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Implement endomorphism optimization for secp256k1_ecmult_const

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This commit is contained in:
Andrew Poelstra 2015-05-22 12:09:36 -05:00
parent ed35d43a0c
commit 92e53fc4c8
3 changed files with 144 additions and 14 deletions
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2
src/bench_internal.c
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@ -241,7 +241,7 @@ void bench_wnaf_const(void* arg) {
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_wnaf_const(data->wnaf, &data->scalar_x, WINDOW_A);
secp256k1_wnaf_const(data->wnaf, data->scalar_x, WINDOW_A);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}

135
src/ecmult_const_impl.h
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@ -12,7 +12,11 @@
#include "ecmult_const.h"
#include "ecmult_impl.h"
#ifdef USE_ENDOMORPHISM
#define WNAF_BITS 128
#else
#define WNAF_BITS 256
#endif
#define WNAF_SIZE(w) ((WNAF_BITS + (w) - 1) / (w))
/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
@ -49,17 +53,47 @@
*
* Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
*/
static void secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar_t *a, int w) {
secp256k1_scalar_t s = *a;
/* Negate to force oddness */
int is_even = secp256k1_scalar_is_even(&s);
int global_sign = secp256k1_scalar_cond_negate(&s, is_even);
static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar_t s, int w) {
int global_sign = 1;
int skew = 0;
int word = 0;
/* 1 2 3 */
int u_last = secp256k1_scalar_shr_int(&s, w);
int u_last;
int u;
#ifdef USE_ENDOMORPHISM
/* If we are using the endomorphism, we cannot handle even numbers by negating
* them, since we are working with 128-bit numbers whose negations would be 256
* bits, eliminating the performance advantage. Instead we use a technique from
* Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
* or 2 (for odd) to the number we are encoding, then compensating after the
* multiplication. */
/* Negative 128-bit numbers will be negated, since otherwise they are 256-bit */
int flip = secp256k1_scalar_is_high(&s);
/* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
int bit = flip ^ (s.d[0] & 1);
/* We check for negative one, since adding 2 to it will cause an overflow */
secp256k1_scalar_t neg_s;
int not_neg_one;
secp256k1_scalar_negate(&neg_s, &s);
not_neg_one = !secp256k1_scalar_is_one(&neg_s);
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
* identical. We only flipped, but since skewing is required (in the sense that
* the skew must be 1 or 2, never zero) and flipping is not, we need to change
* our flags to claim that we only skewed. */
global_sign = secp256k1_scalar_cond_negate(&s, flip);
global_sign *= not_neg_one * 2 - 1;
skew = 1 << bit;
#else
/* Otherwise, we just negate to force oddness */
int is_even = secp256k1_scalar_is_even(&s);
global_sign = secp256k1_scalar_cond_negate(&s, is_even);
#endif
/* 4 */
u_last = secp256k1_scalar_shr_int(&s, w);
while (word * w < WNAF_BITS) {
int sign;
int even;
@ -81,6 +115,7 @@ static void secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar_t *a, int w)
VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
VERIFY_CHECK(word == WNAF_SIZE(w));
return skew;
}
@ -89,17 +124,37 @@ static void secp256k1_ecmult_const(secp256k1_gej_t *r, const secp256k1_ge_t *a,
secp256k1_ge_t tmpa;
secp256k1_fe_t Z;
#ifdef USE_ENDOMORPHISM
secp256k1_ge_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
int skew_1;
int skew_lam;
secp256k1_scalar_t q_1, q_lam;
#else
int wnaf[1 + WNAF_SIZE(WINDOW_A - 1)];
#endif
int i;
int is_zero = secp256k1_scalar_is_zero(scalar);
secp256k1_scalar_t sc = *scalar;
/* build wnaf representation for q. */
#ifdef USE_ENDOMORPHISM
/* 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);
/* no need for zero correction when using endomorphism since even
* numbers have one added to them anyway */
skew_1 = secp256k1_wnaf_const(wnaf_1, q_1, WINDOW_A - 1);
skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1);
#else
int is_zero = secp256k1_scalar_is_zero(scalar);
/* the wNAF ladder cannot handle zero, so bump this to one .. we will
* correct the result after the fact */
sc.d[0] += is_zero;
VERIFY_CHECK(!secp256k1_scalar_is_zero(&sc));
/* build wnaf representation for q. */
secp256k1_wnaf_const(wnaf, &sc, WINDOW_A - 1);
secp256k1_wnaf_const(wnaf, sc, WINDOW_A - 1);
#endif
/* Calculate odd multiples of a.
* All multiples are brought to the same Z 'denominator', which is stored
@ -109,14 +164,31 @@ static void secp256k1_ecmult_const(secp256k1_gej_t *r, const secp256k1_ge_t *a,
*/
secp256k1_gej_set_ge(r, a);
secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
#ifdef USE_ENDOMORPHISM
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
}
#endif
/* first loop iteration (separated out so we can directly set r, rather
* than having it start at infinity, get doubled several times, then have
* its new value added to it) */
#ifdef USE_ENDOMORPHISM
i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)];
VERIFY_CHECK(i != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
secp256k1_gej_set_ge(r, &tmpa);
i = wnaf_lam[WNAF_SIZE(WINDOW_A - 1)];
VERIFY_CHECK(i != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
secp256k1_gej_add_ge(r, r, &tmpa);
#else
i = wnaf[WNAF_SIZE(WINDOW_A - 1)];
VERIFY_CHECK(i != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
secp256k1_gej_set_ge(r, &tmpa);
#endif
/* remaining loop iterations */
for (i = WNAF_SIZE(WINDOW_A - 1) - 1; i >= 0; i--) {
int n;
@ -124,16 +196,59 @@ static void secp256k1_ecmult_const(secp256k1_gej_t *r, const secp256k1_ge_t *a,
for (j = 0; j < WINDOW_A - 1; ++j) {
secp256k1_gej_double_nonzero(r, r, NULL);
}
#ifdef USE_ENDOMORPHISM
n = wnaf_1[i];
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
VERIFY_CHECK(n != 0);
secp256k1_gej_add_ge(r, r, &tmpa);
n = wnaf_lam[i];
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
VERIFY_CHECK(n != 0);
secp256k1_gej_add_ge(r, r, &tmpa);
#else
n = wnaf[i];
VERIFY_CHECK(n != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
secp256k1_gej_add_ge(r, r, &tmpa);
#endif
}
secp256k1_fe_mul(&r->z, &r->z, &Z);
#ifdef USE_ENDOMORPHISM
{
/* Correct for wNAF skew */
secp256k1_ge_t correction = *a;
secp256k1_ge_storage_t correction_1_stor;
secp256k1_ge_storage_t correction_lam_stor;
secp256k1_ge_storage_t a2_stor;
secp256k1_gej_t tmpj;
secp256k1_gej_set_ge(&tmpj, &correction);
secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
secp256k1_ge_set_gej(&correction, &tmpj);
secp256k1_ge_to_storage(&correction_1_stor, a);
secp256k1_ge_to_storage(&correction_lam_stor, a);
secp256k1_ge_to_storage(&a2_stor, &correction);
/* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
/* Apply the correction */
secp256k1_ge_from_storage(&correction, &correction_1_stor);
secp256k1_ge_neg(&correction, &correction);
secp256k1_gej_add_ge(r, r, &correction);
secp256k1_ge_from_storage(&correction, &correction_lam_stor);
secp256k1_ge_neg(&correction, &correction);
secp256k1_ge_mul_lambda(&correction, &correction);
secp256k1_gej_add_ge(r, r, &correction);
}
#else
/* correct for zero */
r->infinity |= is_zero;
#endif
}
#endif

19
src/tests.c
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@ -1550,10 +1550,21 @@ void test_constant_wnaf(const secp256k1_scalar_t *number, int w) {
secp256k1_scalar_t x, shift;
int wnaf[256] = {0};
int i;
#ifdef USE_ENDOMORPHISM
int skew;
#endif
secp256k1_scalar_t num = *number;
secp256k1_scalar_set_int(&x, 0);
secp256k1_scalar_set_int(&shift, 1 << w);
secp256k1_wnaf_const(wnaf, number, w);
/* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
#ifdef USE_ENDOMORPHISM
for (i = 0; i < 16; ++i)
secp256k1_scalar_shr_int(&num, 8);
skew = secp256k1_wnaf_const(wnaf, num, w);
#else
secp256k1_wnaf_const(wnaf, num, w);
#endif
for (i = WNAF_SIZE(w); i >= 0; --i) {
secp256k1_scalar_t t;
@ -1572,7 +1583,11 @@ void test_constant_wnaf(const secp256k1_scalar_t *number, int w) {
}
secp256k1_scalar_add(&x, &x, &t);
}
CHECK(secp256k1_scalar_eq(&x, number));
#ifdef USE_ENDOMORPHISM
/* Skew num because when encoding 128-bit numbers as odd we use an offset */
secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
#endif
CHECK(secp256k1_scalar_eq(&x, &num));
}
void run_wnaf(void) {