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"More" constant time point multiplication

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About the same speed, about the same precomputation table requirements.
Simpler code.
This commit is contained in:
Jochen Hoenicke 2015-03-16 16:29:29 +01:00
parent eb6e74f361
commit ec057a5102
3 changed files with 1711 additions and 1091 deletions
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108
ecdsa.c
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@ -194,83 +194,65 @@ int point_is_negative_of(const curve_point *p, const curve_point *q)
}
#if USE_PRECOMPUTED_CP
#define BITS_AT_A_TIME 3
#else
#define BITS_AT_A_TIME 2
#endif
// res = k * G
void scalar_multiply(const bignum256 *k, curve_point *res)
{
int i;
int i, j;
// result is zero
int is_zero = 1;
#if !USE_PRECOMPUTED_CP
curve_point curr = G256k1;
#endif
assert (bn_is_less(k, &order256k1));
bignum256 a = *k;
int sign = 1;
if ((a.val[8] & 0x8000) != 0) {
// negate k if it is large
int sign = (a.val[0] & 1) ^ 1;
uint32_t lowbits;
// make number odd
if (sign) {
bn_subtract(&order256k1, &a, &a);
sign = -sign;
}
// initial res
point_set_infinity(res);
for (i = 0; i < 256; i++) {
int lowbits = a.val[0] & ((1 << BITS_AT_A_TIME) - 1);
if ((lowbits & 1) != 0) {
int tsign = sign;
int factor = lowbits & 3;
if ((lowbits & (1 << (BITS_AT_A_TIME - 1))) != 0) {
lowbits |= ~((1 << BITS_AT_A_TIME) - 1);
factor ^= ~1;
tsign = -sign;
}
int j = 0;
uint32_t carry = -lowbits;
while (carry) {
carry += a.val[j];
a.val[j] = carry & 0x3fffffff;
carry >>= 30;
j++;
}
a.val[8] |= 0x10000;
assert((a.val[0] & 1) != 0);
assert((a.val[8] & 0x10000) != 0);
const curve_point *summand;
#if USE_PRECOMPUTED_CP
summand = ((factor & 2) != 0 ? secp256k1_cp2 : secp256k1_cp) + i;
#else
summand = &curr;
#endif
// negate summand if necessary
if (is_zero) {
if (tsign < 0) {
res->x = summand->x;
bn_subtract(&prime256k1, &summand->y, &res->y);
} else {
*res = *summand;
}
is_zero = 0;
} else {
curve_point temp;
if (tsign < 0) {
temp.x = summand->x;
bn_subtract(&prime256k1, &summand->y, &temp.y);
summand = &temp;
}
point_add(summand, res);
}
// now compute res = a *G step by step.
// initial res
lowbits = a.val[0] & ((1 << 5) - 1);
lowbits ^= (lowbits >> 4) - 1;
lowbits &= 15;
*res = secp256k1_cp[0][lowbits >> 1];
for (i = 1; i < 64; i ++) {
// invariant res = abs((a % 2*16^i) - 16^i) * G
for (j = 0; j < 8; j++) {
a.val[j] = (a.val[j] >> 4) | ((a.val[j + 1] & 0xf) << 26);
}
bn_rshift(&a);
#if ! USE_PRECOMPUTED_CP
point_double(&curr);
#endif
a.val[j] >>= 4;
lowbits = a.val[0] & ((1 << 5) - 1);
lowbits ^= (lowbits >> 4) - 1;
lowbits &= 15;
if ((lowbits & 1) == 0) {
// negate last result to make signs of this round and the
// last round equal.
bn_subtract(&prime256k1, &res->y, &res->y);
}
// add odd factor
point_add(&secp256k1_cp[i][lowbits >> 1], res);
}
if (sign) {
// negate
bn_subtract(&prime256k1, &res->y, &res->y);
}
}
#else
void scalar_multiply(const bignum256 *k, curve_point *res)
{
point_multiply(k, &G256k1, res);
}
#endif
// generate random K for signing
int generate_k_random(bignum256 *k) {
int i, j;

2691
secp256k1.c
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File diff suppressed because it is too large Load Diff

3
secp256k1.h
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@ -49,8 +49,7 @@ extern const bignum256 order256k1_half;
extern const bignum256 three_over_two256k1;
#if USE_PRECOMPUTED_CP
extern const curve_point secp256k1_cp[256];
extern const curve_point secp256k1_cp2[255];
extern const curve_point secp256k1_cp[64][8];
#endif
#endif