/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
- int m; \
- int abs_n = (n) * (((n) > 0) * 2 - 1); \
- int idx_n = abs_n / 2; \
+ int m = 0; \
+ /* Extract the sign-bit for a constant time absolute-value. */ \
+ int mask = (n) >> (sizeof(n) * CHAR_BIT - 1); \
+ int abs_n = ((n) + mask) ^ mask; \
+ int idx_n = abs_n >> 1; \
secp256k1_fe neg_y; \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
- for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
+ /* Unconditionally set r->x = (pre)[m].x. r->y = (pre)[m].y. because it's either the correct one \
+ * or will get replaced in the later iterations, this is needed to make sure `r` is initialized. */ \
+ (r)->x = (pre)[m].x; \
+ (r)->y = (pre)[m].y; \
+ for (m = 1; m < ECMULT_TABLE_SIZE(w); m++) { \
/* This loop is used to avoid secret data in array indices. See
* the comment in ecmult_gen_impl.h for rationale. */ \
secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
*
* Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
* Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
- * CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
+ * CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlag Berlin Heidelberg 2003
*
* Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
*/
-static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w, int size) {
+static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size) {
int global_sign;
int skew = 0;
int word = 0;
int flip;
int bit;
- secp256k1_scalar neg_s;
+ secp256k1_scalar s;
int not_neg_one;
+
+ VERIFY_CHECK(w > 0);
+ VERIFY_CHECK(size > 0);
+
/* Note that we cannot handle even numbers by negating them to be odd, as is
* done in other implementations, since if our scalars were specified to have
* width < 256 for performance reasons, their negations would have width 256
* {1, 2} we want to add to the scalar when ensuring that it's odd. Further
* complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and
* we need to special-case it in this logic. */
- flip = secp256k1_scalar_is_high(&s);
+ flip = secp256k1_scalar_is_high(scalar);
/* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
- bit = flip ^ !secp256k1_scalar_is_even(&s);
+ bit = flip ^ !secp256k1_scalar_is_even(scalar);
/* We check for negative one, since adding 2 to it will cause an overflow */
- secp256k1_scalar_negate(&neg_s, &s);
- not_neg_one = !secp256k1_scalar_is_one(&neg_s);
+ secp256k1_scalar_negate(&s, scalar);
+ not_neg_one = !secp256k1_scalar_is_one(&s);
+ s = *scalar;
secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
/* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
* that we added two to it and flipped it. In fact for -1 these operations are
/* 4 */
u_last = secp256k1_scalar_shr_int(&s, w);
- while (word * w < size) {
- int sign;
+ do {
int even;
/* 4.1 4.4 */
u = secp256k1_scalar_shr_int(&s, w);
/* 4.2 */
even = ((u & 1) == 0);
- sign = 2 * (u_last > 0) - 1;
- u += sign * even;
- u_last -= sign * even * (1 << w);
+ /* In contrast to the original algorithm, u_last is always > 0 and
+ * therefore we do not need to check its sign. In particular, it's easy
+ * to see that u_last is never < 0 because u is never < 0. Moreover,
+ * u_last is never = 0 because u is never even after a loop
+ * iteration. The same holds analogously for the initial value of
+ * u_last (in the first loop iteration). */
+ VERIFY_CHECK(u_last > 0);
+ VERIFY_CHECK((u_last & 1) == 1);
+ u += even;
+ u_last -= even * (1 << w);
/* 4.3, adapted for global sign change */
wnaf[word++] = u_last * global_sign;
u_last = u;
- }
+ } while (word * w < size);
wnaf[word] = u * global_sign;
VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
int i;
- secp256k1_scalar sc = *scalar;
/* build wnaf representation for q. */
int rsize = size;
if (size > 128) {
rsize = 128;
/* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
- secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
- skew_1 = secp256k1_wnaf_const(wnaf_1, q_1, WINDOW_A - 1, 128);
- skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1, 128);
+ secp256k1_scalar_split_lambda(&q_1, &q_lam, scalar);
+ skew_1 = secp256k1_wnaf_const(wnaf_1, &q_1, WINDOW_A - 1, 128);
+ skew_lam = secp256k1_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128);
} else
#endif
{
- skew_1 = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1, size);
+ skew_1 = secp256k1_wnaf_const(wnaf_1, scalar, WINDOW_A - 1, size);
#ifdef USE_ENDOMORPHISM
skew_lam = 0;
#endif
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
}
+
}
#endif
int n;
int j;
for (j = 0; j < WINDOW_A - 1; ++j) {
- secp256k1_gej_double_nonzero(r, r, NULL);
+ secp256k1_gej_double_nonzero(r, r);
}
n = wnaf_1[i];
projects / secp256k1.git / blobdiff