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parameterize ecmult_const over input size

This commit is contained in:
Andrew Poelstra 2018-03-13 16:32:51 +00:00
parent dbc3ddd5e2
commit 7c1b91ba4b
7 changed files with 78 additions and 49 deletions
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2
src/bench_internal.c
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@ -251,7 +251,7 @@ void bench_wnaf_const(void* arg) {
bench_inv *data = (bench_inv*)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, 256);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}

4
src/ecmult_const.h
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@ -10,6 +10,8 @@
#include "scalar.h"
#include "group.h"
static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
/* Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus
* one because we internally sometimes add 2 to the number during the WNAF conversion. */
static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits);
#endif /* SECP256K1_ECMULT_CONST_H */

90
src/ecmult_const_impl.h
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@ -48,7 +48,7 @@
*
* 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) {
static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w, int size) {
int global_sign;
int skew = 0;
int word = 0;
@ -67,9 +67,14 @@ static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
* and we'd lose any performance benefit. 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, returning a skew value indicating
* this, and having the caller compensate after doing the multiplication. */
/* Negative numbers will be negated to keep their bit representation below the maximum width */
* this, and having the caller compensate after doing the multiplication.
*
* In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in
* particular, to ensure that the outputs from the endomorphism-split fit into
* 128 bits). If we negate, the parity of our number flips, inverting which of
* {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);
/* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
bit = flip ^ !secp256k1_scalar_is_even(&s);
@ -88,7 +93,7 @@ static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
/* 4 */
u_last = secp256k1_scalar_shr_int(&s, w);
while (word * w < WNAF_BITS) {
while (word * w < size) {
int sign;
int even;
@ -108,37 +113,44 @@ static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
wnaf[word] = u * global_sign;
VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
VERIFY_CHECK(word == WNAF_SIZE(w));
VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w));
return skew;
}
static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar) {
static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) {
secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_ge tmpa;
secp256k1_fe Z;
int skew_1;
int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
#ifdef USE_ENDOMORPHISM
secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
int skew_lam;
secp256k1_scalar q_1, q_lam;
#endif
int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
int i;
secp256k1_scalar sc = *scalar;
/* build wnaf representation for q. */
int rsize = size;
#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);
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
skew_1 = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1);
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);
} else
#endif
{
skew_1 = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1, size);
#ifdef USE_ENDOMORPHISM
skew_lam = 0;
#endif
}
/* Calculate odd multiples of a.
* All multiples are brought to the same Z 'denominator', which is stored
@ -152,26 +164,30 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
secp256k1_fe_normalize_weak(&pre_a[i].y);
}
#ifdef USE_ENDOMORPHISM
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
if (size > 128) {
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) */
i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)];
i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
VERIFY_CHECK(i != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
secp256k1_gej_set_ge(r, &tmpa);
#ifdef USE_ENDOMORPHISM
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);
if (size > 128) {
i = wnaf_lam[WNAF_SIZE_BITS(rsize, 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);
}
#endif
/* remaining loop iterations */
for (i = WNAF_SIZE(WINDOW_A - 1) - 1; i >= 0; i--) {
for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) {
int n;
int j;
for (j = 0; j < WINDOW_A - 1; ++j) {
@ -183,10 +199,12 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
VERIFY_CHECK(n != 0);
secp256k1_gej_add_ge(r, r, &tmpa);
#ifdef USE_ENDOMORPHISM
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);
if (size > 128) {
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);
}
#endif
}
@ -206,14 +224,18 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
secp256k1_ge_set_gej(&correction, &tmpj);
secp256k1_ge_to_storage(&correction_1_stor, a);
#ifdef USE_ENDOMORPHISM
secp256k1_ge_to_storage(&correction_lam_stor, a);
if (size > 128) {
secp256k1_ge_to_storage(&correction_lam_stor, a);
}
#endif
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);
#ifdef USE_ENDOMORPHISM
secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
if (size > 128) {
secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
}
#endif
/* Apply the correction */
@ -222,10 +244,12 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
secp256k1_gej_add_ge(r, r, &correction);
#ifdef USE_ENDOMORPHISM
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);
if (size > 128) {
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);
}
#endif
}
}

3
src/ecmult_impl.h
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@ -47,7 +47,8 @@
#else
#define WNAF_BITS 256
#endif
#define WNAF_SIZE(w) ((WNAF_BITS + (w) - 1) / (w))
#define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w))
#define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w)
/** The number of entries a table with precomputed multiples needs to have. */
#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))

2
src/modules/ecdh/main_impl.h
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@ -30,7 +30,7 @@ int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *result, const se
unsigned char y[1];
secp256k1_sha256 sha;
secp256k1_ecmult_const(&res, &pt, &s);
secp256k1_ecmult_const(&res, &pt, &s, 256);
secp256k1_ge_set_gej(&pt, &res);
/* Compute a hash of the point in compressed form
* Note we cannot use secp256k1_eckey_pubkey_serialize here since it does not

24
src/tests.c
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@ -2443,7 +2443,7 @@ void ecmult_const_random_mult(void) {
0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
);
secp256k1_gej b;
secp256k1_ecmult_const(&b, &a, &xn);
secp256k1_ecmult_const(&b, &a, &xn, 256);
CHECK(secp256k1_ge_is_valid_var(&a));
ge_equals_gej(&expected_b, &b);
@ -2459,12 +2459,12 @@ void ecmult_const_commutativity(void) {
random_scalar_order_test(&a);
random_scalar_order_test(&b);
secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a);
secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b);
secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a, 256);
secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b, 256);
secp256k1_ge_set_gej(&mid1, &res1);
secp256k1_ge_set_gej(&mid2, &res2);
secp256k1_ecmult_const(&res1, &mid1, &b);
secp256k1_ecmult_const(&res2, &mid2, &a);
secp256k1_ecmult_const(&res1, &mid1, &b, 256);
secp256k1_ecmult_const(&res2, &mid2, &a, 256);
secp256k1_ge_set_gej(&mid1, &res1);
secp256k1_ge_set_gej(&mid2, &res2);
ge_equals_ge(&mid1, &mid2);
@ -2480,13 +2480,13 @@ void ecmult_const_mult_zero_one(void) {
secp256k1_scalar_negate(&negone, &one);
random_group_element_test(&point);
secp256k1_ecmult_const(&res1, &point, &zero);
secp256k1_ecmult_const(&res1, &point, &zero, 3);
secp256k1_ge_set_gej(&res2, &res1);
CHECK(secp256k1_ge_is_infinity(&res2));
secp256k1_ecmult_const(&res1, &point, &one);
secp256k1_ecmult_const(&res1, &point, &one, 2);
secp256k1_ge_set_gej(&res2, &res1);
ge_equals_ge(&res2, &point);
secp256k1_ecmult_const(&res1, &point, &negone);
secp256k1_ecmult_const(&res1, &point, &negone, 256);
secp256k1_gej_neg(&res1, &res1);
secp256k1_ge_set_gej(&res2, &res1);
ge_equals_ge(&res2, &point);
@ -2512,7 +2512,7 @@ void ecmult_const_chain_multiply(void) {
for (i = 0; i < 100; ++i) {
secp256k1_ge tmp;
secp256k1_ge_set_gej(&tmp, &point);
secp256k1_ecmult_const(&point, &tmp, &scalar);
secp256k1_ecmult_const(&point, &tmp, &scalar, 256);
}
secp256k1_ge_set_gej(&res, &point);
ge_equals_gej(&res, &expected_point);
@ -2968,6 +2968,7 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) {
int wnaf[256] = {0};
int i;
int skew;
int bits = 256;
secp256k1_scalar num = *number;
secp256k1_scalar_set_int(&x, 0);
@ -2977,10 +2978,11 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) {
for (i = 0; i < 16; ++i) {
secp256k1_scalar_shr_int(&num, 8);
}
bits = 128;
#endif
skew = secp256k1_wnaf_const(wnaf, num, w);
skew = secp256k1_wnaf_const(wnaf, num, w, bits);
for (i = WNAF_SIZE(w); i >= 0; --i) {
for (i = WNAF_SIZE_BITS(bits, w); i >= 0; --i) {
secp256k1_scalar t;
int v = wnaf[i];
CHECK(v != 0); /* check nonzero */

2
src/tests_exhaustive.c
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@ -174,7 +174,7 @@ void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *gr
ge_equals_gej(&group[(i * r_log + j) % order], &tmp);
if (i > 0) {
secp256k1_ecmult_const(&tmp, &group[i], &ng);
secp256k1_ecmult_const(&tmp, &group[i], &ng, 256);
ge_equals_gej(&group[(i * j) % order], &tmp);
}
}