 /* Due to the size of curve_n. */
allankliu 0:b6fdeddc0bc9 106 #endif
allankliu 0:b6fdeddc0bc9 107 #if uECC_SUPPORTS_secp192r1
allankliu 0:b6fdeddc0bc9 108 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 109 #define uECC_MAX_WORDS 6
allankliu 0:b6fdeddc0bc9 110 #endif
allankliu 0:b6fdeddc0bc9 111 #if uECC_SUPPORTS_secp224r1
allankliu 0:b6fdeddc0bc9 112 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 113 #define uECC_MAX_WORDS 7
allankliu 0:b6fdeddc0bc9 114 #endif
allankliu 0:b6fdeddc0bc9 115 #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1)
allankliu 0:b6fdeddc0bc9 116 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 117 #define uECC_MAX_WORDS 8
allankliu 0:b6fdeddc0bc9 118 #endif
allankliu 0:b6fdeddc0bc9 119 #elif (uECC_WORD_SIZE == 8)
allankliu 0:b6fdeddc0bc9 120 #if uECC_SUPPORTS_secp160r1
allankliu 0:b6fdeddc0bc9 121 #define uECC_MAX_WORDS 3
allankliu 0:b6fdeddc0bc9 122 #endif
allankliu 0:b6fdeddc0bc9 123 #if uECC_SUPPORTS_secp192r1
allankliu 0:b6fdeddc0bc9 124 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 125 #define uECC_MAX_WORDS 3
allankliu 0:b6fdeddc0bc9 126 #endif
allankliu 0:b6fdeddc0bc9 127 #if uECC_SUPPORTS_secp224r1
allankliu 0:b6fdeddc0bc9 128 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 129 #define uECC_MAX_WORDS 4
allankliu 0:b6fdeddc0bc9 130 #endif
allankliu 0:b6fdeddc0bc9 131 #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1)
allankliu 0:b6fdeddc0bc9 132 #undef uECC_MAX_WORDS
allankliu 0:b6fdeddc0bc9 133 #define uECC_MAX_WORDS 4
allankliu 0:b6fdeddc0bc9 134 #endif
allankliu 0:b6fdeddc0bc9 135 #endif /* uECC_WORD_SIZE */
allankliu 0:b6fdeddc0bc9 136
allankliu 0:b6fdeddc0bc9 137 #define BITS_TO_WORDS(num_bits) ((num_bits + ((uECC_WORD_SIZE * 8) - 1)) / (uECC_WORD_SIZE * 8))
allankliu 0:b6fdeddc0bc9 138 #define BITS_TO_BYTES(num_bits) ((num_bits + 7) / 8)
allankliu 0:b6fdeddc0bc9 139
allankliu 0:b6fdeddc0bc9 140 struct uECC_Curve_t {
allankliu 0:b6fdeddc0bc9 141 wordcount_t num_words;
allankliu 0:b6fdeddc0bc9 142 wordcount_t num_bytes;
allankliu 0:b6fdeddc0bc9 143 bitcount_t num_n_bits;
allankliu 0:b6fdeddc0bc9 144 uECC_word_t p[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 145 uECC_word_t n[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 146 uECC_word_t G[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 147 uECC_word_t b[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 148 void (*double_jacobian)(uECC_word_t * X1,
allankliu 0:b6fdeddc0bc9 149 uECC_word_t * Y1,
allankliu 0:b6fdeddc0bc9 150 uECC_word_t * Z1,
allankliu 0:b6fdeddc0bc9 151 uECC_Curve curve);
allankliu 0:b6fdeddc0bc9 152 #if uECC_SUPPORT_COMPRESSED_POINT
allankliu 0:b6fdeddc0bc9 153 void (*mod_sqrt)(uECC_word_t *a, uECC_Curve curve);
allankliu 0:b6fdeddc0bc9 154 #endif
allankliu 0:b6fdeddc0bc9 155 void (*x_side)(uECC_word_t *result, const uECC_word_t *x, uECC_Curve curve);
allankliu 0:b6fdeddc0bc9 156 #if (uECC_OPTIMIZATION_LEVEL > 0)
allankliu 0:b6fdeddc0bc9 157 void (*mmod_fast)(uECC_word_t *result, uECC_word_t *product);
allankliu 0:b6fdeddc0bc9 158 #endif
allankliu 0:b6fdeddc0bc9 159 };
allankliu 0:b6fdeddc0bc9 160
allankliu 0:b6fdeddc0bc9 161 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 162 static void bcopy(uint8_t *dst,
allankliu 0:b6fdeddc0bc9 163 const uint8_t *src,
allankliu 0:b6fdeddc0bc9 164 unsigned num_bytes) {
allankliu 0:b6fdeddc0bc9 165 while (0 != num_bytes) {
allankliu 0:b6fdeddc0bc9 166 num_bytes--;
allankliu 0:b6fdeddc0bc9 167 dst[num_bytes] = src[num_bytes];
allankliu 0:b6fdeddc0bc9 168 }
allankliu 0:b6fdeddc0bc9 169 }
allankliu 0:b6fdeddc0bc9 170 #endif
allankliu 0:b6fdeddc0bc9 171
allankliu 0:b6fdeddc0bc9 172 static cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 173 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 174 wordcount_t num_words);
allankliu 0:b6fdeddc0bc9 175
allankliu 0:b6fdeddc0bc9 176 #if (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb || \
allankliu 0:b6fdeddc0bc9 177 uECC_PLATFORM == uECC_arm_thumb2)
allankliu 0:b6fdeddc0bc9 178 //#include "asm_arm.inc"
allankliu 0:b6fdeddc0bc9 179 #include "asm_arm.h"
allankliu 0:b6fdeddc0bc9 180 #if (uECC_PLATFORM == uECC_arm)
allankliu 0:b6fdeddc0bc9 181 #warning uECC_arm
allankliu 0:b6fdeddc0bc9 182 #elif (uECC_PLATFORM == uECC_arm_thumb)
allankliu 0:b6fdeddc0bc9 183 #warning uECC_arm_thumb
allankliu 0:b6fdeddc0bc9 184 #elif (uECC_PLATFORM == uECC_arm_thumb2)
allankliu 0:b6fdeddc0bc9 185 #warning uECC_arm_thumb2
allankliu 0:b6fdeddc0bc9 186 #endif
allankliu 0:b6fdeddc0bc9 187 #endif
allankliu 0:b6fdeddc0bc9 188
allankliu 0:b6fdeddc0bc9 189 #if (uECC_PLATFORM == uECC_avr)
allankliu 0:b6fdeddc0bc9 190 #include "asm_avr.inc"
allankliu 0:b6fdeddc0bc9 191 #endif
allankliu 0:b6fdeddc0bc9 192
allankliu 0:b6fdeddc0bc9 193 #if default_RNG_defined
allankliu 0:b6fdeddc0bc9 194 static uECC_RNG_Function g_rng_function = &default_RNG;
allankliu 0:b6fdeddc0bc9 195 #else
allankliu 0:b6fdeddc0bc9 196 static uECC_RNG_Function g_rng_function = 0;
allankliu 0:b6fdeddc0bc9 197 #endif
allankliu 0:b6fdeddc0bc9 198
allankliu 0:b6fdeddc0bc9 199 void uECC_set_rng(uECC_RNG_Function rng_function) {
allankliu 0:b6fdeddc0bc9 200 g_rng_function = rng_function;
allankliu 0:b6fdeddc0bc9 201 }
allankliu 0:b6fdeddc0bc9 202
allankliu 0:b6fdeddc0bc9 203 uECC_RNG_Function uECC_get_rng(void) {
allankliu 0:b6fdeddc0bc9 204 return g_rng_function;
allankliu 0:b6fdeddc0bc9 205 }
allankliu 0:b6fdeddc0bc9 206
allankliu 0:b6fdeddc0bc9 207 int uECC_curve_private_key_size(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 208 return BITS_TO_BYTES(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 209 }
allankliu 0:b6fdeddc0bc9 210
allankliu 0:b6fdeddc0bc9 211 int uECC_curve_public_key_size(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 212 return 2 * curve->num_bytes;
allankliu 0:b6fdeddc0bc9 213 }
allankliu 0:b6fdeddc0bc9 214
allankliu 0:b6fdeddc0bc9 215 #if !asm_clear
allankliu 0:b6fdeddc0bc9 216 uECC_VLI_API void uECC_vli_clear(uECC_word_t *vli, wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 217 wordcount_t i;
allankliu 0:b6fdeddc0bc9 218 for (i = 0; i < num_words; ++i) {
allankliu 0:b6fdeddc0bc9 219 vli[i] = 0;
allankliu 0:b6fdeddc0bc9 220 }
allankliu 0:b6fdeddc0bc9 221 }
allankliu 0:b6fdeddc0bc9 222 #endif /* !asm_clear */
allankliu 0:b6fdeddc0bc9 223
allankliu 0:b6fdeddc0bc9 224 /* Constant-time comparison to zero - secure way to compare long integers */
allankliu 0:b6fdeddc0bc9 225 /* Returns 1 if vli == 0, 0 otherwise. */
allankliu 0:b6fdeddc0bc9 226 uECC_VLI_API uECC_word_t uECC_vli_isZero(const uECC_word_t *vli, wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 227 uECC_word_t bits = 0;
allankliu 0:b6fdeddc0bc9 228 wordcount_t i;
allankliu 0:b6fdeddc0bc9 229 for (i = 0; i < num_words; ++i) {
allankliu 0:b6fdeddc0bc9 230 bits |= vli[i];
allankliu 0:b6fdeddc0bc9 231 }
allankliu 0:b6fdeddc0bc9 232 return (bits == 0);
allankliu 0:b6fdeddc0bc9 233 }
allankliu 0:b6fdeddc0bc9 234
allankliu 0:b6fdeddc0bc9 235 /* Returns nonzero if bit 'bit' of vli is set. */
allankliu 0:b6fdeddc0bc9 236 uECC_VLI_API uECC_word_t uECC_vli_testBit(const uECC_word_t *vli, bitcount_t bit) {
allankliu 0:b6fdeddc0bc9 237 return (vli[bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK)));
allankliu 0:b6fdeddc0bc9 238 }
allankliu 0:b6fdeddc0bc9 239
allankliu 0:b6fdeddc0bc9 240 /* Counts the number of words in vli. */
allankliu 0:b6fdeddc0bc9 241 static wordcount_t vli_numDigits(const uECC_word_t *vli, const wordcount_t max_words) {
allankliu 0:b6fdeddc0bc9 242 wordcount_t i;
allankliu 0:b6fdeddc0bc9 243 /* Search from the end until we find a non-zero digit.
allankliu 0:b6fdeddc0bc9 244 We do it in reverse because we expect that most digits will be nonzero. */
allankliu 0:b6fdeddc0bc9 245 for (i = max_words - 1; i >= 0 && vli[i] == 0; --i) {
allankliu 0:b6fdeddc0bc9 246 }
allankliu 0:b6fdeddc0bc9 247
allankliu 0:b6fdeddc0bc9 248 return (i + 1);
allankliu 0:b6fdeddc0bc9 249 }
allankliu 0:b6fdeddc0bc9 250
allankliu 0:b6fdeddc0bc9 251 /* Counts the number of bits required to represent vli. */
allankliu 0:b6fdeddc0bc9 252 uECC_VLI_API bitcount_t uECC_vli_numBits(const uECC_word_t *vli, const wordcount_t max_words) {
allankliu 0:b6fdeddc0bc9 253 uECC_word_t i;
allankliu 0:b6fdeddc0bc9 254 uECC_word_t digit;
allankliu 0:b6fdeddc0bc9 255
allankliu 0:b6fdeddc0bc9 256 wordcount_t num_digits = vli_numDigits(vli, max_words);
allankliu 0:b6fdeddc0bc9 257 if (num_digits == 0) {
allankliu 0:b6fdeddc0bc9 258 return 0;
allankliu 0:b6fdeddc0bc9 259 }
allankliu 0:b6fdeddc0bc9 260
allankliu 0:b6fdeddc0bc9 261 digit = vli[num_digits - 1];
allankliu 0:b6fdeddc0bc9 262 for (i = 0; digit; ++i) {
allankliu 0:b6fdeddc0bc9 263 digit >>= 1;
allankliu 0:b6fdeddc0bc9 264 }
allankliu 0:b6fdeddc0bc9 265
allankliu 0:b6fdeddc0bc9 266 return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i);
allankliu 0:b6fdeddc0bc9 267 }
allankliu 0:b6fdeddc0bc9 268
allankliu 0:b6fdeddc0bc9 269 /* Sets dest = src. */
allankliu 0:b6fdeddc0bc9 270 #if !asm_set
allankliu 0:b6fdeddc0bc9 271 uECC_VLI_API void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src, wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 272 wordcount_t i;
allankliu 0:b6fdeddc0bc9 273 for (i = 0; i < num_words; ++i) {
allankliu 0:b6fdeddc0bc9 274 dest[i] = src[i];
allankliu 0:b6fdeddc0bc9 275 }
allankliu 0:b6fdeddc0bc9 276 }
allankliu 0:b6fdeddc0bc9 277 #endif /* !asm_set */
allankliu 0:b6fdeddc0bc9 278
allankliu 0:b6fdeddc0bc9 279 /* Returns sign of left - right. */
allankliu 0:b6fdeddc0bc9 280 static cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 281 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 282 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 283 wordcount_t i;
allankliu 0:b6fdeddc0bc9 284 for (i = num_words - 1; i >= 0; --i) {
allankliu 0:b6fdeddc0bc9 285 if (left[i] > right[i]) {
allankliu 0:b6fdeddc0bc9 286 return 1;
allankliu 0:b6fdeddc0bc9 287 } else if (left[i] < right[i]) {
allankliu 0:b6fdeddc0bc9 288 return -1;
allankliu 0:b6fdeddc0bc9 289 }
allankliu 0:b6fdeddc0bc9 290 }
allankliu 0:b6fdeddc0bc9 291 return 0;
allankliu 0:b6fdeddc0bc9 292 }
allankliu 0:b6fdeddc0bc9 293
allankliu 0:b6fdeddc0bc9 294 /* Constant-time comparison function - secure way to compare long integers */
allankliu 0:b6fdeddc0bc9 295 /* Returns one if left == right, zero otherwise. */
allankliu 0:b6fdeddc0bc9 296 uECC_VLI_API uECC_word_t uECC_vli_equal(const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 297 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 298 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 299 uECC_word_t diff = 0;
allankliu 0:b6fdeddc0bc9 300 wordcount_t i;
allankliu 0:b6fdeddc0bc9 301 for (i = num_words - 1; i >= 0; --i) {
allankliu 0:b6fdeddc0bc9 302 diff |= (left[i] ^ right[i]);
allankliu 0:b6fdeddc0bc9 303 }
allankliu 0:b6fdeddc0bc9 304 return (diff == 0);
allankliu 0:b6fdeddc0bc9 305 }
allankliu 0:b6fdeddc0bc9 306
allankliu 0:b6fdeddc0bc9 307 uECC_VLI_API uECC_word_t uECC_vli_sub(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 308 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 309 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 310 wordcount_t num_words);
allankliu 0:b6fdeddc0bc9 311
allankliu 0:b6fdeddc0bc9 312 /* Returns sign of left - right, in constant time. */
allankliu 0:b6fdeddc0bc9 313 uECC_VLI_API cmpresult_t uECC_vli_cmp(const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 314 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 315 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 316 uECC_word_t tmp[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 317 uECC_word_t neg = !!uECC_vli_sub(tmp, left, right, num_words);
allankliu 0:b6fdeddc0bc9 318 uECC_word_t equal = uECC_vli_isZero(tmp, num_words);
allankliu 0:b6fdeddc0bc9 319 return (!equal - 2 * neg);
allankliu 0:b6fdeddc0bc9 320 }
allankliu 0:b6fdeddc0bc9 321
allankliu 0:b6fdeddc0bc9 322 /* Computes vli = vli >> 1. */
allankliu 0:b6fdeddc0bc9 323 #if !asm_rshift1
allankliu 0:b6fdeddc0bc9 324 uECC_VLI_API void uECC_vli_rshift1(uECC_word_t *vli, wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 325 uECC_word_t *end = vli;
allankliu 0:b6fdeddc0bc9 326 uECC_word_t carry = 0;
allankliu 0:b6fdeddc0bc9 327
allankliu 0:b6fdeddc0bc9 328 vli += num_words;
allankliu 0:b6fdeddc0bc9 329 while (vli-- > end) {
allankliu 0:b6fdeddc0bc9 330 uECC_word_t temp = *vli;
allankliu 0:b6fdeddc0bc9 331 *vli = (temp >> 1) | carry;
allankliu 0:b6fdeddc0bc9 332 carry = temp << (uECC_WORD_BITS - 1);
allankliu 0:b6fdeddc0bc9 333 }
allankliu 0:b6fdeddc0bc9 334 }
allankliu 0:b6fdeddc0bc9 335 #endif /* !asm_rshift1 */
allankliu 0:b6fdeddc0bc9 336
allankliu 0:b6fdeddc0bc9 337 /* Computes result = left + right, returning carry. Can modify in place. */
allankliu 0:b6fdeddc0bc9 338 #if !asm_add
allankliu 0:b6fdeddc0bc9 339 uECC_VLI_API uECC_word_t uECC_vli_add(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 340 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 341 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 342 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 343 uECC_word_t carry = 0;
allankliu 0:b6fdeddc0bc9 344 wordcount_t i;
allankliu 0:b6fdeddc0bc9 345 for (i = 0; i < num_words; ++i) {
allankliu 0:b6fdeddc0bc9 346 uECC_word_t sum = left[i] + right[i] + carry;
allankliu 0:b6fdeddc0bc9 347 if (sum != left[i]) {
allankliu 0:b6fdeddc0bc9 348 carry = (sum < left[i]);
allankliu 0:b6fdeddc0bc9 349 }
allankliu 0:b6fdeddc0bc9 350 result[i] = sum;
allankliu 0:b6fdeddc0bc9 351 }
allankliu 0:b6fdeddc0bc9 352 return carry;
allankliu 0:b6fdeddc0bc9 353 }
allankliu 0:b6fdeddc0bc9 354 #endif /* !asm_add */
allankliu 0:b6fdeddc0bc9 355
allankliu 0:b6fdeddc0bc9 356 /* Computes result = left - right, returning borrow. Can modify in place. */
allankliu 0:b6fdeddc0bc9 357 #if !asm_sub
allankliu 0:b6fdeddc0bc9 358 uECC_VLI_API uECC_word_t uECC_vli_sub(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 359 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 360 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 361 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 362 uECC_word_t borrow = 0;
allankliu 0:b6fdeddc0bc9 363 wordcount_t i;
allankliu 0:b6fdeddc0bc9 364 for (i = 0; i < num_words; ++i) {
allankliu 0:b6fdeddc0bc9 365 uECC_word_t diff = left[i] - right[i] - borrow;
allankliu 0:b6fdeddc0bc9 366 if (diff != left[i]) {
allankliu 0:b6fdeddc0bc9 367 borrow = (diff > left[i]);
allankliu 0:b6fdeddc0bc9 368 }
allankliu 0:b6fdeddc0bc9 369 result[i] = diff;
allankliu 0:b6fdeddc0bc9 370 }
allankliu 0:b6fdeddc0bc9 371 return borrow;
allankliu 0:b6fdeddc0bc9 372 }
allankliu 0:b6fdeddc0bc9 373 #endif /* !asm_sub */
allankliu 0:b6fdeddc0bc9 374
allankliu 0:b6fdeddc0bc9 375 #if !asm_mult || (uECC_SQUARE_FUNC && !asm_square) || \
allankliu 0:b6fdeddc0bc9 376 (uECC_SUPPORTS_secp256k1 && (uECC_OPTIMIZATION_LEVEL > 0) && \
allankliu 0:b6fdeddc0bc9 377 ((uECC_WORD_SIZE == 1) || (uECC_WORD_SIZE == 8)))
allankliu 0:b6fdeddc0bc9 378 static void muladd(uECC_word_t a,
allankliu 0:b6fdeddc0bc9 379 uECC_word_t b,
allankliu 0:b6fdeddc0bc9 380 uECC_word_t *r0,
allankliu 0:b6fdeddc0bc9 381 uECC_word_t *r1,
allankliu 0:b6fdeddc0bc9 382 uECC_word_t *r2) {
allankliu 0:b6fdeddc0bc9 383 #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128
allankliu 0:b6fdeddc0bc9 384 uint64_t a0 = a & 0xffffffffull;
allankliu 0:b6fdeddc0bc9 385 uint64_t a1 = a >> 32;
allankliu 0:b6fdeddc0bc9 386 uint64_t b0 = b & 0xffffffffull;
allankliu 0:b6fdeddc0bc9 387 uint64_t b1 = b >> 32;
allankliu 0:b6fdeddc0bc9 388
allankliu 0:b6fdeddc0bc9 389 uint64_t i0 = a0 * b0;
allankliu 0:b6fdeddc0bc9 390 uint64_t i1 = a0 * b1;
allankliu 0:b6fdeddc0bc9 391 uint64_t i2 = a1 * b0;
allankliu 0:b6fdeddc0bc9 392 uint64_t i3 = a1 * b1;
allankliu 0:b6fdeddc0bc9 393
allankliu 0:b6fdeddc0bc9 394 uint64_t p0, p1;
allankliu 0:b6fdeddc0bc9 395
allankliu 0:b6fdeddc0bc9 396 i2 += (i0 >> 32);
allankliu 0:b6fdeddc0bc9 397 i2 += i1;
allankliu 0:b6fdeddc0bc9 398 if (i2 < i1) { /* overflow */
allankliu 0:b6fdeddc0bc9 399 i3 += 0x100000000ull;
allankliu 0:b6fdeddc0bc9 400 }
allankliu 0:b6fdeddc0bc9 401
allankliu 0:b6fdeddc0bc9 402 p0 = (i0 & 0xffffffffull) | (i2 << 32);
allankliu 0:b6fdeddc0bc9 403 p1 = i3 + (i2 >> 32);
allankliu 0:b6fdeddc0bc9 404
allankliu 0:b6fdeddc0bc9 405 *r0 += p0;
allankliu 0:b6fdeddc0bc9 406 *r1 += (p1 + (*r0 < p0));
allankliu 0:b6fdeddc0bc9 407 *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0));
allankliu 0:b6fdeddc0bc9 408 #else
allankliu 0:b6fdeddc0bc9 409 uECC_dword_t p = (uECC_dword_t)a * b;
allankliu 0:b6fdeddc0bc9 410 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
allankliu 0:b6fdeddc0bc9 411 r01 += p;
allankliu 0:b6fdeddc0bc9 412 *r2 += (r01 < p);
allankliu 0:b6fdeddc0bc9 413 *r1 = r01 >> uECC_WORD_BITS;
allankliu 0:b6fdeddc0bc9 414 *r0 = (uECC_word_t)r01;
allankliu 0:b6fdeddc0bc9 415 #endif
allankliu 0:b6fdeddc0bc9 416 }
allankliu 0:b6fdeddc0bc9 417 #endif /* muladd needed */
allankliu 0:b6fdeddc0bc9 418
allankliu 0:b6fdeddc0bc9 419 #if !asm_mult
allankliu 0:b6fdeddc0bc9 420 uECC_VLI_API void uECC_vli_mult(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 421 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 422 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 423 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 424 uECC_word_t r0 = 0;
allankliu 0:b6fdeddc0bc9 425 uECC_word_t r1 = 0;
allankliu 0:b6fdeddc0bc9 426 uECC_word_t r2 = 0;
allankliu 0:b6fdeddc0bc9 427 wordcount_t i, k;
allankliu 0:b6fdeddc0bc9 428
allankliu 0:b6fdeddc0bc9 429 /* Compute each digit of result in sequence, maintaining the carries. */
allankliu 0:b6fdeddc0bc9 430 for (k = 0; k < num_words; ++k) {
allankliu 0:b6fdeddc0bc9 431 for (i = 0; i <= k; ++i) {
allankliu 0:b6fdeddc0bc9 432 muladd(left[i], right[k - i], &r0, &r1, &r2);
allankliu 0:b6fdeddc0bc9 433 }
allankliu 0:b6fdeddc0bc9 434 result[k] = r0;
allankliu 0:b6fdeddc0bc9 435 r0 = r1;
allankliu 0:b6fdeddc0bc9 436 r1 = r2;
allankliu 0:b6fdeddc0bc9 437 r2 = 0;
allankliu 0:b6fdeddc0bc9 438 }
allankliu 0:b6fdeddc0bc9 439 for (k = num_words; k < num_words * 2 - 1; ++k) {
allankliu 0:b6fdeddc0bc9 440 for (i = (k + 1) - num_words; i < num_words; ++i) {
allankliu 0:b6fdeddc0bc9 441 muladd(left[i], right[k - i], &r0, &r1, &r2);
allankliu 0:b6fdeddc0bc9 442 }
allankliu 0:b6fdeddc0bc9 443 result[k] = r0;
allankliu 0:b6fdeddc0bc9 444 r0 = r1;
allankliu 0:b6fdeddc0bc9 445 r1 = r2;
allankliu 0:b6fdeddc0bc9 446 r2 = 0;
allankliu 0:b6fdeddc0bc9 447 }
allankliu 0:b6fdeddc0bc9 448 result[num_words * 2 - 1] = r0;
allankliu 0:b6fdeddc0bc9 449 }
allankliu 0:b6fdeddc0bc9 450 #endif /* !asm_mult */
allankliu 0:b6fdeddc0bc9 451
allankliu 0:b6fdeddc0bc9 452 #if uECC_SQUARE_FUNC
allankliu 0:b6fdeddc0bc9 453
allankliu 0:b6fdeddc0bc9 454 #if !asm_square
allankliu 0:b6fdeddc0bc9 455 static void mul2add(uECC_word_t a,
allankliu 0:b6fdeddc0bc9 456 uECC_word_t b,
allankliu 0:b6fdeddc0bc9 457 uECC_word_t *r0,
allankliu 0:b6fdeddc0bc9 458 uECC_word_t *r1,
allankliu 0:b6fdeddc0bc9 459 uECC_word_t *r2) {
allankliu 0:b6fdeddc0bc9 460 #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128
allankliu 0:b6fdeddc0bc9 461 uint64_t a0 = a & 0xffffffffull;
allankliu 0:b6fdeddc0bc9 462 uint64_t a1 = a >> 32;
allankliu 0:b6fdeddc0bc9 463 uint64_t b0 = b & 0xffffffffull;
allankliu 0:b6fdeddc0bc9 464 uint64_t b1 = b >> 32;
allankliu 0:b6fdeddc0bc9 465
allankliu 0:b6fdeddc0bc9 466 uint64_t i0 = a0 * b0;
allankliu 0:b6fdeddc0bc9 467 uint64_t i1 = a0 * b1;
allankliu 0:b6fdeddc0bc9 468 uint64_t i2 = a1 * b0;
allankliu 0:b6fdeddc0bc9 469 uint64_t i3 = a1 * b1;
allankliu 0:b6fdeddc0bc9 470
allankliu 0:b6fdeddc0bc9 471 uint64_t p0, p1;
allankliu 0:b6fdeddc0bc9 472
allankliu 0:b6fdeddc0bc9 473 i2 += (i0 >> 32);
allankliu 0:b6fdeddc0bc9 474 i2 += i1;
allankliu 0:b6fdeddc0bc9 475 if (i2 < i1)
allankliu 0:b6fdeddc0bc9 476 { /* overflow */
allankliu 0:b6fdeddc0bc9 477 i3 += 0x100000000ull;
allankliu 0:b6fdeddc0bc9 478 }
allankliu 0:b6fdeddc0bc9 479
allankliu 0:b6fdeddc0bc9 480 p0 = (i0 & 0xffffffffull) | (i2 << 32);
allankliu 0:b6fdeddc0bc9 481 p1 = i3 + (i2 >> 32);
allankliu 0:b6fdeddc0bc9 482
allankliu 0:b6fdeddc0bc9 483 *r2 += (p1 >> 63);
allankliu 0:b6fdeddc0bc9 484 p1 = (p1 << 1) | (p0 >> 63);
allankliu 0:b6fdeddc0bc9 485 p0 <<= 1;
allankliu 0:b6fdeddc0bc9 486
allankliu 0:b6fdeddc0bc9 487 *r0 += p0;
allankliu 0:b6fdeddc0bc9 488 *r1 += (p1 + (*r0 < p0));
allankliu 0:b6fdeddc0bc9 489 *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0));
allankliu 0:b6fdeddc0bc9 490 #else
allankliu 0:b6fdeddc0bc9 491 uECC_dword_t p = (uECC_dword_t)a * b;
allankliu 0:b6fdeddc0bc9 492 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
allankliu 0:b6fdeddc0bc9 493 *r2 += (p >> (uECC_WORD_BITS * 2 - 1));
allankliu 0:b6fdeddc0bc9 494 p *= 2;
allankliu 0:b6fdeddc0bc9 495 r01 += p;
allankliu 0:b6fdeddc0bc9 496 *r2 += (r01 < p);
allankliu 0:b6fdeddc0bc9 497 *r1 = r01 >> uECC_WORD_BITS;
allankliu 0:b6fdeddc0bc9 498 *r0 = (uECC_word_t)r01;
allankliu 0:b6fdeddc0bc9 499 #endif
allankliu 0:b6fdeddc0bc9 500 }
allankliu 0:b6fdeddc0bc9 501
allankliu 0:b6fdeddc0bc9 502 uECC_VLI_API void uECC_vli_square(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 503 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 504 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 505 uECC_word_t r0 = 0;
allankliu 0:b6fdeddc0bc9 506 uECC_word_t r1 = 0;
allankliu 0:b6fdeddc0bc9 507 uECC_word_t r2 = 0;
allankliu 0:b6fdeddc0bc9 508
allankliu 0:b6fdeddc0bc9 509 wordcount_t i, k;
allankliu 0:b6fdeddc0bc9 510
allankliu 0:b6fdeddc0bc9 511 for (k = 0; k < num_words * 2 - 1; ++k) {
allankliu 0:b6fdeddc0bc9 512 uECC_word_t min = (k < num_words ? 0 : (k + 1) - num_words);
allankliu 0:b6fdeddc0bc9 513 for (i = min; i <= k && i <= k - i; ++i) {
allankliu 0:b6fdeddc0bc9 514 if (i < k-i) {
allankliu 0:b6fdeddc0bc9 515 mul2add(left[i], left[k - i], &r0, &r1, &r2);
allankliu 0:b6fdeddc0bc9 516 } else {
allankliu 0:b6fdeddc0bc9 517 muladd(left[i], left[k - i], &r0, &r1, &r2);
allankliu 0:b6fdeddc0bc9 518 }
allankliu 0:b6fdeddc0bc9 519 }
allankliu 0:b6fdeddc0bc9 520 result[k] = r0;
allankliu 0:b6fdeddc0bc9 521 r0 = r1;
allankliu 0:b6fdeddc0bc9 522 r1 = r2;
allankliu 0:b6fdeddc0bc9 523 r2 = 0;
allankliu 0:b6fdeddc0bc9 524 }
allankliu 0:b6fdeddc0bc9 525
allankliu 0:b6fdeddc0bc9 526 result[num_words * 2 - 1] = r0;
allankliu 0:b6fdeddc0bc9 527 }
allankliu 0:b6fdeddc0bc9 528 #endif /* !asm_square */
allankliu 0:b6fdeddc0bc9 529
allankliu 0:b6fdeddc0bc9 530 #else /* uECC_SQUARE_FUNC */
allankliu 0:b6fdeddc0bc9 531
allankliu 0:b6fdeddc0bc9 532 #if uECC_ENABLE_VLI_API
allankliu 0:b6fdeddc0bc9 533 uECC_VLI_API void uECC_vli_square(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 534 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 535 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 536 uECC_vli_mult(result, left, left, num_words);
allankliu 0:b6fdeddc0bc9 537 }
allankliu 0:b6fdeddc0bc9 538 #endif /* uECC_ENABLE_VLI_API */
allankliu 0:b6fdeddc0bc9 539
allankliu 0:b6fdeddc0bc9 540 #endif /* uECC_SQUARE_FUNC */
allankliu 0:b6fdeddc0bc9 541
allankliu 0:b6fdeddc0bc9 542 /* Computes result = (left + right) % mod.
allankliu 0:b6fdeddc0bc9 543 Assumes that left < mod and right < mod, and that result does not overlap mod. */
allankliu 0:b6fdeddc0bc9 544 uECC_VLI_API void uECC_vli_modAdd(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 545 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 546 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 547 const uECC_word_t *mod,
allankliu 0:b6fdeddc0bc9 548 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 549 uECC_word_t carry = uECC_vli_add(result, left, right, num_words);
allankliu 0:b6fdeddc0bc9 550 if (carry || uECC_vli_cmp_unsafe(mod, result, num_words) != 1) {
allankliu 0:b6fdeddc0bc9 551 /* result > mod (result = mod + remainder), so subtract mod to get remainder. */
allankliu 0:b6fdeddc0bc9 552 uECC_vli_sub(result, result, mod, num_words);
allankliu 0:b6fdeddc0bc9 553 }
allankliu 0:b6fdeddc0bc9 554 }
allankliu 0:b6fdeddc0bc9 555
allankliu 0:b6fdeddc0bc9 556 /* Computes result = (left - right) % mod.
allankliu 0:b6fdeddc0bc9 557 Assumes that left < mod and right < mod, and that result does not overlap mod. */
allankliu 0:b6fdeddc0bc9 558 uECC_VLI_API void uECC_vli_modSub(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 559 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 560 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 561 const uECC_word_t *mod,
allankliu 0:b6fdeddc0bc9 562 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 563 uECC_word_t l_borrow = uECC_vli_sub(result, left, right, num_words);
allankliu 0:b6fdeddc0bc9 564 if (l_borrow) {
allankliu 0:b6fdeddc0bc9 565 /* In this case, result == -diff == (max int) - diff. Since -x % d == d - x,
allankliu 0:b6fdeddc0bc9 566 we can get the correct result from result + mod (with overflow). */
allankliu 0:b6fdeddc0bc9 567 uECC_vli_add(result, result, mod, num_words);
allankliu 0:b6fdeddc0bc9 568 }
allankliu 0:b6fdeddc0bc9 569 }
allankliu 0:b6fdeddc0bc9 570
allankliu 0:b6fdeddc0bc9 571 /* Computes result = product % mod, where product is 2N words long. */
allankliu 0:b6fdeddc0bc9 572 /* Currently only designed to work for curve_p or curve_n. */
allankliu 0:b6fdeddc0bc9 573 uECC_VLI_API void uECC_vli_mmod(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 574 uECC_word_t *product,
allankliu 0:b6fdeddc0bc9 575 const uECC_word_t *mod,
allankliu 0:b6fdeddc0bc9 576 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 577 uECC_word_t mod_multiple[2 * uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 578 uECC_word_t tmp[2 * uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 579 uECC_word_t *v[2] = {tmp, product};
allankliu 0:b6fdeddc0bc9 580 uECC_word_t index;
allankliu 0:b6fdeddc0bc9 581
allankliu 0:b6fdeddc0bc9 582 /* Shift mod so its highest set bit is at the maximum position. */
allankliu 0:b6fdeddc0bc9 583 bitcount_t shift = (num_words * 2 * uECC_WORD_BITS) - uECC_vli_numBits(mod, num_words);
allankliu 0:b6fdeddc0bc9 584 wordcount_t word_shift = shift / uECC_WORD_BITS;
allankliu 0:b6fdeddc0bc9 585 wordcount_t bit_shift = shift % uECC_WORD_BITS;
allankliu 0:b6fdeddc0bc9 586 uECC_word_t carry = 0;
allankliu 0:b6fdeddc0bc9 587 uECC_vli_clear(mod_multiple, word_shift);
allankliu 0:b6fdeddc0bc9 588 if (bit_shift > 0) {
allankliu 0:b6fdeddc0bc9 589 for(index = 0; index < (uECC_word_t)num_words; ++index) {
allankliu 0:b6fdeddc0bc9 590 mod_multiple[word_shift + index] = (mod[index] << bit_shift) | carry;
allankliu 0:b6fdeddc0bc9 591 carry = mod[index] >> (uECC_WORD_BITS - bit_shift);
allankliu 0:b6fdeddc0bc9 592 }
allankliu 0:b6fdeddc0bc9 593 } else {
allankliu 0:b6fdeddc0bc9 594 uECC_vli_set(mod_multiple + word_shift, mod, num_words);
allankliu 0:b6fdeddc0bc9 595 }
allankliu 0:b6fdeddc0bc9 596
allankliu 0:b6fdeddc0bc9 597 for (index = 1; shift >= 0; --shift) {
allankliu 0:b6fdeddc0bc9 598 uECC_word_t borrow = 0;
allankliu 0:b6fdeddc0bc9 599 wordcount_t i;
allankliu 0:b6fdeddc0bc9 600 for (i = 0; i < num_words * 2; ++i) {
allankliu 0:b6fdeddc0bc9 601 uECC_word_t diff = v[index][i] - mod_multiple[i] - borrow;
allankliu 0:b6fdeddc0bc9 602 if (diff != v[index][i]) {
allankliu 0:b6fdeddc0bc9 603 borrow = (diff > v[index][i]);
allankliu 0:b6fdeddc0bc9 604 }
allankliu 0:b6fdeddc0bc9 605 v[1 - index][i] = diff;
allankliu 0:b6fdeddc0bc9 606 }
allankliu 0:b6fdeddc0bc9 607 index = !(index ^ borrow); /* Swap the index if there was no borrow */
allankliu 0:b6fdeddc0bc9 608 uECC_vli_rshift1(mod_multiple, num_words);
allankliu 0:b6fdeddc0bc9 609 mod_multiple[num_words - 1] |= mod_multiple[num_words] << (uECC_WORD_BITS - 1);
allankliu 0:b6fdeddc0bc9 610 uECC_vli_rshift1(mod_multiple + num_words, num_words);
allankliu 0:b6fdeddc0bc9 611 }
allankliu 0:b6fdeddc0bc9 612 uECC_vli_set(result, v[index], num_words);
allankliu 0:b6fdeddc0bc9 613 }
allankliu 0:b6fdeddc0bc9 614
allankliu 0:b6fdeddc0bc9 615 /* Computes result = (left * right) % mod. */
allankliu 0:b6fdeddc0bc9 616 uECC_VLI_API void uECC_vli_modMult(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 617 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 618 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 619 const uECC_word_t *mod,
allankliu 0:b6fdeddc0bc9 620 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 621 uECC_word_t product[2 * uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 622 uECC_vli_mult(product, left, right, num_words);
allankliu 0:b6fdeddc0bc9 623 uECC_vli_mmod(result, product, mod, num_words);
allankliu 0:b6fdeddc0bc9 624 }
allankliu 0:b6fdeddc0bc9 625
allankliu 0:b6fdeddc0bc9 626 uECC_VLI_API void uECC_vli_modMult_fast(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 627 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 628 const uECC_word_t *right,
allankliu 0:b6fdeddc0bc9 629 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 630 uECC_word_t product[2 * uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 631 uECC_vli_mult(product, left, right, curve->num_words);
allankliu 0:b6fdeddc0bc9 632 #if (uECC_OPTIMIZATION_LEVEL > 0)
allankliu 0:b6fdeddc0bc9 633 curve->mmod_fast(result, product);
allankliu 0:b6fdeddc0bc9 634 #else
allankliu 0:b6fdeddc0bc9 635 uECC_vli_mmod(result, product, curve->p, curve->num_words);
allankliu 0:b6fdeddc0bc9 636 #endif
allankliu 0:b6fdeddc0bc9 637 }
allankliu 0:b6fdeddc0bc9 638
allankliu 0:b6fdeddc0bc9 639 #if uECC_SQUARE_FUNC
allankliu 0:b6fdeddc0bc9 640
allankliu 0:b6fdeddc0bc9 641 #if uECC_ENABLE_VLI_API
allankliu 0:b6fdeddc0bc9 642 /* Computes result = left^2 % mod. */
allankliu 0:b6fdeddc0bc9 643 uECC_VLI_API void uECC_vli_modSquare(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 644 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 645 const uECC_word_t *mod,
allankliu 0:b6fdeddc0bc9 646 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 647 uECC_word_t product[2 * uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 648 uECC_vli_square(product, left, num_words);
allankliu 0:b6fdeddc0bc9 649 uECC_vli_mmod(result, product, mod, num_words);
allankliu 0:b6fdeddc0bc9 650 }
allankliu 0:b6fdeddc0bc9 651 #endif /* uECC_ENABLE_VLI_API */
allankliu 0:b6fdeddc0bc9 652
allankliu 0:b6fdeddc0bc9 653 uECC_VLI_API void uECC_vli_modSquare_fast(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 654 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 655 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 656 uECC_word_t product[2 * uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 657 uECC_vli_square(product, left, curve->num_words);
allankliu 0:b6fdeddc0bc9 658 #if (uECC_OPTIMIZATION_LEVEL > 0)
allankliu 0:b6fdeddc0bc9 659 curve->mmod_fast(result, product);
allankliu 0:b6fdeddc0bc9 660 #else
allankliu 0:b6fdeddc0bc9 661 uECC_vli_mmod(result, product, curve->p, curve->num_words);
allankliu 0:b6fdeddc0bc9 662 #endif
allankliu 0:b6fdeddc0bc9 663 }
allankliu 0:b6fdeddc0bc9 664
allankliu 0:b6fdeddc0bc9 665 #else /* uECC_SQUARE_FUNC */
allankliu 0:b6fdeddc0bc9 666
allankliu 0:b6fdeddc0bc9 667 #if uECC_ENABLE_VLI_API
allankliu 0:b6fdeddc0bc9 668 uECC_VLI_API void uECC_vli_modSquare(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 669 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 670 const uECC_word_t *mod,
allankliu 0:b6fdeddc0bc9 671 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 672 uECC_vli_modMult(result, left, left, mod, num_words);
allankliu 0:b6fdeddc0bc9 673 }
allankliu 0:b6fdeddc0bc9 674 #endif /* uECC_ENABLE_VLI_API */
allankliu 0:b6fdeddc0bc9 675
allankliu 0:b6fdeddc0bc9 676 uECC_VLI_API void uECC_vli_modSquare_fast(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 677 const uECC_word_t *left,
allankliu 0:b6fdeddc0bc9 678 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 679 uECC_vli_modMult_fast(result, left, left, curve);
allankliu 0:b6fdeddc0bc9 680 }
allankliu 0:b6fdeddc0bc9 681
allankliu 0:b6fdeddc0bc9 682 #endif /* uECC_SQUARE_FUNC */
allankliu 0:b6fdeddc0bc9 683
allankliu 0:b6fdeddc0bc9 684 #define EVEN(vli) (!(vli[0] & 1))
allankliu 0:b6fdeddc0bc9 685 static void vli_modInv_update(uECC_word_t *uv,
allankliu 0:b6fdeddc0bc9 686 const uECC_word_t *mod,
allankliu 0:b6fdeddc0bc9 687 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 688 uECC_word_t carry = 0;
allankliu 0:b6fdeddc0bc9 689 if (!EVEN(uv)) {
allankliu 0:b6fdeddc0bc9 690 carry = uECC_vli_add(uv, uv, mod, num_words);
allankliu 0:b6fdeddc0bc9 691 }
allankliu 0:b6fdeddc0bc9 692 uECC_vli_rshift1(uv, num_words);
allankliu 0:b6fdeddc0bc9 693 if (carry) {
allankliu 0:b6fdeddc0bc9 694 uv[num_words - 1] |= HIGH_BIT_SET;
allankliu 0:b6fdeddc0bc9 695 }
allankliu 0:b6fdeddc0bc9 696 }
allankliu 0:b6fdeddc0bc9 697
allankliu 0:b6fdeddc0bc9 698 /* Computes result = (1 / input) % mod. All VLIs are the same size.
allankliu 0:b6fdeddc0bc9 699 See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" */
allankliu 0:b6fdeddc0bc9 700 uECC_VLI_API void uECC_vli_modInv(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 701 const uECC_word_t *input,
allankliu 0:b6fdeddc0bc9 702 const uECC_word_t *mod,
allankliu 0:b6fdeddc0bc9 703 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 704 uECC_word_t a[uECC_MAX_WORDS], b[uECC_MAX_WORDS], u[uECC_MAX_WORDS], v[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 705 cmpresult_t cmpResult;
allankliu 0:b6fdeddc0bc9 706
allankliu 0:b6fdeddc0bc9 707 if (uECC_vli_isZero(input, num_words)) {
allankliu 0:b6fdeddc0bc9 708 uECC_vli_clear(result, num_words);
allankliu 0:b6fdeddc0bc9 709 return;
allankliu 0:b6fdeddc0bc9 710 }
allankliu 0:b6fdeddc0bc9 711
allankliu 0:b6fdeddc0bc9 712 uECC_vli_set(a, input, num_words);
allankliu 0:b6fdeddc0bc9 713 uECC_vli_set(b, mod, num_words);
allankliu 0:b6fdeddc0bc9 714 uECC_vli_clear(u, num_words);
allankliu 0:b6fdeddc0bc9 715 u[0] = 1;
allankliu 0:b6fdeddc0bc9 716 uECC_vli_clear(v, num_words);
allankliu 0:b6fdeddc0bc9 717 while ((cmpResult = uECC_vli_cmp_unsafe(a, b, num_words)) != 0) {
allankliu 0:b6fdeddc0bc9 718 if (EVEN(a)) {
allankliu 0:b6fdeddc0bc9 719 uECC_vli_rshift1(a, num_words);
allankliu 0:b6fdeddc0bc9 720 vli_modInv_update(u, mod, num_words);
allankliu 0:b6fdeddc0bc9 721 } else if (EVEN(b)) {
allankliu 0:b6fdeddc0bc9 722 uECC_vli_rshift1(b, num_words);
allankliu 0:b6fdeddc0bc9 723 vli_modInv_update(v, mod, num_words);
allankliu 0:b6fdeddc0bc9 724 } else if (cmpResult > 0) {
allankliu 0:b6fdeddc0bc9 725 uECC_vli_sub(a, a, b, num_words);
allankliu 0:b6fdeddc0bc9 726 uECC_vli_rshift1(a, num_words);
allankliu 0:b6fdeddc0bc9 727 if (uECC_vli_cmp_unsafe(u, v, num_words) < 0) {
allankliu 0:b6fdeddc0bc9 728 uECC_vli_add(u, u, mod, num_words);
allankliu 0:b6fdeddc0bc9 729 }
allankliu 0:b6fdeddc0bc9 730 uECC_vli_sub(u, u, v, num_words);
allankliu 0:b6fdeddc0bc9 731 vli_modInv_update(u, mod, num_words);
allankliu 0:b6fdeddc0bc9 732 } else {
allankliu 0:b6fdeddc0bc9 733 uECC_vli_sub(b, b, a, num_words);
allankliu 0:b6fdeddc0bc9 734 uECC_vli_rshift1(b, num_words);
allankliu 0:b6fdeddc0bc9 735 if (uECC_vli_cmp_unsafe(v, u, num_words) < 0) {
allankliu 0:b6fdeddc0bc9 736 uECC_vli_add(v, v, mod, num_words);
allankliu 0:b6fdeddc0bc9 737 }
allankliu 0:b6fdeddc0bc9 738 uECC_vli_sub(v, v, u, num_words);
allankliu 0:b6fdeddc0bc9 739 vli_modInv_update(v, mod, num_words);
allankliu 0:b6fdeddc0bc9 740 }
allankliu 0:b6fdeddc0bc9 741 }
allankliu 0:b6fdeddc0bc9 742 uECC_vli_set(result, u, num_words);
allankliu 0:b6fdeddc0bc9 743 }
allankliu 0:b6fdeddc0bc9 744
allankliu 0:b6fdeddc0bc9 745 /* ------ Point operations ------ */
allankliu 0:b6fdeddc0bc9 746
allankliu 0:b6fdeddc0bc9 747 //#include "curve-specific.inc"
allankliu 0:b6fdeddc0bc9 748 #include "curve-specific.h"
allankliu 0:b6fdeddc0bc9 749
allankliu 0:b6fdeddc0bc9 750 /* Returns 1 if 'point' is the point at infinity, 0 otherwise. */
allankliu 0:b6fdeddc0bc9 751 #define EccPoint_isZero(point, curve) uECC_vli_isZero((point), (curve)->num_words * 2)
allankliu 0:b6fdeddc0bc9 752
allankliu 0:b6fdeddc0bc9 753 /* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates.
allankliu 0:b6fdeddc0bc9 754 From http://eprint.iacr.org/2011/338.pdf
allankliu 0:b6fdeddc0bc9 755 */
allankliu 0:b6fdeddc0bc9 756
allankliu 0:b6fdeddc0bc9 757 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
allankliu 0:b6fdeddc0bc9 758 static void apply_z(uECC_word_t * X1,
allankliu 0:b6fdeddc0bc9 759 uECC_word_t * Y1,
allankliu 0:b6fdeddc0bc9 760 const uECC_word_t * const Z,
allankliu 0:b6fdeddc0bc9 761 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 762 uECC_word_t t1[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 763
allankliu 0:b6fdeddc0bc9 764 uECC_vli_modSquare_fast(t1, Z, curve); /* z^2 */
allankliu 0:b6fdeddc0bc9 765 uECC_vli_modMult_fast(X1, X1, t1, curve); /* x1 * z^2 */
allankliu 0:b6fdeddc0bc9 766 uECC_vli_modMult_fast(t1, t1, Z, curve); /* z^3 */
allankliu 0:b6fdeddc0bc9 767 uECC_vli_modMult_fast(Y1, Y1, t1, curve); /* y1 * z^3 */
allankliu 0:b6fdeddc0bc9 768 }
allankliu 0:b6fdeddc0bc9 769
allankliu 0:b6fdeddc0bc9 770 /* P = (x1, y1) => 2P, (x2, y2) => P' */
allankliu 0:b6fdeddc0bc9 771 static void XYcZ_initial_double(uECC_word_t * X1,
allankliu 0:b6fdeddc0bc9 772 uECC_word_t * Y1,
allankliu 0:b6fdeddc0bc9 773 uECC_word_t * X2,
allankliu 0:b6fdeddc0bc9 774 uECC_word_t * Y2,
allankliu 0:b6fdeddc0bc9 775 const uECC_word_t * const initial_Z,
allankliu 0:b6fdeddc0bc9 776 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 777 uECC_word_t z[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 778 wordcount_t num_words = curve->num_words;
allankliu 0:b6fdeddc0bc9 779 if (initial_Z) {
allankliu 0:b6fdeddc0bc9 780 uECC_vli_set(z, initial_Z, num_words);
allankliu 0:b6fdeddc0bc9 781 } else {
allankliu 0:b6fdeddc0bc9 782 uECC_vli_clear(z, num_words);
allankliu 0:b6fdeddc0bc9 783 z[0] = 1;
allankliu 0:b6fdeddc0bc9 784 }
allankliu 0:b6fdeddc0bc9 785
allankliu 0:b6fdeddc0bc9 786 uECC_vli_set(X2, X1, num_words);
allankliu 0:b6fdeddc0bc9 787 uECC_vli_set(Y2, Y1, num_words);
allankliu 0:b6fdeddc0bc9 788
allankliu 0:b6fdeddc0bc9 789 apply_z(X1, Y1, z, curve);
allankliu 0:b6fdeddc0bc9 790 curve->double_jacobian(X1, Y1, z, curve);
allankliu 0:b6fdeddc0bc9 791 apply_z(X2, Y2, z, curve);
allankliu 0:b6fdeddc0bc9 792 }
allankliu 0:b6fdeddc0bc9 793
allankliu 0:b6fdeddc0bc9 794 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
allankliu 0:b6fdeddc0bc9 795 Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
allankliu 0:b6fdeddc0bc9 796 or P => P', Q => P + Q
allankliu 0:b6fdeddc0bc9 797 */
allankliu 0:b6fdeddc0bc9 798 static void XYcZ_add(uECC_word_t * X1,
allankliu 0:b6fdeddc0bc9 799 uECC_word_t * Y1,
allankliu 0:b6fdeddc0bc9 800 uECC_word_t * X2,
allankliu 0:b6fdeddc0bc9 801 uECC_word_t * Y2,
allankliu 0:b6fdeddc0bc9 802 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 803 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
allankliu 0:b6fdeddc0bc9 804 uECC_word_t t5[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 805 wordcount_t num_words = curve->num_words;
allankliu 0:b6fdeddc0bc9 806
allankliu 0:b6fdeddc0bc9 807 uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */
allankliu 0:b6fdeddc0bc9 808 uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */
allankliu 0:b6fdeddc0bc9 809 uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */
allankliu 0:b6fdeddc0bc9 810 uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */
allankliu 0:b6fdeddc0bc9 811 uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */
allankliu 0:b6fdeddc0bc9 812 uECC_vli_modSquare_fast(t5, Y2, curve); /* t5 = (y2 - y1)^2 = D */
allankliu 0:b6fdeddc0bc9 813
allankliu 0:b6fdeddc0bc9 814 uECC_vli_modSub(t5, t5, X1, curve->p, num_words); /* t5 = D - B */
allankliu 0:b6fdeddc0bc9 815 uECC_vli_modSub(t5, t5, X2, curve->p, num_words); /* t5 = D - B - C = x3 */
allankliu 0:b6fdeddc0bc9 816 uECC_vli_modSub(X2, X2, X1, curve->p, num_words); /* t3 = C - B */
allankliu 0:b6fdeddc0bc9 817 uECC_vli_modMult_fast(Y1, Y1, X2, curve); /* t2 = y1*(C - B) */
allankliu 0:b6fdeddc0bc9 818 uECC_vli_modSub(X2, X1, t5, curve->p, num_words); /* t3 = B - x3 */
allankliu 0:b6fdeddc0bc9 819 uECC_vli_modMult_fast(Y2, Y2, X2, curve); /* t4 = (y2 - y1)*(B - x3) */
allankliu 0:b6fdeddc0bc9 820 uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y3 */
allankliu 0:b6fdeddc0bc9 821
allankliu 0:b6fdeddc0bc9 822 uECC_vli_set(X2, t5, num_words);
allankliu 0:b6fdeddc0bc9 823 }
allankliu 0:b6fdeddc0bc9 824
allankliu 0:b6fdeddc0bc9 825 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
allankliu 0:b6fdeddc0bc9 826 Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
allankliu 0:b6fdeddc0bc9 827 or P => P - Q, Q => P + Q
allankliu 0:b6fdeddc0bc9 828 */
allankliu 0:b6fdeddc0bc9 829 static void XYcZ_addC(uECC_word_t * X1,
allankliu 0:b6fdeddc0bc9 830 uECC_word_t * Y1,
allankliu 0:b6fdeddc0bc9 831 uECC_word_t * X2,
allankliu 0:b6fdeddc0bc9 832 uECC_word_t * Y2,
allankliu 0:b6fdeddc0bc9 833 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 834 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
allankliu 0:b6fdeddc0bc9 835 uECC_word_t t5[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 836 uECC_word_t t6[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 837 uECC_word_t t7[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 838 wordcount_t num_words = curve->num_words;
allankliu 0:b6fdeddc0bc9 839
allankliu 0:b6fdeddc0bc9 840 uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */
allankliu 0:b6fdeddc0bc9 841 uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */
allankliu 0:b6fdeddc0bc9 842 uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */
allankliu 0:b6fdeddc0bc9 843 uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */
allankliu 0:b6fdeddc0bc9 844 uECC_vli_modAdd(t5, Y2, Y1, curve->p, num_words); /* t5 = y2 + y1 */
allankliu 0:b6fdeddc0bc9 845 uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */
allankliu 0:b6fdeddc0bc9 846
allankliu 0:b6fdeddc0bc9 847 uECC_vli_modSub(t6, X2, X1, curve->p, num_words); /* t6 = C - B */
allankliu 0:b6fdeddc0bc9 848 uECC_vli_modMult_fast(Y1, Y1, t6, curve); /* t2 = y1 * (C - B) = E */
allankliu 0:b6fdeddc0bc9 849 uECC_vli_modAdd(t6, X1, X2, curve->p, num_words); /* t6 = B + C */
allankliu 0:b6fdeddc0bc9 850 uECC_vli_modSquare_fast(X2, Y2, curve); /* t3 = (y2 - y1)^2 = D */
allankliu 0:b6fdeddc0bc9 851 uECC_vli_modSub(X2, X2, t6, curve->p, num_words); /* t3 = D - (B + C) = x3 */
allankliu 0:b6fdeddc0bc9 852
allankliu 0:b6fdeddc0bc9 853 uECC_vli_modSub(t7, X1, X2, curve->p, num_words); /* t7 = B - x3 */
allankliu 0:b6fdeddc0bc9 854 uECC_vli_modMult_fast(Y2, Y2, t7, curve); /* t4 = (y2 - y1)*(B - x3) */
allankliu 0:b6fdeddc0bc9 855 uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = (y2 - y1)*(B - x3) - E = y3 */
allankliu 0:b6fdeddc0bc9 856
allankliu 0:b6fdeddc0bc9 857 uECC_vli_modSquare_fast(t7, t5, curve); /* t7 = (y2 + y1)^2 = F */
allankliu 0:b6fdeddc0bc9 858 uECC_vli_modSub(t7, t7, t6, curve->p, num_words); /* t7 = F - (B + C) = x3' */
allankliu 0:b6fdeddc0bc9 859 uECC_vli_modSub(t6, t7, X1, curve->p, num_words); /* t6 = x3' - B */
allankliu 0:b6fdeddc0bc9 860 uECC_vli_modMult_fast(t6, t6, t5, curve); /* t6 = (y2+y1)*(x3' - B) */
allankliu 0:b6fdeddc0bc9 861 uECC_vli_modSub(Y1, t6, Y1, curve->p, num_words); /* t2 = (y2+y1)*(x3' - B) - E = y3' */
allankliu 0:b6fdeddc0bc9 862
allankliu 0:b6fdeddc0bc9 863 uECC_vli_set(X1, t7, num_words);
allankliu 0:b6fdeddc0bc9 864 }
allankliu 0:b6fdeddc0bc9 865
allankliu 0:b6fdeddc0bc9 866 /* result may overlap point. */
allankliu 0:b6fdeddc0bc9 867 static void EccPoint_mult(uECC_word_t * result,
allankliu 0:b6fdeddc0bc9 868 const uECC_word_t * point,
allankliu 0:b6fdeddc0bc9 869 const uECC_word_t * scalar,
allankliu 0:b6fdeddc0bc9 870 const uECC_word_t * initial_Z,
allankliu 0:b6fdeddc0bc9 871 bitcount_t num_bits,
allankliu 0:b6fdeddc0bc9 872 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 873 /* R0 and R1 */
allankliu 0:b6fdeddc0bc9 874 uECC_word_t Rx[2][uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 875 uECC_word_t Ry[2][uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 876 uECC_word_t z[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 877 bitcount_t i;
allankliu 0:b6fdeddc0bc9 878 uECC_word_t nb;
allankliu 0:b6fdeddc0bc9 879 wordcount_t num_words = curve->num_words;
allankliu 0:b6fdeddc0bc9 880
allankliu 0:b6fdeddc0bc9 881 uECC_vli_set(Rx[1], point, num_words);
allankliu 0:b6fdeddc0bc9 882 uECC_vli_set(Ry[1], point + num_words, num_words);
allankliu 0:b6fdeddc0bc9 883
allankliu 0:b6fdeddc0bc9 884 XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initial_Z, curve);
allankliu 0:b6fdeddc0bc9 885
allankliu 0:b6fdeddc0bc9 886 for (i = num_bits - 2; i > 0; --i) {
allankliu 0:b6fdeddc0bc9 887 nb = !uECC_vli_testBit(scalar, i);
allankliu 0:b6fdeddc0bc9 888 XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve);
allankliu 0:b6fdeddc0bc9 889 XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve);
allankliu 0:b6fdeddc0bc9 890 }
allankliu 0:b6fdeddc0bc9 891
allankliu 0:b6fdeddc0bc9 892 nb = !uECC_vli_testBit(scalar, 0);
allankliu 0:b6fdeddc0bc9 893 XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve);
allankliu 0:b6fdeddc0bc9 894
allankliu 0:b6fdeddc0bc9 895 /* Find final 1/Z value. */
allankliu 0:b6fdeddc0bc9 896 uECC_vli_modSub(z, Rx[1], Rx[0], curve->p, num_words); /* X1 - X0 */
allankliu 0:b6fdeddc0bc9 897 uECC_vli_modMult_fast(z, z, Ry[1 - nb], curve); /* Yb * (X1 - X0) */
allankliu 0:b6fdeddc0bc9 898 uECC_vli_modMult_fast(z, z, point, curve); /* xP * Yb * (X1 - X0) */
allankliu 0:b6fdeddc0bc9 899 uECC_vli_modInv(z, z, curve->p, num_words); /* 1 / (xP * Yb * (X1 - X0)) */
allankliu 0:b6fdeddc0bc9 900 /* yP / (xP * Yb * (X1 - X0)) */
allankliu 0:b6fdeddc0bc9 901 uECC_vli_modMult_fast(z, z, point + num_words, curve);
allankliu 0:b6fdeddc0bc9 902 uECC_vli_modMult_fast(z, z, Rx[1 - nb], curve); /* Xb * yP / (xP * Yb * (X1 - X0)) */
allankliu 0:b6fdeddc0bc9 903 /* End 1/Z calculation */
allankliu 0:b6fdeddc0bc9 904
allankliu 0:b6fdeddc0bc9 905 XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve);
allankliu 0:b6fdeddc0bc9 906 apply_z(Rx[0], Ry[0], z, curve);
allankliu 0:b6fdeddc0bc9 907
allankliu 0:b6fdeddc0bc9 908 uECC_vli_set(result, Rx[0], num_words);
allankliu 0:b6fdeddc0bc9 909 uECC_vli_set(result + num_words, Ry[0], num_words);
allankliu 0:b6fdeddc0bc9 910 }
allankliu 0:b6fdeddc0bc9 911
allankliu 0:b6fdeddc0bc9 912 static uECC_word_t regularize_k(const uECC_word_t * const k,
allankliu 0:b6fdeddc0bc9 913 uECC_word_t *k0,
allankliu 0:b6fdeddc0bc9 914 uECC_word_t *k1,
allankliu 0:b6fdeddc0bc9 915 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 916 wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 917 bitcount_t num_n_bits = curve->num_n_bits;
allankliu 0:b6fdeddc0bc9 918 uECC_word_t carry = uECC_vli_add(k0, k, curve->n, num_n_words) ||
allankliu 0:b6fdeddc0bc9 919 (num_n_bits < ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8) &&
allankliu 0:b6fdeddc0bc9 920 uECC_vli_testBit(k0, num_n_bits));
allankliu 0:b6fdeddc0bc9 921 uECC_vli_add(k1, k0, curve->n, num_n_words);
allankliu 0:b6fdeddc0bc9 922 return carry;
allankliu 0:b6fdeddc0bc9 923 }
allankliu 0:b6fdeddc0bc9 924
allankliu 0:b6fdeddc0bc9 925 static uECC_word_t EccPoint_compute_public_key(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 926 uECC_word_t *private_key,
allankliu 0:b6fdeddc0bc9 927 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 928 uECC_word_t tmp1[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 929 uECC_word_t tmp2[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 930 uECC_word_t *p2[2] = {tmp1, tmp2};
allankliu 0:b6fdeddc0bc9 931 uECC_word_t carry;
allankliu 0:b6fdeddc0bc9 932
allankliu 0:b6fdeddc0bc9 933 /* Regularize the bitcount for the private key so that attackers cannot use a side channel
allankliu 0:b6fdeddc0bc9 934 attack to learn the number of leading zeros. */
allankliu 0:b6fdeddc0bc9 935 carry = regularize_k(private_key, tmp1, tmp2, curve);
allankliu 0:b6fdeddc0bc9 936
allankliu 0:b6fdeddc0bc9 937 EccPoint_mult(result, curve->G, p2[!carry], 0, curve->num_n_bits + 1, curve);
allankliu 0:b6fdeddc0bc9 938
allankliu 0:b6fdeddc0bc9 939 if (EccPoint_isZero(result, curve)) {
allankliu 0:b6fdeddc0bc9 940 return 0;
allankliu 0:b6fdeddc0bc9 941 }
allankliu 0:b6fdeddc0bc9 942 return 1;
allankliu 0:b6fdeddc0bc9 943 }
allankliu 0:b6fdeddc0bc9 944
allankliu 0:b6fdeddc0bc9 945 #if uECC_WORD_SIZE == 1
allankliu 0:b6fdeddc0bc9 946
allankliu 0:b6fdeddc0bc9 947 uECC_VLI_API void uECC_vli_nativeToBytes(uint8_t *bytes,
allankliu 0:b6fdeddc0bc9 948 int num_bytes,
allankliu 0:b6fdeddc0bc9 949 const uint8_t *native) {
allankliu 0:b6fdeddc0bc9 950 wordcount_t i;
allankliu 0:b6fdeddc0bc9 951 for (i = 0; i < num_bytes; ++i) {
allankliu 0:b6fdeddc0bc9 952 bytes[i] = native[(num_bytes - 1) - i];
allankliu 0:b6fdeddc0bc9 953 }
allankliu 0:b6fdeddc0bc9 954 }
allankliu 0:b6fdeddc0bc9 955
allankliu 0:b6fdeddc0bc9 956 uECC_VLI_API void uECC_vli_bytesToNative(uint8_t *native,
allankliu 0:b6fdeddc0bc9 957 const uint8_t *bytes,
allankliu 0:b6fdeddc0bc9 958 int num_bytes) {
allankliu 0:b6fdeddc0bc9 959 uECC_vli_nativeToBytes(native, num_bytes, bytes);
allankliu 0:b6fdeddc0bc9 960 }
allankliu 0:b6fdeddc0bc9 961
allankliu 0:b6fdeddc0bc9 962 #else
allankliu 0:b6fdeddc0bc9 963
allankliu 0:b6fdeddc0bc9 964 uECC_VLI_API void uECC_vli_nativeToBytes(uint8_t *bytes,
allankliu 0:b6fdeddc0bc9 965 int num_bytes,
allankliu 0:b6fdeddc0bc9 966 const uECC_word_t *native) {
allankliu 0:b6fdeddc0bc9 967 wordcount_t i;
allankliu 0:b6fdeddc0bc9 968 for (i = 0; i < num_bytes; ++i) {
allankliu 0:b6fdeddc0bc9 969 unsigned b = num_bytes - 1 - i;
allankliu 0:b6fdeddc0bc9 970 bytes[i] = native[b / uECC_WORD_SIZE] >> (8 * (b % uECC_WORD_SIZE));
allankliu 0:b6fdeddc0bc9 971 }
allankliu 0:b6fdeddc0bc9 972 }
allankliu 0:b6fdeddc0bc9 973
allankliu 0:b6fdeddc0bc9 974 uECC_VLI_API void uECC_vli_bytesToNative(uECC_word_t *native,
allankliu 0:b6fdeddc0bc9 975 const uint8_t *bytes,
allankliu 0:b6fdeddc0bc9 976 int num_bytes) {
allankliu 0:b6fdeddc0bc9 977 wordcount_t i;
allankliu 0:b6fdeddc0bc9 978 uECC_vli_clear(native, (num_bytes + (uECC_WORD_SIZE - 1)) / uECC_WORD_SIZE);
allankliu 0:b6fdeddc0bc9 979 for (i = 0; i < num_bytes; ++i) {
allankliu 0:b6fdeddc0bc9 980 unsigned b = num_bytes - 1 - i;
allankliu 0:b6fdeddc0bc9 981 native[b / uECC_WORD_SIZE] |=
allankliu 0:b6fdeddc0bc9 982 (uECC_word_t)bytes[i] << (8 * (b % uECC_WORD_SIZE));
allankliu 0:b6fdeddc0bc9 983 }
allankliu 0:b6fdeddc0bc9 984 }
allankliu 0:b6fdeddc0bc9 985
allankliu 0:b6fdeddc0bc9 986 #endif /* uECC_WORD_SIZE */
allankliu 0:b6fdeddc0bc9 987
allankliu 0:b6fdeddc0bc9 988 /* Generates a random integer in the range 0 < random < top.
allankliu 0:b6fdeddc0bc9 989 Both random and top have num_words words. */
allankliu 0:b6fdeddc0bc9 990 uECC_VLI_API int uECC_generate_random_int(uECC_word_t *random,
allankliu 0:b6fdeddc0bc9 991 const uECC_word_t *top,
allankliu 0:b6fdeddc0bc9 992 wordcount_t num_words) {
allankliu 0:b6fdeddc0bc9 993 uECC_word_t mask = (uECC_word_t)-1;
allankliu 0:b6fdeddc0bc9 994 uECC_word_t tries;
allankliu 0:b6fdeddc0bc9 995 bitcount_t num_bits = uECC_vli_numBits(top, num_words);
allankliu 0:b6fdeddc0bc9 996
allankliu 0:b6fdeddc0bc9 997 if (!g_rng_function) {
allankliu 0:b6fdeddc0bc9 998 return 0;
allankliu 0:b6fdeddc0bc9 999 }
allankliu 0:b6fdeddc0bc9 1000
allankliu 0:b6fdeddc0bc9 1001 for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) {
allankliu 0:b6fdeddc0bc9 1002 if (!g_rng_function((uint8_t *)random, num_words * uECC_WORD_SIZE)) {
allankliu 0:b6fdeddc0bc9 1003 return 0;
allankliu 0:b6fdeddc0bc9 1004 }
allankliu 0:b6fdeddc0bc9 1005 random[num_words - 1] &= mask >> ((bitcount_t)(num_words * uECC_WORD_SIZE * 8 - num_bits));
allankliu 0:b6fdeddc0bc9 1006 if (!uECC_vli_isZero(random, num_words) &&
allankliu 0:b6fdeddc0bc9 1007 uECC_vli_cmp(top, random, num_words) == 1) {
allankliu 0:b6fdeddc0bc9 1008 return 1;
allankliu 0:b6fdeddc0bc9 1009 }
allankliu 0:b6fdeddc0bc9 1010 }
allankliu 0:b6fdeddc0bc9 1011 return 0;
allankliu 0:b6fdeddc0bc9 1012 }
allankliu 0:b6fdeddc0bc9 1013
allankliu 0:b6fdeddc0bc9 1014 int uECC_make_key(uint8_t *public_key,
allankliu 0:b6fdeddc0bc9 1015 uint8_t *private_key,
allankliu 0:b6fdeddc0bc9 1016 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1017 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1018 uECC_word_t *_private = (uECC_word_t *)private_key;
allankliu 0:b6fdeddc0bc9 1019 uECC_word_t *_public = (uECC_word_t *)public_key;
allankliu 0:b6fdeddc0bc9 1020 #else
allankliu 0:b6fdeddc0bc9 1021 uECC_word_t _private[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1022 uECC_word_t _public[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 1023 #endif
allankliu 0:b6fdeddc0bc9 1024 uECC_word_t tries;
allankliu 0:b6fdeddc0bc9 1025
allankliu 0:b6fdeddc0bc9 1026 for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) {
allankliu 0:b6fdeddc0bc9 1027 if (!uECC_generate_random_int(_private, curve->n, BITS_TO_WORDS(curve->num_n_bits))) {
allankliu 0:b6fdeddc0bc9 1028 return 0;
allankliu 0:b6fdeddc0bc9 1029 }
allankliu 0:b6fdeddc0bc9 1030
allankliu 0:b6fdeddc0bc9 1031 if (EccPoint_compute_public_key(_public, _private, curve)) {
allankliu 0:b6fdeddc0bc9 1032 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0
allankliu 0:b6fdeddc0bc9 1033 uECC_vli_nativeToBytes(private_key, BITS_TO_BYTES(curve->num_n_bits), _private);
allankliu 0:b6fdeddc0bc9 1034 uECC_vli_nativeToBytes(public_key, curve->num_bytes, _public);
allankliu 0:b6fdeddc0bc9 1035 uECC_vli_nativeToBytes(
allankliu 0:b6fdeddc0bc9 1036 public_key + curve->num_bytes, curve->num_bytes, _public + curve->num_words);
allankliu 0:b6fdeddc0bc9 1037 #endif
allankliu 0:b6fdeddc0bc9 1038 return 1;
allankliu 0:b6fdeddc0bc9 1039 }
allankliu 0:b6fdeddc0bc9 1040 }
allankliu 0:b6fdeddc0bc9 1041 return 0;
allankliu 0:b6fdeddc0bc9 1042 }
allankliu 0:b6fdeddc0bc9 1043
allankliu 0:b6fdeddc0bc9 1044 int uECC_shared_secret(const uint8_t *public_key,
allankliu 0:b6fdeddc0bc9 1045 const uint8_t *private_key,
allankliu 0:b6fdeddc0bc9 1046 uint8_t *secret,
allankliu 0:b6fdeddc0bc9 1047 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1048 uECC_word_t _public[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 1049 uECC_word_t _private[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1050
allankliu 0:b6fdeddc0bc9 1051 uECC_word_t tmp[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1052 uECC_word_t *p2[2] = {_private, tmp};
allankliu 0:b6fdeddc0bc9 1053 uECC_word_t *initial_Z = 0;
allankliu 0:b6fdeddc0bc9 1054 uECC_word_t carry;
allankliu 0:b6fdeddc0bc9 1055 wordcount_t num_words = curve->num_words;
allankliu 0:b6fdeddc0bc9 1056 wordcount_t num_bytes = curve->num_bytes;
allankliu 0:b6fdeddc0bc9 1057
allankliu 0:b6fdeddc0bc9 1058 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1059 bcopy((uint8_t *) _private, private_key, num_bytes);
allankliu 0:b6fdeddc0bc9 1060 bcopy((uint8_t *) _public, public_key, num_bytes*2);
allankliu 0:b6fdeddc0bc9 1061 #else
allankliu 0:b6fdeddc0bc9 1062 uECC_vli_bytesToNative(_private, private_key, BITS_TO_BYTES(curve->num_n_bits));
allankliu 0:b6fdeddc0bc9 1063 uECC_vli_bytesToNative(_public, public_key, num_bytes);
allankliu 0:b6fdeddc0bc9 1064 uECC_vli_bytesToNative(_public + num_words, public_key + num_bytes, num_bytes);
allankliu 0:b6fdeddc0bc9 1065 #endif
allankliu 0:b6fdeddc0bc9 1066
allankliu 0:b6fdeddc0bc9 1067 /* Regularize the bitcount for the private key so that attackers cannot use a side channel
allankliu 0:b6fdeddc0bc9 1068 attack to learn the number of leading zeros. */
allankliu 0:b6fdeddc0bc9 1069 carry = regularize_k(_private, _private, tmp, curve);
allankliu 0:b6fdeddc0bc9 1070
allankliu 0:b6fdeddc0bc9 1071 /* If an RNG function was specified, try to get a random initial Z value to improve
allankliu 0:b6fdeddc0bc9 1072 protection against side-channel attacks. */
allankliu 0:b6fdeddc0bc9 1073 if (g_rng_function) {
allankliu 0:b6fdeddc0bc9 1074 if (!uECC_generate_random_int(p2[carry], curve->p, num_words)) {
allankliu 0:b6fdeddc0bc9 1075 return 0;
allankliu 0:b6fdeddc0bc9 1076 }
allankliu 0:b6fdeddc0bc9 1077 initial_Z = p2[carry];
allankliu 0:b6fdeddc0bc9 1078 }
allankliu 0:b6fdeddc0bc9 1079
allankliu 0:b6fdeddc0bc9 1080 EccPoint_mult(_public, _public, p2[!carry], initial_Z, curve->num_n_bits + 1, curve);
allankliu 0:b6fdeddc0bc9 1081 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1082 bcopy((uint8_t *) secret, (uint8_t *) _public, num_bytes);
allankliu 0:b6fdeddc0bc9 1083 #else
allankliu 0:b6fdeddc0bc9 1084 uECC_vli_nativeToBytes(secret, num_bytes, _public);
allankliu 0:b6fdeddc0bc9 1085 #endif
allankliu 0:b6fdeddc0bc9 1086 return !EccPoint_isZero(_public, curve);
allankliu 0:b6fdeddc0bc9 1087 }
allankliu 0:b6fdeddc0bc9 1088
allankliu 0:b6fdeddc0bc9 1089 #if uECC_SUPPORT_COMPRESSED_POINT
allankliu 0:b6fdeddc0bc9 1090 void uECC_compress(const uint8_t *public_key, uint8_t *compressed, uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1091 wordcount_t i;
allankliu 0:b6fdeddc0bc9 1092 for (i = 0; i < curve->num_bytes; ++i) {
allankliu 0:b6fdeddc0bc9 1093 compressed[i+1] = public_key[i];
allankliu 0:b6fdeddc0bc9 1094 }
allankliu 0:b6fdeddc0bc9 1095 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1096 compressed[0] = 2 + (public_key[curve->num_bytes] & 0x01);
allankliu 0:b6fdeddc0bc9 1097 #else
allankliu 0:b6fdeddc0bc9 1098 compressed[0] = 2 + (public_key[curve->num_bytes * 2 - 1] & 0x01);
allankliu 0:b6fdeddc0bc9 1099 #endif
allankliu 0:b6fdeddc0bc9 1100 }
allankliu 0:b6fdeddc0bc9 1101
allankliu 0:b6fdeddc0bc9 1102 void uECC_decompress(const uint8_t *compressed, uint8_t *public_key, uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1103 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1104 uECC_word_t *point = (uECC_word_t *)public_key;
allankliu 0:b6fdeddc0bc9 1105 #else
allankliu 0:b6fdeddc0bc9 1106 uECC_word_t point[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 1107 #endif
allankliu 0:b6fdeddc0bc9 1108 uECC_word_t *y = point + curve->num_words;
allankliu 0:b6fdeddc0bc9 1109 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1110 bcopy(public_key, compressed+1, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1111 #else
allankliu 0:b6fdeddc0bc9 1112 uECC_vli_bytesToNative(point, compressed + 1, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1113 #endif
allankliu 0:b6fdeddc0bc9 1114 curve->x_side(y, point, curve);
allankliu 0:b6fdeddc0bc9 1115 curve->mod_sqrt(y, curve);
allankliu 0:b6fdeddc0bc9 1116
allankliu 0:b6fdeddc0bc9 1117 if ((y[0] & 0x01) != (compressed[0] & 0x01)) {
allankliu 0:b6fdeddc0bc9 1118 uECC_vli_sub(y, curve->p, y, curve->num_words);
allankliu 0:b6fdeddc0bc9 1119 }
allankliu 0:b6fdeddc0bc9 1120
allankliu 0:b6fdeddc0bc9 1121 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0
allankliu 0:b6fdeddc0bc9 1122 uECC_vli_nativeToBytes(public_key, curve->num_bytes, point);
allankliu 0:b6fdeddc0bc9 1123 uECC_vli_nativeToBytes(public_key + curve->num_bytes, curve->num_bytes, y);
allankliu 0:b6fdeddc0bc9 1124 #endif
allankliu 0:b6fdeddc0bc9 1125 }
allankliu 0:b6fdeddc0bc9 1126 #endif /* uECC_SUPPORT_COMPRESSED_POINT */
allankliu 0:b6fdeddc0bc9 1127
allankliu 0:b6fdeddc0bc9 1128 int uECC_valid_point(const uECC_word_t *point, uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1129 uECC_word_t tmp1[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1130 uECC_word_t tmp2[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1131 wordcount_t num_words = curve->num_words;
allankliu 0:b6fdeddc0bc9 1132
allankliu 0:b6fdeddc0bc9 1133 /* The point at infinity is invalid. */
allankliu 0:b6fdeddc0bc9 1134 if (EccPoint_isZero(point, curve)) {
allankliu 0:b6fdeddc0bc9 1135 return 0;
allankliu 0:b6fdeddc0bc9 1136 }
allankliu 0:b6fdeddc0bc9 1137
allankliu 0:b6fdeddc0bc9 1138 /* x and y must be smaller than p. */
allankliu 0:b6fdeddc0bc9 1139 if (uECC_vli_cmp_unsafe(curve->p, point, num_words) != 1 ||
allankliu 0:b6fdeddc0bc9 1140 uECC_vli_cmp_unsafe(curve->p, point + num_words, num_words) != 1) {
allankliu 0:b6fdeddc0bc9 1141 return 0;
allankliu 0:b6fdeddc0bc9 1142 }
allankliu 0:b6fdeddc0bc9 1143
allankliu 0:b6fdeddc0bc9 1144 uECC_vli_modSquare_fast(tmp1, point + num_words, curve);
allankliu 0:b6fdeddc0bc9 1145 curve->x_side(tmp2, point, curve); /* tmp2 = x^3 + ax + b */
allankliu 0:b6fdeddc0bc9 1146
allankliu 0:b6fdeddc0bc9 1147 /* Make sure that y^2 == x^3 + ax + b */
allankliu 0:b6fdeddc0bc9 1148 return (int)(uECC_vli_equal(tmp1, tmp2, num_words));
allankliu 0:b6fdeddc0bc9 1149 }
allankliu 0:b6fdeddc0bc9 1150
allankliu 0:b6fdeddc0bc9 1151 int uECC_valid_public_key(const uint8_t *public_key, uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1152 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1153 uECC_word_t *_public = (uECC_word_t *)public_key;
allankliu 0:b6fdeddc0bc9 1154 #else
allankliu 0:b6fdeddc0bc9 1155 uECC_word_t _public[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 1156 #endif
allankliu 0:b6fdeddc0bc9 1157
allankliu 0:b6fdeddc0bc9 1158 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0
allankliu 0:b6fdeddc0bc9 1159 uECC_vli_bytesToNative(_public, public_key, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1160 uECC_vli_bytesToNative(
allankliu 0:b6fdeddc0bc9 1161 _public + curve->num_words, public_key + curve->num_bytes, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1162 #endif
allankliu 0:b6fdeddc0bc9 1163 return uECC_valid_point(_public, curve);
allankliu 0:b6fdeddc0bc9 1164 }
allankliu 0:b6fdeddc0bc9 1165
allankliu 0:b6fdeddc0bc9 1166 int uECC_compute_public_key(const uint8_t *private_key, uint8_t *public_key, uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1167 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1168 uECC_word_t *_private = (uECC_word_t *)private_key;
allankliu 0:b6fdeddc0bc9 1169 uECC_word_t *_public = (uECC_word_t *)public_key;
allankliu 0:b6fdeddc0bc9 1170 #else
allankliu 0:b6fdeddc0bc9 1171 uECC_word_t _private[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1172 uECC_word_t _public[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 1173 #endif
allankliu 0:b6fdeddc0bc9 1174
allankliu 0:b6fdeddc0bc9 1175 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0
allankliu 0:b6fdeddc0bc9 1176 uECC_vli_bytesToNative(_private, private_key, BITS_TO_BYTES(curve->num_n_bits));
allankliu 0:b6fdeddc0bc9 1177 #endif
allankliu 0:b6fdeddc0bc9 1178
allankliu 0:b6fdeddc0bc9 1179 /* Make sure the private key is in the range [1, n-1]. */
allankliu 0:b6fdeddc0bc9 1180 if (uECC_vli_isZero(_private, BITS_TO_WORDS(curve->num_n_bits))) {
allankliu 0:b6fdeddc0bc9 1181 return 0;
allankliu 0:b6fdeddc0bc9 1182 }
allankliu 0:b6fdeddc0bc9 1183
allankliu 0:b6fdeddc0bc9 1184 if (uECC_vli_cmp(curve->n, _private, BITS_TO_WORDS(curve->num_n_bits)) != 1) {
allankliu 0:b6fdeddc0bc9 1185 return 0;
allankliu 0:b6fdeddc0bc9 1186 }
allankliu 0:b6fdeddc0bc9 1187
allankliu 0:b6fdeddc0bc9 1188 /* Compute public key. */
allankliu 0:b6fdeddc0bc9 1189 if (!EccPoint_compute_public_key(_public, _private, curve)) {
allankliu 0:b6fdeddc0bc9 1190 return 0;
allankliu 0:b6fdeddc0bc9 1191 }
allankliu 0:b6fdeddc0bc9 1192
allankliu 0:b6fdeddc0bc9 1193 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0
allankliu 0:b6fdeddc0bc9 1194 uECC_vli_nativeToBytes(public_key, curve->num_bytes, _public);
allankliu 0:b6fdeddc0bc9 1195 uECC_vli_nativeToBytes(
allankliu 0:b6fdeddc0bc9 1196 public_key + curve->num_bytes, curve->num_bytes, _public + curve->num_words);
allankliu 0:b6fdeddc0bc9 1197 #endif
allankliu 0:b6fdeddc0bc9 1198 return 1;
allankliu 0:b6fdeddc0bc9 1199 }
allankliu 0:b6fdeddc0bc9 1200
allankliu 0:b6fdeddc0bc9 1201
allankliu 0:b6fdeddc0bc9 1202 /* -------- ECDSA code -------- */
allankliu 0:b6fdeddc0bc9 1203
allankliu 0:b6fdeddc0bc9 1204 static void bits2int(uECC_word_t *native,
allankliu 0:b6fdeddc0bc9 1205 const uint8_t *bits,
allankliu 0:b6fdeddc0bc9 1206 unsigned bits_size,
allankliu 0:b6fdeddc0bc9 1207 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1208 unsigned num_n_bytes = BITS_TO_BYTES(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 1209 unsigned num_n_words = BITS_TO_WORDS(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 1210 int shift;
allankliu 0:b6fdeddc0bc9 1211 uECC_word_t carry;
allankliu 0:b6fdeddc0bc9 1212 uECC_word_t *ptr;
allankliu 0:b6fdeddc0bc9 1213
allankliu 0:b6fdeddc0bc9 1214 if (bits_size > num_n_bytes) {
allankliu 0:b6fdeddc0bc9 1215 bits_size = num_n_bytes;
allankliu 0:b6fdeddc0bc9 1216 }
allankliu 0:b6fdeddc0bc9 1217
allankliu 0:b6fdeddc0bc9 1218 uECC_vli_clear(native, num_n_words);
allankliu 0:b6fdeddc0bc9 1219 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1220 bcopy((uint8_t *) native, bits, bits_size);
allankliu 0:b6fdeddc0bc9 1221 #else
allankliu 0:b6fdeddc0bc9 1222 uECC_vli_bytesToNative(native, bits, bits_size);
allankliu 0:b6fdeddc0bc9 1223 #endif
allankliu 0:b6fdeddc0bc9 1224 if (bits_size * 8 <= (unsigned)curve->num_n_bits) {
allankliu 0:b6fdeddc0bc9 1225 return;
allankliu 0:b6fdeddc0bc9 1226 }
allankliu 0:b6fdeddc0bc9 1227 shift = bits_size * 8 - curve->num_n_bits;
allankliu 0:b6fdeddc0bc9 1228 carry = 0;
allankliu 0:b6fdeddc0bc9 1229 ptr = native + num_n_words;
allankliu 0:b6fdeddc0bc9 1230 while (ptr-- > native) {
allankliu 0:b6fdeddc0bc9 1231 uECC_word_t temp = *ptr;
allankliu 0:b6fdeddc0bc9 1232 *ptr = (temp >> shift) | carry;
allankliu 0:b6fdeddc0bc9 1233 carry = temp << (uECC_WORD_BITS - shift);
allankliu 0:b6fdeddc0bc9 1234 }
allankliu 0:b6fdeddc0bc9 1235
allankliu 0:b6fdeddc0bc9 1236 /* Reduce mod curve_n */
allankliu 0:b6fdeddc0bc9 1237 if (uECC_vli_cmp_unsafe(curve->n, native, num_n_words) != 1) {
allankliu 0:b6fdeddc0bc9 1238 uECC_vli_sub(native, native, curve->n, num_n_words);
allankliu 0:b6fdeddc0bc9 1239 }
allankliu 0:b6fdeddc0bc9 1240 }
allankliu 0:b6fdeddc0bc9 1241
allankliu 0:b6fdeddc0bc9 1242 static int uECC_sign_with_k(const uint8_t *private_key,
allankliu 0:b6fdeddc0bc9 1243 const uint8_t *message_hash,
allankliu 0:b6fdeddc0bc9 1244 unsigned hash_size,
allankliu 0:b6fdeddc0bc9 1245 uECC_word_t *k,
allankliu 0:b6fdeddc0bc9 1246 uint8_t *signature,
allankliu 0:b6fdeddc0bc9 1247 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1248
allankliu 0:b6fdeddc0bc9 1249 uECC_word_t tmp[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1250 uECC_word_t s[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1251 uECC_word_t *k2[2] = {tmp, s};
allankliu 0:b6fdeddc0bc9 1252 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1253 uECC_word_t *p = (uECC_word_t *)signature;
allankliu 0:b6fdeddc0bc9 1254 #else
allankliu 0:b6fdeddc0bc9 1255 uECC_word_t p[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 1256 #endif
allankliu 0:b6fdeddc0bc9 1257 uECC_word_t carry;
allankliu 0:b6fdeddc0bc9 1258 wordcount_t num_words = curve->num_words;
allankliu 0:b6fdeddc0bc9 1259 wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 1260 bitcount_t num_n_bits = curve->num_n_bits;
allankliu 0:b6fdeddc0bc9 1261
allankliu 0:b6fdeddc0bc9 1262 /* Make sure 0 < k < curve_n */
allankliu 0:b6fdeddc0bc9 1263 if (uECC_vli_isZero(k, num_words) || uECC_vli_cmp(curve->n, k, num_n_words) != 1) {
allankliu 0:b6fdeddc0bc9 1264 return 0;
allankliu 0:b6fdeddc0bc9 1265 }
allankliu 0:b6fdeddc0bc9 1266
allankliu 0:b6fdeddc0bc9 1267 carry = regularize_k(k, tmp, s, curve);
allankliu 0:b6fdeddc0bc9 1268 EccPoint_mult(p, curve->G, k2[!carry], 0, num_n_bits + 1, curve);
allankliu 0:b6fdeddc0bc9 1269 if (uECC_vli_isZero(p, num_words)) {
allankliu 0:b6fdeddc0bc9 1270 return 0;
allankliu 0:b6fdeddc0bc9 1271 }
allankliu 0:b6fdeddc0bc9 1272
allankliu 0:b6fdeddc0bc9 1273 /* If an RNG function was specified, get a random number
allankliu 0:b6fdeddc0bc9 1274 to prevent side channel analysis of k. */
allankliu 0:b6fdeddc0bc9 1275 if (!g_rng_function) {
allankliu 0:b6fdeddc0bc9 1276 uECC_vli_clear(tmp, num_n_words);
allankliu 0:b6fdeddc0bc9 1277 tmp[0] = 1;
allankliu 0:b6fdeddc0bc9 1278 } else if (!uECC_generate_random_int(tmp, curve->n, num_n_words)) {
allankliu 0:b6fdeddc0bc9 1279 return 0;
allankliu 0:b6fdeddc0bc9 1280 }
allankliu 0:b6fdeddc0bc9 1281
allankliu 0:b6fdeddc0bc9 1282 /* Prevent side channel analysis of uECC_vli_modInv() to determine
allankliu 0:b6fdeddc0bc9 1283 bits of k / the private key by premultiplying by a random number */
allankliu 0:b6fdeddc0bc9 1284 uECC_vli_modMult(k, k, tmp, curve->n, num_n_words); /* k' = rand * k */
allankliu 0:b6fdeddc0bc9 1285 uECC_vli_modInv(k, k, curve->n, num_n_words); /* k = 1 / k' */
allankliu 0:b6fdeddc0bc9 1286 uECC_vli_modMult(k, k, tmp, curve->n, num_n_words); /* k = 1 / k */
allankliu 0:b6fdeddc0bc9 1287
allankliu 0:b6fdeddc0bc9 1288 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0
allankliu 0:b6fdeddc0bc9 1289 uECC_vli_nativeToBytes(signature, curve->num_bytes, p); /* store r */
allankliu 0:b6fdeddc0bc9 1290 #endif
allankliu 0:b6fdeddc0bc9 1291
allankliu 0:b6fdeddc0bc9 1292 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1293 bcopy((uint8_t *) tmp, private_key, BITS_TO_BYTES(curve->num_n_bits));
allankliu 0:b6fdeddc0bc9 1294 #else
allankliu 0:b6fdeddc0bc9 1295 uECC_vli_bytesToNative(tmp, private_key, BITS_TO_BYTES(curve->num_n_bits)); /* tmp = d */
allankliu 0:b6fdeddc0bc9 1296 #endif
allankliu 0:b6fdeddc0bc9 1297
allankliu 0:b6fdeddc0bc9 1298 s[num_n_words - 1] = 0;
allankliu 0:b6fdeddc0bc9 1299 uECC_vli_set(s, p, num_words);
allankliu 0:b6fdeddc0bc9 1300 uECC_vli_modMult(s, tmp, s, curve->n, num_n_words); /* s = r*d */
allankliu 0:b6fdeddc0bc9 1301
allankliu 0:b6fdeddc0bc9 1302 bits2int(tmp, message_hash, hash_size, curve);
allankliu 0:b6fdeddc0bc9 1303 uECC_vli_modAdd(s, tmp, s, curve->n, num_n_words); /* s = e + r*d */
allankliu 0:b6fdeddc0bc9 1304 uECC_vli_modMult(s, s, k, curve->n, num_n_words); /* s = (e + r*d) / k */
allankliu 0:b6fdeddc0bc9 1305 if (uECC_vli_numBits(s, num_n_words) > (bitcount_t)curve->num_bytes * 8) {
allankliu 0:b6fdeddc0bc9 1306 return 0;
allankliu 0:b6fdeddc0bc9 1307 }
allankliu 0:b6fdeddc0bc9 1308 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1309 bcopy((uint8_t *) signature + curve->num_bytes, (uint8_t *) s, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1310 #else
allankliu 0:b6fdeddc0bc9 1311 uECC_vli_nativeToBytes(signature + curve->num_bytes, curve->num_bytes, s);
allankliu 0:b6fdeddc0bc9 1312 #endif
allankliu 0:b6fdeddc0bc9 1313 return 1;
allankliu 0:b6fdeddc0bc9 1314 }
allankliu 0:b6fdeddc0bc9 1315
allankliu 0:b6fdeddc0bc9 1316 int uECC_sign(const uint8_t *private_key,
allankliu 0:b6fdeddc0bc9 1317 const uint8_t *message_hash,
allankliu 0:b6fdeddc0bc9 1318 unsigned hash_size,
allankliu 0:b6fdeddc0bc9 1319 uint8_t *signature,
allankliu 0:b6fdeddc0bc9 1320 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1321 uECC_word_t k[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1322 uECC_word_t tries;
allankliu 0:b6fdeddc0bc9 1323
allankliu 0:b6fdeddc0bc9 1324 for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) {
allankliu 0:b6fdeddc0bc9 1325 if (!uECC_generate_random_int(k, curve->n, BITS_TO_WORDS(curve->num_n_bits))) {
allankliu 0:b6fdeddc0bc9 1326 return 0;
allankliu 0:b6fdeddc0bc9 1327 }
allankliu 0:b6fdeddc0bc9 1328
allankliu 0:b6fdeddc0bc9 1329 if (uECC_sign_with_k(private_key, message_hash, hash_size, k, signature, curve)) {
allankliu 0:b6fdeddc0bc9 1330 return 1;
allankliu 0:b6fdeddc0bc9 1331 }
allankliu 0:b6fdeddc0bc9 1332 }
allankliu 0:b6fdeddc0bc9 1333 return 0;
allankliu 0:b6fdeddc0bc9 1334 }
allankliu 0:b6fdeddc0bc9 1335
allankliu 0:b6fdeddc0bc9 1336 /* Compute an HMAC using K as a key (as in RFC 6979). Note that K is always
allankliu 0:b6fdeddc0bc9 1337 the same size as the hash result size. */
allankliu 0:b6fdeddc0bc9 1338 static void HMAC_init(const uECC_HashContext *hash_context, const uint8_t *K) {
allankliu 0:b6fdeddc0bc9 1339 uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size;
allankliu 0:b6fdeddc0bc9 1340 unsigned i;
allankliu 0:b6fdeddc0bc9 1341 for (i = 0; i < hash_context->result_size; ++i)
allankliu 0:b6fdeddc0bc9 1342 pad[i] = K[i] ^ 0x36;
allankliu 0:b6fdeddc0bc9 1343 for (; i < hash_context->block_size; ++i)
allankliu 0:b6fdeddc0bc9 1344 pad[i] = 0x36;
allankliu 0:b6fdeddc0bc9 1345
allankliu 0:b6fdeddc0bc9 1346 hash_context->init_hash(hash_context);
allankliu 0:b6fdeddc0bc9 1347 hash_context->update_hash(hash_context, pad, hash_context->block_size);
allankliu 0:b6fdeddc0bc9 1348 }
allankliu 0:b6fdeddc0bc9 1349
allankliu 0:b6fdeddc0bc9 1350 static void HMAC_update(const uECC_HashContext *hash_context,
allankliu 0:b6fdeddc0bc9 1351 const uint8_t *message,
allankliu 0:b6fdeddc0bc9 1352 unsigned message_size) {
allankliu 0:b6fdeddc0bc9 1353 hash_context->update_hash(hash_context, message, message_size);
allankliu 0:b6fdeddc0bc9 1354 }
allankliu 0:b6fdeddc0bc9 1355
allankliu 0:b6fdeddc0bc9 1356 static void HMAC_finish(const uECC_HashContext *hash_context,
allankliu 0:b6fdeddc0bc9 1357 const uint8_t *K,
allankliu 0:b6fdeddc0bc9 1358 uint8_t *result) {
allankliu 0:b6fdeddc0bc9 1359 uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size;
allankliu 0:b6fdeddc0bc9 1360 unsigned i;
allankliu 0:b6fdeddc0bc9 1361 for (i = 0; i < hash_context->result_size; ++i)
allankliu 0:b6fdeddc0bc9 1362 pad[i] = K[i] ^ 0x5c;
allankliu 0:b6fdeddc0bc9 1363 for (; i < hash_context->block_size; ++i)
allankliu 0:b6fdeddc0bc9 1364 pad[i] = 0x5c;
allankliu 0:b6fdeddc0bc9 1365
allankliu 0:b6fdeddc0bc9 1366 hash_context->finish_hash(hash_context, result);
allankliu 0:b6fdeddc0bc9 1367
allankliu 0:b6fdeddc0bc9 1368 hash_context->init_hash(hash_context);
allankliu 0:b6fdeddc0bc9 1369 hash_context->update_hash(hash_context, pad, hash_context->block_size);
allankliu 0:b6fdeddc0bc9 1370 hash_context->update_hash(hash_context, result, hash_context->result_size);
allankliu 0:b6fdeddc0bc9 1371 hash_context->finish_hash(hash_context, result);
allankliu 0:b6fdeddc0bc9 1372 }
allankliu 0:b6fdeddc0bc9 1373
allankliu 0:b6fdeddc0bc9 1374 /* V = HMAC_K(V) */
allankliu 0:b6fdeddc0bc9 1375 static void update_V(const uECC_HashContext *hash_context, uint8_t *K, uint8_t *V) {
allankliu 0:b6fdeddc0bc9 1376 HMAC_init(hash_context, K);
allankliu 0:b6fdeddc0bc9 1377 HMAC_update(hash_context, V, hash_context->result_size);
allankliu 0:b6fdeddc0bc9 1378 HMAC_finish(hash_context, K, V);
allankliu 0:b6fdeddc0bc9 1379 }
allankliu 0:b6fdeddc0bc9 1380
allankliu 0:b6fdeddc0bc9 1381 /* Deterministic signing, similar to RFC 6979. Differences are:
allankliu 0:b6fdeddc0bc9 1382 * We just use H(m) directly rather than bits2octets(H(m))
allankliu 0:b6fdeddc0bc9 1383 (it is not reduced modulo curve_n).
allankliu 0:b6fdeddc0bc9 1384 * We generate a value for k (aka T) directly rather than converting endianness.
allankliu 0:b6fdeddc0bc9 1385
allankliu 0:b6fdeddc0bc9 1386 Layout of hash_context->tmp: <K> | <V> | (1 byte overlapped 0x00 or 0x01) / <HMAC pad> */
allankliu 0:b6fdeddc0bc9 1387 int uECC_sign_deterministic(const uint8_t *private_key,
allankliu 0:b6fdeddc0bc9 1388 const uint8_t *message_hash,
allankliu 0:b6fdeddc0bc9 1389 unsigned hash_size,
allankliu 0:b6fdeddc0bc9 1390 const uECC_HashContext *hash_context,
allankliu 0:b6fdeddc0bc9 1391 uint8_t *signature,
allankliu 0:b6fdeddc0bc9 1392 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1393 uint8_t *K = hash_context->tmp;
allankliu 0:b6fdeddc0bc9 1394 uint8_t *V = K + hash_context->result_size;
allankliu 0:b6fdeddc0bc9 1395 wordcount_t num_bytes = curve->num_bytes;
allankliu 0:b6fdeddc0bc9 1396 wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 1397 bitcount_t num_n_bits = curve->num_n_bits;
allankliu 0:b6fdeddc0bc9 1398 uECC_word_t tries;
allankliu 0:b6fdeddc0bc9 1399 unsigned i;
allankliu 0:b6fdeddc0bc9 1400 for (i = 0; i < hash_context->result_size; ++i) {
allankliu 0:b6fdeddc0bc9 1401 V[i] = 0x01;
allankliu 0:b6fdeddc0bc9 1402 K[i] = 0;
allankliu 0:b6fdeddc0bc9 1403 }
allankliu 0:b6fdeddc0bc9 1404
allankliu 0:b6fdeddc0bc9 1405 /* K = HMAC_K(V || 0x00 || int2octets(x) || h(m)) */
allankliu 0:b6fdeddc0bc9 1406 HMAC_init(hash_context, K);
allankliu 0:b6fdeddc0bc9 1407 V[hash_context->result_size] = 0x00;
allankliu 0:b6fdeddc0bc9 1408 HMAC_update(hash_context, V, hash_context->result_size + 1);
allankliu 0:b6fdeddc0bc9 1409 HMAC_update(hash_context, private_key, num_bytes);
allankliu 0:b6fdeddc0bc9 1410 HMAC_update(hash_context, message_hash, hash_size);
allankliu 0:b6fdeddc0bc9 1411 HMAC_finish(hash_context, K, K);
allankliu 0:b6fdeddc0bc9 1412
allankliu 0:b6fdeddc0bc9 1413 update_V(hash_context, K, V);
allankliu 0:b6fdeddc0bc9 1414
allankliu 0:b6fdeddc0bc9 1415 /* K = HMAC_K(V || 0x01 || int2octets(x) || h(m)) */
allankliu 0:b6fdeddc0bc9 1416 HMAC_init(hash_context, K);
allankliu 0:b6fdeddc0bc9 1417 V[hash_context->result_size] = 0x01;
allankliu 0:b6fdeddc0bc9 1418 HMAC_update(hash_context, V, hash_context->result_size + 1);
allankliu 0:b6fdeddc0bc9 1419 HMAC_update(hash_context, private_key, num_bytes);
allankliu 0:b6fdeddc0bc9 1420 HMAC_update(hash_context, message_hash, hash_size);
allankliu 0:b6fdeddc0bc9 1421 HMAC_finish(hash_context, K, K);
allankliu 0:b6fdeddc0bc9 1422
allankliu 0:b6fdeddc0bc9 1423 update_V(hash_context, K, V);
allankliu 0:b6fdeddc0bc9 1424
allankliu 0:b6fdeddc0bc9 1425 for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) {
allankliu 0:b6fdeddc0bc9 1426 uECC_word_t T[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1427 uint8_t *T_ptr = (uint8_t *)T;
allankliu 0:b6fdeddc0bc9 1428 wordcount_t T_bytes = 0;
allankliu 0:b6fdeddc0bc9 1429 for (;;) {
allankliu 0:b6fdeddc0bc9 1430 update_V(hash_context, K, V);
allankliu 0:b6fdeddc0bc9 1431 for (i = 0; i < hash_context->result_size; ++i) {
allankliu 0:b6fdeddc0bc9 1432 T_ptr[T_bytes++] = V[i];
allankliu 0:b6fdeddc0bc9 1433 if (T_bytes >= num_n_words * uECC_WORD_SIZE) {
allankliu 0:b6fdeddc0bc9 1434 goto filled;
allankliu 0:b6fdeddc0bc9 1435 }
allankliu 0:b6fdeddc0bc9 1436 }
allankliu 0:b6fdeddc0bc9 1437 }
allankliu 0:b6fdeddc0bc9 1438 filled:
allankliu 0:b6fdeddc0bc9 1439 if ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8 > num_n_bits) {
allankliu 0:b6fdeddc0bc9 1440 uECC_word_t mask = (uECC_word_t)-1;
allankliu 0:b6fdeddc0bc9 1441 T[num_n_words - 1] &=
allankliu 0:b6fdeddc0bc9 1442 mask >> ((bitcount_t)(num_n_words * uECC_WORD_SIZE * 8 - num_n_bits));
allankliu 0:b6fdeddc0bc9 1443 }
allankliu 0:b6fdeddc0bc9 1444
allankliu 0:b6fdeddc0bc9 1445 if (uECC_sign_with_k(private_key, message_hash, hash_size, T, signature, curve)) {
allankliu 0:b6fdeddc0bc9 1446 return 1;
allankliu 0:b6fdeddc0bc9 1447 }
allankliu 0:b6fdeddc0bc9 1448
allankliu 0:b6fdeddc0bc9 1449 /* K = HMAC_K(V || 0x00) */
allankliu 0:b6fdeddc0bc9 1450 HMAC_init(hash_context, K);
allankliu 0:b6fdeddc0bc9 1451 V[hash_context->result_size] = 0x00;
allankliu 0:b6fdeddc0bc9 1452 HMAC_update(hash_context, V, hash_context->result_size + 1);
allankliu 0:b6fdeddc0bc9 1453 HMAC_finish(hash_context, K, K);
allankliu 0:b6fdeddc0bc9 1454
allankliu 0:b6fdeddc0bc9 1455 update_V(hash_context, K, V);
allankliu 0:b6fdeddc0bc9 1456 }
allankliu 0:b6fdeddc0bc9 1457 return 0;
allankliu 0:b6fdeddc0bc9 1458 }
allankliu 0:b6fdeddc0bc9 1459
allankliu 0:b6fdeddc0bc9 1460 static bitcount_t smax(bitcount_t a, bitcount_t b) {
allankliu 0:b6fdeddc0bc9 1461 return (a > b ? a : b);
allankliu 0:b6fdeddc0bc9 1462 }
allankliu 0:b6fdeddc0bc9 1463
allankliu 0:b6fdeddc0bc9 1464 int uECC_verify(const uint8_t *public_key,
allankliu 0:b6fdeddc0bc9 1465 const uint8_t *message_hash,
allankliu 0:b6fdeddc0bc9 1466 unsigned hash_size,
allankliu 0:b6fdeddc0bc9 1467 const uint8_t *signature,
allankliu 0:b6fdeddc0bc9 1468 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1469 uECC_word_t u1[uECC_MAX_WORDS], u2[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1470 uECC_word_t z[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1471 uECC_word_t sum[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 1472 uECC_word_t rx[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1473 uECC_word_t ry[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1474 uECC_word_t tx[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1475 uECC_word_t ty[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1476 uECC_word_t tz[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1477 const uECC_word_t *points[4];
allankliu 0:b6fdeddc0bc9 1478 const uECC_word_t *point;
allankliu 0:b6fdeddc0bc9 1479 bitcount_t num_bits;
allankliu 0:b6fdeddc0bc9 1480 bitcount_t i;
allankliu 0:b6fdeddc0bc9 1481 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1482 uECC_word_t *_public = (uECC_word_t *)public_key;
allankliu 0:b6fdeddc0bc9 1483 #else
allankliu 0:b6fdeddc0bc9 1484 uECC_word_t _public[uECC_MAX_WORDS * 2];
allankliu 0:b6fdeddc0bc9 1485 #endif
allankliu 0:b6fdeddc0bc9 1486 uECC_word_t r[uECC_MAX_WORDS], s[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1487 wordcount_t num_words = curve->num_words;
allankliu 0:b6fdeddc0bc9 1488 wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 1489
allankliu 0:b6fdeddc0bc9 1490 rx[num_n_words - 1] = 0;
allankliu 0:b6fdeddc0bc9 1491 r[num_n_words - 1] = 0;
allankliu 0:b6fdeddc0bc9 1492 s[num_n_words - 1] = 0;
allankliu 0:b6fdeddc0bc9 1493
allankliu 0:b6fdeddc0bc9 1494 #if uECC_VLI_NATIVE_LITTLE_ENDIAN
allankliu 0:b6fdeddc0bc9 1495 bcopy((uint8_t *) r, signature, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1496 bcopy((uint8_t *) s, signature + curve->num_bytes, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1497 #else
allankliu 0:b6fdeddc0bc9 1498 uECC_vli_bytesToNative(_public, public_key, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1499 uECC_vli_bytesToNative(
allankliu 0:b6fdeddc0bc9 1500 _public + num_words, public_key + curve->num_bytes, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1501 uECC_vli_bytesToNative(r, signature, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1502 uECC_vli_bytesToNative(s, signature + curve->num_bytes, curve->num_bytes);
allankliu 0:b6fdeddc0bc9 1503 #endif
allankliu 0:b6fdeddc0bc9 1504
allankliu 0:b6fdeddc0bc9 1505 /* r, s must not be 0. */
allankliu 0:b6fdeddc0bc9 1506 if (uECC_vli_isZero(r, num_words) || uECC_vli_isZero(s, num_words)) {
allankliu 0:b6fdeddc0bc9 1507 return 0;
allankliu 0:b6fdeddc0bc9 1508 }
allankliu 0:b6fdeddc0bc9 1509
allankliu 0:b6fdeddc0bc9 1510 /* r, s must be < n. */
allankliu 0:b6fdeddc0bc9 1511 if (uECC_vli_cmp_unsafe(curve->n, r, num_n_words) != 1 ||
allankliu 0:b6fdeddc0bc9 1512 uECC_vli_cmp_unsafe(curve->n, s, num_n_words) != 1) {
allankliu 0:b6fdeddc0bc9 1513 return 0;
allankliu 0:b6fdeddc0bc9 1514 }
allankliu 0:b6fdeddc0bc9 1515
allankliu 0:b6fdeddc0bc9 1516 /* Calculate u1 and u2. */
allankliu 0:b6fdeddc0bc9 1517 uECC_vli_modInv(z, s, curve->n, num_n_words); /* z = 1/s */
allankliu 0:b6fdeddc0bc9 1518 u1[num_n_words - 1] = 0;
allankliu 0:b6fdeddc0bc9 1519 bits2int(u1, message_hash, hash_size, curve);
allankliu 0:b6fdeddc0bc9 1520 uECC_vli_modMult(u1, u1, z, curve->n, num_n_words); /* u1 = e/s */
allankliu 0:b6fdeddc0bc9 1521 uECC_vli_modMult(u2, r, z, curve->n, num_n_words); /* u2 = r/s */
allankliu 0:b6fdeddc0bc9 1522
allankliu 0:b6fdeddc0bc9 1523 /* Calculate sum = G + Q. */
allankliu 0:b6fdeddc0bc9 1524 uECC_vli_set(sum, _public, num_words);
allankliu 0:b6fdeddc0bc9 1525 uECC_vli_set(sum + num_words, _public + num_words, num_words);
allankliu 0:b6fdeddc0bc9 1526 uECC_vli_set(tx, curve->G, num_words);
allankliu 0:b6fdeddc0bc9 1527 uECC_vli_set(ty, curve->G + num_words, num_words);
allankliu 0:b6fdeddc0bc9 1528 uECC_vli_modSub(z, sum, tx, curve->p, num_words); /* z = x2 - x1 */
allankliu 0:b6fdeddc0bc9 1529 XYcZ_add(tx, ty, sum, sum + num_words, curve);
allankliu 0:b6fdeddc0bc9 1530 uECC_vli_modInv(z, z, curve->p, num_words); /* z = 1/z */
allankliu 0:b6fdeddc0bc9 1531 apply_z(sum, sum + num_words, z, curve);
allankliu 0:b6fdeddc0bc9 1532
allankliu 0:b6fdeddc0bc9 1533 /* Use Shamir's trick to calculate u1*G + u2*Q */
allankliu 0:b6fdeddc0bc9 1534 points[0] = 0;
allankliu 0:b6fdeddc0bc9 1535 points[1] = curve->G;
allankliu 0:b6fdeddc0bc9 1536 points[2] = _public;
allankliu 0:b6fdeddc0bc9 1537 points[3] = sum;
allankliu 0:b6fdeddc0bc9 1538 num_bits = smax(uECC_vli_numBits(u1, num_n_words),
allankliu 0:b6fdeddc0bc9 1539 uECC_vli_numBits(u2, num_n_words));
allankliu 0:b6fdeddc0bc9 1540
allankliu 0:b6fdeddc0bc9 1541 point = points[(!!uECC_vli_testBit(u1, num_bits - 1)) |
allankliu 0:b6fdeddc0bc9 1542 ((!!uECC_vli_testBit(u2, num_bits - 1)) << 1)];
allankliu 0:b6fdeddc0bc9 1543 uECC_vli_set(rx, point, num_words);
allankliu 0:b6fdeddc0bc9 1544 uECC_vli_set(ry, point + num_words, num_words);
allankliu 0:b6fdeddc0bc9 1545 uECC_vli_clear(z, num_words);
allankliu 0:b6fdeddc0bc9 1546 z[0] = 1;
allankliu 0:b6fdeddc0bc9 1547
allankliu 0:b6fdeddc0bc9 1548 for (i = num_bits - 2; i >= 0; --i) {
allankliu 0:b6fdeddc0bc9 1549 uECC_word_t index;
allankliu 0:b6fdeddc0bc9 1550 curve->double_jacobian(rx, ry, z, curve);
allankliu 0:b6fdeddc0bc9 1551
allankliu 0:b6fdeddc0bc9 1552 index = (!!uECC_vli_testBit(u1, i)) | ((!!uECC_vli_testBit(u2, i)) << 1);
allankliu 0:b6fdeddc0bc9 1553 point = points[index];
allankliu 0:b6fdeddc0bc9 1554 if (point) {
allankliu 0:b6fdeddc0bc9 1555 uECC_vli_set(tx, point, num_words);
allankliu 0:b6fdeddc0bc9 1556 uECC_vli_set(ty, point + num_words, num_words);
allankliu 0:b6fdeddc0bc9 1557 apply_z(tx, ty, z, curve);
allankliu 0:b6fdeddc0bc9 1558 uECC_vli_modSub(tz, rx, tx, curve->p, num_words); /* Z = x2 - x1 */
allankliu 0:b6fdeddc0bc9 1559 XYcZ_add(tx, ty, rx, ry, curve);
allankliu 0:b6fdeddc0bc9 1560 uECC_vli_modMult_fast(z, z, tz, curve);
allankliu 0:b6fdeddc0bc9 1561 }
allankliu 0:b6fdeddc0bc9 1562 }
allankliu 0:b6fdeddc0bc9 1563
allankliu 0:b6fdeddc0bc9 1564 uECC_vli_modInv(z, z, curve->p, num_words); /* Z = 1/Z */
allankliu 0:b6fdeddc0bc9 1565 apply_z(rx, ry, z, curve);
allankliu 0:b6fdeddc0bc9 1566
allankliu 0:b6fdeddc0bc9 1567 /* v = x1 (mod n) */
allankliu 0:b6fdeddc0bc9 1568 if (uECC_vli_cmp_unsafe(curve->n, rx, num_n_words) != 1) {
allankliu 0:b6fdeddc0bc9 1569 uECC_vli_sub(rx, rx, curve->n, num_n_words);
allankliu 0:b6fdeddc0bc9 1570 }
allankliu 0:b6fdeddc0bc9 1571
allankliu 0:b6fdeddc0bc9 1572 /* Accept only if v == r. */
allankliu 0:b6fdeddc0bc9 1573 return (int)(uECC_vli_equal(rx, r, num_words));
allankliu 0:b6fdeddc0bc9 1574 }
allankliu 0:b6fdeddc0bc9 1575
allankliu 0:b6fdeddc0bc9 1576 #if uECC_ENABLE_VLI_API
allankliu 0:b6fdeddc0bc9 1577
allankliu 0:b6fdeddc0bc9 1578 unsigned uECC_curve_num_words(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1579 return curve->num_words;
allankliu 0:b6fdeddc0bc9 1580 }
allankliu 0:b6fdeddc0bc9 1581
allankliu 0:b6fdeddc0bc9 1582 unsigned uECC_curve_num_bytes(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1583 return curve->num_bytes;
allankliu 0:b6fdeddc0bc9 1584 }
allankliu 0:b6fdeddc0bc9 1585
allankliu 0:b6fdeddc0bc9 1586 unsigned uECC_curve_num_bits(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1587 return curve->num_bytes * 8;
allankliu 0:b6fdeddc0bc9 1588 }
allankliu 0:b6fdeddc0bc9 1589
allankliu 0:b6fdeddc0bc9 1590 unsigned uECC_curve_num_n_words(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1591 return BITS_TO_WORDS(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 1592 }
allankliu 0:b6fdeddc0bc9 1593
allankliu 0:b6fdeddc0bc9 1594 unsigned uECC_curve_num_n_bytes(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1595 return BITS_TO_BYTES(curve->num_n_bits);
allankliu 0:b6fdeddc0bc9 1596 }
allankliu 0:b6fdeddc0bc9 1597
allankliu 0:b6fdeddc0bc9 1598 unsigned uECC_curve_num_n_bits(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1599 return curve->num_n_bits;
allankliu 0:b6fdeddc0bc9 1600 }
allankliu 0:b6fdeddc0bc9 1601
allankliu 0:b6fdeddc0bc9 1602 const uECC_word_t *uECC_curve_p(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1603 return curve->p;
allankliu 0:b6fdeddc0bc9 1604 }
allankliu 0:b6fdeddc0bc9 1605
allankliu 0:b6fdeddc0bc9 1606 const uECC_word_t *uECC_curve_n(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1607 return curve->n;
allankliu 0:b6fdeddc0bc9 1608 }
allankliu 0:b6fdeddc0bc9 1609
allankliu 0:b6fdeddc0bc9 1610 const uECC_word_t *uECC_curve_G(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1611 return curve->G;
allankliu 0:b6fdeddc0bc9 1612 }
allankliu 0:b6fdeddc0bc9 1613
allankliu 0:b6fdeddc0bc9 1614 const uECC_word_t *uECC_curve_b(uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1615 return curve->b;
allankliu 0:b6fdeddc0bc9 1616 }
allankliu 0:b6fdeddc0bc9 1617
allankliu 0:b6fdeddc0bc9 1618 #if uECC_SUPPORT_COMPRESSED_POINT
allankliu 0:b6fdeddc0bc9 1619 void uECC_vli_mod_sqrt(uECC_word_t *a, uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1620 curve->mod_sqrt(a, curve);
allankliu 0:b6fdeddc0bc9 1621 }
allankliu 0:b6fdeddc0bc9 1622 #endif
allankliu 0:b6fdeddc0bc9 1623
allankliu 0:b6fdeddc0bc9 1624 void uECC_vli_mmod_fast(uECC_word_t *result, uECC_word_t *product, uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1625 #if (uECC_OPTIMIZATION_LEVEL > 0)
allankliu 0:b6fdeddc0bc9 1626 curve->mmod_fast(result, product);
allankliu 0:b6fdeddc0bc9 1627 #else
allankliu 0:b6fdeddc0bc9 1628 uECC_vli_mmod(result, product, curve->p, curve->num_words);
allankliu 0:b6fdeddc0bc9 1629 #endif
allankliu 0:b6fdeddc0bc9 1630 }
allankliu 0:b6fdeddc0bc9 1631
allankliu 0:b6fdeddc0bc9 1632 void uECC_point_mult(uECC_word_t *result,
allankliu 0:b6fdeddc0bc9 1633 const uECC_word_t *point,
allankliu 0:b6fdeddc0bc9 1634 const uECC_word_t *scalar,
allankliu 0:b6fdeddc0bc9 1635 uECC_Curve curve) {
allankliu 0:b6fdeddc0bc9 1636 uECC_word_t tmp1[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1637 uECC_word_t tmp2[uECC_MAX_WORDS];
allankliu 0:b6fdeddc0bc9 1638 uECC_word_t *p2[2] = {tmp1, tmp2};
allankliu 0:b6fdeddc0bc9 1639 uECC_word_t carry = regularize_k(scalar, tmp1, tmp2, curve);
allankliu 0:b6fdeddc0bc9 1640
allankliu 0:b6fdeddc0bc9 1641 EccPoint_mult(result, point, p2[!carry], 0, curve->num_n_bits + 1, curve);
allankliu 0:b6fdeddc0bc9 1642 }
allankliu 0:b6fdeddc0bc9 1643
allankliu 0:b6fdeddc0bc9 1644 #endif /* uECC_ENABLE_VLI_API */