/* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */ #include "uECC.h" #include "uECC_vli.h" #ifndef uECC_RNG_MAX_TRIES #define uECC_RNG_MAX_TRIES 64 #endif #if uECC_ENABLE_VLI_API #define uECC_VLI_API #else #define uECC_VLI_API static #endif #define CONCATX(a, ...) a ## __VA_ARGS__ #define CONCAT(a, ...) CONCATX(a, __VA_ARGS__) #define STRX(a) #a #define STR(a) STRX(a) #define EVAL(...) EVAL1(EVAL1(EVAL1(EVAL1(__VA_ARGS__)))) #define EVAL1(...) EVAL2(EVAL2(EVAL2(EVAL2(__VA_ARGS__)))) #define EVAL2(...) EVAL3(EVAL3(EVAL3(EVAL3(__VA_ARGS__)))) #define EVAL3(...) EVAL4(EVAL4(EVAL4(EVAL4(__VA_ARGS__)))) #define EVAL4(...) __VA_ARGS__ #define DEC_1 0 #define DEC_2 1 #define DEC_3 2 #define DEC_4 3 #define DEC_5 4 #define DEC_6 5 #define DEC_7 6 #define DEC_8 7 #define DEC_9 8 #define DEC_10 9 #define DEC_11 10 #define DEC_12 11 #define DEC_13 12 #define DEC_14 13 #define DEC_15 14 #define DEC_16 15 #define DEC_17 16 #define DEC_18 17 #define DEC_19 18 #define DEC_20 19 #define DEC_21 20 #define DEC_22 21 #define DEC_23 22 #define DEC_24 23 #define DEC_25 24 #define DEC_26 25 #define DEC_27 26 #define DEC_28 27 #define DEC_29 28 #define DEC_30 29 #define DEC_31 30 #define DEC_32 31 #define DEC(N) CONCAT(DEC_, N) #define SECOND_ARG(_, val, ...) val #define SOME_CHECK_0 ~, 0 #define GET_SECOND_ARG(...) SECOND_ARG(__VA_ARGS__, SOME,) #define SOME_OR_0(N) GET_SECOND_ARG(CONCAT(SOME_CHECK_, N)) #define EMPTY(...) #define DEFER(...) __VA_ARGS__ EMPTY() #define REPEAT_NAME_0() REPEAT_0 #define REPEAT_NAME_SOME() REPEAT_SOME #define REPEAT_0(...) #define REPEAT_SOME(N, stuff) DEFER(CONCAT(REPEAT_NAME_, SOME_OR_0(DEC(N))))()(DEC(N), stuff) stuff #define REPEAT(N, stuff) EVAL(REPEAT_SOME(N, stuff)) #define REPEATM_NAME_0() REPEATM_0 #define REPEATM_NAME_SOME() REPEATM_SOME #define REPEATM_0(...) #define REPEATM_SOME(N, macro) macro(N) \ DEFER(CONCAT(REPEATM_NAME_, SOME_OR_0(DEC(N))))()(DEC(N), macro) #define REPEATM(N, macro) EVAL(REPEATM_SOME(N, macro)) #include "platform-specific.inc" #if (uECC_WORD_SIZE == 1) #if uECC_SUPPORTS_secp160r1 #define uECC_MAX_WORDS 21 /* Due to the size of curve_n. */ #endif #if uECC_SUPPORTS_secp192r1 #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 24 #endif #if uECC_SUPPORTS_secp224r1 #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 28 #endif #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1) #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 32 #endif #elif (uECC_WORD_SIZE == 4) #if uECC_SUPPORTS_secp160r1 #define uECC_MAX_WORDS 6 /* Due to the size of curve_n. */ #endif #if uECC_SUPPORTS_secp192r1 #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 6 #endif #if uECC_SUPPORTS_secp224r1 #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 7 #endif #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1) #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 8 #endif #elif (uECC_WORD_SIZE == 8) #if uECC_SUPPORTS_secp160r1 #define uECC_MAX_WORDS 3 #endif #if uECC_SUPPORTS_secp192r1 #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 3 #endif #if uECC_SUPPORTS_secp224r1 #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 4 #endif #if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1) #undef uECC_MAX_WORDS #define uECC_MAX_WORDS 4 #endif #endif /* uECC_WORD_SIZE */ #define BITS_TO_WORDS(num_bits) ((num_bits + ((uECC_WORD_SIZE * 8) - 1)) / (uECC_WORD_SIZE * 8)) #define BITS_TO_BYTES(num_bits) ((num_bits + 7) / 8) struct uECC_Curve_t { wordcount_t num_words; wordcount_t num_bytes; bitcount_t num_n_bits; uECC_word_t p[uECC_MAX_WORDS]; uECC_word_t n[uECC_MAX_WORDS]; uECC_word_t G[uECC_MAX_WORDS * 2]; uECC_word_t b[uECC_MAX_WORDS]; void (*double_jacobian)(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * Z1, uECC_Curve curve); #if uECC_SUPPORT_COMPRESSED_POINT void (*mod_sqrt)(uECC_word_t *a, uECC_Curve curve); #endif void (*x_side)(uECC_word_t *result, const uECC_word_t *x, uECC_Curve curve); #if (uECC_OPTIMIZATION_LEVEL > 0) void (*mmod_fast)(uECC_word_t *result, uECC_word_t *product); #endif }; #if uECC_VLI_NATIVE_LITTLE_ENDIAN static void bcopy(uint8_t *dst, const uint8_t *src, unsigned num_bytes) { while (0 != num_bytes) { num_bytes--; dst[num_bytes] = src[num_bytes]; } } #endif static cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left, const uECC_word_t *right, wordcount_t num_words); #if (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb || \ uECC_PLATFORM == uECC_arm_thumb2) #include "asm_arm.inc" #endif #if (uECC_PLATFORM == uECC_avr) #include "asm_avr.inc" #endif #if default_RNG_defined static uECC_RNG_Function g_rng_function = &default_RNG; #else static uECC_RNG_Function g_rng_function = 0; #endif void uECC_set_rng(uECC_RNG_Function rng_function) { g_rng_function = rng_function; } uECC_RNG_Function uECC_get_rng(void) { return g_rng_function; } int uECC_curve_private_key_size(uECC_Curve curve) { return BITS_TO_BYTES(curve->num_n_bits); } int uECC_curve_public_key_size(uECC_Curve curve) { return 2 * curve->num_bytes; } #if !asm_clear uECC_VLI_API void uECC_vli_clear(uECC_word_t *vli, wordcount_t num_words) { wordcount_t i; for (i = 0; i < num_words; ++i) { vli[i] = 0; } } #endif /* !asm_clear */ /* Constant-time comparison to zero - secure way to compare long integers */ /* Returns 1 if vli == 0, 0 otherwise. */ uECC_VLI_API uECC_word_t uECC_vli_isZero(const uECC_word_t *vli, wordcount_t num_words) { uECC_word_t bits = 0; wordcount_t i; for (i = 0; i < num_words; ++i) { bits |= vli[i]; } return (bits == 0); } /* Returns nonzero if bit 'bit' of vli is set. */ uECC_VLI_API uECC_word_t uECC_vli_testBit(const uECC_word_t *vli, bitcount_t bit) { return (vli[bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK))); } /* Counts the number of words in vli. */ static wordcount_t vli_numDigits(const uECC_word_t *vli, const wordcount_t max_words) { wordcount_t i; /* Search from the end until we find a non-zero digit. We do it in reverse because we expect that most digits will be nonzero. */ for (i = max_words - 1; i >= 0 && vli[i] == 0; --i) { } return (i + 1); } /* Counts the number of bits required to represent vli. */ uECC_VLI_API bitcount_t uECC_vli_numBits(const uECC_word_t *vli, const wordcount_t max_words) { uECC_word_t i; uECC_word_t digit; wordcount_t num_digits = vli_numDigits(vli, max_words); if (num_digits == 0) { return 0; } digit = vli[num_digits - 1]; for (i = 0; digit; ++i) { digit >>= 1; } return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i); } /* Sets dest = src. */ #if !asm_set uECC_VLI_API void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src, wordcount_t num_words) { wordcount_t i; for (i = 0; i < num_words; ++i) { dest[i] = src[i]; } } #endif /* !asm_set */ /* Returns sign of left - right. */ static cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left, const uECC_word_t *right, wordcount_t num_words) { wordcount_t i; for (i = num_words - 1; i >= 0; --i) { if (left[i] > right[i]) { return 1; } else if (left[i] < right[i]) { return -1; } } return 0; } /* Constant-time comparison function - secure way to compare long integers */ /* Returns one if left == right, zero otherwise. */ uECC_VLI_API uECC_word_t uECC_vli_equal(const uECC_word_t *left, const uECC_word_t *right, wordcount_t num_words) { uECC_word_t diff = 0; wordcount_t i; for (i = num_words - 1; i >= 0; --i) { diff |= (left[i] ^ right[i]); } return (diff == 0); } uECC_VLI_API uECC_word_t uECC_vli_sub(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right, wordcount_t num_words); /* Returns sign of left - right, in constant time. */ uECC_VLI_API cmpresult_t uECC_vli_cmp(const uECC_word_t *left, const uECC_word_t *right, wordcount_t num_words) { uECC_word_t tmp[uECC_MAX_WORDS]; uECC_word_t neg = !!uECC_vli_sub(tmp, left, right, num_words); uECC_word_t equal = uECC_vli_isZero(tmp, num_words); return (!equal - 2 * neg); } /* Computes vli = vli >> 1. */ #if !asm_rshift1 uECC_VLI_API void uECC_vli_rshift1(uECC_word_t *vli, wordcount_t num_words) { uECC_word_t *end = vli; uECC_word_t carry = 0; vli += num_words; while (vli-- > end) { uECC_word_t temp = *vli; *vli = (temp >> 1) | carry; carry = temp << (uECC_WORD_BITS - 1); } } #endif /* !asm_rshift1 */ /* Computes result = left + right, returning carry. Can modify in place. */ #if !asm_add uECC_VLI_API uECC_word_t uECC_vli_add(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right, wordcount_t num_words) { uECC_word_t carry = 0; wordcount_t i; for (i = 0; i < num_words; ++i) { uECC_word_t sum = left[i] + right[i] + carry; if (sum != left[i]) { carry = (sum < left[i]); } result[i] = sum; } return carry; } #endif /* !asm_add */ /* Computes result = left - right, returning borrow. Can modify in place. */ #if !asm_sub uECC_VLI_API uECC_word_t uECC_vli_sub(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right, wordcount_t num_words) { uECC_word_t borrow = 0; wordcount_t i; for (i = 0; i < num_words; ++i) { uECC_word_t diff = left[i] - right[i] - borrow; if (diff != left[i]) { borrow = (diff > left[i]); } result[i] = diff; } return borrow; } #endif /* !asm_sub */ #if !asm_mult || (uECC_SQUARE_FUNC && !asm_square) || \ (uECC_SUPPORTS_secp256k1 && (uECC_OPTIMIZATION_LEVEL > 0) && \ ((uECC_WORD_SIZE == 1) || (uECC_WORD_SIZE == 8))) static void muladd(uECC_word_t a, uECC_word_t b, uECC_word_t *r0, uECC_word_t *r1, uECC_word_t *r2) { #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128 uint64_t a0 = a & 0xffffffffull; uint64_t a1 = a >> 32; uint64_t b0 = b & 0xffffffffull; uint64_t b1 = b >> 32; uint64_t i0 = a0 * b0; uint64_t i1 = a0 * b1; uint64_t i2 = a1 * b0; uint64_t i3 = a1 * b1; uint64_t p0, p1; i2 += (i0 >> 32); i2 += i1; if (i2 < i1) { /* overflow */ i3 += 0x100000000ull; } p0 = (i0 & 0xffffffffull) | (i2 << 32); p1 = i3 + (i2 >> 32); *r0 += p0; *r1 += (p1 + (*r0 < p0)); *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0)); #else uECC_dword_t p = (uECC_dword_t)a * b; uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; r01 += p; *r2 += (r01 < p); *r1 = r01 >> uECC_WORD_BITS; *r0 = (uECC_word_t)r01; #endif } #endif /* muladd needed */ #if !asm_mult uECC_VLI_API void uECC_vli_mult(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right, wordcount_t num_words) { uECC_word_t r0 = 0; uECC_word_t r1 = 0; uECC_word_t r2 = 0; wordcount_t i, k; /* Compute each digit of result in sequence, maintaining the carries. */ for (k = 0; k < num_words; ++k) { for (i = 0; i <= k; ++i) { muladd(left[i], right[k - i], &r0, &r1, &r2); } result[k] = r0; r0 = r1; r1 = r2; r2 = 0; } for (k = num_words; k < num_words * 2 - 1; ++k) { for (i = (k + 1) - num_words; i < num_words; ++i) { muladd(left[i], right[k - i], &r0, &r1, &r2); } result[k] = r0; r0 = r1; r1 = r2; r2 = 0; } result[num_words * 2 - 1] = r0; } #endif /* !asm_mult */ #if uECC_SQUARE_FUNC #if !asm_square static void mul2add(uECC_word_t a, uECC_word_t b, uECC_word_t *r0, uECC_word_t *r1, uECC_word_t *r2) { #if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128 uint64_t a0 = a & 0xffffffffull; uint64_t a1 = a >> 32; uint64_t b0 = b & 0xffffffffull; uint64_t b1 = b >> 32; uint64_t i0 = a0 * b0; uint64_t i1 = a0 * b1; uint64_t i2 = a1 * b0; uint64_t i3 = a1 * b1; uint64_t p0, p1; i2 += (i0 >> 32); i2 += i1; if (i2 < i1) { /* overflow */ i3 += 0x100000000ull; } p0 = (i0 & 0xffffffffull) | (i2 << 32); p1 = i3 + (i2 >> 32); *r2 += (p1 >> 63); p1 = (p1 << 1) | (p0 >> 63); p0 <<= 1; *r0 += p0; *r1 += (p1 + (*r0 < p0)); *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0)); #else uECC_dword_t p = (uECC_dword_t)a * b; uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; *r2 += (p >> (uECC_WORD_BITS * 2 - 1)); p *= 2; r01 += p; *r2 += (r01 < p); *r1 = r01 >> uECC_WORD_BITS; *r0 = (uECC_word_t)r01; #endif } uECC_VLI_API void uECC_vli_square(uECC_word_t *result, const uECC_word_t *left, wordcount_t num_words) { uECC_word_t r0 = 0; uECC_word_t r1 = 0; uECC_word_t r2 = 0; wordcount_t i, k; for (k = 0; k < num_words * 2 - 1; ++k) { uECC_word_t min = (k < num_words ? 0 : (k + 1) - num_words); for (i = min; i <= k && i <= k - i; ++i) { if (i < k-i) { mul2add(left[i], left[k - i], &r0, &r1, &r2); } else { muladd(left[i], left[k - i], &r0, &r1, &r2); } } result[k] = r0; r0 = r1; r1 = r2; r2 = 0; } result[num_words * 2 - 1] = r0; } #endif /* !asm_square */ #else /* uECC_SQUARE_FUNC */ #if uECC_ENABLE_VLI_API uECC_VLI_API void uECC_vli_square(uECC_word_t *result, const uECC_word_t *left, wordcount_t num_words) { uECC_vli_mult(result, left, left, num_words); } #endif /* uECC_ENABLE_VLI_API */ #endif /* uECC_SQUARE_FUNC */ /* Computes result = (left + right) % mod. Assumes that left < mod and right < mod, and that result does not overlap mod. */ uECC_VLI_API void uECC_vli_modAdd(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right, const uECC_word_t *mod, wordcount_t num_words) { uECC_word_t carry = uECC_vli_add(result, left, right, num_words); if (carry || uECC_vli_cmp_unsafe(mod, result, num_words) != 1) { /* result > mod (result = mod + remainder), so subtract mod to get remainder. */ uECC_vli_sub(result, result, mod, num_words); } } /* Computes result = (left - right) % mod. Assumes that left < mod and right < mod, and that result does not overlap mod. */ uECC_VLI_API void uECC_vli_modSub(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right, const uECC_word_t *mod, wordcount_t num_words) { uECC_word_t l_borrow = uECC_vli_sub(result, left, right, num_words); if (l_borrow) { /* In this case, result == -diff == (max int) - diff. Since -x % d == d - x, we can get the correct result from result + mod (with overflow). */ uECC_vli_add(result, result, mod, num_words); } } /* Computes result = product % mod, where product is 2N words long. */ /* Currently only designed to work for curve_p or curve_n. */ uECC_VLI_API void uECC_vli_mmod(uECC_word_t *result, uECC_word_t *product, const uECC_word_t *mod, wordcount_t num_words) { uECC_word_t mod_multiple[2 * uECC_MAX_WORDS]; uECC_word_t tmp[2 * uECC_MAX_WORDS]; uECC_word_t *v[2] = {tmp, product}; uECC_word_t index; /* Shift mod so its highest set bit is at the maximum position. */ bitcount_t shift = (num_words * 2 * uECC_WORD_BITS) - uECC_vli_numBits(mod, num_words); wordcount_t word_shift = shift / uECC_WORD_BITS; wordcount_t bit_shift = shift % uECC_WORD_BITS; uECC_word_t carry = 0; uECC_vli_clear(mod_multiple, word_shift); if (bit_shift > 0) { for(index = 0; index < (uECC_word_t)num_words; ++index) { mod_multiple[word_shift + index] = (mod[index] << bit_shift) | carry; carry = mod[index] >> (uECC_WORD_BITS - bit_shift); } } else { uECC_vli_set(mod_multiple + word_shift, mod, num_words); } for (index = 1; shift >= 0; --shift) { uECC_word_t borrow = 0; wordcount_t i; for (i = 0; i < num_words * 2; ++i) { uECC_word_t diff = v[index][i] - mod_multiple[i] - borrow; if (diff != v[index][i]) { borrow = (diff > v[index][i]); } v[1 - index][i] = diff; } index = !(index ^ borrow); /* Swap the index if there was no borrow */ uECC_vli_rshift1(mod_multiple, num_words); mod_multiple[num_words - 1] |= mod_multiple[num_words] << (uECC_WORD_BITS - 1); uECC_vli_rshift1(mod_multiple + num_words, num_words); } uECC_vli_set(result, v[index], num_words); } /* Computes result = (left * right) % mod. */ uECC_VLI_API void uECC_vli_modMult(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right, const uECC_word_t *mod, wordcount_t num_words) { uECC_word_t product[2 * uECC_MAX_WORDS]; uECC_vli_mult(product, left, right, num_words); uECC_vli_mmod(result, product, mod, num_words); } uECC_VLI_API void uECC_vli_modMult_fast(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right, uECC_Curve curve) { uECC_word_t product[2 * uECC_MAX_WORDS]; uECC_vli_mult(product, left, right, curve->num_words); #if (uECC_OPTIMIZATION_LEVEL > 0) curve->mmod_fast(result, product); #else uECC_vli_mmod(result, product, curve->p, curve->num_words); #endif } #if uECC_SQUARE_FUNC #if uECC_ENABLE_VLI_API /* Computes result = left^2 % mod. */ uECC_VLI_API void uECC_vli_modSquare(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *mod, wordcount_t num_words) { uECC_word_t product[2 * uECC_MAX_WORDS]; uECC_vli_square(product, left, num_words); uECC_vli_mmod(result, product, mod, num_words); } #endif /* uECC_ENABLE_VLI_API */ uECC_VLI_API void uECC_vli_modSquare_fast(uECC_word_t *result, const uECC_word_t *left, uECC_Curve curve) { uECC_word_t product[2 * uECC_MAX_WORDS]; uECC_vli_square(product, left, curve->num_words); #if (uECC_OPTIMIZATION_LEVEL > 0) curve->mmod_fast(result, product); #else uECC_vli_mmod(result, product, curve->p, curve->num_words); #endif } #else /* uECC_SQUARE_FUNC */ #if uECC_ENABLE_VLI_API uECC_VLI_API void uECC_vli_modSquare(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *mod, wordcount_t num_words) { uECC_vli_modMult(result, left, left, mod, num_words); } #endif /* uECC_ENABLE_VLI_API */ uECC_VLI_API void uECC_vli_modSquare_fast(uECC_word_t *result, const uECC_word_t *left, uECC_Curve curve) { uECC_vli_modMult_fast(result, left, left, curve); } #endif /* uECC_SQUARE_FUNC */ #define EVEN(vli) (!(vli[0] & 1)) static void vli_modInv_update(uECC_word_t *uv, const uECC_word_t *mod, wordcount_t num_words) { uECC_word_t carry = 0; if (!EVEN(uv)) { carry = uECC_vli_add(uv, uv, mod, num_words); } uECC_vli_rshift1(uv, num_words); if (carry) { uv[num_words - 1] |= HIGH_BIT_SET; } } /* Computes result = (1 / input) % mod. All VLIs are the same size. See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" */ uECC_VLI_API void uECC_vli_modInv(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod, wordcount_t num_words) { uECC_word_t a[uECC_MAX_WORDS], b[uECC_MAX_WORDS], u[uECC_MAX_WORDS], v[uECC_MAX_WORDS]; cmpresult_t cmpResult; if (uECC_vli_isZero(input, num_words)) { uECC_vli_clear(result, num_words); return; } uECC_vli_set(a, input, num_words); uECC_vli_set(b, mod, num_words); uECC_vli_clear(u, num_words); u[0] = 1; uECC_vli_clear(v, num_words); while ((cmpResult = uECC_vli_cmp_unsafe(a, b, num_words)) != 0) { if (EVEN(a)) { uECC_vli_rshift1(a, num_words); vli_modInv_update(u, mod, num_words); } else if (EVEN(b)) { uECC_vli_rshift1(b, num_words); vli_modInv_update(v, mod, num_words); } else if (cmpResult > 0) { uECC_vli_sub(a, a, b, num_words); uECC_vli_rshift1(a, num_words); if (uECC_vli_cmp_unsafe(u, v, num_words) < 0) { uECC_vli_add(u, u, mod, num_words); } uECC_vli_sub(u, u, v, num_words); vli_modInv_update(u, mod, num_words); } else { uECC_vli_sub(b, b, a, num_words); uECC_vli_rshift1(b, num_words); if (uECC_vli_cmp_unsafe(v, u, num_words) < 0) { uECC_vli_add(v, v, mod, num_words); } uECC_vli_sub(v, v, u, num_words); vli_modInv_update(v, mod, num_words); } } uECC_vli_set(result, u, num_words); } /* ------ Point operations ------ */ #include "curve-specific.inc" /* Returns 1 if 'point' is the point at infinity, 0 otherwise. */ #define EccPoint_isZero(point, curve) uECC_vli_isZero((point), (curve)->num_words * 2) /* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates. From http://eprint.iacr.org/2011/338.pdf */ /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ static void apply_z(uECC_word_t * X1, uECC_word_t * Y1, const uECC_word_t * const Z, uECC_Curve curve) { uECC_word_t t1[uECC_MAX_WORDS]; uECC_vli_modSquare_fast(t1, Z, curve); /* z^2 */ uECC_vli_modMult_fast(X1, X1, t1, curve); /* x1 * z^2 */ uECC_vli_modMult_fast(t1, t1, Z, curve); /* z^3 */ uECC_vli_modMult_fast(Y1, Y1, t1, curve); /* y1 * z^3 */ } /* P = (x1, y1) => 2P, (x2, y2) => P' */ static void XYcZ_initial_double(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * X2, uECC_word_t * Y2, const uECC_word_t * const initial_Z, uECC_Curve curve) { uECC_word_t z[uECC_MAX_WORDS]; wordcount_t num_words = curve->num_words; if (initial_Z) { uECC_vli_set(z, initial_Z, num_words); } else { uECC_vli_clear(z, num_words); z[0] = 1; } uECC_vli_set(X2, X1, num_words); uECC_vli_set(Y2, Y1, num_words); apply_z(X1, Y1, z, curve); curve->double_jacobian(X1, Y1, z, curve); apply_z(X2, Y2, z, curve); } /* Input P = (x1, y1, Z), Q = (x2, y2, Z) Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) or P => P', Q => P + Q */ static void XYcZ_add(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * X2, uECC_word_t * Y2, uECC_Curve curve) { /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ uECC_word_t t5[uECC_MAX_WORDS]; wordcount_t num_words = curve->num_words; uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ uECC_vli_modSquare_fast(t5, Y2, curve); /* t5 = (y2 - y1)^2 = D */ uECC_vli_modSub(t5, t5, X1, curve->p, num_words); /* t5 = D - B */ uECC_vli_modSub(t5, t5, X2, curve->p, num_words); /* t5 = D - B - C = x3 */ uECC_vli_modSub(X2, X2, X1, curve->p, num_words); /* t3 = C - B */ uECC_vli_modMult_fast(Y1, Y1, X2, curve); /* t2 = y1*(C - B) */ uECC_vli_modSub(X2, X1, t5, curve->p, num_words); /* t3 = B - x3 */ uECC_vli_modMult_fast(Y2, Y2, X2, curve); /* t4 = (y2 - y1)*(B - x3) */ uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y3 */ uECC_vli_set(X2, t5, num_words); } /* Input P = (x1, y1, Z), Q = (x2, y2, Z) Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) or P => P - Q, Q => P + Q */ static void XYcZ_addC(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * X2, uECC_word_t * Y2, uECC_Curve curve) { /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ uECC_word_t t5[uECC_MAX_WORDS]; uECC_word_t t6[uECC_MAX_WORDS]; uECC_word_t t7[uECC_MAX_WORDS]; wordcount_t num_words = curve->num_words; uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ uECC_vli_modAdd(t5, Y2, Y1, curve->p, num_words); /* t5 = y2 + y1 */ uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ uECC_vli_modSub(t6, X2, X1, curve->p, num_words); /* t6 = C - B */ uECC_vli_modMult_fast(Y1, Y1, t6, curve); /* t2 = y1 * (C - B) = E */ uECC_vli_modAdd(t6, X1, X2, curve->p, num_words); /* t6 = B + C */ uECC_vli_modSquare_fast(X2, Y2, curve); /* t3 = (y2 - y1)^2 = D */ uECC_vli_modSub(X2, X2, t6, curve->p, num_words); /* t3 = D - (B + C) = x3 */ uECC_vli_modSub(t7, X1, X2, curve->p, num_words); /* t7 = B - x3 */ uECC_vli_modMult_fast(Y2, Y2, t7, curve); /* t4 = (y2 - y1)*(B - x3) */ uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = (y2 - y1)*(B - x3) - E = y3 */ uECC_vli_modSquare_fast(t7, t5, curve); /* t7 = (y2 + y1)^2 = F */ uECC_vli_modSub(t7, t7, t6, curve->p, num_words); /* t7 = F - (B + C) = x3' */ uECC_vli_modSub(t6, t7, X1, curve->p, num_words); /* t6 = x3' - B */ uECC_vli_modMult_fast(t6, t6, t5, curve); /* t6 = (y2+y1)*(x3' - B) */ uECC_vli_modSub(Y1, t6, Y1, curve->p, num_words); /* t2 = (y2+y1)*(x3' - B) - E = y3' */ uECC_vli_set(X1, t7, num_words); } /* result may overlap point. */ static void EccPoint_mult(uECC_word_t * result, const uECC_word_t * point, const uECC_word_t * scalar, const uECC_word_t * initial_Z, bitcount_t num_bits, uECC_Curve curve) { /* R0 and R1 */ uECC_word_t Rx[2][uECC_MAX_WORDS]; uECC_word_t Ry[2][uECC_MAX_WORDS]; uECC_word_t z[uECC_MAX_WORDS]; bitcount_t i; uECC_word_t nb; wordcount_t num_words = curve->num_words; uECC_vli_set(Rx[1], point, num_words); uECC_vli_set(Ry[1], point + num_words, num_words); XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initial_Z, curve); for (i = num_bits - 2; i > 0; --i) { nb = !uECC_vli_testBit(scalar, i); XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve); XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve); } nb = !uECC_vli_testBit(scalar, 0); XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve); /* Find final 1/Z value. */ uECC_vli_modSub(z, Rx[1], Rx[0], curve->p, num_words); /* X1 - X0 */ uECC_vli_modMult_fast(z, z, Ry[1 - nb], curve); /* Yb * (X1 - X0) */ uECC_vli_modMult_fast(z, z, point, curve); /* xP * Yb * (X1 - X0) */ uECC_vli_modInv(z, z, curve->p, num_words); /* 1 / (xP * Yb * (X1 - X0)) */ /* yP / (xP * Yb * (X1 - X0)) */ uECC_vli_modMult_fast(z, z, point + num_words, curve); uECC_vli_modMult_fast(z, z, Rx[1 - nb], curve); /* Xb * yP / (xP * Yb * (X1 - X0)) */ /* End 1/Z calculation */ XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve); apply_z(Rx[0], Ry[0], z, curve); uECC_vli_set(result, Rx[0], num_words); uECC_vli_set(result + num_words, Ry[0], num_words); } static uECC_word_t regularize_k(const uECC_word_t * const k, uECC_word_t *k0, uECC_word_t *k1, uECC_Curve curve) { wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); bitcount_t num_n_bits = curve->num_n_bits; uECC_word_t carry = uECC_vli_add(k0, k, curve->n, num_n_words) || (num_n_bits < ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8) && uECC_vli_testBit(k0, num_n_bits)); uECC_vli_add(k1, k0, curve->n, num_n_words); return carry; } static uECC_word_t EccPoint_compute_public_key(uECC_word_t *result, uECC_word_t *private_key, uECC_Curve curve) { uECC_word_t tmp1[uECC_MAX_WORDS]; uECC_word_t tmp2[uECC_MAX_WORDS]; uECC_word_t *p2[2] = {tmp1, tmp2}; uECC_word_t carry; /* Regularize the bitcount for the private key so that attackers cannot use a side channel attack to learn the number of leading zeros. */ carry = regularize_k(private_key, tmp1, tmp2, curve); EccPoint_mult(result, curve->G, p2[!carry], 0, curve->num_n_bits + 1, curve); if (EccPoint_isZero(result, curve)) { return 0; } return 1; } #if uECC_WORD_SIZE == 1 uECC_VLI_API void uECC_vli_nativeToBytes(uint8_t *bytes, int num_bytes, const uint8_t *native) { wordcount_t i; for (i = 0; i < num_bytes; ++i) { bytes[i] = native[(num_bytes - 1) - i]; } } uECC_VLI_API void uECC_vli_bytesToNative(uint8_t *native, const uint8_t *bytes, int num_bytes) { uECC_vli_nativeToBytes(native, num_bytes, bytes); } #else uECC_VLI_API void uECC_vli_nativeToBytes(uint8_t *bytes, int num_bytes, const uECC_word_t *native) { wordcount_t i; for (i = 0; i < num_bytes; ++i) { unsigned b = num_bytes - 1 - i; bytes[i] = native[b / uECC_WORD_SIZE] >> (8 * (b % uECC_WORD_SIZE)); } } uECC_VLI_API void uECC_vli_bytesToNative(uECC_word_t *native, const uint8_t *bytes, int num_bytes) { wordcount_t i; uECC_vli_clear(native, (num_bytes + (uECC_WORD_SIZE - 1)) / uECC_WORD_SIZE); for (i = 0; i < num_bytes; ++i) { unsigned b = num_bytes - 1 - i; native[b / uECC_WORD_SIZE] |= (uECC_word_t)bytes[i] << (8 * (b % uECC_WORD_SIZE)); } } #endif /* uECC_WORD_SIZE */ /* Generates a random integer in the range 0 < random < top. Both random and top have num_words words. */ uECC_VLI_API int uECC_generate_random_int(uECC_word_t *random, const uECC_word_t *top, wordcount_t num_words) { uECC_word_t mask = (uECC_word_t)-1; uECC_word_t tries; bitcount_t num_bits = uECC_vli_numBits(top, num_words); if (!g_rng_function) { return 0; } for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { if (!g_rng_function((uint8_t *)random, num_words * uECC_WORD_SIZE)) { return 0; } random[num_words - 1] &= mask >> ((bitcount_t)(num_words * uECC_WORD_SIZE * 8 - num_bits)); if (!uECC_vli_isZero(random, num_words) && uECC_vli_cmp(top, random, num_words) == 1) { return 1; } } return 0; } int uECC_make_key(uint8_t *public_key, uint8_t *private_key, uECC_Curve curve) { #if uECC_VLI_NATIVE_LITTLE_ENDIAN uECC_word_t *_private = (uECC_word_t *)private_key; uECC_word_t *_public = (uECC_word_t *)public_key; #else uECC_word_t _private[uECC_MAX_WORDS]; uECC_word_t _public[uECC_MAX_WORDS * 2]; #endif uECC_word_t tries; for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { if (!uECC_generate_random_int(_private, curve->n, BITS_TO_WORDS(curve->num_n_bits))) { return 0; } if (EccPoint_compute_public_key(_public, _private, curve)) { #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 uECC_vli_nativeToBytes(private_key, BITS_TO_BYTES(curve->num_n_bits), _private); uECC_vli_nativeToBytes(public_key, curve->num_bytes, _public); uECC_vli_nativeToBytes( public_key + curve->num_bytes, curve->num_bytes, _public + curve->num_words); #endif return 1; } } return 0; } int uECC_shared_secret(const uint8_t *public_key, const uint8_t *private_key, uint8_t *secret, uECC_Curve curve) { uECC_word_t _public[uECC_MAX_WORDS * 2]; uECC_word_t _private[uECC_MAX_WORDS]; uECC_word_t tmp[uECC_MAX_WORDS]; uECC_word_t *p2[2] = {_private, tmp}; uECC_word_t *initial_Z = 0; uECC_word_t carry; wordcount_t num_words = curve->num_words; wordcount_t num_bytes = curve->num_bytes; #if uECC_VLI_NATIVE_LITTLE_ENDIAN bcopy((uint8_t *) _private, private_key, num_bytes); bcopy((uint8_t *) _public, public_key, num_bytes*2); #else uECC_vli_bytesToNative(_private, private_key, BITS_TO_BYTES(curve->num_n_bits)); uECC_vli_bytesToNative(_public, public_key, num_bytes); uECC_vli_bytesToNative(_public + num_words, public_key + num_bytes, num_bytes); #endif /* Regularize the bitcount for the private key so that attackers cannot use a side channel attack to learn the number of leading zeros. */ carry = regularize_k(_private, _private, tmp, curve); /* If an RNG function was specified, try to get a random initial Z value to improve protection against side-channel attacks. */ if (g_rng_function) { if (!uECC_generate_random_int(p2[carry], curve->p, num_words)) { return 0; } initial_Z = p2[carry]; } EccPoint_mult(_public, _public, p2[!carry], initial_Z, curve->num_n_bits + 1, curve); #if uECC_VLI_NATIVE_LITTLE_ENDIAN bcopy((uint8_t *) secret, (uint8_t *) _public, num_bytes); #else uECC_vli_nativeToBytes(secret, num_bytes, _public); #endif return !EccPoint_isZero(_public, curve); } #if uECC_SUPPORT_COMPRESSED_POINT void uECC_compress(const uint8_t *public_key, uint8_t *compressed, uECC_Curve curve) { wordcount_t i; for (i = 0; i < curve->num_bytes; ++i) { compressed[i+1] = public_key[i]; } #if uECC_VLI_NATIVE_LITTLE_ENDIAN compressed[0] = 2 + (public_key[curve->num_bytes] & 0x01); #else compressed[0] = 2 + (public_key[curve->num_bytes * 2 - 1] & 0x01); #endif } void uECC_decompress(const uint8_t *compressed, uint8_t *public_key, uECC_Curve curve) { #if uECC_VLI_NATIVE_LITTLE_ENDIAN uECC_word_t *point = (uECC_word_t *)public_key; #else uECC_word_t point[uECC_MAX_WORDS * 2]; #endif uECC_word_t *y = point + curve->num_words; #if uECC_VLI_NATIVE_LITTLE_ENDIAN bcopy(public_key, compressed+1, curve->num_bytes); #else uECC_vli_bytesToNative(point, compressed + 1, curve->num_bytes); #endif curve->x_side(y, point, curve); curve->mod_sqrt(y, curve); if ((y[0] & 0x01) != (compressed[0] & 0x01)) { uECC_vli_sub(y, curve->p, y, curve->num_words); } #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 uECC_vli_nativeToBytes(public_key, curve->num_bytes, point); uECC_vli_nativeToBytes(public_key + curve->num_bytes, curve->num_bytes, y); #endif } #endif /* uECC_SUPPORT_COMPRESSED_POINT */ int uECC_valid_point(const uECC_word_t *point, uECC_Curve curve) { uECC_word_t tmp1[uECC_MAX_WORDS]; uECC_word_t tmp2[uECC_MAX_WORDS]; wordcount_t num_words = curve->num_words; /* The point at infinity is invalid. */ if (EccPoint_isZero(point, curve)) { return 0; } /* x and y must be smaller than p. */ if (uECC_vli_cmp_unsafe(curve->p, point, num_words) != 1 || uECC_vli_cmp_unsafe(curve->p, point + num_words, num_words) != 1) { return 0; } uECC_vli_modSquare_fast(tmp1, point + num_words, curve); curve->x_side(tmp2, point, curve); /* tmp2 = x^3 + ax + b */ /* Make sure that y^2 == x^3 + ax + b */ return (int)(uECC_vli_equal(tmp1, tmp2, num_words)); } int uECC_valid_public_key(const uint8_t *public_key, uECC_Curve curve) { #if uECC_VLI_NATIVE_LITTLE_ENDIAN uECC_word_t *_public = (uECC_word_t *)public_key; #else uECC_word_t _public[uECC_MAX_WORDS * 2]; #endif #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 uECC_vli_bytesToNative(_public, public_key, curve->num_bytes); uECC_vli_bytesToNative( _public + curve->num_words, public_key + curve->num_bytes, curve->num_bytes); #endif return uECC_valid_point(_public, curve); } int uECC_compute_public_key(const uint8_t *private_key, uint8_t *public_key, uECC_Curve curve) { #if uECC_VLI_NATIVE_LITTLE_ENDIAN uECC_word_t *_private = (uECC_word_t *)private_key; uECC_word_t *_public = (uECC_word_t *)public_key; #else uECC_word_t _private[uECC_MAX_WORDS]; uECC_word_t _public[uECC_MAX_WORDS * 2]; #endif #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 uECC_vli_bytesToNative(_private, private_key, BITS_TO_BYTES(curve->num_n_bits)); #endif /* Make sure the private key is in the range [1, n-1]. */ if (uECC_vli_isZero(_private, BITS_TO_WORDS(curve->num_n_bits))) { return 0; } if (uECC_vli_cmp(curve->n, _private, BITS_TO_WORDS(curve->num_n_bits)) != 1) { return 0; } /* Compute public key. */ if (!EccPoint_compute_public_key(_public, _private, curve)) { return 0; } #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 uECC_vli_nativeToBytes(public_key, curve->num_bytes, _public); uECC_vli_nativeToBytes( public_key + curve->num_bytes, curve->num_bytes, _public + curve->num_words); #endif return 1; } /* -------- ECDSA code -------- */ static void bits2int(uECC_word_t *native, const uint8_t *bits, unsigned bits_size, uECC_Curve curve) { unsigned num_n_bytes = BITS_TO_BYTES(curve->num_n_bits); unsigned num_n_words = BITS_TO_WORDS(curve->num_n_bits); int shift; uECC_word_t carry; uECC_word_t *ptr; if (bits_size > num_n_bytes) { bits_size = num_n_bytes; } uECC_vli_clear(native, num_n_words); #if uECC_VLI_NATIVE_LITTLE_ENDIAN bcopy((uint8_t *) native, bits, bits_size); #else uECC_vli_bytesToNative(native, bits, bits_size); #endif if (bits_size * 8 <= (unsigned)curve->num_n_bits) { return; } shift = bits_size * 8 - curve->num_n_bits; carry = 0; ptr = native + num_n_words; while (ptr-- > native) { uECC_word_t temp = *ptr; *ptr = (temp >> shift) | carry; carry = temp << (uECC_WORD_BITS - shift); } /* Reduce mod curve_n */ if (uECC_vli_cmp_unsafe(curve->n, native, num_n_words) != 1) { uECC_vli_sub(native, native, curve->n, num_n_words); } } static int uECC_sign_with_k(const uint8_t *private_key, const uint8_t *message_hash, unsigned hash_size, uECC_word_t *k, uint8_t *signature, uECC_Curve curve) { uECC_word_t tmp[uECC_MAX_WORDS]; uECC_word_t s[uECC_MAX_WORDS]; uECC_word_t *k2[2] = {tmp, s}; #if uECC_VLI_NATIVE_LITTLE_ENDIAN uECC_word_t *p = (uECC_word_t *)signature; #else uECC_word_t p[uECC_MAX_WORDS * 2]; #endif uECC_word_t carry; wordcount_t num_words = curve->num_words; wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); bitcount_t num_n_bits = curve->num_n_bits; /* Make sure 0 < k < curve_n */ if (uECC_vli_isZero(k, num_words) || uECC_vli_cmp(curve->n, k, num_n_words) != 1) { return 0; } carry = regularize_k(k, tmp, s, curve); EccPoint_mult(p, curve->G, k2[!carry], 0, num_n_bits + 1, curve); if (uECC_vli_isZero(p, num_words)) { return 0; } /* If an RNG function was specified, get a random number to prevent side channel analysis of k. */ if (!g_rng_function) { uECC_vli_clear(tmp, num_n_words); tmp[0] = 1; } else if (!uECC_generate_random_int(tmp, curve->n, num_n_words)) { return 0; } /* Prevent side channel analysis of uECC_vli_modInv() to determine bits of k / the private key by premultiplying by a random number */ uECC_vli_modMult(k, k, tmp, curve->n, num_n_words); /* k' = rand * k */ uECC_vli_modInv(k, k, curve->n, num_n_words); /* k = 1 / k' */ uECC_vli_modMult(k, k, tmp, curve->n, num_n_words); /* k = 1 / k */ #if uECC_VLI_NATIVE_LITTLE_ENDIAN == 0 uECC_vli_nativeToBytes(signature, curve->num_bytes, p); /* store r */ #endif #if uECC_VLI_NATIVE_LITTLE_ENDIAN bcopy((uint8_t *) tmp, private_key, BITS_TO_BYTES(curve->num_n_bits)); #else uECC_vli_bytesToNative(tmp, private_key, BITS_TO_BYTES(curve->num_n_bits)); /* tmp = d */ #endif s[num_n_words - 1] = 0; uECC_vli_set(s, p, num_words); uECC_vli_modMult(s, tmp, s, curve->n, num_n_words); /* s = r*d */ bits2int(tmp, message_hash, hash_size, curve); uECC_vli_modAdd(s, tmp, s, curve->n, num_n_words); /* s = e + r*d */ uECC_vli_modMult(s, s, k, curve->n, num_n_words); /* s = (e + r*d) / k */ if (uECC_vli_numBits(s, num_n_words) > (bitcount_t)curve->num_bytes * 8) { return 0; } #if uECC_VLI_NATIVE_LITTLE_ENDIAN bcopy((uint8_t *) signature + curve->num_bytes, (uint8_t *) s, curve->num_bytes); #else uECC_vli_nativeToBytes(signature + curve->num_bytes, curve->num_bytes, s); #endif return 1; } int uECC_sign(const uint8_t *private_key, const uint8_t *message_hash, unsigned hash_size, uint8_t *signature, uECC_Curve curve) { uECC_word_t k[uECC_MAX_WORDS]; uECC_word_t tries; for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { if (!uECC_generate_random_int(k, curve->n, BITS_TO_WORDS(curve->num_n_bits))) { return 0; } if (uECC_sign_with_k(private_key, message_hash, hash_size, k, signature, curve)) { return 1; } } return 0; } /* Compute an HMAC using K as a key (as in RFC 6979). Note that K is always the same size as the hash result size. */ static void HMAC_init(const uECC_HashContext *hash_context, const uint8_t *K) { uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size; unsigned i; for (i = 0; i < hash_context->result_size; ++i) pad[i] = K[i] ^ 0x36; for (; i < hash_context->block_size; ++i) pad[i] = 0x36; hash_context->init_hash(hash_context); hash_context->update_hash(hash_context, pad, hash_context->block_size); } static void HMAC_update(const uECC_HashContext *hash_context, const uint8_t *message, unsigned message_size) { hash_context->update_hash(hash_context, message, message_size); } static void HMAC_finish(const uECC_HashContext *hash_context, const uint8_t *K, uint8_t *result) { uint8_t *pad = hash_context->tmp + 2 * hash_context->result_size; unsigned i; for (i = 0; i < hash_context->result_size; ++i) pad[i] = K[i] ^ 0x5c; for (; i < hash_context->block_size; ++i) pad[i] = 0x5c; hash_context->finish_hash(hash_context, result); hash_context->init_hash(hash_context); hash_context->update_hash(hash_context, pad, hash_context->block_size); hash_context->update_hash(hash_context, result, hash_context->result_size); hash_context->finish_hash(hash_context, result); } /* V = HMAC_K(V) */ static void update_V(const uECC_HashContext *hash_context, uint8_t *K, uint8_t *V) { HMAC_init(hash_context, K); HMAC_update(hash_context, V, hash_context->result_size); HMAC_finish(hash_context, K, V); } /* Deterministic signing, similar to RFC 6979. Differences are: * We just use H(m) directly rather than bits2octets(H(m)) (it is not reduced modulo curve_n). * We generate a value for k (aka T) directly rather than converting endianness. Layout of hash_context->tmp: | | (1 byte overlapped 0x00 or 0x01) / */ int uECC_sign_deterministic(const uint8_t *private_key, const uint8_t *message_hash, unsigned hash_size, const uECC_HashContext *hash_context, uint8_t *signature, uECC_Curve curve) { uint8_t *K = hash_context->tmp; uint8_t *V = K + hash_context->result_size; wordcount_t num_bytes = curve->num_bytes; wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); bitcount_t num_n_bits = curve->num_n_bits; uECC_word_t tries; unsigned i; for (i = 0; i < hash_context->result_size; ++i) { V[i] = 0x01; K[i] = 0; } /* K = HMAC_K(V || 0x00 || int2octets(x) || h(m)) */ HMAC_init(hash_context, K); V[hash_context->result_size] = 0x00; HMAC_update(hash_context, V, hash_context->result_size + 1); HMAC_update(hash_context, private_key, num_bytes); HMAC_update(hash_context, message_hash, hash_size); HMAC_finish(hash_context, K, K); update_V(hash_context, K, V); /* K = HMAC_K(V || 0x01 || int2octets(x) || h(m)) */ HMAC_init(hash_context, K); V[hash_context->result_size] = 0x01; HMAC_update(hash_context, V, hash_context->result_size + 1); HMAC_update(hash_context, private_key, num_bytes); HMAC_update(hash_context, message_hash, hash_size); HMAC_finish(hash_context, K, K); update_V(hash_context, K, V); for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { uECC_word_t T[uECC_MAX_WORDS]; uint8_t *T_ptr = (uint8_t *)T; wordcount_t T_bytes = 0; for (;;) { update_V(hash_context, K, V); for (i = 0; i < hash_context->result_size; ++i) { T_ptr[T_bytes++] = V[i]; if (T_bytes >= num_n_words * uECC_WORD_SIZE) { goto filled; } } } filled: if ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8 > num_n_bits) { uECC_word_t mask = (uECC_word_t)-1; T[num_n_words - 1] &= mask >> ((bitcount_t)(num_n_words * uECC_WORD_SIZE * 8 - num_n_bits)); } if (uECC_sign_with_k(private_key, message_hash, hash_size, T, signature, curve)) { return 1; } /* K = HMAC_K(V || 0x00) */ HMAC_init(hash_context, K); V[hash_context->result_size] = 0x00; HMAC_update(hash_context, V, hash_context->result_size + 1); HMAC_finish(hash_context, K, K); update_V(hash_context, K, V); } return 0; } static bitcount_t smax(bitcount_t a, bitcount_t b) { return (a > b ? a : b); } int uECC_verify(const uint8_t *public_key, const uint8_t *message_hash, unsigned hash_size, const uint8_t *signature, uECC_Curve curve) { uECC_word_t u1[uECC_MAX_WORDS], u2[uECC_MAX_WORDS]; uECC_word_t z[uECC_MAX_WORDS]; uECC_word_t sum[uECC_MAX_WORDS * 2]; uECC_word_t rx[uECC_MAX_WORDS]; uECC_word_t ry[uECC_MAX_WORDS]; uECC_word_t tx[uECC_MAX_WORDS]; uECC_word_t ty[uECC_MAX_WORDS]; uECC_word_t tz[uECC_MAX_WORDS]; const uECC_word_t *points[4]; const uECC_word_t *point; bitcount_t num_bits; bitcount_t i; #if uECC_VLI_NATIVE_LITTLE_ENDIAN uECC_word_t *_public = (uECC_word_t *)public_key; #else uECC_word_t _public[uECC_MAX_WORDS * 2]; #endif uECC_word_t r[uECC_MAX_WORDS], s[uECC_MAX_WORDS]; wordcount_t num_words = curve->num_words; wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); rx[num_n_words - 1] = 0; r[num_n_words - 1] = 0; s[num_n_words - 1] = 0; #if uECC_VLI_NATIVE_LITTLE_ENDIAN bcopy((uint8_t *) r, signature, curve->num_bytes); bcopy((uint8_t *) s, signature + curve->num_bytes, curve->num_bytes); #else uECC_vli_bytesToNative(_public, public_key, curve->num_bytes); uECC_vli_bytesToNative( _public + num_words, public_key + curve->num_bytes, curve->num_bytes); uECC_vli_bytesToNative(r, signature, curve->num_bytes); uECC_vli_bytesToNative(s, signature + curve->num_bytes, curve->num_bytes); #endif /* r, s must not be 0. */ if (uECC_vli_isZero(r, num_words) || uECC_vli_isZero(s, num_words)) { return 0; } /* r, s must be < n. */ if (uECC_vli_cmp_unsafe(curve->n, r, num_n_words) != 1 || uECC_vli_cmp_unsafe(curve->n, s, num_n_words) != 1) { return 0; } /* Calculate u1 and u2. */ uECC_vli_modInv(z, s, curve->n, num_n_words); /* z = 1/s */ u1[num_n_words - 1] = 0; bits2int(u1, message_hash, hash_size, curve); uECC_vli_modMult(u1, u1, z, curve->n, num_n_words); /* u1 = e/s */ uECC_vli_modMult(u2, r, z, curve->n, num_n_words); /* u2 = r/s */ /* Calculate sum = G + Q. */ uECC_vli_set(sum, _public, num_words); uECC_vli_set(sum + num_words, _public + num_words, num_words); uECC_vli_set(tx, curve->G, num_words); uECC_vli_set(ty, curve->G + num_words, num_words); uECC_vli_modSub(z, sum, tx, curve->p, num_words); /* z = x2 - x1 */ XYcZ_add(tx, ty, sum, sum + num_words, curve); uECC_vli_modInv(z, z, curve->p, num_words); /* z = 1/z */ apply_z(sum, sum + num_words, z, curve); /* Use Shamir's trick to calculate u1*G + u2*Q */ points[0] = 0; points[1] = curve->G; points[2] = _public; points[3] = sum; num_bits = smax(uECC_vli_numBits(u1, num_n_words), uECC_vli_numBits(u2, num_n_words)); point = points[(!!uECC_vli_testBit(u1, num_bits - 1)) | ((!!uECC_vli_testBit(u2, num_bits - 1)) << 1)]; uECC_vli_set(rx, point, num_words); uECC_vli_set(ry, point + num_words, num_words); uECC_vli_clear(z, num_words); z[0] = 1; for (i = num_bits - 2; i >= 0; --i) { uECC_word_t index; curve->double_jacobian(rx, ry, z, curve); index = (!!uECC_vli_testBit(u1, i)) | ((!!uECC_vli_testBit(u2, i)) << 1); point = points[index]; if (point) { uECC_vli_set(tx, point, num_words); uECC_vli_set(ty, point + num_words, num_words); apply_z(tx, ty, z, curve); uECC_vli_modSub(tz, rx, tx, curve->p, num_words); /* Z = x2 - x1 */ XYcZ_add(tx, ty, rx, ry, curve); uECC_vli_modMult_fast(z, z, tz, curve); } } uECC_vli_modInv(z, z, curve->p, num_words); /* Z = 1/Z */ apply_z(rx, ry, z, curve); /* v = x1 (mod n) */ if (uECC_vli_cmp_unsafe(curve->n, rx, num_n_words) != 1) { uECC_vli_sub(rx, rx, curve->n, num_n_words); } /* Accept only if v == r. */ return (int)(uECC_vli_equal(rx, r, num_words)); } #if uECC_ENABLE_VLI_API unsigned uECC_curve_num_words(uECC_Curve curve) { return curve->num_words; } unsigned uECC_curve_num_bytes(uECC_Curve curve) { return curve->num_bytes; } unsigned uECC_curve_num_bits(uECC_Curve curve) { return curve->num_bytes * 8; } unsigned uECC_curve_num_n_words(uECC_Curve curve) { return BITS_TO_WORDS(curve->num_n_bits); } unsigned uECC_curve_num_n_bytes(uECC_Curve curve) { return BITS_TO_BYTES(curve->num_n_bits); } unsigned uECC_curve_num_n_bits(uECC_Curve curve) { return curve->num_n_bits; } const uECC_word_t *uECC_curve_p(uECC_Curve curve) { return curve->p; } const uECC_word_t *uECC_curve_n(uECC_Curve curve) { return curve->n; } const uECC_word_t *uECC_curve_G(uECC_Curve curve) { return curve->G; } const uECC_word_t *uECC_curve_b(uECC_Curve curve) { return curve->b; } #if uECC_SUPPORT_COMPRESSED_POINT void uECC_vli_mod_sqrt(uECC_word_t *a, uECC_Curve curve) { curve->mod_sqrt(a, curve); } #endif void uECC_vli_mmod_fast(uECC_word_t *result, uECC_word_t *product, uECC_Curve curve) { #if (uECC_OPTIMIZATION_LEVEL > 0) curve->mmod_fast(result, product); #else uECC_vli_mmod(result, product, curve->p, curve->num_words); #endif } void uECC_point_mult(uECC_word_t *result, const uECC_word_t *point, const uECC_word_t *scalar, uECC_Curve curve) { uECC_word_t tmp1[uECC_MAX_WORDS]; uECC_word_t tmp2[uECC_MAX_WORDS]; uECC_word_t *p2[2] = {tmp1, tmp2}; uECC_word_t carry = regularize_k(scalar, tmp1, tmp2, curve); EccPoint_mult(result, point, p2[!carry], 0, curve->num_n_bits + 1, curve); } #endif /* uECC_ENABLE_VLI_API */