| /* 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 (cmpresult_t)(!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] = (uint8_t)(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: <K> | <V> | (1 byte overlapped 0x00 or 0x01) / <HMAC pad> */ |
| 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 */ |
