diff options
Diffstat (limited to 'src/ecmult_impl.h')
-rw-r--r-- | src/ecmult_impl.h | 268 |
1 files changed, 170 insertions, 98 deletions
diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h index 1b2856f83d..e6e5f47188 100644 --- a/src/ecmult_impl.h +++ b/src/ecmult_impl.h @@ -24,62 +24,107 @@ #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(n, prea, prej, zr); + /* 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)); \ @@ -92,15 +137,15 @@ static void secp256k1_ecmult_table_precomp_ge_storage_var(secp256k1_ge_storage_t } \ } 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; @@ -109,35 +154,35 @@ static void secp256k1_ecmult_context_build(secp256k1_ecmult_context_t *ctx) { /* 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 @@ -145,17 +190,17 @@ static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context_t *dst, 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); @@ -168,54 +213,68 @@ static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context_t *ctx) { * - 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; @@ -227,7 +286,7 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge #else int wnaf_na[256]; int bits_na; - int wnaf_ng[257]; + int wnaf_ng[256]; int bits_ng; #endif int i; @@ -235,11 +294,11 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge #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; @@ -248,24 +307,33 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge } #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; } @@ -273,7 +341,7 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge 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; } @@ -281,37 +349,41 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge 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 |