#define WINDOW_G 16
#endif
-/** Fill a table 'pre' with precomputed odd multiples of a. W determines the size of the table.
- * pre will contains the values [1*a,3*a,5*a,...,(2^(w-1)-1)*a], so it needs place for
- * 2^(w-2) entries.
- *
- * There are two versions of this function:
- * - secp256k1_ecmult_precomp_wnaf_gej, which operates on group elements in jacobian notation,
- * fast to precompute, but slower to use in later additions.
- * - secp256k1_ecmult_precomp_wnaf_ge, which operates on group elements in affine notations,
- * (much) slower to precompute, but a bit faster to use in later additions.
- * To compute a*P + b*G, we use the jacobian version for P, and the affine version for G, as
- * G is constant, so it only needs to be done once in advance.
+/** The number of entries a table with precomputed multiples needs to have. */
+#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
+
+/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
+ * the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
+ * contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
+ * Prej's Z values are undefined, except for the last value.
*/
-static void secp256k1_ecmult_table_precomp_gej_var(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) {
- secp256k1_gej_t d;
+static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) {
+ secp256k1_gej d;
+ secp256k1_ge a_ge, d_ge;
int i;
- pre[0] = *a;
- secp256k1_gej_double_var(&d, &pre[0]);
- for (i = 1; i < (1 << (w-2)); i++) {
- secp256k1_gej_add_var(&pre[i], &d, &pre[i-1]);
+
+ VERIFY_CHECK(!a->infinity);
+
+ secp256k1_gej_double_var(&d, a, NULL);
+
+ /*
+ * Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
+ * of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
+ */
+ d_ge.x = d.x;
+ d_ge.y = d.y;
+ d_ge.infinity = 0;
+
+ secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
+ prej[0].x = a_ge.x;
+ prej[0].y = a_ge.y;
+ prej[0].z = a->z;
+ prej[0].infinity = 0;
+
+ zr[0] = d.z;
+ for (i = 1; i < n; i++) {
+ secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
}
+
+ /*
+ * Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
+ * the final point's z coordinate is actually used though, so just update that.
+ */
+ secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
+}
+
+/** Fill a table 'pre' with precomputed odd multiples of a.
+ *
+ * There are two versions of this function:
+ * - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
+ * resulting point set to a single constant Z denominator, stores the X and Y
+ * coordinates as ge_storage points in pre, and stores the global Z in rz.
+ * It only operates on tables sized for WINDOW_A wnaf multiples.
+ * - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
+ * resulting point set to actually affine points, and stores those in pre.
+ * It operates on tables of any size, but uses heap-allocated temporaries.
+ *
+ * To compute a*P + b*G, we compute a table for P using the first function,
+ * and for G using the second (which requires an inverse, but it only needs to
+ * happen once).
+ */
+static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
+ secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
+ secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
+
+ /* Compute the odd multiples in Jacobian form. */
+ secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
+ /* Bring them to the same Z denominator. */
+ secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
}
-static void secp256k1_ecmult_table_precomp_ge_storage_var(secp256k1_ge_storage_t *pre, const secp256k1_gej_t *a, int w) {
- secp256k1_gej_t d;
+static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage *pre, const secp256k1_gej *a, const secp256k1_callback *cb) {
+ secp256k1_gej *prej = (secp256k1_gej*)checked_malloc(cb, sizeof(secp256k1_gej) * n);
+ secp256k1_ge *prea = (secp256k1_ge*)checked_malloc(cb, sizeof(secp256k1_ge) * n);
+ secp256k1_fe *zr = (secp256k1_fe*)checked_malloc(cb, sizeof(secp256k1_fe) * n);
int i;
- const int table_size = 1 << (w-2);
- secp256k1_gej_t *prej = (secp256k1_gej_t *)checked_malloc(sizeof(secp256k1_gej_t) * table_size);
- secp256k1_ge_t *prea = (secp256k1_ge_t *)checked_malloc(sizeof(secp256k1_ge_t) * table_size);
- prej[0] = *a;
- secp256k1_gej_double_var(&d, a);
- for (i = 1; i < table_size; i++) {
- secp256k1_gej_add_var(&prej[i], &d, &prej[i-1]);
- }
- secp256k1_ge_set_all_gej_var(table_size, prea, prej);
- for (i = 0; i < table_size; i++) {
+
+ /* Compute the odd multiples in Jacobian form. */
+ secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
+ /* Convert them in batch to affine coordinates. */
+ secp256k1_ge_set_table_gej_var(prea, prej, zr, n);
+ /* Convert them to compact storage form. */
+ for (i = 0; i < n; i++) {
secp256k1_ge_to_storage(&pre[i], &prea[i]);
}
- free(prej);
+
free(prea);
+ free(prej);
+ free(zr);
}
-/** The number of entries a table with precomputed multiples needs to have. */
-#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
-
/** The following two macro retrieves a particular odd multiple from a table
* of precomputed multiples. */
-#define ECMULT_TABLE_GET_GEJ(r,pre,n,w) do { \
+#define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
if ((n) > 0) { \
*(r) = (pre)[((n)-1)/2]; \
} else { \
- secp256k1_gej_neg((r), &(pre)[(-(n)-1)/2]); \
+ secp256k1_ge_neg((r), &(pre)[(-(n)-1)/2]); \
} \
} while(0)
+
#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
} \
} while(0)
-static void secp256k1_ecmult_context_init(secp256k1_ecmult_context_t *ctx) {
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
ctx->pre_g = NULL;
#ifdef USE_ENDOMORPHISM
ctx->pre_g_128 = NULL;
#endif
}
-static void secp256k1_ecmult_context_build(secp256k1_ecmult_context_t *ctx) {
- secp256k1_gej_t gj;
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb) {
+ secp256k1_gej gj;
if (ctx->pre_g != NULL) {
return;
/* get the generator */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
- ctx->pre_g = (secp256k1_ge_storage_t (*)[])checked_malloc(sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
+ ctx->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
/* precompute the tables with odd multiples */
- secp256k1_ecmult_table_precomp_ge_storage_var(*ctx->pre_g, &gj, WINDOW_G);
+ secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb);
#ifdef USE_ENDOMORPHISM
{
- secp256k1_gej_t g_128j;
+ secp256k1_gej g_128j;
int i;
- ctx->pre_g_128 = (secp256k1_ge_storage_t (*)[])checked_malloc(sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
+ ctx->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
/* calculate 2^128*generator */
g_128j = gj;
for (i = 0; i < 128; i++) {
- secp256k1_gej_double_var(&g_128j, &g_128j);
+ secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
}
- secp256k1_ecmult_table_precomp_ge_storage_var(*ctx->pre_g_128, &g_128j, WINDOW_G);
+ secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb);
}
#endif
}
-static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context_t *dst,
- const secp256k1_ecmult_context_t *src) {
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+ const secp256k1_ecmult_context *src, const secp256k1_callback *cb) {
if (src->pre_g == NULL) {
dst->pre_g = NULL;
} else {
size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
- dst->pre_g = (secp256k1_ge_storage_t (*)[])checked_malloc(size);
+ dst->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
memcpy(dst->pre_g, src->pre_g, size);
}
#ifdef USE_ENDOMORPHISM
dst->pre_g_128 = NULL;
} else {
size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
- dst->pre_g_128 = (secp256k1_ge_storage_t (*)[])checked_malloc(size);
+ dst->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
memcpy(dst->pre_g_128, src->pre_g_128, size);
}
#endif
}
-static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context_t *ctx) {
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
return ctx->pre_g != NULL;
}
-static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context_t *ctx) {
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
free(ctx->pre_g);
#ifdef USE_ENDOMORPHISM
free(ctx->pre_g_128);
* - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
* - two non-zero entries in wnaf are separated by at least w-1 zeroes.
* - the number of set values in wnaf is returned. This number is at most 256, and at most one more
- * - than the number of bits in the (absolute value) of the input.
+ * than the number of bits in the (absolute value) of the input.
*/
-static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_scalar_t *a, int w) {
- secp256k1_scalar_t s = *a;
- int set_bits = 0;
+static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) {
+ secp256k1_scalar s = *a;
+ int last_set_bit = -1;
int bit = 0;
int sign = 1;
+ int carry = 0;
+
+ VERIFY_CHECK(wnaf != NULL);
+ VERIFY_CHECK(0 <= len && len <= 256);
+ VERIFY_CHECK(a != NULL);
+ VERIFY_CHECK(2 <= w && w <= 31);
+
+ memset(wnaf, 0, len * sizeof(wnaf[0]));
if (secp256k1_scalar_get_bits(&s, 255, 1)) {
secp256k1_scalar_negate(&s, &s);
sign = -1;
}
- while (bit < 256) {
+ while (bit < len) {
int now;
int word;
- if (secp256k1_scalar_get_bits(&s, bit, 1) == 0) {
+ if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
bit++;
continue;
}
- while (set_bits < bit) {
- wnaf[set_bits++] = 0;
- }
+
now = w;
- if (bit + now > 256) {
- now = 256 - bit;
- }
- word = secp256k1_scalar_get_bits_var(&s, bit, now);
- if (word & (1 << (w-1))) {
- secp256k1_scalar_add_bit(&s, bit + w);
- wnaf[set_bits++] = sign * (word - (1 << w));
- } else {
- wnaf[set_bits++] = sign * word;
+ if (now > len - bit) {
+ now = len - bit;
}
+
+ word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
+
+ carry = (word >> (w-1)) & 1;
+ word -= carry << w;
+
+ wnaf[bit] = sign * word;
+ last_set_bit = bit;
+
bit += now;
}
- return set_bits;
+#ifdef VERIFY
+ CHECK(carry == 0);
+ while (bit < 256) {
+ CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
+ }
+#endif
+ return last_set_bit + 1;
}
-static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng) {
- secp256k1_gej_t tmpj;
- secp256k1_gej_t pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
- secp256k1_ge_t tmpa;
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
+ secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+ secp256k1_ge tmpa;
+ secp256k1_fe Z;
#ifdef USE_ENDOMORPHISM
- secp256k1_gej_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
- secp256k1_scalar_t na_1, na_lam;
+ secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+ secp256k1_scalar na_1, na_lam;
/* Splitted G factors. */
- secp256k1_scalar_t ng_1, ng_128;
+ secp256k1_scalar ng_1, ng_128;
int wnaf_na_1[130];
int wnaf_na_lam[130];
int bits_na_1;
#else
int wnaf_na[256];
int bits_na;
- int wnaf_ng[257];
+ int wnaf_ng[256];
int bits_ng;
#endif
int i;
#ifdef USE_ENDOMORPHISM
/* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
- secp256k1_scalar_split_lambda_var(&na_1, &na_lam, na);
+ secp256k1_scalar_split_lambda(&na_1, &na_lam, na);
/* build wnaf representation for na_1 and na_lam. */
- bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, &na_1, WINDOW_A);
- bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
+ bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, 130, &na_1, WINDOW_A);
+ bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, 130, &na_lam, WINDOW_A);
VERIFY_CHECK(bits_na_1 <= 130);
VERIFY_CHECK(bits_na_lam <= 130);
bits = bits_na_1;
}
#else
/* build wnaf representation for na. */
- bits_na = secp256k1_ecmult_wnaf(wnaf_na, na, WINDOW_A);
+ bits_na = secp256k1_ecmult_wnaf(wnaf_na, 256, na, WINDOW_A);
bits = bits_na;
#endif
- /* calculate odd multiples of a */
- secp256k1_ecmult_table_precomp_gej_var(pre_a, a, WINDOW_A);
+ /* Calculate odd multiples of a.
+ * All multiples are brought to the same Z 'denominator', which is stored
+ * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+ * that the Z coordinate was 1, use affine addition formulae, and correct
+ * the Z coordinate of the result once at the end.
+ * The exception is the precomputed G table points, which are actually
+ * affine. Compared to the base used for other points, they have a Z ratio
+ * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
+ * isomorphism to efficiently add with a known Z inverse.
+ */
+ secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, a);
#ifdef USE_ENDOMORPHISM
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
- secp256k1_gej_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+ secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
}
/* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
/* Build wnaf representation for ng_1 and ng_128 */
- bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, &ng_1, WINDOW_G);
- bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, &ng_128, WINDOW_G);
+ bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G);
+ bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
if (bits_ng_1 > bits) {
bits = bits_ng_1;
}
bits = bits_ng_128;
}
#else
- bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, ng, WINDOW_G);
+ bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G);
if (bits_ng > bits) {
bits = bits_ng;
}
secp256k1_gej_set_infinity(r);
- for (i = bits-1; i >= 0; i--) {
+ for (i = bits - 1; i >= 0; i--) {
int n;
- secp256k1_gej_double_var(r, r);
+ secp256k1_gej_double_var(r, r, NULL);
#ifdef USE_ENDOMORPHISM
if (i < bits_na_1 && (n = wnaf_na_1[i])) {
- ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
- secp256k1_gej_add_var(r, r, &tmpj);
+ ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+ secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
- ECMULT_TABLE_GET_GEJ(&tmpj, pre_a_lam, n, WINDOW_A);
- secp256k1_gej_add_var(r, r, &tmpj);
+ ECMULT_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+ secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
- secp256k1_gej_add_ge_var(r, r, &tmpa);
+ secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
- secp256k1_gej_add_ge_var(r, r, &tmpa);
+ secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
#else
if (i < bits_na && (n = wnaf_na[i])) {
- ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
- secp256k1_gej_add_var(r, r, &tmpj);
+ ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+ secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
if (i < bits_ng && (n = wnaf_ng[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
- secp256k1_gej_add_ge_var(r, r, &tmpa);
+ secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
#endif
}
+
+ if (!r->infinity) {
+ secp256k1_fe_mul(&r->z, &r->z, &Z);
+ }
}
#endif
projects / secp256k1.git / blobdiff