Kai Liu
micro-ECC for mbed, ported from GCC version from Github,
Dependents: mbed_microECC Wallet_v1
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uECC.cpp
00001 /* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */ 00002 00003 #include "uECC.h" 00004 #include "uECC_vli.h" 00005 00006 #ifndef uECC_RNG_MAX_TRIES 00007 #define uECC_RNG_MAX_TRIES 64 00008 #endif 00009 00010 #if uECC_ENABLE_VLI_API 00011 #define uECC_VLI_API 00012 #else 00013 #define uECC_VLI_API static 00014 #endif 00015 00016 #define CONCATX(a, ...) a ## __VA_ARGS__ 00017 #define CONCAT(a, ...) CONCATX(a, __VA_ARGS__) 00018 00019 #define STRX(a) #a 00020 #define STR(a) STRX(a) 00021 00022 #define EVAL(...) EVAL1(EVAL1(EVAL1(EVAL1(__VA_ARGS__)))) 00023 #define EVAL1(...) EVAL2(EVAL2(EVAL2(EVAL2(__VA_ARGS__)))) 00024 #define EVAL2(...) EVAL3(EVAL3(EVAL3(EVAL3(__VA_ARGS__)))) 00025 #define EVAL3(...) EVAL4(EVAL4(EVAL4(EVAL4(__VA_ARGS__)))) 00026 #define EVAL4(...) __VA_ARGS__ 00027 00028 #define DEC_1 0 00029 #define DEC_2 1 00030 #define DEC_3 2 00031 #define DEC_4 3 00032 #define DEC_5 4 00033 #define DEC_6 5 00034 #define DEC_7 6 00035 #define DEC_8 7 00036 #define DEC_9 8 00037 #define DEC_10 9 00038 #define DEC_11 10 00039 #define DEC_12 11 00040 #define DEC_13 12 00041 #define DEC_14 13 00042 #define DEC_15 14 00043 #define DEC_16 15 00044 #define DEC_17 16 00045 #define DEC_18 17 00046 #define DEC_19 18 00047 #define DEC_20 19 00048 #define DEC_21 20 00049 #define DEC_22 21 00050 #define DEC_23 22 00051 #define DEC_24 23 00052 #define DEC_25 24 00053 #define DEC_26 25 00054 #define DEC_27 26 00055 #define DEC_28 27 00056 #define DEC_29 28 00057 #define DEC_30 29 00058 #define DEC_31 30 00059 #define DEC_32 31 00060 00061 #define DEC(N) CONCAT(DEC_, N) 00062 00063 #define SECOND_ARG(_, val, ...) val 00064 #define SOME_CHECK_0 ~, 0 00065 #define GET_SECOND_ARG(...) SECOND_ARG(__VA_ARGS__, SOME,) 00066 #define SOME_OR_0(N) GET_SECOND_ARG(CONCAT(SOME_CHECK_, N)) 00067 00068 #define EMPTY(...) 00069 #define DEFER(...) __VA_ARGS__ EMPTY() 00070 00071 #define REPEAT_NAME_0() REPEAT_0 00072 #define REPEAT_NAME_SOME() REPEAT_SOME 00073 #define REPEAT_0(...) 00074 #define REPEAT_SOME(N, stuff) DEFER(CONCAT(REPEAT_NAME_, SOME_OR_0(DEC(N))))()(DEC(N), stuff) stuff 00075 #define REPEAT(N, stuff) EVAL(REPEAT_SOME(N, stuff)) 00076 00077 #define REPEATM_NAME_0() REPEATM_0 00078 #define REPEATM_NAME_SOME() REPEATM_SOME 00079 #define REPEATM_0(...) 00080 #define REPEATM_SOME(N, macro) macro(N) \ 00081 DEFER(CONCAT(REPEATM_NAME_, SOME_OR_0(DEC(N))))()(DEC(N), macro) 00082 #define REPEATM(N, macro) EVAL(REPEATM_SOME(N, macro)) 00083 00084 //#include "platform-specific.inc" 00085 #include "platform-specific.h" 00086 00087 #if (uECC_WORD_SIZE == 1) 00088 #if uECC_SUPPORTS_secp160r1 00089 #define uECC_MAX_WORDS 21 /* Due to the size of curve_n. */ 00090 #endif 00091 #if uECC_SUPPORTS_secp192r1 00092 #undef uECC_MAX_WORDS 00093 #define uECC_MAX_WORDS 24 00094 #endif 00095 #if uECC_SUPPORTS_secp224r1 00096 #undef uECC_MAX_WORDS 00097 #define uECC_MAX_WORDS 28 00098 #endif 00099 #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1) 00100 #undef uECC_MAX_WORDS 00101 #define uECC_MAX_WORDS 32 00102 #endif 00103 #elif (uECC_WORD_SIZE == 4) 00104 #if uECC_SUPPORTS_secp160r1 00105 #define uECC_MAX_WORDS 6 /* Due to the size of curve_n. */ 00106 #endif 00107 #if uECC_SUPPORTS_secp192r1 00108 #undef uECC_MAX_WORDS 00109 #define uECC_MAX_WORDS 6 00110 #endif 00111 #if uECC_SUPPORTS_secp224r1 00112 #undef uECC_MAX_WORDS 00113 #define uECC_MAX_WORDS 7 00114 #endif 00115 #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1) 00116 #undef uECC_MAX_WORDS 00117 #define uECC_MAX_WORDS 8 00118 #endif 00119 #elif (uECC_WORD_SIZE == 8) 00120 #if uECC_SUPPORTS_secp160r1 00121 #define uECC_MAX_WORDS 3 00122 #endif 00123 #if uECC_SUPPORTS_secp192r1 00124 #undef uECC_MAX_WORDS 00125 #define uECC_MAX_WORDS 3 00126 #endif 00127 #if uECC_SUPPORTS_secp224r1 00128 #undef uECC_MAX_WORDS 00129 #define uECC_MAX_WORDS 4 00130 #endif 00131 #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1) 00132 #undef uECC_MAX_WORDS 00133 #define uECC_MAX_WORDS 4 00134 #endif 00135 #endif /* uECC_WORD_SIZE */ 00136 00137 #define BITS_TO_WORDS(num_bits) ((num_bits + ((uECC_WORD_SIZE * 8) - 1)) / (uECC_WORD_SIZE * 8)) 00138 #define BITS_TO_BYTES(num_bits) ((num_bits + 7) / 8) 00139 00140 struct uECC_Curve_t { 00141 wordcount_t num_words; 00142 wordcount_t num_bytes; 00143 bitcount_t num_n_bits; 00144 uECC_word_t p[uECC_MAX_WORDS]; 00145 uECC_word_t n[uECC_MAX_WORDS]; 00146 uECC_word_t G[uECC_MAX_WORDS * 2]; 00147 uECC_word_t b[uECC_MAX_WORDS]; 00148 void (*double_jacobian)(uECC_word_t * X1, 00149 uECC_word_t * Y1, 00150 uECC_word_t * Z1, 00151 uECC_Curve curve); 00152 #if uECC_SUPPORT_COMPRESSED_POINT 00153 void (*mod_sqrt)(uECC_word_t *a, uECC_Curve curve); 00154 #endif 00155 void (*x_side)(uECC_word_t *result, const uECC_word_t *x, uECC_Curve curve); 00156 #if (uECC_OPTIMIZATION_LEVEL > 0) 00157 void (*mmod_fast)(uECC_word_t *result, uECC_word_t *product); 00158 #endif 00159 }; 00160 00161 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 00162 static void bcopy(uint8_t *dst, 00163 const uint8_t *src, 00164 unsigned num_bytes) { 00165 while (0 != num_bytes) { 00166 num_bytes--; 00167 dst[num_bytes] = src[num_bytes]; 00168 } 00169 } 00170 #endif 00171 00172 static cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left, 00173 const uECC_word_t *right, 00174 wordcount_t num_words); 00175 00176 #if (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb || \ 00177 uECC_PLATFORM == uECC_arm_thumb2) 00178 //#include "asm_arm.inc" 00179 #include "asm_arm.h" 00180 #if (uECC_PLATFORM == uECC_arm) 00181 #warning uECC_arm 00182 #elif (uECC_PLATFORM == uECC_arm_thumb) 00183 #warning uECC_arm_thumb 00184 #elif (uECC_PLATFORM == uECC_arm_thumb2) 00185 #warning uECC_arm_thumb2 00186 #endif 00187 #endif 00188 00189 #if (uECC_PLATFORM == uECC_avr) 00190 #include "asm_avr.inc" 00191 #endif 00192 00193 #if default_RNG_defined 00194 static uECC_RNG_Function g_rng_function = &default_RNG; 00195 #else 00196 static uECC_RNG_Function g_rng_function = 0; 00197 #endif 00198 00199 void uECC_set_rng(uECC_RNG_Function rng_function) { 00200 g_rng_function = rng_function; 00201 } 00202 00203 uECC_RNG_Function uECC_get_rng(void) { 00204 return g_rng_function; 00205 } 00206 00207 int uECC_curve_private_key_size(uECC_Curve curve) { 00208 return BITS_TO_BYTES(curve->num_n_bits); 00209 } 00210 00211 int uECC_curve_public_key_size(uECC_Curve curve) { 00212 return 2 * curve->num_bytes; 00213 } 00214 00215 #if !asm_clear 00216 uECC_VLI_API void uECC_vli_clear(uECC_word_t *vli, wordcount_t num_words) { 00217 wordcount_t i; 00218 for (i = 0; i < num_words; ++i) { 00219 vli[i] = 0; 00220 } 00221 } 00222 #endif /* !asm_clear */ 00223 00224 /* Constant-time comparison to zero - secure way to compare long integers */ 00225 /* Returns 1 if vli == 0, 0 otherwise. */ 00226 uECC_VLI_API uECC_word_t uECC_vli_isZero(const uECC_word_t *vli, wordcount_t num_words) { 00227 uECC_word_t bits = 0; 00228 wordcount_t i; 00229 for (i = 0; i < num_words; ++i) { 00230 bits |= vli[i]; 00231 } 00232 return (bits == 0); 00233 } 00234 00235 /* Returns nonzero if bit 'bit' of vli is set. */ 00236 uECC_VLI_API uECC_word_t uECC_vli_testBit(const uECC_word_t *vli, bitcount_t bit) { 00237 return (vli[bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK))); 00238 } 00239 00240 /* Counts the number of words in vli. */ 00241 static wordcount_t vli_numDigits(const uECC_word_t *vli, const wordcount_t max_words) { 00242 wordcount_t i; 00243 /* Search from the end until we find a non-zero digit. 00244 We do it in reverse because we expect that most digits will be nonzero. */ 00245 for (i = max_words - 1; i >= 0 && vli[i] == 0; --i) { 00246 } 00247 00248 return (i + 1); 00249 } 00250 00251 /* Counts the number of bits required to represent vli. */ 00252 uECC_VLI_API bitcount_t uECC_vli_numBits(const uECC_word_t *vli, const wordcount_t max_words) { 00253 uECC_word_t i; 00254 uECC_word_t digit; 00255 00256 wordcount_t num_digits = vli_numDigits(vli, max_words); 00257 if (num_digits == 0) { 00258 return 0; 00259 } 00260 00261 digit = vli[num_digits - 1]; 00262 for (i = 0; digit; ++i) { 00263 digit >>= 1; 00264 } 00265 00266 return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i); 00267 } 00268 00269 /* Sets dest = src. */ 00270 #if !asm_set 00271 uECC_VLI_API void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src, wordcount_t num_words) { 00272 wordcount_t i; 00273 for (i = 0; i < num_words; ++i) { 00274 dest[i] = src[i]; 00275 } 00276 } 00277 #endif /* !asm_set */ 00278 00279 /* Returns sign of left - right. */ 00280 static cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left, 00281 const uECC_word_t *right, 00282 wordcount_t num_words) { 00283 wordcount_t i; 00284 for (i = num_words - 1; i >= 0; --i) { 00285 if (left[i] > right[i]) { 00286 return 1; 00287 } else if (left[i] < right[i]) { 00288 return -1; 00289 } 00290 } 00291 return 0; 00292 } 00293 00294 /* Constant-time comparison function - secure way to compare long integers */ 00295 /* Returns one if left == right, zero otherwise. */ 00296 uECC_VLI_API uECC_word_t uECC_vli_equal(const uECC_word_t *left, 00297 const uECC_word_t *right, 00298 wordcount_t num_words) { 00299 uECC_word_t diff = 0; 00300 wordcount_t i; 00301 for (i = num_words - 1; i >= 0; --i) { 00302 diff |= (left[i] ^ right[i]); 00303 } 00304 return (diff == 0); 00305 } 00306 00307 uECC_VLI_API uECC_word_t uECC_vli_sub(uECC_word_t *result, 00308 const uECC_word_t *left, 00309 const uECC_word_t *right, 00310 wordcount_t num_words); 00311 00312 /* Returns sign of left - right, in constant time. */ 00313 uECC_VLI_API cmpresult_t uECC_vli_cmp(const uECC_word_t *left, 00314 const uECC_word_t *right, 00315 wordcount_t num_words) { 00316 uECC_word_t tmp[uECC_MAX_WORDS]; 00317 uECC_word_t neg = !!uECC_vli_sub(tmp, left, right, num_words); 00318 uECC_word_t equal = uECC_vli_isZero(tmp, num_words); 00319 return (!equal - 2 * neg); 00320 } 00321 00322 /* Computes vli = vli >> 1. */ 00323 #if !asm_rshift1 00324 uECC_VLI_API void uECC_vli_rshift1(uECC_word_t *vli, wordcount_t num_words) { 00325 uECC_word_t *end = vli; 00326 uECC_word_t carry = 0; 00327 00328 vli += num_words; 00329 while (vli-- > end) { 00330 uECC_word_t temp = *vli; 00331 *vli = (temp >> 1) | carry; 00332 carry = temp << (uECC_WORD_BITS - 1); 00333 } 00334 } 00335 #endif /* !asm_rshift1 */ 00336 00337 /* Computes result = left + right, returning carry. Can modify in place. */ 00338 #if !asm_add 00339 uECC_VLI_API uECC_word_t uECC_vli_add(uECC_word_t *result, 00340 const uECC_word_t *left, 00341 const uECC_word_t *right, 00342 wordcount_t num_words) { 00343 uECC_word_t carry = 0; 00344 wordcount_t i; 00345 for (i = 0; i < num_words; ++i) { 00346 uECC_word_t sum = left[i] + right[i] + carry; 00347 if (sum != left[i]) { 00348 carry = (sum < left[i]); 00349 } 00350 result[i] = sum; 00351 } 00352 return carry; 00353 } 00354 #endif /* !asm_add */ 00355 00356 /* Computes result = left - right, returning borrow. Can modify in place. */ 00357 #if !asm_sub 00358 uECC_VLI_API uECC_word_t uECC_vli_sub(uECC_word_t *result, 00359 const uECC_word_t *left, 00360 const uECC_word_t *right, 00361 wordcount_t num_words) { 00362 uECC_word_t borrow = 0; 00363 wordcount_t i; 00364 for (i = 0; i < num_words; ++i) { 00365 uECC_word_t diff = left[i] - right[i] - borrow; 00366 if (diff != left[i]) { 00367 borrow = (diff > left[i]); 00368 } 00369 result[i] = diff; 00370 } 00371 return borrow; 00372 } 00373 #endif /* !asm_sub */ 00374 00375 #if !asm_mult || (uECC_SQUARE_FUNC && !asm_square) || \ 00376 (uECC_SUPPORTS_secp256k1 && (uECC_OPTIMIZATION_LEVEL > 0) && \ 00377 ((uECC_WORD_SIZE == 1) || (uECC_WORD_SIZE == 8))) 00378 static void muladd(uECC_word_t a, 00379 uECC_word_t b, 00380 uECC_word_t *r0, 00381 uECC_word_t *r1, 00382 uECC_word_t *r2) { 00383 #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128 00384 uint64_t a0 = a & 0xffffffffull; 00385 uint64_t a1 = a >> 32; 00386 uint64_t b0 = b & 0xffffffffull; 00387 uint64_t b1 = b >> 32; 00388 00389 uint64_t i0 = a0 * b0; 00390 uint64_t i1 = a0 * b1; 00391 uint64_t i2 = a1 * b0; 00392 uint64_t i3 = a1 * b1; 00393 00394 uint64_t p0, p1; 00395 00396 i2 += (i0 >> 32); 00397 i2 += i1; 00398 if (i2 < i1) { /* overflow */ 00399 i3 += 0x100000000ull; 00400 } 00401 00402 p0 = (i0 & 0xffffffffull) | (i2 << 32); 00403 p1 = i3 + (i2 >> 32); 00404 00405 *r0 += p0; 00406 *r1 += (p1 + (*r0 < p0)); 00407 *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0)); 00408 #else 00409 uECC_dword_t p = (uECC_dword_t)a * b; 00410 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; 00411 r01 += p; 00412 *r2 += (r01 < p); 00413 *r1 = r01 >> uECC_WORD_BITS; 00414 *r0 = (uECC_word_t)r01; 00415 #endif 00416 } 00417 #endif /* muladd needed */ 00418 00419 #if !asm_mult 00420 uECC_VLI_API void uECC_vli_mult(uECC_word_t *result, 00421 const uECC_word_t *left, 00422 const uECC_word_t *right, 00423 wordcount_t num_words) { 00424 uECC_word_t r0 = 0; 00425 uECC_word_t r1 = 0; 00426 uECC_word_t r2 = 0; 00427 wordcount_t i, k; 00428 00429 /* Compute each digit of result in sequence, maintaining the carries. */ 00430 for (k = 0; k < num_words; ++k) { 00431 for (i = 0; i <= k; ++i) { 00432 muladd(left[i], right[k - i], &r0, &r1, &r2); 00433 } 00434 result[k] = r0; 00435 r0 = r1; 00436 r1 = r2; 00437 r2 = 0; 00438 } 00439 for (k = num_words; k < num_words * 2 - 1; ++k) { 00440 for (i = (k + 1) - num_words; i < num_words; ++i) { 00441 muladd(left[i], right[k - i], &r0, &r1, &r2); 00442 } 00443 result[k] = r0; 00444 r0 = r1; 00445 r1 = r2; 00446 r2 = 0; 00447 } 00448 result[num_words * 2 - 1] = r0; 00449 } 00450 #endif /* !asm_mult */ 00451 00452 #if uECC_SQUARE_FUNC 00453 00454 #if !asm_square 00455 static void mul2add(uECC_word_t a, 00456 uECC_word_t b, 00457 uECC_word_t *r0, 00458 uECC_word_t *r1, 00459 uECC_word_t *r2) { 00460 #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128 00461 uint64_t a0 = a & 0xffffffffull; 00462 uint64_t a1 = a >> 32; 00463 uint64_t b0 = b & 0xffffffffull; 00464 uint64_t b1 = b >> 32; 00465 00466 uint64_t i0 = a0 * b0; 00467 uint64_t i1 = a0 * b1; 00468 uint64_t i2 = a1 * b0; 00469 uint64_t i3 = a1 * b1; 00470 00471 uint64_t p0, p1; 00472 00473 i2 += (i0 >> 32); 00474 i2 += i1; 00475 if (i2 < i1) 00476 { /* overflow */ 00477 i3 += 0x100000000ull; 00478 } 00479 00480 p0 = (i0 & 0xffffffffull) | (i2 << 32); 00481 p1 = i3 + (i2 >> 32); 00482 00483 *r2 += (p1 >> 63); 00484 p1 = (p1 << 1) | (p0 >> 63); 00485 p0 <<= 1; 00486 00487 *r0 += p0; 00488 *r1 += (p1 + (*r0 < p0)); 00489 *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0)); 00490 #else 00491 uECC_dword_t p = (uECC_dword_t)a * b; 00492 uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; 00493 *r2 += (p >> (uECC_WORD_BITS * 2 - 1)); 00494 p *= 2; 00495 r01 += p; 00496 *r2 += (r01 < p); 00497 *r1 = r01 >> uECC_WORD_BITS; 00498 *r0 = (uECC_word_t)r01; 00499 #endif 00500 } 00501 00502 uECC_VLI_API void uECC_vli_square(uECC_word_t *result, 00503 const uECC_word_t *left, 00504 wordcount_t num_words) { 00505 uECC_word_t r0 = 0; 00506 uECC_word_t r1 = 0; 00507 uECC_word_t r2 = 0; 00508 00509 wordcount_t i, k; 00510 00511 for (k = 0; k < num_words * 2 - 1; ++k) { 00512 uECC_word_t min = (k < num_words ? 0 : (k + 1) - num_words); 00513 for (i = min; i <= k && i <= k - i; ++i) { 00514 if (i < k-i) { 00515 mul2add(left[i], left[k - i], &r0, &r1, &r2); 00516 } else { 00517 muladd(left[i], left[k - i], &r0, &r1, &r2); 00518 } 00519 } 00520 result[k] = r0; 00521 r0 = r1; 00522 r1 = r2; 00523 r2 = 0; 00524 } 00525 00526 result[num_words * 2 - 1] = r0; 00527 } 00528 #endif /* !asm_square */ 00529 00530 #else /* uECC_SQUARE_FUNC */ 00531 00532 #if uECC_ENABLE_VLI_API 00533 uECC_VLI_API void uECC_vli_square(uECC_word_t *result, 00534 const uECC_word_t *left, 00535 wordcount_t num_words) { 00536 uECC_vli_mult(result, left, left, num_words); 00537 } 00538 #endif /* uECC_ENABLE_VLI_API */ 00539 00540 #endif /* uECC_SQUARE_FUNC */ 00541 00542 /* Computes result = (left + right) % mod. 00543 Assumes that left < mod and right < mod, and that result does not overlap mod. */ 00544 uECC_VLI_API void uECC_vli_modAdd(uECC_word_t *result, 00545 const uECC_word_t *left, 00546 const uECC_word_t *right, 00547 const uECC_word_t *mod, 00548 wordcount_t num_words) { 00549 uECC_word_t carry = uECC_vli_add(result, left, right, num_words); 00550 if (carry || uECC_vli_cmp_unsafe(mod, result, num_words) != 1) { 00551 /* result > mod (result = mod + remainder), so subtract mod to get remainder. */ 00552 uECC_vli_sub(result, result, mod, num_words); 00553 } 00554 } 00555 00556 /* Computes result = (left - right) % mod. 00557 Assumes that left < mod and right < mod, and that result does not overlap mod. */ 00558 uECC_VLI_API void uECC_vli_modSub(uECC_word_t *result, 00559 const uECC_word_t *left, 00560 const uECC_word_t *right, 00561 const uECC_word_t *mod, 00562 wordcount_t num_words) { 00563 uECC_word_t l_borrow = uECC_vli_sub(result, left, right, num_words); 00564 if (l_borrow) { 00565 /* In this case, result == -diff == (max int) - diff. Since -x % d == d - x, 00566 we can get the correct result from result + mod (with overflow). */ 00567 uECC_vli_add(result, result, mod, num_words); 00568 } 00569 } 00570 00571 /* Computes result = product % mod, where product is 2N words long. */ 00572 /* Currently only designed to work for curve_p or curve_n. */ 00573 uECC_VLI_API void uECC_vli_mmod(uECC_word_t *result, 00574 uECC_word_t *product, 00575 const uECC_word_t *mod, 00576 wordcount_t num_words) { 00577 uECC_word_t mod_multiple[2 * uECC_MAX_WORDS]; 00578 uECC_word_t tmp[2 * uECC_MAX_WORDS]; 00579 uECC_word_t *v[2] = {tmp, product}; 00580 uECC_word_t index; 00581 00582 /* Shift mod so its highest set bit is at the maximum position. */ 00583 bitcount_t shift = (num_words * 2 * uECC_WORD_BITS) - uECC_vli_numBits(mod, num_words); 00584 wordcount_t word_shift = shift / uECC_WORD_BITS; 00585 wordcount_t bit_shift = shift % uECC_WORD_BITS; 00586 uECC_word_t carry = 0; 00587 uECC_vli_clear(mod_multiple, word_shift); 00588 if (bit_shift > 0) { 00589 for(index = 0; index < (uECC_word_t)num_words; ++index) { 00590 mod_multiple[word_shift + index] = (mod[index] << bit_shift) | carry; 00591 carry = mod[index] >> (uECC_WORD_BITS - bit_shift); 00592 } 00593 } else { 00594 uECC_vli_set(mod_multiple + word_shift, mod, num_words); 00595 } 00596 00597 for (index = 1; shift >= 0; --shift) { 00598 uECC_word_t borrow = 0; 00599 wordcount_t i; 00600 for (i = 0; i < num_words * 2; ++i) { 00601 uECC_word_t diff = v[index][i] - mod_multiple[i] - borrow; 00602 if (diff != v[index][i]) { 00603 borrow = (diff > v[index][i]); 00604 } 00605 v[1 - index][i] = diff; 00606 } 00607 index = !(index ^ borrow); /* Swap the index if there was no borrow */ 00608 uECC_vli_rshift1(mod_multiple, num_words); 00609 mod_multiple[num_words - 1] |= mod_multiple[num_words] << (uECC_WORD_BITS - 1); 00610 uECC_vli_rshift1(mod_multiple + num_words, num_words); 00611 } 00612 uECC_vli_set(result, v[index], num_words); 00613 } 00614 00615 /* Computes result = (left * right) % mod. */ 00616 uECC_VLI_API void uECC_vli_modMult(uECC_word_t *result, 00617 const uECC_word_t *left, 00618 const uECC_word_t *right, 00619 const uECC_word_t *mod, 00620 wordcount_t num_words) { 00621 uECC_word_t product[2 * uECC_MAX_WORDS]; 00622 uECC_vli_mult(product, left, right, num_words); 00623 uECC_vli_mmod(result, product, mod, num_words); 00624 } 00625 00626 uECC_VLI_API void uECC_vli_modMult_fast(uECC_word_t *result, 00627 const uECC_word_t *left, 00628 const uECC_word_t *right, 00629 uECC_Curve curve) { 00630 uECC_word_t product[2 * uECC_MAX_WORDS]; 00631 uECC_vli_mult(product, left, right, curve->num_words); 00632 #if (uECC_OPTIMIZATION_LEVEL > 0) 00633 curve->mmod_fast(result, product); 00634 #else 00635 uECC_vli_mmod(result, product, curve->p, curve->num_words); 00636 #endif 00637 } 00638 00639 #if uECC_SQUARE_FUNC 00640 00641 #if uECC_ENABLE_VLI_API 00642 /* Computes result = left^2 % mod. */ 00643 uECC_VLI_API void uECC_vli_modSquare(uECC_word_t *result, 00644 const uECC_word_t *left, 00645 const uECC_word_t *mod, 00646 wordcount_t num_words) { 00647 uECC_word_t product[2 * uECC_MAX_WORDS]; 00648 uECC_vli_square(product, left, num_words); 00649 uECC_vli_mmod(result, product, mod, num_words); 00650 } 00651 #endif /* uECC_ENABLE_VLI_API */ 00652 00653 uECC_VLI_API void uECC_vli_modSquare_fast(uECC_word_t *result, 00654 const uECC_word_t *left, 00655 uECC_Curve curve) { 00656 uECC_word_t product[2 * uECC_MAX_WORDS]; 00657 uECC_vli_square(product, left, curve->num_words); 00658 #if (uECC_OPTIMIZATION_LEVEL > 0) 00659 curve->mmod_fast(result, product); 00660 #else 00661 uECC_vli_mmod(result, product, curve->p, curve->num_words); 00662 #endif 00663 } 00664 00665 #else /* uECC_SQUARE_FUNC */ 00666 00667 #if uECC_ENABLE_VLI_API 00668 uECC_VLI_API void uECC_vli_modSquare(uECC_word_t *result, 00669 const uECC_word_t *left, 00670 const uECC_word_t *mod, 00671 wordcount_t num_words) { 00672 uECC_vli_modMult(result, left, left, mod, num_words); 00673 } 00674 #endif /* uECC_ENABLE_VLI_API */ 00675 00676 uECC_VLI_API void uECC_vli_modSquare_fast(uECC_word_t *result, 00677 const uECC_word_t *left, 00678 uECC_Curve curve) { 00679 uECC_vli_modMult_fast(result, left, left, curve); 00680 } 00681 00682 #endif /* uECC_SQUARE_FUNC */ 00683 00684 #define EVEN(vli) (!(vli[0] & 1)) 00685 static void vli_modInv_update(uECC_word_t *uv, 00686 const uECC_word_t *mod, 00687 wordcount_t num_words) { 00688 uECC_word_t carry = 0; 00689 if (!EVEN(uv)) { 00690 carry = uECC_vli_add(uv, uv, mod, num_words); 00691 } 00692 uECC_vli_rshift1(uv, num_words); 00693 if (carry) { 00694 uv[num_words - 1] |= HIGH_BIT_SET; 00695 } 00696 } 00697 00698 /* Computes result = (1 / input) % mod. All VLIs are the same size. 00699 See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" */ 00700 uECC_VLI_API void uECC_vli_modInv(uECC_word_t *result, 00701 const uECC_word_t *input, 00702 const uECC_word_t *mod, 00703 wordcount_t num_words) { 00704 uECC_word_t a[uECC_MAX_WORDS], b[uECC_MAX_WORDS], u[uECC_MAX_WORDS], v[uECC_MAX_WORDS]; 00705 cmpresult_t cmpResult; 00706 00707 if (uECC_vli_isZero(input, num_words)) { 00708 uECC_vli_clear(result, num_words); 00709 return; 00710 } 00711 00712 uECC_vli_set(a, input, num_words); 00713 uECC_vli_set(b, mod, num_words); 00714 uECC_vli_clear(u, num_words); 00715 u[0] = 1; 00716 uECC_vli_clear(v, num_words); 00717 while ((cmpResult = uECC_vli_cmp_unsafe(a, b, num_words)) != 0) { 00718 if (EVEN(a)) { 00719 uECC_vli_rshift1(a, num_words); 00720 vli_modInv_update(u, mod, num_words); 00721 } else if (EVEN(b)) { 00722 uECC_vli_rshift1(b, num_words); 00723 vli_modInv_update(v, mod, num_words); 00724 } else if (cmpResult > 0) { 00725 uECC_vli_sub(a, a, b, num_words); 00726 uECC_vli_rshift1(a, num_words); 00727 if (uECC_vli_cmp_unsafe(u, v, num_words) < 0) { 00728 uECC_vli_add(u, u, mod, num_words); 00729 } 00730 uECC_vli_sub(u, u, v, num_words); 00731 vli_modInv_update(u, mod, num_words); 00732 } else { 00733 uECC_vli_sub(b, b, a, num_words); 00734 uECC_vli_rshift1(b, num_words); 00735 if (uECC_vli_cmp_unsafe(v, u, num_words) < 0) { 00736 uECC_vli_add(v, v, mod, num_words); 00737 } 00738 uECC_vli_sub(v, v, u, num_words); 00739 vli_modInv_update(v, mod, num_words); 00740 } 00741 } 00742 uECC_vli_set(result, u, num_words); 00743 } 00744 00745 /* ------ Point operations ------ */ 00746 00747 //#include "curve-specific.inc" 00748 #include "curve-specific.h" 00749 00750 /* Returns 1 if 'point' is the point at infinity, 0 otherwise. */ 00751 #define EccPoint_isZero(point, curve) uECC_vli_isZero((point), (curve)->num_words * 2) 00752 00753 /* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates. 00754 From http://eprint.iacr.org/2011/338.pdf 00755 */ 00756 00757 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ 00758 static void apply_z(uECC_word_t * X1, 00759 uECC_word_t * Y1, 00760 const uECC_word_t * const Z, 00761 uECC_Curve curve) { 00762 uECC_word_t t1[uECC_MAX_WORDS]; 00763 00764 uECC_vli_modSquare_fast(t1, Z, curve); /* z^2 */ 00765 uECC_vli_modMult_fast(X1, X1, t1, curve); /* x1 * z^2 */ 00766 uECC_vli_modMult_fast(t1, t1, Z, curve); /* z^3 */ 00767 uECC_vli_modMult_fast(Y1, Y1, t1, curve); /* y1 * z^3 */ 00768 } 00769 00770 /* P = (x1, y1) => 2P, (x2, y2) => P' */ 00771 static void XYcZ_initial_double(uECC_word_t * X1, 00772 uECC_word_t * Y1, 00773 uECC_word_t * X2, 00774 uECC_word_t * Y2, 00775 const uECC_word_t * const initial_Z, 00776 uECC_Curve curve) { 00777 uECC_word_t z[uECC_MAX_WORDS]; 00778 wordcount_t num_words = curve->num_words; 00779 if (initial_Z) { 00780 uECC_vli_set(z, initial_Z, num_words); 00781 } else { 00782 uECC_vli_clear(z, num_words); 00783 z[0] = 1; 00784 } 00785 00786 uECC_vli_set(X2, X1, num_words); 00787 uECC_vli_set(Y2, Y1, num_words); 00788 00789 apply_z(X1, Y1, z, curve); 00790 curve->double_jacobian(X1, Y1, z, curve); 00791 apply_z(X2, Y2, z, curve); 00792 } 00793 00794 /* Input P = (x1, y1, Z), Q = (x2, y2, Z) 00795 Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) 00796 or P => P', Q => P + Q 00797 */ 00798 static void XYcZ_add(uECC_word_t * X1, 00799 uECC_word_t * Y1, 00800 uECC_word_t * X2, 00801 uECC_word_t * Y2, 00802 uECC_Curve curve) { 00803 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 00804 uECC_word_t t5[uECC_MAX_WORDS]; 00805 wordcount_t num_words = curve->num_words; 00806 00807 uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ 00808 uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ 00809 uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ 00810 uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ 00811 uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ 00812 uECC_vli_modSquare_fast(t5, Y2, curve); /* t5 = (y2 - y1)^2 = D */ 00813 00814 uECC_vli_modSub(t5, t5, X1, curve->p, num_words); /* t5 = D - B */ 00815 uECC_vli_modSub(t5, t5, X2, curve->p, num_words); /* t5 = D - B - C = x3 */ 00816 uECC_vli_modSub(X2, X2, X1, curve->p, num_words); /* t3 = C - B */ 00817 uECC_vli_modMult_fast(Y1, Y1, X2, curve); /* t2 = y1*(C - B) */ 00818 uECC_vli_modSub(X2, X1, t5, curve->p, num_words); /* t3 = B - x3 */ 00819 uECC_vli_modMult_fast(Y2, Y2, X2, curve); /* t4 = (y2 - y1)*(B - x3) */ 00820 uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y3 */ 00821 00822 uECC_vli_set(X2, t5, num_words); 00823 } 00824 00825 /* Input P = (x1, y1, Z), Q = (x2, y2, Z) 00826 Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) 00827 or P => P - Q, Q => P + Q 00828 */ 00829 static void XYcZ_addC(uECC_word_t * X1, 00830 uECC_word_t * Y1, 00831 uECC_word_t * X2, 00832 uECC_word_t * Y2, 00833 uECC_Curve curve) { 00834 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 00835 uECC_word_t t5[uECC_MAX_WORDS]; 00836 uECC_word_t t6[uECC_MAX_WORDS]; 00837 uECC_word_t t7[uECC_MAX_WORDS]; 00838 wordcount_t num_words = curve->num_words; 00839 00840 uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ 00841 uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ 00842 uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ 00843 uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ 00844 uECC_vli_modAdd(t5, Y2, Y1, curve->p, num_words); /* t5 = y2 + y1 */ 00845 uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ 00846 00847 uECC_vli_modSub(t6, X2, X1, curve->p, num_words); /* t6 = C - B */ 00848 uECC_vli_modMult_fast(Y1, Y1, t6, curve); /* t2 = y1 * (C - B) = E */ 00849 uECC_vli_modAdd(t6, X1, X2, curve->p, num_words); /* t6 = B + C */ 00850 uECC_vli_modSquare_fast(X2, Y2, curve); /* t3 = (y2 - y1)^2 = D */ 00851 uECC_vli_modSub(X2, X2, t6, curve->p, num_words); /* t3 = D - (B + C) = x3 */ 00852 00853 uECC_vli_modSub(t7, X1, X2, curve->p, num_words); /* t7 = B - x3 */ 00854 uECC_vli_modMult_fast(Y2, Y2, t7, curve); /* t4 = (y2 - y1)*(B - x3) */ 00855 uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = (y2 - y1)*(B - x3) - E = y3 */ 00856 00857 uECC_vli_modSquare_fast(t7, t5, curve); /* t7 = (y2 + y1)^2 = F */ 00858 uECC_vli_modSub(t7, t7, t6, curve->p, num_words); /* t7 = F - (B + C) = x3' */ 00859 uECC_vli_modSub(t6, t7, X1, curve->p, num_words); /* t6 = x3' - B */ 00860 uECC_vli_modMult_fast(t6, t6, t5, curve); /* t6 = (y2+y1)*(x3' - B) */ 00861 uECC_vli_modSub(Y1, t6, Y1, curve->p, num_words); /* t2 = (y2+y1)*(x3' - B) - E = y3' */ 00862 00863 uECC_vli_set(X1, t7, num_words); 00864 } 00865 00866 /* result may overlap point. */ 00867 static void EccPoint_mult(uECC_word_t * result, 00868 const uECC_word_t * point, 00869 const uECC_word_t * scalar, 00870 const uECC_word_t * initial_Z, 00871 bitcount_t num_bits, 00872 uECC_Curve curve) { 00873 /* R0 and R1 */ 00874 uECC_word_t Rx[2][uECC_MAX_WORDS]; 00875 uECC_word_t Ry[2][uECC_MAX_WORDS]; 00876 uECC_word_t z[uECC_MAX_WORDS]; 00877 bitcount_t i; 00878 uECC_word_t nb; 00879 wordcount_t num_words = curve->num_words; 00880 00881 uECC_vli_set(Rx[1], point, num_words); 00882 uECC_vli_set(Ry[1], point + num_words, num_words); 00883 00884 XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initial_Z, curve); 00885 00886 for (i = num_bits - 2; i > 0; --i) { 00887 nb = !uECC_vli_testBit(scalar, i); 00888 XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve); 00889 XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve); 00890 } 00891 00892 nb = !uECC_vli_testBit(scalar, 0); 00893 XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve); 00894 00895 /* Find final 1/Z value. */ 00896 uECC_vli_modSub(z, Rx[1], Rx[0], curve->p, num_words); /* X1 - X0 */ 00897 uECC_vli_modMult_fast(z, z, Ry[1 - nb], curve); /* Yb * (X1 - X0) */ 00898 uECC_vli_modMult_fast(z, z, point, curve); /* xP * Yb * (X1 - X0) */ 00899 uECC_vli_modInv(z, z, curve->p, num_words); /* 1 / (xP * Yb * (X1 - X0)) */ 00900 /* yP / (xP * Yb * (X1 - X0)) */ 00901 uECC_vli_modMult_fast(z, z, point + num_words, curve); 00902 uECC_vli_modMult_fast(z, z, Rx[1 - nb], curve); /* Xb * yP / (xP * Yb * (X1 - X0)) */ 00903 /* End 1/Z calculation */ 00904 00905 XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve); 00906 apply_z(Rx[0], Ry[0], z, curve); 00907 00908 uECC_vli_set(result, Rx[0], num_words); 00909 uECC_vli_set(result + num_words, Ry[0], num_words); 00910 } 00911 00912 static uECC_word_t regularize_k(const uECC_word_t * const k, 00913 uECC_word_t *k0, 00914 uECC_word_t *k1, 00915 uECC_Curve curve) { 00916 wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); 00917 bitcount_t num_n_bits = curve->num_n_bits; 00918 uECC_word_t carry = uECC_vli_add(k0, k, curve->n, num_n_words) || 00919 (num_n_bits < ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8) && 00920 uECC_vli_testBit(k0, num_n_bits)); 00921 uECC_vli_add(k1, k0, curve->n, num_n_words); 00922 return carry; 00923 } 00924 00925 static uECC_word_t EccPoint_compute_public_key(uECC_word_t *result, 00926 uECC_word_t *private_key, 00927 uECC_Curve curve) { 00928 uECC_word_t tmp1[uECC_MAX_WORDS]; 00929 uECC_word_t tmp2[uECC_MAX_WORDS]; 00930 uECC_word_t *p2[2] = {tmp1, tmp2}; 00931 uECC_word_t carry; 00932 00933 /* Regularize the bitcount for the private key so that attackers cannot use a side channel 00934 attack to learn the number of leading zeros. */ 00935 carry = regularize_k(private_key, tmp1, tmp2, curve); 00936 00937 EccPoint_mult(result, curve->G, p2[!carry], 0, curve->num_n_bits + 1, curve); 00938 00939 if (EccPoint_isZero(result, curve)) { 00940 return 0; 00941 } 00942 return 1; 00943 } 00944 00945 #if uECC_WORD_SIZE == 1 00946 00947 uECC_VLI_API void uECC_vli_nativeToBytes(uint8_t *bytes, 00948 int num_bytes, 00949 const uint8_t *native) { 00950 wordcount_t i; 00951 for (i = 0; i < num_bytes; ++i) { 00952 bytes[i] = native[(num_bytes - 1) - i]; 00953 } 00954 } 00955 00956 uECC_VLI_API void uECC_vli_bytesToNative(uint8_t *native, 00957 const uint8_t *bytes, 00958 int num_bytes) { 00959 uECC_vli_nativeToBytes(native, num_bytes, bytes); 00960 } 00961 00962 #else 00963 00964 uECC_VLI_API void uECC_vli_nativeToBytes(uint8_t *bytes, 00965 int num_bytes, 00966 const uECC_word_t *native) { 00967 wordcount_t i; 00968 for (i = 0; i < num_bytes; ++i) { 00969 unsigned b = num_bytes - 1 - i; 00970 bytes[i] = native[b / uECC_WORD_SIZE] >> (8 * (b % uECC_WORD_SIZE)); 00971 } 00972 } 00973 00974 uECC_VLI_API void uECC_vli_bytesToNative(uECC_word_t *native, 00975 const uint8_t *bytes, 00976 int num_bytes) { 00977 wordcount_t i; 00978 uECC_vli_clear(native, (num_bytes + (uECC_WORD_SIZE - 1)) / uECC_WORD_SIZE); 00979 for (i = 0; i < num_bytes; ++i) { 00980 unsigned b = num_bytes - 1 - i; 00981 native[b / uECC_WORD_SIZE] |= 00982 (uECC_word_t)bytes[i] << (8 * (b % uECC_WORD_SIZE)); 00983 } 00984 } 00985 00986 #endif /* uECC_WORD_SIZE */ 00987 00988 /* Generates a random integer in the range 0 < random < top. 00989 Both random and top have num_words words. */ 00990 uECC_VLI_API int uECC_generate_random_int(uECC_word_t *random, 00991 const uECC_word_t *top, 00992 wordcount_t num_words) { 00993 uECC_word_t mask = (uECC_word_t)-1; 00994 uECC_word_t tries; 00995 bitcount_t num_bits = uECC_vli_numBits(top, num_words); 00996 00997 if (!g_rng_function) { 00998 return 0; 00999 } 01000 01001 for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { 01002 if (!g_rng_function((uint8_t *)random, num_words * uECC_WORD_SIZE)) { 01003 return 0; 01004 } 01005 random[num_words - 1] &= mask >> ((bitcount_t)(num_words * uECC_WORD_SIZE * 8 - num_bits)); 01006 if (!uECC_vli_isZero(random, num_words) && 01007 uECC_vli_cmp(top, random, num_words) == 1) { 01008 return 1; 01009 } 01010 } 01011 return 0; 01012 } 01013 01014 int uECC_make_key(uint8_t *public_key, 01015 uint8_t *private_key, 01016 uECC_Curve curve) { 01017 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01018 uECC_word_t *_private = (uECC_word_t *)private_key; 01019 uECC_word_t *_public = (uECC_word_t *)public_key; 01020 #else 01021 uECC_word_t _private[uECC_MAX_WORDS]; 01022 uECC_word_t _public[uECC_MAX_WORDS * 2]; 01023 #endif 01024 uECC_word_t tries; 01025 01026 for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { 01027 if (!uECC_generate_random_int(_private, curve->n, BITS_TO_WORDS(curve->num_n_bits))) { 01028 return 0; 01029 } 01030 01031 if (EccPoint_compute_public_key(_public, _private, curve)) { 01032 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 01033 uECC_vli_nativeToBytes(private_key, BITS_TO_BYTES(curve->num_n_bits), _private); 01034 uECC_vli_nativeToBytes(public_key, curve->num_bytes, _public); 01035 uECC_vli_nativeToBytes( 01036 public_key + curve->num_bytes, curve->num_bytes, _public + curve->num_words); 01037 #endif 01038 return 1; 01039 } 01040 } 01041 return 0; 01042 } 01043 01044 int uECC_shared_secret(const uint8_t *public_key, 01045 const uint8_t *private_key, 01046 uint8_t *secret, 01047 uECC_Curve curve) { 01048 uECC_word_t _public[uECC_MAX_WORDS * 2]; 01049 uECC_word_t _private[uECC_MAX_WORDS]; 01050 01051 uECC_word_t tmp[uECC_MAX_WORDS]; 01052 uECC_word_t *p2[2] = {_private, tmp}; 01053 uECC_word_t *initial_Z = 0; 01054 uECC_word_t carry; 01055 wordcount_t num_words = curve->num_words; 01056 wordcount_t num_bytes = curve->num_bytes; 01057 01058 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01059 bcopy((uint8_t *) _private, private_key, num_bytes); 01060 bcopy((uint8_t *) _public, public_key, num_bytes*2); 01061 #else 01062 uECC_vli_bytesToNative(_private, private_key, BITS_TO_BYTES(curve->num_n_bits)); 01063 uECC_vli_bytesToNative(_public, public_key, num_bytes); 01064 uECC_vli_bytesToNative(_public + num_words, public_key + num_bytes, num_bytes); 01065 #endif 01066 01067 /* Regularize the bitcount for the private key so that attackers cannot use a side channel 01068 attack to learn the number of leading zeros. */ 01069 carry = regularize_k(_private, _private, tmp, curve); 01070 01071 /* If an RNG function was specified, try to get a random initial Z value to improve 01072 protection against side-channel attacks. */ 01073 if (g_rng_function) { 01074 if (!uECC_generate_random_int(p2[carry], curve->p, num_words)) { 01075 return 0; 01076 } 01077 initial_Z = p2[carry]; 01078 } 01079 01080 EccPoint_mult(_public, _public, p2[!carry], initial_Z, curve->num_n_bits + 1, curve); 01081 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01082 bcopy((uint8_t *) secret, (uint8_t *) _public, num_bytes); 01083 #else 01084 uECC_vli_nativeToBytes(secret, num_bytes, _public); 01085 #endif 01086 return !EccPoint_isZero(_public, curve); 01087 } 01088 01089 #if uECC_SUPPORT_COMPRESSED_POINT 01090 void uECC_compress(const uint8_t *public_key, uint8_t *compressed, uECC_Curve curve) { 01091 wordcount_t i; 01092 for (i = 0; i < curve->num_bytes; ++i) { 01093 compressed[i+1] = public_key[i]; 01094 } 01095 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01096 compressed[0] = 2 + (public_key[curve->num_bytes] & 0x01); 01097 #else 01098 compressed[0] = 2 + (public_key[curve->num_bytes * 2 - 1] & 0x01); 01099 #endif 01100 } 01101 01102 void uECC_decompress(const uint8_t *compressed, uint8_t *public_key, uECC_Curve curve) { 01103 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01104 uECC_word_t *point = (uECC_word_t *)public_key; 01105 #else 01106 uECC_word_t point[uECC_MAX_WORDS * 2]; 01107 #endif 01108 uECC_word_t *y = point + curve->num_words; 01109 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01110 bcopy(public_key, compressed+1, curve->num_bytes); 01111 #else 01112 uECC_vli_bytesToNative(point, compressed + 1, curve->num_bytes); 01113 #endif 01114 curve->x_side(y, point, curve); 01115 curve->mod_sqrt(y, curve); 01116 01117 if ((y[0] & 0x01) != (compressed[0] & 0x01)) { 01118 uECC_vli_sub(y, curve->p, y, curve->num_words); 01119 } 01120 01121 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 01122 uECC_vli_nativeToBytes(public_key, curve->num_bytes, point); 01123 uECC_vli_nativeToBytes(public_key + curve->num_bytes, curve->num_bytes, y); 01124 #endif 01125 } 01126 #endif /* uECC_SUPPORT_COMPRESSED_POINT */ 01127 01128 int uECC_valid_point(const uECC_word_t *point, uECC_Curve curve) { 01129 uECC_word_t tmp1[uECC_MAX_WORDS]; 01130 uECC_word_t tmp2[uECC_MAX_WORDS]; 01131 wordcount_t num_words = curve->num_words; 01132 01133 /* The point at infinity is invalid. */ 01134 if (EccPoint_isZero(point, curve)) { 01135 return 0; 01136 } 01137 01138 /* x and y must be smaller than p. */ 01139 if (uECC_vli_cmp_unsafe(curve->p, point, num_words) != 1 || 01140 uECC_vli_cmp_unsafe(curve->p, point + num_words, num_words) != 1) { 01141 return 0; 01142 } 01143 01144 uECC_vli_modSquare_fast(tmp1, point + num_words, curve); 01145 curve->x_side(tmp2, point, curve); /* tmp2 = x^3 + ax + b */ 01146 01147 /* Make sure that y^2 == x^3 + ax + b */ 01148 return (int)(uECC_vli_equal(tmp1, tmp2, num_words)); 01149 } 01150 01151 int uECC_valid_public_key(const uint8_t *public_key, uECC_Curve curve) { 01152 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01153 uECC_word_t *_public = (uECC_word_t *)public_key; 01154 #else 01155 uECC_word_t _public[uECC_MAX_WORDS * 2]; 01156 #endif 01157 01158 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 01159 uECC_vli_bytesToNative(_public, public_key, curve->num_bytes); 01160 uECC_vli_bytesToNative( 01161 _public + curve->num_words, public_key + curve->num_bytes, curve->num_bytes); 01162 #endif 01163 return uECC_valid_point(_public, curve); 01164 } 01165 01166 int uECC_compute_public_key(const uint8_t *private_key, uint8_t *public_key, uECC_Curve curve) { 01167 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01168 uECC_word_t *_private = (uECC_word_t *)private_key; 01169 uECC_word_t *_public = (uECC_word_t *)public_key; 01170 #else 01171 uECC_word_t _private[uECC_MAX_WORDS]; 01172 uECC_word_t _public[uECC_MAX_WORDS * 2]; 01173 #endif 01174 01175 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 01176 uECC_vli_bytesToNative(_private, private_key, BITS_TO_BYTES(curve->num_n_bits)); 01177 #endif 01178 01179 /* Make sure the private key is in the range [1, n-1]. */ 01180 if (uECC_vli_isZero(_private, BITS_TO_WORDS(curve->num_n_bits))) { 01181 return 0; 01182 } 01183 01184 if (uECC_vli_cmp(curve->n, _private, BITS_TO_WORDS(curve->num_n_bits)) != 1) { 01185 return 0; 01186 } 01187 01188 /* Compute public key. */ 01189 if (!EccPoint_compute_public_key(_public, _private, curve)) { 01190 return 0; 01191 } 01192 01193 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 01194 uECC_vli_nativeToBytes(public_key, curve->num_bytes, _public); 01195 uECC_vli_nativeToBytes( 01196 public_key + curve->num_bytes, curve->num_bytes, _public + curve->num_words); 01197 #endif 01198 return 1; 01199 } 01200 01201 01202 /* -------- ECDSA code -------- */ 01203 01204 static void bits2int(uECC_word_t *native, 01205 const uint8_t *bits, 01206 unsigned bits_size, 01207 uECC_Curve curve) { 01208 unsigned num_n_bytes = BITS_TO_BYTES(curve->num_n_bits); 01209 unsigned num_n_words = BITS_TO_WORDS(curve->num_n_bits); 01210 int shift; 01211 uECC_word_t carry; 01212 uECC_word_t *ptr; 01213 01214 if (bits_size > num_n_bytes) { 01215 bits_size = num_n_bytes; 01216 } 01217 01218 uECC_vli_clear(native, num_n_words); 01219 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01220 bcopy((uint8_t *) native, bits, bits_size); 01221 #else 01222 uECC_vli_bytesToNative(native, bits, bits_size); 01223 #endif 01224 if (bits_size * 8 <= (unsigned)curve->num_n_bits) { 01225 return; 01226 } 01227 shift = bits_size * 8 - curve->num_n_bits; 01228 carry = 0; 01229 ptr = native + num_n_words; 01230 while (ptr-- > native) { 01231 uECC_word_t temp = *ptr; 01232 *ptr = (temp >> shift) | carry; 01233 carry = temp << (uECC_WORD_BITS - shift); 01234 } 01235 01236 /* Reduce mod curve_n */ 01237 if (uECC_vli_cmp_unsafe(curve->n, native, num_n_words) != 1) { 01238 uECC_vli_sub(native, native, curve->n, num_n_words); 01239 } 01240 } 01241 01242 static int uECC_sign_with_k(const uint8_t *private_key, 01243 const uint8_t *message_hash, 01244 unsigned hash_size, 01245 uECC_word_t *k, 01246 uint8_t *signature, 01247 uECC_Curve curve) { 01248 01249 uECC_word_t tmp[uECC_MAX_WORDS]; 01250 uECC_word_t s[uECC_MAX_WORDS]; 01251 uECC_word_t *k2[2] = {tmp, s}; 01252 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01253 uECC_word_t *p = (uECC_word_t *)signature; 01254 #else 01255 uECC_word_t p[uECC_MAX_WORDS * 2]; 01256 #endif 01257 uECC_word_t carry; 01258 wordcount_t num_words = curve->num_words; 01259 wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); 01260 bitcount_t num_n_bits = curve->num_n_bits; 01261 01262 /* Make sure 0 < k < curve_n */ 01263 if (uECC_vli_isZero(k, num_words) || uECC_vli_cmp(curve->n, k, num_n_words) != 1) { 01264 return 0; 01265 } 01266 01267 carry = regularize_k(k, tmp, s, curve); 01268 EccPoint_mult(p, curve->G, k2[!carry], 0, num_n_bits + 1, curve); 01269 if (uECC_vli_isZero(p, num_words)) { 01270 return 0; 01271 } 01272 01273 /* If an RNG function was specified, get a random number 01274 to prevent side channel analysis of k. */ 01275 if (!g_rng_function) { 01276 uECC_vli_clear(tmp, num_n_words); 01277 tmp[0] = 1; 01278 } else if (!uECC_generate_random_int(tmp, curve->n, num_n_words)) { 01279 return 0; 01280 } 01281 01282 /* Prevent side channel analysis of uECC_vli_modInv() to determine 01283 bits of k / the private key by premultiplying by a random number */ 01284 uECC_vli_modMult(k, k, tmp, curve->n, num_n_words); /* k' = rand * k */ 01285 uECC_vli_modInv(k, k, curve->n, num_n_words); /* k = 1 / k' */ 01286 uECC_vli_modMult(k, k, tmp, curve->n, num_n_words); /* k = 1 / k */ 01287 01288 #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 01289 uECC_vli_nativeToBytes(signature, curve->num_bytes, p); /* store r */ 01290 #endif 01291 01292 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01293 bcopy((uint8_t *) tmp, private_key, BITS_TO_BYTES(curve->num_n_bits)); 01294 #else 01295 uECC_vli_bytesToNative(tmp, private_key, BITS_TO_BYTES(curve->num_n_bits)); /* tmp = d */ 01296 #endif 01297 01298 s[num_n_words - 1] = 0; 01299 uECC_vli_set(s, p, num_words); 01300 uECC_vli_modMult(s, tmp, s, curve->n, num_n_words); /* s = r*d */ 01301 01302 bits2int(tmp, message_hash, hash_size, curve); 01303 uECC_vli_modAdd(s, tmp, s, curve->n, num_n_words); /* s = e + r*d */ 01304 uECC_vli_modMult(s, s, k, curve->n, num_n_words); /* s = (e + r*d) / k */ 01305 if (uECC_vli_numBits(s, num_n_words) > (bitcount_t)curve->num_bytes * 8) { 01306 return 0; 01307 } 01308 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01309 bcopy((uint8_t *) signature + curve->num_bytes, (uint8_t *) s, curve->num_bytes); 01310 #else 01311 uECC_vli_nativeToBytes(signature + curve->num_bytes, curve->num_bytes, s); 01312 #endif 01313 return 1; 01314 } 01315 01316 int uECC_sign(const uint8_t *private_key, 01317 const uint8_t *message_hash, 01318 unsigned hash_size, 01319 uint8_t *signature, 01320 uECC_Curve curve) { 01321 uECC_word_t k[uECC_MAX_WORDS]; 01322 uECC_word_t tries; 01323 01324 for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { 01325 if (!uECC_generate_random_int(k, curve->n, BITS_TO_WORDS(curve->num_n_bits))) { 01326 return 0; 01327 } 01328 01329 if (uECC_sign_with_k(private_key, message_hash, hash_size, k, signature, curve)) { 01330 return 1; 01331 } 01332 } 01333 return 0; 01334 } 01335 01336 /* Compute an HMAC using K as a key (as in RFC 6979). Note that K is always 01337 the same size as the hash result size. */ 01338 static void HMAC_init(const uECC_HashContext *hash_context, const uint8_t *K) { 01339 uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size; 01340 unsigned i; 01341 for (i = 0; i < hash_context->result_size; ++i) 01342 pad[i] = K[i] ^ 0x36; 01343 for (; i < hash_context->block_size; ++i) 01344 pad[i] = 0x36; 01345 01346 hash_context->init_hash(hash_context); 01347 hash_context->update_hash(hash_context, pad, hash_context->block_size); 01348 } 01349 01350 static void HMAC_update(const uECC_HashContext *hash_context, 01351 const uint8_t *message, 01352 unsigned message_size) { 01353 hash_context->update_hash(hash_context, message, message_size); 01354 } 01355 01356 static void HMAC_finish(const uECC_HashContext *hash_context, 01357 const uint8_t *K, 01358 uint8_t *result) { 01359 uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size; 01360 unsigned i; 01361 for (i = 0; i < hash_context->result_size; ++i) 01362 pad[i] = K[i] ^ 0x5c; 01363 for (; i < hash_context->block_size; ++i) 01364 pad[i] = 0x5c; 01365 01366 hash_context->finish_hash(hash_context, result); 01367 01368 hash_context->init_hash(hash_context); 01369 hash_context->update_hash(hash_context, pad, hash_context->block_size); 01370 hash_context->update_hash(hash_context, result, hash_context->result_size); 01371 hash_context->finish_hash(hash_context, result); 01372 } 01373 01374 /* V = HMAC_K(V) */ 01375 static void update_V(const uECC_HashContext *hash_context, uint8_t *K, uint8_t *V) { 01376 HMAC_init(hash_context, K); 01377 HMAC_update(hash_context, V, hash_context->result_size); 01378 HMAC_finish(hash_context, K, V); 01379 } 01380 01381 /* Deterministic signing, similar to RFC 6979. Differences are: 01382 * We just use H(m) directly rather than bits2octets(H(m)) 01383 (it is not reduced modulo curve_n). 01384 * We generate a value for k (aka T) directly rather than converting endianness. 01385 01386 Layout of hash_context->tmp: <K> | <V> | (1 byte overlapped 0x00 or 0x01) / <HMAC pad> */ 01387 int uECC_sign_deterministic(const uint8_t *private_key, 01388 const uint8_t *message_hash, 01389 unsigned hash_size, 01390 const uECC_HashContext *hash_context, 01391 uint8_t *signature, 01392 uECC_Curve curve) { 01393 uint8_t *K = hash_context->tmp; 01394 uint8_t *V = K + hash_context->result_size; 01395 wordcount_t num_bytes = curve->num_bytes; 01396 wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); 01397 bitcount_t num_n_bits = curve->num_n_bits; 01398 uECC_word_t tries; 01399 unsigned i; 01400 for (i = 0; i < hash_context->result_size; ++i) { 01401 V[i] = 0x01; 01402 K[i] = 0; 01403 } 01404 01405 /* K = HMAC_K(V || 0x00 || int2octets(x) || h(m)) */ 01406 HMAC_init(hash_context, K); 01407 V[hash_context->result_size] = 0x00; 01408 HMAC_update(hash_context, V, hash_context->result_size + 1); 01409 HMAC_update(hash_context, private_key, num_bytes); 01410 HMAC_update(hash_context, message_hash, hash_size); 01411 HMAC_finish(hash_context, K, K); 01412 01413 update_V(hash_context, K, V); 01414 01415 /* K = HMAC_K(V || 0x01 || int2octets(x) || h(m)) */ 01416 HMAC_init(hash_context, K); 01417 V[hash_context->result_size] = 0x01; 01418 HMAC_update(hash_context, V, hash_context->result_size + 1); 01419 HMAC_update(hash_context, private_key, num_bytes); 01420 HMAC_update(hash_context, message_hash, hash_size); 01421 HMAC_finish(hash_context, K, K); 01422 01423 update_V(hash_context, K, V); 01424 01425 for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { 01426 uECC_word_t T[uECC_MAX_WORDS]; 01427 uint8_t *T_ptr = (uint8_t *)T; 01428 wordcount_t T_bytes = 0; 01429 for (;;) { 01430 update_V(hash_context, K, V); 01431 for (i = 0; i < hash_context->result_size; ++i) { 01432 T_ptr[T_bytes++] = V[i]; 01433 if (T_bytes >= num_n_words * uECC_WORD_SIZE) { 01434 goto filled; 01435 } 01436 } 01437 } 01438 filled: 01439 if ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8 > num_n_bits) { 01440 uECC_word_t mask = (uECC_word_t)-1; 01441 T[num_n_words - 1] &= 01442 mask >> ((bitcount_t)(num_n_words * uECC_WORD_SIZE * 8 - num_n_bits)); 01443 } 01444 01445 if (uECC_sign_with_k(private_key, message_hash, hash_size, T, signature, curve)) { 01446 return 1; 01447 } 01448 01449 /* K = HMAC_K(V || 0x00) */ 01450 HMAC_init(hash_context, K); 01451 V[hash_context->result_size] = 0x00; 01452 HMAC_update(hash_context, V, hash_context->result_size + 1); 01453 HMAC_finish(hash_context, K, K); 01454 01455 update_V(hash_context, K, V); 01456 } 01457 return 0; 01458 } 01459 01460 static bitcount_t smax(bitcount_t a, bitcount_t b) { 01461 return (a > b ? a : b); 01462 } 01463 01464 int uECC_verify(const uint8_t *public_key, 01465 const uint8_t *message_hash, 01466 unsigned hash_size, 01467 const uint8_t *signature, 01468 uECC_Curve curve) { 01469 uECC_word_t u1[uECC_MAX_WORDS], u2[uECC_MAX_WORDS]; 01470 uECC_word_t z[uECC_MAX_WORDS]; 01471 uECC_word_t sum[uECC_MAX_WORDS * 2]; 01472 uECC_word_t rx[uECC_MAX_WORDS]; 01473 uECC_word_t ry[uECC_MAX_WORDS]; 01474 uECC_word_t tx[uECC_MAX_WORDS]; 01475 uECC_word_t ty[uECC_MAX_WORDS]; 01476 uECC_word_t tz[uECC_MAX_WORDS]; 01477 const uECC_word_t *points[4]; 01478 const uECC_word_t *point; 01479 bitcount_t num_bits; 01480 bitcount_t i; 01481 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01482 uECC_word_t *_public = (uECC_word_t *)public_key; 01483 #else 01484 uECC_word_t _public[uECC_MAX_WORDS * 2]; 01485 #endif 01486 uECC_word_t r[uECC_MAX_WORDS], s[uECC_MAX_WORDS]; 01487 wordcount_t num_words = curve->num_words; 01488 wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); 01489 01490 rx[num_n_words - 1] = 0; 01491 r[num_n_words - 1] = 0; 01492 s[num_n_words - 1] = 0; 01493 01494 #if uECC_VLI_NATIVE_LITTLE_ENDIAN 01495 bcopy((uint8_t *) r, signature, curve->num_bytes); 01496 bcopy((uint8_t *) s, signature + curve->num_bytes, curve->num_bytes); 01497 #else 01498 uECC_vli_bytesToNative(_public, public_key, curve->num_bytes); 01499 uECC_vli_bytesToNative( 01500 _public + num_words, public_key + curve->num_bytes, curve->num_bytes); 01501 uECC_vli_bytesToNative(r, signature, curve->num_bytes); 01502 uECC_vli_bytesToNative(s, signature + curve->num_bytes, curve->num_bytes); 01503 #endif 01504 01505 /* r, s must not be 0. */ 01506 if (uECC_vli_isZero(r, num_words) || uECC_vli_isZero(s, num_words)) { 01507 return 0; 01508 } 01509 01510 /* r, s must be < n. */ 01511 if (uECC_vli_cmp_unsafe(curve->n, r, num_n_words) != 1 || 01512 uECC_vli_cmp_unsafe(curve->n, s, num_n_words) != 1) { 01513 return 0; 01514 } 01515 01516 /* Calculate u1 and u2. */ 01517 uECC_vli_modInv(z, s, curve->n, num_n_words); /* z = 1/s */ 01518 u1[num_n_words - 1] = 0; 01519 bits2int(u1, message_hash, hash_size, curve); 01520 uECC_vli_modMult(u1, u1, z, curve->n, num_n_words); /* u1 = e/s */ 01521 uECC_vli_modMult(u2, r, z, curve->n, num_n_words); /* u2 = r/s */ 01522 01523 /* Calculate sum = G + Q. */ 01524 uECC_vli_set(sum, _public, num_words); 01525 uECC_vli_set(sum + num_words, _public + num_words, num_words); 01526 uECC_vli_set(tx, curve->G, num_words); 01527 uECC_vli_set(ty, curve->G + num_words, num_words); 01528 uECC_vli_modSub(z, sum, tx, curve->p, num_words); /* z = x2 - x1 */ 01529 XYcZ_add(tx, ty, sum, sum + num_words, curve); 01530 uECC_vli_modInv(z, z, curve->p, num_words); /* z = 1/z */ 01531 apply_z(sum, sum + num_words, z, curve); 01532 01533 /* Use Shamir's trick to calculate u1*G + u2*Q */ 01534 points[0] = 0; 01535 points[1] = curve->G; 01536 points[2] = _public; 01537 points[3] = sum; 01538 num_bits = smax(uECC_vli_numBits(u1, num_n_words), 01539 uECC_vli_numBits(u2, num_n_words)); 01540 01541 point = points[(!!uECC_vli_testBit(u1, num_bits - 1)) | 01542 ((!!uECC_vli_testBit(u2, num_bits - 1)) << 1)]; 01543 uECC_vli_set(rx, point, num_words); 01544 uECC_vli_set(ry, point + num_words, num_words); 01545 uECC_vli_clear(z, num_words); 01546 z[0] = 1; 01547 01548 for (i = num_bits - 2; i >= 0; --i) { 01549 uECC_word_t index; 01550 curve->double_jacobian(rx, ry, z, curve); 01551 01552 index = (!!uECC_vli_testBit(u1, i)) | ((!!uECC_vli_testBit(u2, i)) << 1); 01553 point = points[index]; 01554 if (point) { 01555 uECC_vli_set(tx, point, num_words); 01556 uECC_vli_set(ty, point + num_words, num_words); 01557 apply_z(tx, ty, z, curve); 01558 uECC_vli_modSub(tz, rx, tx, curve->p, num_words); /* Z = x2 - x1 */ 01559 XYcZ_add(tx, ty, rx, ry, curve); 01560 uECC_vli_modMult_fast(z, z, tz, curve); 01561 } 01562 } 01563 01564 uECC_vli_modInv(z, z, curve->p, num_words); /* Z = 1/Z */ 01565 apply_z(rx, ry, z, curve); 01566 01567 /* v = x1 (mod n) */ 01568 if (uECC_vli_cmp_unsafe(curve->n, rx, num_n_words) != 1) { 01569 uECC_vli_sub(rx, rx, curve->n, num_n_words); 01570 } 01571 01572 /* Accept only if v == r. */ 01573 return (int)(uECC_vli_equal(rx, r, num_words)); 01574 } 01575 01576 #if uECC_ENABLE_VLI_API 01577 01578 unsigned uECC_curve_num_words(uECC_Curve curve) { 01579 return curve->num_words; 01580 } 01581 01582 unsigned uECC_curve_num_bytes(uECC_Curve curve) { 01583 return curve->num_bytes; 01584 } 01585 01586 unsigned uECC_curve_num_bits(uECC_Curve curve) { 01587 return curve->num_bytes * 8; 01588 } 01589 01590 unsigned uECC_curve_num_n_words(uECC_Curve curve) { 01591 return BITS_TO_WORDS(curve->num_n_bits); 01592 } 01593 01594 unsigned uECC_curve_num_n_bytes(uECC_Curve curve) { 01595 return BITS_TO_BYTES(curve->num_n_bits); 01596 } 01597 01598 unsigned uECC_curve_num_n_bits(uECC_Curve curve) { 01599 return curve->num_n_bits; 01600 } 01601 01602 const uECC_word_t *uECC_curve_p(uECC_Curve curve) { 01603 return curve->p; 01604 } 01605 01606 const uECC_word_t *uECC_curve_n(uECC_Curve curve) { 01607 return curve->n; 01608 } 01609 01610 const uECC_word_t *uECC_curve_G(uECC_Curve curve) { 01611 return curve->G; 01612 } 01613 01614 const uECC_word_t *uECC_curve_b(uECC_Curve curve) { 01615 return curve->b; 01616 } 01617 01618 #if uECC_SUPPORT_COMPRESSED_POINT 01619 void uECC_vli_mod_sqrt(uECC_word_t *a, uECC_Curve curve) { 01620 curve->mod_sqrt(a, curve); 01621 } 01622 #endif 01623 01624 void uECC_vli_mmod_fast(uECC_word_t *result, uECC_word_t *product, uECC_Curve curve) { 01625 #if (uECC_OPTIMIZATION_LEVEL > 0) 01626 curve->mmod_fast(result, product); 01627 #else 01628 uECC_vli_mmod(result, product, curve->p, curve->num_words); 01629 #endif 01630 } 01631 01632 void uECC_point_mult(uECC_word_t *result, 01633 const uECC_word_t *point, 01634 const uECC_word_t *scalar, 01635 uECC_Curve curve) { 01636 uECC_word_t tmp1[uECC_MAX_WORDS]; 01637 uECC_word_t tmp2[uECC_MAX_WORDS]; 01638 uECC_word_t *p2[2] = {tmp1, tmp2}; 01639 uECC_word_t carry = regularize_k(scalar, tmp1, tmp2, curve); 01640 01641 EccPoint_mult(result, point, p2[!carry], 0, curve->num_n_bits + 1, curve); 01642 } 01643 01644 #endif /* uECC_ENABLE_VLI_API */
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