Kai Liu
micro-ECC for mbed, ported from GCC version from Github,
Dependents: mbed_microECC Wallet_v1
Diff: uECC.cpp
- Revision:
- 0:b6fdeddc0bc9
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/uECC.cpp Thu Sep 07 12:10:11 2017 +0000
@@ -0,0 +1,1644 @@
+/* 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"
+#include "platform-specific.h"
+
+#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"
+ #include "asm_arm.h"
+#if (uECC_PLATFORM == uECC_arm)
+ #warning uECC_arm
+#elif (uECC_PLATFORM == uECC_arm_thumb)
+ #warning uECC_arm_thumb
+#elif (uECC_PLATFORM == uECC_arm_thumb2)
+ #warning uECC_arm_thumb2
+#endif
+#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"
+#include "curve-specific.h"
+
+/* 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: <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 */