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mongoose/src/tls_uecc.c
Sergio R. Caprile 285dc63c5c reformat comments
2023-12-20 16:40:31 -03:00

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/* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */
#include "tls_uecc.h"
#include "tls.h"
#if MG_TLS == MG_TLS_BUILTIN
#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
#if (uECC_PLATFORM == uECC_avr) || (uECC_PLATFORM == uECC_arm) || \
(uECC_PLATFORM == uECC_arm_thumb) || (uECC_PLATFORM == uECC_arm_thumb2)
#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))
#endif
//#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) \
((wordcount_t) ((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
#ifndef asm_clear
#define asm_clear 0
#endif
#ifndef asm_set
#define asm_set 0
#endif
#ifndef asm_add
#define asm_add 0
#endif
#ifndef asm_sub
#define asm_sub 0
#endif
#ifndef asm_mult
#define asm_mult 0
#endif
#ifndef asm_rshift1
#define asm_rshift1 0
#endif
#ifndef asm_mmod_fast_secp256r1
#define asm_mmod_fast_secp256r1 0
#endif
#if defined(default_RNG_defined) && 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)) +
(bitcount_t) 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
uint64_t a0 = a & 0xffffffff;
uint64_t a1 = a >> 32;
uint64_t b0 = b & 0xffffffff;
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 += 0x100000000;
}
p0 = (i0 & 0xffffffff) | (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 = (uECC_word_t) (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 = (wordcount_t) ((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
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 = (bitcount_t) (
(num_words * 2 * uECC_WORD_BITS) - uECC_vli_numBits(mod, num_words));
wordcount_t word_shift = (wordcount_t) (shift / uECC_WORD_BITS);
wordcount_t bit_shift = (wordcount_t) (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[(uECC_word_t) word_shift + index] =
(uECC_word_t) (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 ------ */
/* Copyright 2015, Kenneth MacKay. Licensed under the BSD 2-clause license. */
#ifndef _UECC_CURVE_SPECIFIC_H_
#define _UECC_CURVE_SPECIFIC_H_
#define num_bytes_secp160r1 20
#define num_bytes_secp192r1 24
#define num_bytes_secp224r1 28
#define num_bytes_secp256r1 32
#define num_bytes_secp256k1 32
#if (uECC_WORD_SIZE == 1)
#define num_words_secp160r1 20
#define num_words_secp192r1 24
#define num_words_secp224r1 28
#define num_words_secp256r1 32
#define num_words_secp256k1 32
#define BYTES_TO_WORDS_8(a, b, c, d, e, f, g, h) \
0x##a, 0x##b, 0x##c, 0x##d, 0x##e, 0x##f, 0x##g, 0x##h
#define BYTES_TO_WORDS_4(a, b, c, d) 0x##a, 0x##b, 0x##c, 0x##d
#elif (uECC_WORD_SIZE == 4)
#define num_words_secp160r1 5
#define num_words_secp192r1 6
#define num_words_secp224r1 7
#define num_words_secp256r1 8
#define num_words_secp256k1 8
#define BYTES_TO_WORDS_8(a, b, c, d, e, f, g, h) 0x##d##c##b##a, 0x##h##g##f##e
#define BYTES_TO_WORDS_4(a, b, c, d) 0x##d##c##b##a
#elif (uECC_WORD_SIZE == 8)
#define num_words_secp160r1 3
#define num_words_secp192r1 3
#define num_words_secp224r1 4
#define num_words_secp256r1 4
#define num_words_secp256k1 4
#define BYTES_TO_WORDS_8(a, b, c, d, e, f, g, h) 0x##h##g##f##e##d##c##b##a##U
#define BYTES_TO_WORDS_4(a, b, c, d) 0x##d##c##b##a##U
#endif /* uECC_WORD_SIZE */
#if uECC_SUPPORTS_secp160r1 || uECC_SUPPORTS_secp192r1 || \
uECC_SUPPORTS_secp224r1 || uECC_SUPPORTS_secp256r1
static void double_jacobian_default(uECC_word_t *X1, uECC_word_t *Y1,
uECC_word_t *Z1, uECC_Curve curve) {
/* t1 = X, t2 = Y, t3 = Z */
uECC_word_t t4[uECC_MAX_WORDS];
uECC_word_t t5[uECC_MAX_WORDS];
wordcount_t num_words = curve->num_words;
if (uECC_vli_isZero(Z1, num_words)) {
return;
}
uECC_vli_modSquare_fast(t4, Y1, curve); /* t4 = y1^2 */
uECC_vli_modMult_fast(t5, X1, t4, curve); /* t5 = x1*y1^2 = A */
uECC_vli_modSquare_fast(t4, t4, curve); /* t4 = y1^4 */
uECC_vli_modMult_fast(Y1, Y1, Z1, curve); /* t2 = y1*z1 = z3 */
uECC_vli_modSquare_fast(Z1, Z1, curve); /* t3 = z1^2 */
uECC_vli_modAdd(X1, X1, Z1, curve->p, num_words); /* t1 = x1 + z1^2 */
uECC_vli_modAdd(Z1, Z1, Z1, curve->p, num_words); /* t3 = 2*z1^2 */
uECC_vli_modSub(Z1, X1, Z1, curve->p, num_words); /* t3 = x1 - z1^2 */
uECC_vli_modMult_fast(X1, X1, Z1, curve); /* t1 = x1^2 - z1^4 */
uECC_vli_modAdd(Z1, X1, X1, curve->p, num_words); /* t3 = 2*(x1^2 - z1^4) */
uECC_vli_modAdd(X1, X1, Z1, curve->p, num_words); /* t1 = 3*(x1^2 - z1^4) */
if (uECC_vli_testBit(X1, 0)) {
uECC_word_t l_carry = uECC_vli_add(X1, X1, curve->p, num_words);
uECC_vli_rshift1(X1, num_words);
X1[num_words - 1] |= l_carry << (uECC_WORD_BITS - 1);
} else {
uECC_vli_rshift1(X1, num_words);
}
/* t1 = 3/2*(x1^2 - z1^4) = B */
uECC_vli_modSquare_fast(Z1, X1, curve); /* t3 = B^2 */
uECC_vli_modSub(Z1, Z1, t5, curve->p, num_words); /* t3 = B^2 - A */
uECC_vli_modSub(Z1, Z1, t5, curve->p, num_words); /* t3 = B^2 - 2A = x3 */
uECC_vli_modSub(t5, t5, Z1, curve->p, num_words); /* t5 = A - x3 */
uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = B * (A - x3) */
uECC_vli_modSub(t4, X1, t4, curve->p,
num_words); /* t4 = B * (A - x3) - y1^4 = y3 */
uECC_vli_set(X1, Z1, num_words);
uECC_vli_set(Z1, Y1, num_words);
uECC_vli_set(Y1, t4, num_words);
}
/* Computes result = x^3 + ax + b. result must not overlap x. */
static void x_side_default(uECC_word_t *result, const uECC_word_t *x,
uECC_Curve curve) {
uECC_word_t _3[uECC_MAX_WORDS] = {3}; /* -a = 3 */
wordcount_t num_words = curve->num_words;
uECC_vli_modSquare_fast(result, x, curve); /* r = x^2 */
uECC_vli_modSub(result, result, _3, curve->p, num_words); /* r = x^2 - 3 */
uECC_vli_modMult_fast(result, result, x, curve); /* r = x^3 - 3x */
uECC_vli_modAdd(result, result, curve->b, curve->p,
num_words); /* r = x^3 - 3x + b */
}
#endif /* uECC_SUPPORTS_secp... */
#if uECC_SUPPORT_COMPRESSED_POINT
#if uECC_SUPPORTS_secp160r1 || uECC_SUPPORTS_secp192r1 || \
uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1
/* Compute a = sqrt(a) (mod curve_p). */
static void mod_sqrt_default(uECC_word_t *a, uECC_Curve curve) {
bitcount_t i;
uECC_word_t p1[uECC_MAX_WORDS] = {1};
uECC_word_t l_result[uECC_MAX_WORDS] = {1};
wordcount_t num_words = curve->num_words;
/* When curve->p == 3 (mod 4), we can compute
sqrt(a) = a^((curve->p + 1) / 4) (mod curve->p). */
uECC_vli_add(p1, curve->p, p1, num_words); /* p1 = curve_p + 1 */
for (i = uECC_vli_numBits(p1, num_words) - 1; i > 1; --i) {
uECC_vli_modSquare_fast(l_result, l_result, curve);
if (uECC_vli_testBit(p1, i)) {
uECC_vli_modMult_fast(l_result, l_result, a, curve);
}
}
uECC_vli_set(a, l_result, num_words);
}
#endif /* uECC_SUPPORTS_secp... */
#endif /* uECC_SUPPORT_COMPRESSED_POINT */
#if uECC_SUPPORTS_secp160r1
#if (uECC_OPTIMIZATION_LEVEL > 0)
static void vli_mmod_fast_secp160r1(uECC_word_t *result, uECC_word_t *product);
#endif
static const struct uECC_Curve_t curve_secp160r1 = {
num_words_secp160r1,
num_bytes_secp160r1,
161, /* num_n_bits */
{BYTES_TO_WORDS_8(FF, FF, FF, 7F, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_4(FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(57, 22, 75, CA, D3, AE, 27, F9),
BYTES_TO_WORDS_8(C8, F4, 01, 00, 00, 00, 00, 00),
BYTES_TO_WORDS_8(00, 00, 00, 00, 01, 00, 00, 00)},
{BYTES_TO_WORDS_8(82, FC, CB, 13, B9, 8B, C3, 68),
BYTES_TO_WORDS_8(89, 69, 64, 46, 28, 73, F5, 8E),
BYTES_TO_WORDS_4(68, B5, 96, 4A),
BYTES_TO_WORDS_8(32, FB, C5, 7A, 37, 51, 23, 04),
BYTES_TO_WORDS_8(12, C9, DC, 59, 7D, 94, 68, 31),
BYTES_TO_WORDS_4(55, 28, A6, 23)},
{BYTES_TO_WORDS_8(45, FA, 65, C5, AD, D4, D4, 81),
BYTES_TO_WORDS_8(9F, F8, AC, 65, 8B, 7A, BD, 54),
BYTES_TO_WORDS_4(FC, BE, 97, 1C)},
&double_jacobian_default,
#if uECC_SUPPORT_COMPRESSED_POINT
&mod_sqrt_default,
#endif
&x_side_default,
#if (uECC_OPTIMIZATION_LEVEL > 0)
&vli_mmod_fast_secp160r1
#endif
};
uECC_Curve uECC_secp160r1(void) {
return &curve_secp160r1;
}
#if (uECC_OPTIMIZATION_LEVEL > 0 && !asm_mmod_fast_secp160r1)
/* Computes result = product % curve_p
see http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf page 354
Note that this only works if log2(omega) < log2(p) / 2 */
static void omega_mult_secp160r1(uECC_word_t *result, const uECC_word_t *right);
#if uECC_WORD_SIZE == 8
static void vli_mmod_fast_secp160r1(uECC_word_t *result, uECC_word_t *product) {
uECC_word_t tmp[2 * num_words_secp160r1];
uECC_word_t copy;
uECC_vli_clear(tmp, num_words_secp160r1);
uECC_vli_clear(tmp + num_words_secp160r1, num_words_secp160r1);
omega_mult_secp160r1(tmp,
product + num_words_secp160r1 - 1); /* (Rq, q) = q * c */
product[num_words_secp160r1 - 1] &= 0xffffffff;
copy = tmp[num_words_secp160r1 - 1];
tmp[num_words_secp160r1 - 1] &= 0xffffffff;
uECC_vli_add(result, product, tmp, num_words_secp160r1); /* (C, r) = r + q */
uECC_vli_clear(product, num_words_secp160r1);
tmp[num_words_secp160r1 - 1] = copy;
omega_mult_secp160r1(product, tmp + num_words_secp160r1 - 1); /* Rq*c */
uECC_vli_add(result, result, product,
num_words_secp160r1); /* (C1, r) = r + Rq*c */
while (uECC_vli_cmp_unsafe(result, curve_secp160r1.p, num_words_secp160r1) >
0) {
uECC_vli_sub(result, result, curve_secp160r1.p, num_words_secp160r1);
}
}
static void omega_mult_secp160r1(uint64_t *result, const uint64_t *right) {
uint32_t carry;
unsigned i;
/* Multiply by (2^31 + 1). */
carry = 0;
for (i = 0; i < num_words_secp160r1; ++i) {
uint64_t tmp = (right[i] >> 32) | (right[i + 1] << 32);
result[i] = (tmp << 31) + tmp + carry;
carry = (tmp >> 33) + (result[i] < tmp || (carry && result[i] == tmp));
}
result[i] = carry;
}
#else
static void vli_mmod_fast_secp160r1(uECC_word_t *result, uECC_word_t *product) {
uECC_word_t tmp[2 * num_words_secp160r1];
uECC_word_t carry;
uECC_vli_clear(tmp, num_words_secp160r1);
uECC_vli_clear(tmp + num_words_secp160r1, num_words_secp160r1);
omega_mult_secp160r1(tmp,
product + num_words_secp160r1); /* (Rq, q) = q * c */
carry = uECC_vli_add(result, product, tmp,
num_words_secp160r1); /* (C, r) = r + q */
uECC_vli_clear(product, num_words_secp160r1);
omega_mult_secp160r1(product, tmp + num_words_secp160r1); /* Rq*c */
carry += uECC_vli_add(result, result, product,
num_words_secp160r1); /* (C1, r) = r + Rq*c */
while (carry > 0) {
--carry;
uECC_vli_sub(result, result, curve_secp160r1.p, num_words_secp160r1);
}
if (uECC_vli_cmp_unsafe(result, curve_secp160r1.p, num_words_secp160r1) > 0) {
uECC_vli_sub(result, result, curve_secp160r1.p, num_words_secp160r1);
}
}
#endif
#if uECC_WORD_SIZE == 1
static void omega_mult_secp160r1(uint8_t *result, const uint8_t *right) {
uint8_t carry;
uint8_t i;
/* Multiply by (2^31 + 1). */
uECC_vli_set(result + 4, right, num_words_secp160r1); /* 2^32 */
uECC_vli_rshift1(result + 4, num_words_secp160r1); /* 2^31 */
result[3] = right[0] << 7; /* get last bit from shift */
carry =
uECC_vli_add(result, result, right, num_words_secp160r1); /* 2^31 + 1 */
for (i = num_words_secp160r1; carry; ++i) {
uint16_t sum = (uint16_t) result[i] + carry;
result[i] = (uint8_t) sum;
carry = sum >> 8;
}
}
#elif uECC_WORD_SIZE == 4
static void omega_mult_secp160r1(uint32_t *result, const uint32_t *right) {
uint32_t carry;
unsigned i;
/* Multiply by (2^31 + 1). */
uECC_vli_set(result + 1, right, num_words_secp160r1); /* 2^32 */
uECC_vli_rshift1(result + 1, num_words_secp160r1); /* 2^31 */
result[0] = right[0] << 31; /* get last bit from shift */
carry =
uECC_vli_add(result, result, right, num_words_secp160r1); /* 2^31 + 1 */
for (i = num_words_secp160r1; carry; ++i) {
uint64_t sum = (uint64_t) result[i] + carry;
result[i] = (uint32_t) sum;
carry = sum >> 32;
}
}
#endif /* uECC_WORD_SIZE */
#endif /* (uECC_OPTIMIZATION_LEVEL > 0 && !asm_mmod_fast_secp160r1) */
#endif /* uECC_SUPPORTS_secp160r1 */
#if uECC_SUPPORTS_secp192r1
#if (uECC_OPTIMIZATION_LEVEL > 0)
static void vli_mmod_fast_secp192r1(uECC_word_t *result, uECC_word_t *product);
#endif
static const struct uECC_Curve_t curve_secp192r1 = {
num_words_secp192r1,
num_bytes_secp192r1,
192, /* num_n_bits */
{BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FE, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(31, 28, D2, B4, B1, C9, 6B, 14),
BYTES_TO_WORDS_8(36, F8, DE, 99, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(12, 10, FF, 82, FD, 0A, FF, F4),
BYTES_TO_WORDS_8(00, 88, A1, 43, EB, 20, BF, 7C),
BYTES_TO_WORDS_8(F6, 90, 30, B0, 0E, A8, 8D, 18),
BYTES_TO_WORDS_8(11, 48, 79, 1E, A1, 77, F9, 73),
BYTES_TO_WORDS_8(D5, CD, 24, 6B, ED, 11, 10, 63),
BYTES_TO_WORDS_8(78, DA, C8, FF, 95, 2B, 19, 07)},
{BYTES_TO_WORDS_8(B1, B9, 46, C1, EC, DE, B8, FE),
BYTES_TO_WORDS_8(49, 30, 24, 72, AB, E9, A7, 0F),
BYTES_TO_WORDS_8(E7, 80, 9C, E5, 19, 05, 21, 64)},
&double_jacobian_default,
#if uECC_SUPPORT_COMPRESSED_POINT
&mod_sqrt_default,
#endif
&x_side_default,
#if (uECC_OPTIMIZATION_LEVEL > 0)
&vli_mmod_fast_secp192r1
#endif
};
uECC_Curve uECC_secp192r1(void) {
return &curve_secp192r1;
}
#if (uECC_OPTIMIZATION_LEVEL > 0)
/* Computes result = product % curve_p.
See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
*/
#if uECC_WORD_SIZE == 1
static void vli_mmod_fast_secp192r1(uint8_t *result, uint8_t *product) {
uint8_t tmp[num_words_secp192r1];
uint8_t carry;
uECC_vli_set(result, product, num_words_secp192r1);
uECC_vli_set(tmp, &product[24], num_words_secp192r1);
carry = uECC_vli_add(result, result, tmp, num_words_secp192r1);
tmp[0] = tmp[1] = tmp[2] = tmp[3] = tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0;
tmp[8] = product[24];
tmp[9] = product[25];
tmp[10] = product[26];
tmp[11] = product[27];
tmp[12] = product[28];
tmp[13] = product[29];
tmp[14] = product[30];
tmp[15] = product[31];
tmp[16] = product[32];
tmp[17] = product[33];
tmp[18] = product[34];
tmp[19] = product[35];
tmp[20] = product[36];
tmp[21] = product[37];
tmp[22] = product[38];
tmp[23] = product[39];
carry += uECC_vli_add(result, result, tmp, num_words_secp192r1);
tmp[0] = tmp[8] = product[40];
tmp[1] = tmp[9] = product[41];
tmp[2] = tmp[10] = product[42];
tmp[3] = tmp[11] = product[43];
tmp[4] = tmp[12] = product[44];
tmp[5] = tmp[13] = product[45];
tmp[6] = tmp[14] = product[46];
tmp[7] = tmp[15] = product[47];
tmp[16] = tmp[17] = tmp[18] = tmp[19] = tmp[20] = tmp[21] = tmp[22] =
tmp[23] = 0;
carry += uECC_vli_add(result, result, tmp, num_words_secp192r1);
while (carry || uECC_vli_cmp_unsafe(curve_secp192r1.p, result,
num_words_secp192r1) != 1) {
carry -=
uECC_vli_sub(result, result, curve_secp192r1.p, num_words_secp192r1);
}
}
#elif uECC_WORD_SIZE == 4
static void vli_mmod_fast_secp192r1(uint32_t *result, uint32_t *product) {
uint32_t tmp[num_words_secp192r1];
int carry;
uECC_vli_set(result, product, num_words_secp192r1);
uECC_vli_set(tmp, &product[6], num_words_secp192r1);
carry = uECC_vli_add(result, result, tmp, num_words_secp192r1);
tmp[0] = tmp[1] = 0;
tmp[2] = product[6];
tmp[3] = product[7];
tmp[4] = product[8];
tmp[5] = product[9];
carry += uECC_vli_add(result, result, tmp, num_words_secp192r1);
tmp[0] = tmp[2] = product[10];
tmp[1] = tmp[3] = product[11];
tmp[4] = tmp[5] = 0;
carry += uECC_vli_add(result, result, tmp, num_words_secp192r1);
while (carry || uECC_vli_cmp_unsafe(curve_secp192r1.p, result,
num_words_secp192r1) != 1) {
carry -=
uECC_vli_sub(result, result, curve_secp192r1.p, num_words_secp192r1);
}
}
#else
static void vli_mmod_fast_secp192r1(uint64_t *result, uint64_t *product) {
uint64_t tmp[num_words_secp192r1];
int carry;
uECC_vli_set(result, product, num_words_secp192r1);
uECC_vli_set(tmp, &product[3], num_words_secp192r1);
carry = (int) uECC_vli_add(result, result, tmp, num_words_secp192r1);
tmp[0] = 0;
tmp[1] = product[3];
tmp[2] = product[4];
carry += uECC_vli_add(result, result, tmp, num_words_secp192r1);
tmp[0] = tmp[1] = product[5];
tmp[2] = 0;
carry += uECC_vli_add(result, result, tmp, num_words_secp192r1);
while (carry || uECC_vli_cmp_unsafe(curve_secp192r1.p, result,
num_words_secp192r1) != 1) {
carry -=
uECC_vli_sub(result, result, curve_secp192r1.p, num_words_secp192r1);
}
}
#endif /* uECC_WORD_SIZE */
#endif /* (uECC_OPTIMIZATION_LEVEL > 0) */
#endif /* uECC_SUPPORTS_secp192r1 */
#if uECC_SUPPORTS_secp224r1
#if uECC_SUPPORT_COMPRESSED_POINT
static void mod_sqrt_secp224r1(uECC_word_t *a, uECC_Curve curve);
#endif
#if (uECC_OPTIMIZATION_LEVEL > 0)
static void vli_mmod_fast_secp224r1(uECC_word_t *result, uECC_word_t *product);
#endif
static const struct uECC_Curve_t curve_secp224r1 = {
num_words_secp224r1,
num_bytes_secp224r1,
224, /* num_n_bits */
{BYTES_TO_WORDS_8(01, 00, 00, 00, 00, 00, 00, 00),
BYTES_TO_WORDS_8(00, 00, 00, 00, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_4(FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(3D, 2A, 5C, 5C, 45, 29, DD, 13),
BYTES_TO_WORDS_8(3E, F0, B8, E0, A2, 16, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_4(FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(21, 1D, 5C, 11, D6, 80, 32, 34),
BYTES_TO_WORDS_8(22, 11, C2, 56, D3, C1, 03, 4A),
BYTES_TO_WORDS_8(B9, 90, 13, 32, 7F, BF, B4, 6B),
BYTES_TO_WORDS_4(BD, 0C, 0E, B7),
BYTES_TO_WORDS_8(34, 7E, 00, 85, 99, 81, D5, 44),
BYTES_TO_WORDS_8(64, 47, 07, 5A, A0, 75, 43, CD),
BYTES_TO_WORDS_8(E6, DF, 22, 4C, FB, 23, F7, B5),
BYTES_TO_WORDS_4(88, 63, 37, BD)},
{BYTES_TO_WORDS_8(B4, FF, 55, 23, 43, 39, 0B, 27),
BYTES_TO_WORDS_8(BA, D8, BF, D7, B7, B0, 44, 50),
BYTES_TO_WORDS_8(56, 32, 41, F5, AB, B3, 04, 0C),
BYTES_TO_WORDS_4(85, 0A, 05, B4)},
&double_jacobian_default,
#if uECC_SUPPORT_COMPRESSED_POINT
&mod_sqrt_secp224r1,
#endif
&x_side_default,
#if (uECC_OPTIMIZATION_LEVEL > 0)
&vli_mmod_fast_secp224r1
#endif
};
uECC_Curve uECC_secp224r1(void) {
return &curve_secp224r1;
}
#if uECC_SUPPORT_COMPRESSED_POINT
/* Routine 3.2.4 RS; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1_rs(uECC_word_t *d1, uECC_word_t *e1,
uECC_word_t *f1, const uECC_word_t *d0,
const uECC_word_t *e0,
const uECC_word_t *f0) {
uECC_word_t t[num_words_secp224r1];
uECC_vli_modSquare_fast(t, d0, &curve_secp224r1); /* t <-- d0 ^ 2 */
uECC_vli_modMult_fast(e1, d0, e0, &curve_secp224r1); /* e1 <-- d0 * e0 */
uECC_vli_modAdd(d1, t, f0, curve_secp224r1.p,
num_words_secp224r1); /* d1 <-- t + f0 */
uECC_vli_modAdd(e1, e1, e1, curve_secp224r1.p,
num_words_secp224r1); /* e1 <-- e1 + e1 */
uECC_vli_modMult_fast(f1, t, f0, &curve_secp224r1); /* f1 <-- t * f0 */
uECC_vli_modAdd(f1, f1, f1, curve_secp224r1.p,
num_words_secp224r1); /* f1 <-- f1 + f1 */
uECC_vli_modAdd(f1, f1, f1, curve_secp224r1.p,
num_words_secp224r1); /* f1 <-- f1 + f1 */
}
/* Routine 3.2.5 RSS; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1_rss(uECC_word_t *d1, uECC_word_t *e1,
uECC_word_t *f1, const uECC_word_t *d0,
const uECC_word_t *e0, const uECC_word_t *f0,
const bitcount_t j) {
bitcount_t i;
uECC_vli_set(d1, d0, num_words_secp224r1); /* d1 <-- d0 */
uECC_vli_set(e1, e0, num_words_secp224r1); /* e1 <-- e0 */
uECC_vli_set(f1, f0, num_words_secp224r1); /* f1 <-- f0 */
for (i = 1; i <= j; i++) {
mod_sqrt_secp224r1_rs(d1, e1, f1, d1, e1, f1); /* RS (d1,e1,f1,d1,e1,f1) */
}
}
/* Routine 3.2.6 RM; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1_rm(uECC_word_t *d2, uECC_word_t *e2,
uECC_word_t *f2, const uECC_word_t *c,
const uECC_word_t *d0, const uECC_word_t *e0,
const uECC_word_t *d1,
const uECC_word_t *e1) {
uECC_word_t t1[num_words_secp224r1];
uECC_word_t t2[num_words_secp224r1];
uECC_vli_modMult_fast(t1, e0, e1, &curve_secp224r1); /* t1 <-- e0 * e1 */
uECC_vli_modMult_fast(t1, t1, c, &curve_secp224r1); /* t1 <-- t1 * c */
/* t1 <-- p - t1 */
uECC_vli_modSub(t1, curve_secp224r1.p, t1, curve_secp224r1.p,
num_words_secp224r1);
uECC_vli_modMult_fast(t2, d0, d1, &curve_secp224r1); /* t2 <-- d0 * d1 */
uECC_vli_modAdd(t2, t2, t1, curve_secp224r1.p,
num_words_secp224r1); /* t2 <-- t2 + t1 */
uECC_vli_modMult_fast(t1, d0, e1, &curve_secp224r1); /* t1 <-- d0 * e1 */
uECC_vli_modMult_fast(e2, d1, e0, &curve_secp224r1); /* e2 <-- d1 * e0 */
uECC_vli_modAdd(e2, e2, t1, curve_secp224r1.p,
num_words_secp224r1); /* e2 <-- e2 + t1 */
uECC_vli_modSquare_fast(f2, e2, &curve_secp224r1); /* f2 <-- e2^2 */
uECC_vli_modMult_fast(f2, f2, c, &curve_secp224r1); /* f2 <-- f2 * c */
/* f2 <-- p - f2 */
uECC_vli_modSub(f2, curve_secp224r1.p, f2, curve_secp224r1.p,
num_words_secp224r1);
uECC_vli_set(d2, t2, num_words_secp224r1); /* d2 <-- t2 */
}
/* Routine 3.2.7 RP; from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1_rp(uECC_word_t *d1, uECC_word_t *e1,
uECC_word_t *f1, const uECC_word_t *c,
const uECC_word_t *r) {
wordcount_t i;
wordcount_t pow2i = 1;
uECC_word_t d0[num_words_secp224r1];
uECC_word_t e0[num_words_secp224r1] = {1}; /* e0 <-- 1 */
uECC_word_t f0[num_words_secp224r1];
uECC_vli_set(d0, r, num_words_secp224r1); /* d0 <-- r */
/* f0 <-- p - c */
uECC_vli_modSub(f0, curve_secp224r1.p, c, curve_secp224r1.p,
num_words_secp224r1);
for (i = 0; i <= 6; i++) {
mod_sqrt_secp224r1_rss(d1, e1, f1, d0, e0, f0,
pow2i); /* RSS (d1,e1,f1,d0,e0,f0,2^i) */
mod_sqrt_secp224r1_rm(d1, e1, f1, c, d1, e1, d0,
e0); /* RM (d1,e1,f1,c,d1,e1,d0,e0) */
uECC_vli_set(d0, d1, num_words_secp224r1); /* d0 <-- d1 */
uECC_vli_set(e0, e1, num_words_secp224r1); /* e0 <-- e1 */
uECC_vli_set(f0, f1, num_words_secp224r1); /* f0 <-- f1 */
pow2i *= 2;
}
}
/* Compute a = sqrt(a) (mod curve_p). */
/* Routine 3.2.8 mp_mod_sqrt_224; from
* http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void mod_sqrt_secp224r1(uECC_word_t *a, uECC_Curve curve) {
(void) curve;
bitcount_t i;
uECC_word_t e1[num_words_secp224r1];
uECC_word_t f1[num_words_secp224r1];
uECC_word_t d0[num_words_secp224r1];
uECC_word_t e0[num_words_secp224r1];
uECC_word_t f0[num_words_secp224r1];
uECC_word_t d1[num_words_secp224r1];
/* s = a; using constant instead of random value */
mod_sqrt_secp224r1_rp(d0, e0, f0, a, a); /* RP (d0, e0, f0, c, s) */
mod_sqrt_secp224r1_rs(d1, e1, f1, d0, e0,
f0); /* RS (d1, e1, f1, d0, e0, f0) */
for (i = 1; i <= 95; i++) {
uECC_vli_set(d0, d1, num_words_secp224r1); /* d0 <-- d1 */
uECC_vli_set(e0, e1, num_words_secp224r1); /* e0 <-- e1 */
uECC_vli_set(f0, f1, num_words_secp224r1); /* f0 <-- f1 */
mod_sqrt_secp224r1_rs(d1, e1, f1, d0, e0,
f0); /* RS (d1, e1, f1, d0, e0, f0) */
if (uECC_vli_isZero(d1, num_words_secp224r1)) { /* if d1 == 0 */
break;
}
}
uECC_vli_modInv(f1, e0, curve_secp224r1.p,
num_words_secp224r1); /* f1 <-- 1 / e0 */
uECC_vli_modMult_fast(a, d0, f1, &curve_secp224r1); /* a <-- d0 / e0 */
}
#endif /* uECC_SUPPORT_COMPRESSED_POINT */
#if (uECC_OPTIMIZATION_LEVEL > 0)
/* Computes result = product % curve_p
from http://www.nsa.gov/ia/_files/nist-routines.pdf */
#if uECC_WORD_SIZE == 1
static void vli_mmod_fast_secp224r1(uint8_t *result, uint8_t *product) {
uint8_t tmp[num_words_secp224r1];
int8_t carry;
/* t */
uECC_vli_set(result, product, num_words_secp224r1);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0;
tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0;
tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0;
tmp[12] = product[28];
tmp[13] = product[29];
tmp[14] = product[30];
tmp[15] = product[31];
tmp[16] = product[32];
tmp[17] = product[33];
tmp[18] = product[34];
tmp[19] = product[35];
tmp[20] = product[36];
tmp[21] = product[37];
tmp[22] = product[38];
tmp[23] = product[39];
tmp[24] = product[40];
tmp[25] = product[41];
tmp[26] = product[42];
tmp[27] = product[43];
carry = uECC_vli_add(result, result, tmp, num_words_secp224r1);
/* s2 */
tmp[12] = product[44];
tmp[13] = product[45];
tmp[14] = product[46];
tmp[15] = product[47];
tmp[16] = product[48];
tmp[17] = product[49];
tmp[18] = product[50];
tmp[19] = product[51];
tmp[20] = product[52];
tmp[21] = product[53];
tmp[22] = product[54];
tmp[23] = product[55];
tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
carry += uECC_vli_add(result, result, tmp, num_words_secp224r1);
/* d1 */
tmp[0] = product[28];
tmp[1] = product[29];
tmp[2] = product[30];
tmp[3] = product[31];
tmp[4] = product[32];
tmp[5] = product[33];
tmp[6] = product[34];
tmp[7] = product[35];
tmp[8] = product[36];
tmp[9] = product[37];
tmp[10] = product[38];
tmp[11] = product[39];
tmp[12] = product[40];
tmp[13] = product[41];
tmp[14] = product[42];
tmp[15] = product[43];
tmp[16] = product[44];
tmp[17] = product[45];
tmp[18] = product[46];
tmp[19] = product[47];
tmp[20] = product[48];
tmp[21] = product[49];
tmp[22] = product[50];
tmp[23] = product[51];
tmp[24] = product[52];
tmp[25] = product[53];
tmp[26] = product[54];
tmp[27] = product[55];
carry -= uECC_vli_sub(result, result, tmp, num_words_secp224r1);
/* d2 */
tmp[0] = product[44];
tmp[1] = product[45];
tmp[2] = product[46];
tmp[3] = product[47];
tmp[4] = product[48];
tmp[5] = product[49];
tmp[6] = product[50];
tmp[7] = product[51];
tmp[8] = product[52];
tmp[9] = product[53];
tmp[10] = product[54];
tmp[11] = product[55];
tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0;
tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
carry -= uECC_vli_sub(result, result, tmp, num_words_secp224r1);
if (carry < 0) {
do {
carry +=
uECC_vli_add(result, result, curve_secp224r1.p, num_words_secp224r1);
} while (carry < 0);
} else {
while (carry || uECC_vli_cmp_unsafe(curve_secp224r1.p, result,
num_words_secp224r1) != 1) {
carry -=
uECC_vli_sub(result, result, curve_secp224r1.p, num_words_secp224r1);
}
}
}
#elif uECC_WORD_SIZE == 4
static void vli_mmod_fast_secp224r1(uint32_t *result, uint32_t *product) {
uint32_t tmp[num_words_secp224r1];
int carry;
/* t */
uECC_vli_set(result, product, num_words_secp224r1);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = 0;
tmp[3] = product[7];
tmp[4] = product[8];
tmp[5] = product[9];
tmp[6] = product[10];
carry = uECC_vli_add(result, result, tmp, num_words_secp224r1);
/* s2 */
tmp[3] = product[11];
tmp[4] = product[12];
tmp[5] = product[13];
tmp[6] = 0;
carry += uECC_vli_add(result, result, tmp, num_words_secp224r1);
/* d1 */
tmp[0] = product[7];
tmp[1] = product[8];
tmp[2] = product[9];
tmp[3] = product[10];
tmp[4] = product[11];
tmp[5] = product[12];
tmp[6] = product[13];
carry -= uECC_vli_sub(result, result, tmp, num_words_secp224r1);
/* d2 */
tmp[0] = product[11];
tmp[1] = product[12];
tmp[2] = product[13];
tmp[3] = tmp[4] = tmp[5] = tmp[6] = 0;
carry -= uECC_vli_sub(result, result, tmp, num_words_secp224r1);
if (carry < 0) {
do {
carry +=
uECC_vli_add(result, result, curve_secp224r1.p, num_words_secp224r1);
} while (carry < 0);
} else {
while (carry || uECC_vli_cmp_unsafe(curve_secp224r1.p, result,
num_words_secp224r1) != 1) {
carry -=
uECC_vli_sub(result, result, curve_secp224r1.p, num_words_secp224r1);
}
}
}
#else
static void vli_mmod_fast_secp224r1(uint64_t *result, uint64_t *product) {
uint64_t tmp[num_words_secp224r1];
int carry = 0;
/* t */
uECC_vli_set(result, product, num_words_secp224r1);
result[num_words_secp224r1 - 1] &= 0xffffffff;
/* s1 */
tmp[0] = 0;
tmp[1] = product[3] & 0xffffffff00000000ull;
tmp[2] = product[4];
tmp[3] = product[5] & 0xffffffff;
uECC_vli_add(result, result, tmp, num_words_secp224r1);
/* s2 */
tmp[1] = product[5] & 0xffffffff00000000ull;
tmp[2] = product[6];
tmp[3] = 0;
uECC_vli_add(result, result, tmp, num_words_secp224r1);
/* d1 */
tmp[0] = (product[3] >> 32) | (product[4] << 32);
tmp[1] = (product[4] >> 32) | (product[5] << 32);
tmp[2] = (product[5] >> 32) | (product[6] << 32);
tmp[3] = product[6] >> 32;
carry -= uECC_vli_sub(result, result, tmp, num_words_secp224r1);
/* d2 */
tmp[0] = (product[5] >> 32) | (product[6] << 32);
tmp[1] = product[6] >> 32;
tmp[2] = tmp[3] = 0;
carry -= uECC_vli_sub(result, result, tmp, num_words_secp224r1);
if (carry < 0) {
do {
carry +=
uECC_vli_add(result, result, curve_secp224r1.p, num_words_secp224r1);
} while (carry < 0);
} else {
while (uECC_vli_cmp_unsafe(curve_secp224r1.p, result,
num_words_secp224r1) != 1) {
uECC_vli_sub(result, result, curve_secp224r1.p, num_words_secp224r1);
}
}
}
#endif /* uECC_WORD_SIZE */
#endif /* (uECC_OPTIMIZATION_LEVEL > 0) */
#endif /* uECC_SUPPORTS_secp224r1 */
#if uECC_SUPPORTS_secp256r1
#if (uECC_OPTIMIZATION_LEVEL > 0)
static void vli_mmod_fast_secp256r1(uECC_word_t *result, uECC_word_t *product);
#endif
static const struct uECC_Curve_t curve_secp256r1 = {
num_words_secp256r1,
num_bytes_secp256r1,
256, /* num_n_bits */
{BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, 00, 00, 00, 00),
BYTES_TO_WORDS_8(00, 00, 00, 00, 00, 00, 00, 00),
BYTES_TO_WORDS_8(01, 00, 00, 00, FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(51, 25, 63, FC, C2, CA, B9, F3),
BYTES_TO_WORDS_8(84, 9E, 17, A7, AD, FA, E6, BC),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(00, 00, 00, 00, FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(96, C2, 98, D8, 45, 39, A1, F4),
BYTES_TO_WORDS_8(A0, 33, EB, 2D, 81, 7D, 03, 77),
BYTES_TO_WORDS_8(F2, 40, A4, 63, E5, E6, BC, F8),
BYTES_TO_WORDS_8(47, 42, 2C, E1, F2, D1, 17, 6B),
BYTES_TO_WORDS_8(F5, 51, BF, 37, 68, 40, B6, CB),
BYTES_TO_WORDS_8(CE, 5E, 31, 6B, 57, 33, CE, 2B),
BYTES_TO_WORDS_8(16, 9E, 0F, 7C, 4A, EB, E7, 8E),
BYTES_TO_WORDS_8(9B, 7F, 1A, FE, E2, 42, E3, 4F)},
{BYTES_TO_WORDS_8(4B, 60, D2, 27, 3E, 3C, CE, 3B),
BYTES_TO_WORDS_8(F6, B0, 53, CC, B0, 06, 1D, 65),
BYTES_TO_WORDS_8(BC, 86, 98, 76, 55, BD, EB, B3),
BYTES_TO_WORDS_8(E7, 93, 3A, AA, D8, 35, C6, 5A)},
&double_jacobian_default,
#if uECC_SUPPORT_COMPRESSED_POINT
&mod_sqrt_default,
#endif
&x_side_default,
#if (uECC_OPTIMIZATION_LEVEL > 0)
&vli_mmod_fast_secp256r1
#endif
};
uECC_Curve uECC_secp256r1(void) {
return &curve_secp256r1;
}
#if (uECC_OPTIMIZATION_LEVEL > 0 && !asm_mmod_fast_secp256r1)
/* Computes result = product % curve_p
from http://www.nsa.gov/ia/_files/nist-routines.pdf */
#if uECC_WORD_SIZE == 1
static void vli_mmod_fast_secp256r1(uint8_t *result, uint8_t *product) {
uint8_t tmp[num_words_secp256r1];
int8_t carry;
/* t */
uECC_vli_set(result, product, num_words_secp256r1);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0;
tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0;
tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0;
tmp[12] = product[44];
tmp[13] = product[45];
tmp[14] = product[46];
tmp[15] = product[47];
tmp[16] = product[48];
tmp[17] = product[49];
tmp[18] = product[50];
tmp[19] = product[51];
tmp[20] = product[52];
tmp[21] = product[53];
tmp[22] = product[54];
tmp[23] = product[55];
tmp[24] = product[56];
tmp[25] = product[57];
tmp[26] = product[58];
tmp[27] = product[59];
tmp[28] = product[60];
tmp[29] = product[61];
tmp[30] = product[62];
tmp[31] = product[63];
carry = uECC_vli_add(tmp, tmp, tmp, num_words_secp256r1);
carry += uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s2 */
tmp[12] = product[48];
tmp[13] = product[49];
tmp[14] = product[50];
tmp[15] = product[51];
tmp[16] = product[52];
tmp[17] = product[53];
tmp[18] = product[54];
tmp[19] = product[55];
tmp[20] = product[56];
tmp[21] = product[57];
tmp[22] = product[58];
tmp[23] = product[59];
tmp[24] = product[60];
tmp[25] = product[61];
tmp[26] = product[62];
tmp[27] = product[63];
tmp[28] = tmp[29] = tmp[30] = tmp[31] = 0;
carry += uECC_vli_add(tmp, tmp, tmp, num_words_secp256r1);
carry += uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s3 */
tmp[0] = product[32];
tmp[1] = product[33];
tmp[2] = product[34];
tmp[3] = product[35];
tmp[4] = product[36];
tmp[5] = product[37];
tmp[6] = product[38];
tmp[7] = product[39];
tmp[8] = product[40];
tmp[9] = product[41];
tmp[10] = product[42];
tmp[11] = product[43];
tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0;
tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
tmp[24] = product[56];
tmp[25] = product[57];
tmp[26] = product[58];
tmp[27] = product[59];
tmp[28] = product[60];
tmp[29] = product[61];
tmp[30] = product[62];
tmp[31] = product[63];
carry += uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s4 */
tmp[0] = product[36];
tmp[1] = product[37];
tmp[2] = product[38];
tmp[3] = product[39];
tmp[4] = product[40];
tmp[5] = product[41];
tmp[6] = product[42];
tmp[7] = product[43];
tmp[8] = product[44];
tmp[9] = product[45];
tmp[10] = product[46];
tmp[11] = product[47];
tmp[12] = product[52];
tmp[13] = product[53];
tmp[14] = product[54];
tmp[15] = product[55];
tmp[16] = product[56];
tmp[17] = product[57];
tmp[18] = product[58];
tmp[19] = product[59];
tmp[20] = product[60];
tmp[21] = product[61];
tmp[22] = product[62];
tmp[23] = product[63];
tmp[24] = product[52];
tmp[25] = product[53];
tmp[26] = product[54];
tmp[27] = product[55];
tmp[28] = product[32];
tmp[29] = product[33];
tmp[30] = product[34];
tmp[31] = product[35];
carry += uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* d1 */
tmp[0] = product[44];
tmp[1] = product[45];
tmp[2] = product[46];
tmp[3] = product[47];
tmp[4] = product[48];
tmp[5] = product[49];
tmp[6] = product[50];
tmp[7] = product[51];
tmp[8] = product[52];
tmp[9] = product[53];
tmp[10] = product[54];
tmp[11] = product[55];
tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0;
tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
tmp[24] = product[32];
tmp[25] = product[33];
tmp[26] = product[34];
tmp[27] = product[35];
tmp[28] = product[40];
tmp[29] = product[41];
tmp[30] = product[42];
tmp[31] = product[43];
carry -= uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d2 */
tmp[0] = product[48];
tmp[1] = product[49];
tmp[2] = product[50];
tmp[3] = product[51];
tmp[4] = product[52];
tmp[5] = product[53];
tmp[6] = product[54];
tmp[7] = product[55];
tmp[8] = product[56];
tmp[9] = product[57];
tmp[10] = product[58];
tmp[11] = product[59];
tmp[12] = product[60];
tmp[13] = product[61];
tmp[14] = product[62];
tmp[15] = product[63];
tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
tmp[24] = product[36];
tmp[25] = product[37];
tmp[26] = product[38];
tmp[27] = product[39];
tmp[28] = product[44];
tmp[29] = product[45];
tmp[30] = product[46];
tmp[31] = product[47];
carry -= uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d3 */
tmp[0] = product[52];
tmp[1] = product[53];
tmp[2] = product[54];
tmp[3] = product[55];
tmp[4] = product[56];
tmp[5] = product[57];
tmp[6] = product[58];
tmp[7] = product[59];
tmp[8] = product[60];
tmp[9] = product[61];
tmp[10] = product[62];
tmp[11] = product[63];
tmp[12] = product[32];
tmp[13] = product[33];
tmp[14] = product[34];
tmp[15] = product[35];
tmp[16] = product[36];
tmp[17] = product[37];
tmp[18] = product[38];
tmp[19] = product[39];
tmp[20] = product[40];
tmp[21] = product[41];
tmp[22] = product[42];
tmp[23] = product[43];
tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
tmp[28] = product[48];
tmp[29] = product[49];
tmp[30] = product[50];
tmp[31] = product[51];
carry -= uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d4 */
tmp[0] = product[56];
tmp[1] = product[57];
tmp[2] = product[58];
tmp[3] = product[59];
tmp[4] = product[60];
tmp[5] = product[61];
tmp[6] = product[62];
tmp[7] = product[63];
tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0;
tmp[12] = product[36];
tmp[13] = product[37];
tmp[14] = product[38];
tmp[15] = product[39];
tmp[16] = product[40];
tmp[17] = product[41];
tmp[18] = product[42];
tmp[19] = product[43];
tmp[20] = product[44];
tmp[21] = product[45];
tmp[22] = product[46];
tmp[23] = product[47];
tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
tmp[28] = product[52];
tmp[29] = product[53];
tmp[30] = product[54];
tmp[31] = product[55];
carry -= uECC_vli_sub(result, result, tmp, num_words_secp256r1);
if (carry < 0) {
do {
carry +=
uECC_vli_add(result, result, curve_secp256r1.p, num_words_secp256r1);
} while (carry < 0);
} else {
while (carry || uECC_vli_cmp_unsafe(curve_secp256r1.p, result,
num_words_secp256r1) != 1) {
carry -=
uECC_vli_sub(result, result, curve_secp256r1.p, num_words_secp256r1);
}
}
}
#elif uECC_WORD_SIZE == 4
static void vli_mmod_fast_secp256r1(uint32_t *result, uint32_t *product) {
uint32_t tmp[num_words_secp256r1];
int carry;
/* t */
uECC_vli_set(result, product, num_words_secp256r1);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = 0;
tmp[3] = product[11];
tmp[4] = product[12];
tmp[5] = product[13];
tmp[6] = product[14];
tmp[7] = product[15];
carry = (int) uECC_vli_add(tmp, tmp, tmp, num_words_secp256r1);
carry += (int) uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s2 */
tmp[3] = product[12];
tmp[4] = product[13];
tmp[5] = product[14];
tmp[6] = product[15];
tmp[7] = 0;
carry += (int) uECC_vli_add(tmp, tmp, tmp, num_words_secp256r1);
carry += (int) uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s3 */
tmp[0] = product[8];
tmp[1] = product[9];
tmp[2] = product[10];
tmp[3] = tmp[4] = tmp[5] = 0;
tmp[6] = product[14];
tmp[7] = product[15];
carry += (int) uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s4 */
tmp[0] = product[9];
tmp[1] = product[10];
tmp[2] = product[11];
tmp[3] = product[13];
tmp[4] = product[14];
tmp[5] = product[15];
tmp[6] = product[13];
tmp[7] = product[8];
carry += (int) uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* d1 */
tmp[0] = product[11];
tmp[1] = product[12];
tmp[2] = product[13];
tmp[3] = tmp[4] = tmp[5] = 0;
tmp[6] = product[8];
tmp[7] = product[10];
carry -= (int) uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d2 */
tmp[0] = product[12];
tmp[1] = product[13];
tmp[2] = product[14];
tmp[3] = product[15];
tmp[4] = tmp[5] = 0;
tmp[6] = product[9];
tmp[7] = product[11];
carry -= (int) uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d3 */
tmp[0] = product[13];
tmp[1] = product[14];
tmp[2] = product[15];
tmp[3] = product[8];
tmp[4] = product[9];
tmp[5] = product[10];
tmp[6] = 0;
tmp[7] = product[12];
carry -= (int) uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d4 */
tmp[0] = product[14];
tmp[1] = product[15];
tmp[2] = 0;
tmp[3] = product[9];
tmp[4] = product[10];
tmp[5] = product[11];
tmp[6] = 0;
tmp[7] = product[13];
carry -= (int) uECC_vli_sub(result, result, tmp, num_words_secp256r1);
if (carry < 0) {
do {
carry +=
(int) uECC_vli_add(result, result, curve_secp256r1.p, num_words_secp256r1);
} while (carry < 0);
} else {
while (carry || uECC_vli_cmp_unsafe(curve_secp256r1.p, result,
num_words_secp256r1) != 1) {
carry -=
(int) uECC_vli_sub(result, result, curve_secp256r1.p, num_words_secp256r1);
}
}
}
#else
static void vli_mmod_fast_secp256r1(uint64_t *result, uint64_t *product) {
uint64_t tmp[num_words_secp256r1];
int carry;
/* t */
uECC_vli_set(result, product, num_words_secp256r1);
/* s1 */
tmp[0] = 0;
tmp[1] = product[5] & 0xffffffff00000000U;
tmp[2] = product[6];
tmp[3] = product[7];
carry = (int) uECC_vli_add(tmp, tmp, tmp, num_words_secp256r1);
carry += (int) uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s2 */
tmp[1] = product[6] << 32;
tmp[2] = (product[6] >> 32) | (product[7] << 32);
tmp[3] = product[7] >> 32;
carry += (int) uECC_vli_add(tmp, tmp, tmp, num_words_secp256r1);
carry += (int) uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s3 */
tmp[0] = product[4];
tmp[1] = product[5] & 0xffffffff;
tmp[2] = 0;
tmp[3] = product[7];
carry += (int) uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* s4 */
tmp[0] = (product[4] >> 32) | (product[5] << 32);
tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000U);
tmp[2] = product[7];
tmp[3] = (product[6] >> 32) | (product[4] << 32);
carry += (int) uECC_vli_add(result, result, tmp, num_words_secp256r1);
/* d1 */
tmp[0] = (product[5] >> 32) | (product[6] << 32);
tmp[1] = (product[6] >> 32);
tmp[2] = 0;
tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
carry -= (int) uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d2 */
tmp[0] = product[6];
tmp[1] = product[7];
tmp[2] = 0;
tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000);
carry -= (int) uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d3 */
tmp[0] = (product[6] >> 32) | (product[7] << 32);
tmp[1] = (product[7] >> 32) | (product[4] << 32);
tmp[2] = (product[4] >> 32) | (product[5] << 32);
tmp[3] = (product[6] << 32);
carry -= (int) uECC_vli_sub(result, result, tmp, num_words_secp256r1);
/* d4 */
tmp[0] = product[7];
tmp[1] = product[4] & 0xffffffff00000000U;
tmp[2] = product[5];
tmp[3] = product[6] & 0xffffffff00000000U;
carry -= (int) uECC_vli_sub(result, result, tmp, num_words_secp256r1);
if (carry < 0) {
do {
carry +=
(int) uECC_vli_add(result, result, curve_secp256r1.p, num_words_secp256r1);
} while (carry < 0);
} else {
while (carry || uECC_vli_cmp_unsafe(curve_secp256r1.p, result,
num_words_secp256r1) != 1) {
carry -=
(int) uECC_vli_sub(result, result, curve_secp256r1.p, num_words_secp256r1);
}
}
}
#endif /* uECC_WORD_SIZE */
#endif /* (uECC_OPTIMIZATION_LEVEL > 0 && !asm_mmod_fast_secp256r1) */
#endif /* uECC_SUPPORTS_secp256r1 */
#if uECC_SUPPORTS_secp256k1
static void double_jacobian_secp256k1(uECC_word_t *X1, uECC_word_t *Y1,
uECC_word_t *Z1, uECC_Curve curve);
static void x_side_secp256k1(uECC_word_t *result, const uECC_word_t *x,
uECC_Curve curve);
#if (uECC_OPTIMIZATION_LEVEL > 0)
static void vli_mmod_fast_secp256k1(uECC_word_t *result, uECC_word_t *product);
#endif
static const struct uECC_Curve_t curve_secp256k1 = {
num_words_secp256k1,
num_bytes_secp256k1,
256, /* num_n_bits */
{BYTES_TO_WORDS_8(2F, FC, FF, FF, FE, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(41, 41, 36, D0, 8C, 5E, D2, BF),
BYTES_TO_WORDS_8(3B, A0, 48, AF, E6, DC, AE, BA),
BYTES_TO_WORDS_8(FE, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF)},
{BYTES_TO_WORDS_8(98, 17, F8, 16, 5B, 81, F2, 59),
BYTES_TO_WORDS_8(D9, 28, CE, 2D, DB, FC, 9B, 02),
BYTES_TO_WORDS_8(07, 0B, 87, CE, 95, 62, A0, 55),
BYTES_TO_WORDS_8(AC, BB, DC, F9, 7E, 66, BE, 79),
BYTES_TO_WORDS_8(B8, D4, 10, FB, 8F, D0, 47, 9C),
BYTES_TO_WORDS_8(19, 54, 85, A6, 48, B4, 17, FD),
BYTES_TO_WORDS_8(A8, 08, 11, 0E, FC, FB, A4, 5D),
BYTES_TO_WORDS_8(65, C4, A3, 26, 77, DA, 3A, 48)},
{BYTES_TO_WORDS_8(07, 00, 00, 00, 00, 00, 00, 00),
BYTES_TO_WORDS_8(00, 00, 00, 00, 00, 00, 00, 00),
BYTES_TO_WORDS_8(00, 00, 00, 00, 00, 00, 00, 00),
BYTES_TO_WORDS_8(00, 00, 00, 00, 00, 00, 00, 00)},
&double_jacobian_secp256k1,
#if uECC_SUPPORT_COMPRESSED_POINT
&mod_sqrt_default,
#endif
&x_side_secp256k1,
#if (uECC_OPTIMIZATION_LEVEL > 0)
&vli_mmod_fast_secp256k1
#endif
};
uECC_Curve uECC_secp256k1(void) {
return &curve_secp256k1;
}
/* Double in place */
static void double_jacobian_secp256k1(uECC_word_t *X1, uECC_word_t *Y1,
uECC_word_t *Z1, uECC_Curve curve) {
/* t1 = X, t2 = Y, t3 = Z */
uECC_word_t t4[num_words_secp256k1];
uECC_word_t t5[num_words_secp256k1];
if (uECC_vli_isZero(Z1, num_words_secp256k1)) {
return;
}
uECC_vli_modSquare_fast(t5, Y1, curve); /* t5 = y1^2 */
uECC_vli_modMult_fast(t4, X1, t5, curve); /* t4 = x1*y1^2 = A */
uECC_vli_modSquare_fast(X1, X1, curve); /* t1 = x1^2 */
uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = y1^4 */
uECC_vli_modMult_fast(Z1, Y1, Z1, curve); /* t3 = y1*z1 = z3 */
uECC_vli_modAdd(Y1, X1, X1, curve->p, num_words_secp256k1); /* t2 = 2*x1^2 */
uECC_vli_modAdd(Y1, Y1, X1, curve->p, num_words_secp256k1); /* t2 = 3*x1^2 */
if (uECC_vli_testBit(Y1, 0)) {
uECC_word_t carry = uECC_vli_add(Y1, Y1, curve->p, num_words_secp256k1);
uECC_vli_rshift1(Y1, num_words_secp256k1);
Y1[num_words_secp256k1 - 1] |= carry << (uECC_WORD_BITS - 1);
} else {
uECC_vli_rshift1(Y1, num_words_secp256k1);
}
/* t2 = 3/2*(x1^2) = B */
uECC_vli_modSquare_fast(X1, Y1, curve); /* t1 = B^2 */
uECC_vli_modSub(X1, X1, t4, curve->p, num_words_secp256k1); /* t1 = B^2 - A */
uECC_vli_modSub(X1, X1, t4, curve->p,
num_words_secp256k1); /* t1 = B^2 - 2A = x3 */
uECC_vli_modSub(t4, t4, X1, curve->p, num_words_secp256k1); /* t4 = A - x3 */
uECC_vli_modMult_fast(Y1, Y1, t4, curve); /* t2 = B * (A - x3) */
uECC_vli_modSub(Y1, Y1, t5, curve->p,
num_words_secp256k1); /* t2 = B * (A - x3) - y1^4 = y3 */
}
/* Computes result = x^3 + b. result must not overlap x. */
static void x_side_secp256k1(uECC_word_t *result, const uECC_word_t *x,
uECC_Curve curve) {
uECC_vli_modSquare_fast(result, x, curve); /* r = x^2 */
uECC_vli_modMult_fast(result, result, x, curve); /* r = x^3 */
uECC_vli_modAdd(result, result, curve->b, curve->p,
num_words_secp256k1); /* r = x^3 + b */
}
#if (uECC_OPTIMIZATION_LEVEL > 0 && !asm_mmod_fast_secp256k1)
static void omega_mult_secp256k1(uECC_word_t *result, const uECC_word_t *right);
static void vli_mmod_fast_secp256k1(uECC_word_t *result, uECC_word_t *product) {
uECC_word_t tmp[2 * num_words_secp256k1];
uECC_word_t carry;
uECC_vli_clear(tmp, num_words_secp256k1);
uECC_vli_clear(tmp + num_words_secp256k1, num_words_secp256k1);
omega_mult_secp256k1(tmp,
product + num_words_secp256k1); /* (Rq, q) = q * c */
carry = uECC_vli_add(result, product, tmp,
num_words_secp256k1); /* (C, r) = r + q */
uECC_vli_clear(product, num_words_secp256k1);
omega_mult_secp256k1(product, tmp + num_words_secp256k1); /* Rq*c */
carry += uECC_vli_add(result, result, product,
num_words_secp256k1); /* (C1, r) = r + Rq*c */
while (carry > 0) {
--carry;
uECC_vli_sub(result, result, curve_secp256k1.p, num_words_secp256k1);
}
if (uECC_vli_cmp_unsafe(result, curve_secp256k1.p, num_words_secp256k1) > 0) {
uECC_vli_sub(result, result, curve_secp256k1.p, num_words_secp256k1);
}
}
#if uECC_WORD_SIZE == 1
static void omega_mult_secp256k1(uint8_t *result, const uint8_t *right) {
/* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t k;
/* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
muladd(0xD1, right[0], &r0, &r1, &r2);
result[0] = r0;
r0 = r1;
r1 = r2;
/* r2 is still 0 */
for (k = 1; k < num_words_secp256k1; ++k) {
muladd(0x03, right[k - 1], &r0, &r1, &r2);
muladd(0xD1, right[k], &r0, &r1, &r2);
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
muladd(0x03, right[num_words_secp256k1 - 1], &r0, &r1, &r2);
result[num_words_secp256k1] = r0;
result[num_words_secp256k1 + 1] = r1;
/* add the 2^32 multiple */
result[4 + num_words_secp256k1] =
uECC_vli_add(result + 4, result + 4, right, num_words_secp256k1);
}
#elif uECC_WORD_SIZE == 4
static void omega_mult_secp256k1(uint32_t *result, const uint32_t *right) {
/* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
uint32_t carry = 0;
wordcount_t k;
for (k = 0; k < num_words_secp256k1; ++k) {
uint64_t p = (uint64_t) 0x3D1 * right[k] + carry;
result[k] = (uint32_t) p;
carry = p >> 32;
}
result[num_words_secp256k1] = carry;
/* add the 2^32 multiple */
result[1 + num_words_secp256k1] =
uECC_vli_add(result + 1, result + 1, right, num_words_secp256k1);
}
#else
static void omega_mult_secp256k1(uint64_t *result, const uint64_t *right) {
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t k;
/* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
for (k = 0; k < num_words_secp256k1; ++k) {
muladd(0x1000003D1ull, right[k], &r0, &r1, &r2);
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
result[num_words_secp256k1] = r0;
}
#endif /* uECC_WORD_SIZE */
#endif /* (uECC_OPTIMIZATION_LEVEL > 0 && && !asm_mmod_fast_secp256k1) */
#endif /* uECC_SUPPORTS_secp256k1 */
#endif /* _UECC_CURVE_SPECIFIC_H_ */
/* Returns 1 if 'point' is the point at infinity, 0 otherwise. */
#define EccPoint_isZero(point, curve) \
uECC_vli_isZero((point), (wordcount_t) ((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] = {0};
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] = {0};
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;
}
/* 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,
(unsigned int) (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;
}
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 *initial_Z = 0;
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);
/* 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, curve->num_words)) {
return 0;
}
initial_Z = p2[carry];
}
EccPoint_mult(result, curve->G, p2[!carry], initial_Z,
(bitcount_t) (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) {
int i;
for (i = 0; i < num_bytes; ++i) {
unsigned b = (unsigned) (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) {
int i;
uECC_vli_clear(native, (wordcount_t) ((num_bytes + (uECC_WORD_SIZE - 1)) /
uECC_WORD_SIZE));
for (i = 0; i < num_bytes; ++i) {
unsigned b = (unsigned) (num_bytes - 1 - i);
native[b / uECC_WORD_SIZE] |= (uECC_word_t) bytes[i]
<< (8 * (b % uECC_WORD_SIZE));
}
}
#endif /* uECC_WORD_SIZE */
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,
(bitcount_t) (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 ((uint8_t) (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 */
uECC_VLI_API 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 = (unsigned) BITS_TO_BYTES(curve->num_n_bits);
unsigned num_n_words = (unsigned) 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, (wordcount_t) num_n_words);
#if uECC_VLI_NATIVE_LITTLE_ENDIAN
bcopy((uint8_t *) native, bits, bits_size);
#else
uECC_vli_bytesToNative(native, bits, (int) bits_size);
#endif
if (bits_size * 8 <= (unsigned) curve->num_n_bits) {
return;
}
shift = (int) 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, (wordcount_t) num_n_words) != 1) {
uECC_vli_sub(native, native, curve->n, (wordcount_t) num_n_words);
}
}
static int uECC_sign_with_k_internal(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};
uECC_word_t *initial_Z = 0;
#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);
/* 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(k2[carry], curve->p, num_words)) {
return 0;
}
initial_Z = k2[carry];
}
EccPoint_mult(p, curve->G, k2[!carry], initial_Z,
(bitcount_t) (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;
}
#if 0
/* For testing - sign with an explicitly specified k value */
int uECC_sign_with_k(const uint8_t *private_key, const uint8_t *message_hash,
unsigned hash_size, const uint8_t *k, uint8_t *signature,
uECC_Curve curve) {
uECC_word_t k2[uECC_MAX_WORDS];
bits2int(k2, k, (unsigned) BITS_TO_BYTES(curve->num_n_bits), curve);
return uECC_sign_with_k_internal(private_key, message_hash, hash_size, k2,
signature, curve);
}
#endif
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_internal(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, (unsigned int) 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, (unsigned int) 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_internal(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, (bitcount_t) (num_bits - 1))) |
((!!uECC_vli_testBit(u2, (bitcount_t) (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_word_t) ((!!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 */
#endif // MG_TLS_BUILTIN
// End of uecc BSD-2
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