From 8c1c831bdb083dfa8b50fac16a0e17a7e1df4064 Mon Sep 17 00:00:00 2001 From: Pieter Wuille Date: Wed, 16 Aug 2017 14:45:27 -0700 Subject: [PATCH] Generalize Strauss to support multiple points API by Andrew Poelstra. --- src/ecmult.h | 9 +- src/ecmult_impl.h | 252 ++++++++++++++++++++++++++++++++++++---------- src/group.h | 3 + src/group_impl.h | 6 ++ 4 files changed, 215 insertions(+), 55 deletions(-) diff --git a/src/ecmult.h b/src/ecmult.h index 6d44aba..12e5463 100644 --- a/src/ecmult.h +++ b/src/ecmult.h @@ -1,5 +1,5 @@ /********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * + * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra * * Distributed under the MIT software license, see the accompanying * * file COPYING or http://www.opensource.org/licenses/mit-license.php.* **********************************************************************/ @@ -9,6 +9,8 @@ #include "num.h" #include "group.h" +#include "scalar.h" +#include "scratch.h" typedef struct { /* For accelerating the computation of a*P + b*G: */ @@ -28,4 +30,9 @@ static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx /** Double multiply: R = na*A + ng*G */ static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng); +typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data); + +/** Multi-multiply: R = inp_g_sc * G + sum_i ni * Ai. */ +static int secp256k1_ecmult_multi(const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n); + #endif /* SECP256K1_ECMULT_H */ diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h index 93d3794..44a2734 100644 --- a/src/ecmult_impl.h +++ b/src/ecmult_impl.h @@ -1,5 +1,5 @@ /********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * + * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra * * Distributed under the MIT software license, see the accompanying * * file COPYING or http://www.opensource.org/licenses/mit-license.php.* **********************************************************************/ @@ -283,50 +283,78 @@ static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, return last_set_bit + 1; } -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; +struct secp256k1_strauss_point_state { #ifdef USE_ENDOMORPHISM - secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; secp256k1_scalar na_1, na_lam; - /* Splitted G factors. */ - secp256k1_scalar ng_1, ng_128; int wnaf_na_1[130]; int wnaf_na_lam[130]; int bits_na_1; int bits_na_lam; - int wnaf_ng_1[129]; - int bits_ng_1; - int wnaf_ng_128[129]; - int bits_ng_128; #else int wnaf_na[256]; int bits_na; +#endif + size_t input_pos; +}; + +struct secp256k1_strauss_state { + secp256k1_gej* prej; + secp256k1_fe* zr; + secp256k1_ge* pre_a; +#ifdef USE_ENDOMORPHISM + secp256k1_ge* pre_a_lam; +#endif + struct secp256k1_strauss_point_state* ps; +}; + +static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, const struct secp256k1_strauss_state *state, secp256k1_gej *r, int num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { + secp256k1_ge tmpa; + secp256k1_fe Z; +#ifdef USE_ENDOMORPHISM + /* Splitted G factors. */ + secp256k1_scalar ng_1, ng_128; + int wnaf_ng_1[129]; + int bits_ng_1 = 0; + int wnaf_ng_128[129]; + int bits_ng_128 = 0; +#else int wnaf_ng[256]; - int bits_ng; + int bits_ng = 0; #endif int i; - int bits; + int bits = 0; + int np; + int no = 0; + for (np = 0; np < num; ++np) { + if (secp256k1_scalar_is_zero(&na[np]) || secp256k1_gej_is_infinity(&a[np])) { + continue; + } + state->ps[no].input_pos = np; #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(&na_1, &na_lam, na); + /* 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(&state->ps[no].na_1, &state->ps[no].na_lam, &na[np]); - /* build wnaf representation for na_1 and na_lam. */ - 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; - if (bits_na_lam > bits) { - bits = bits_na_lam; - } + /* build wnaf representation for na_1 and na_lam. */ + state->ps[no].bits_na_1 = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1, 130, &state->ps[no].na_1, WINDOW_A); + state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 130, &state->ps[no].na_lam, WINDOW_A); + VERIFY_CHECK(state->ps[no].bits_na_1 <= 130); + VERIFY_CHECK(state->ps[no].bits_na_lam <= 130); + if (state->ps[no].bits_na_1 > bits) { + bits = state->ps[no].bits_na_1; + } + if (state->ps[no].bits_na_lam > bits) { + bits = state->ps[no].bits_na_lam; + } #else - /* build wnaf representation for na. */ - bits_na = secp256k1_ecmult_wnaf(wnaf_na, 256, na, WINDOW_A); - bits = bits_na; + /* build wnaf representation for na. */ + state->ps[no].bits_na = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na, 256, &na[np], WINDOW_A); + if (state->ps[no].bits_na > bits) { + bits = state->ps[no].bits_na; + } #endif + ++no; + } /* Calculate odd multiples of a. * All multiples are brought to the same Z 'denominator', which is stored @@ -338,29 +366,51 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej * 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); + if (no > 0) { + /* Compute the odd multiples in Jacobian form. */ + secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->prej, state->zr, &a[state->ps[0].input_pos]); + for (np = 1; np < no; ++np) { + secp256k1_gej tmp = a[state->ps[np].input_pos]; +#ifdef VERIFY + secp256k1_fe_normalize_var(&(state->prej[(np - 1) * ECMULT_TABLE_SIZE(WINDOW_A) + ECMULT_TABLE_SIZE(WINDOW_A) - 1].z)); +#endif + secp256k1_gej_rescale(&tmp, &(state->prej[(np - 1) * ECMULT_TABLE_SIZE(WINDOW_A) + ECMULT_TABLE_SIZE(WINDOW_A) - 1].z)); + secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->prej + np * ECMULT_TABLE_SIZE(WINDOW_A), state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), &tmp); + secp256k1_fe_mul(state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), &(a[state->ps[np].input_pos].z)); + } + /* Bring them to the same Z denominator. */ + secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, &Z, state->prej, state->zr); + } else { + secp256k1_fe_set_int(&Z, 1); + } #ifdef USE_ENDOMORPHISM - for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { - secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]); + for (np = 0; np < no; ++np) { + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_ge_mul_lambda(&state->pre_a_lam[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_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); + if (ng) { + /* 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, 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; - } - if (bits_ng_128 > bits) { - bits = bits_ng_128; + /* Build wnaf representation for ng_1 and ng_128 */ + 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; + } + if (bits_ng_128 > bits) { + bits = bits_ng_128; + } } #else - bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G); - if (bits_ng > bits) { - bits = bits_ng; + if (ng) { + bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G); + if (bits_ng > bits) { + bits = bits_ng; + } } #endif @@ -370,13 +420,15 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej int n; secp256k1_gej_double_var(r, r, NULL); #ifdef USE_ENDOMORPHISM - if (i < bits_na_1 && (n = wnaf_na_1[i])) { - 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_GE(&tmpa, pre_a_lam, n, WINDOW_A); - secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); + for (np = 0; np < no; ++np) { + if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) { + ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A); + secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); + } + if (i < state->ps[np].bits_na_lam && (n = state->ps[np].wnaf_na_lam[i])) { + ECMULT_TABLE_GET_GE(&tmpa, state->pre_a_lam + np * ECMULT_TABLE_SIZE(WINDOW_A), 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); @@ -387,9 +439,11 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); } #else - if (i < bits_na && (n = wnaf_na[i])) { - ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A); - secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); + for (np = 0; np < no; ++np) { + if (i < state->ps[np].bits_na && (n = state->ps[np].wnaf_na[i])) { + ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_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); @@ -403,4 +457,94 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej } } +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_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + struct secp256k1_strauss_point_state ps[1]; +#ifdef USE_ENDOMORPHISM + secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; +#endif + struct secp256k1_strauss_state state; + + state.prej = prej; + state.zr = zr; + state.pre_a = pre_a; +#ifdef USE_ENDOMORPHISM + state.pre_a_lam = pre_a_lam; +#endif + state.ps = ps; + secp256k1_ecmult_strauss_wnaf(ctx, &state, r, 1, a, na, ng); +} + +static int secp256k1_ecmult_multi_split_strauss_wnaf(const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { + secp256k1_gej* points; + secp256k1_scalar* scalars; + secp256k1_gej acc; + size_t in_pos = 0, out_pos = 0; + int first = 1; + +#ifdef USE_ENDOMORPHISM + static const size_t point_size = (sizeof(secp256k1_gej) + sizeof(secp256k1_fe) + sizeof(secp256k1_ge) * 2) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar); +#else + static const size_t point_size = (sizeof(secp256k1_gej) + sizeof(secp256k1_fe) + sizeof(secp256k1_ge)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar); +#endif + + size_t max_points = secp256k1_scratch_max_allocation(scratch, 6) / point_size; + size_t n_batches, points_per_batch; + struct secp256k1_strauss_state state; + + if (max_points == 0) return 0; + if (max_points > 160) max_points = 160; /* At this point, gains are not longer compensating for locality degradation */ + n_batches = (n + max_points - 1) / max_points; + points_per_batch = (n + n_batches - 1) / n_batches; + + /* Attempt to allocate sufficient space for Strauss */ + while (!secp256k1_scratch_resize(scratch, max_points * point_size, 6)) { + max_points /= 2; + if (max_points == 0) { + return 0; + } + } + + secp256k1_scratch_reset(scratch); + points = (secp256k1_gej*)secp256k1_scratch_alloc(scratch, max_points * sizeof(secp256k1_gej)); + scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(scratch, max_points * sizeof(secp256k1_scalar)); + state.prej = (secp256k1_gej*)secp256k1_scratch_alloc(scratch, max_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_gej)); + state.zr = (secp256k1_fe*)secp256k1_scratch_alloc(scratch, max_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe)); +#ifdef USE_ENDOMORPHISM + state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(scratch, max_points * 2 * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); + state.pre_a_lam = state.pre_a + max_points * ECMULT_TABLE_SIZE(WINDOW_A); +#else + state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(scratch, max_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); +#endif + state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(scratch, max_points * sizeof(struct secp256k1_strauss_point_state)); + + if (n == 0 && inp_g_sc) { + secp256k1_ecmult_strauss_wnaf(ctx, &state, r, 0, NULL, NULL, inp_g_sc); + return 1; + } + + while (in_pos < n) { + secp256k1_ge point; + if (!cb(&scalars[out_pos], &point, in_pos, cbdata)) return 0; + secp256k1_gej_set_ge(&points[out_pos], &point); + ++in_pos; + ++out_pos; + if (out_pos == points_per_batch || in_pos == n) { + secp256k1_ecmult_strauss_wnaf(ctx, &state, first ? r : &acc, out_pos, points, scalars, first ? inp_g_sc : NULL); + if (!first) { + secp256k1_gej_add_var(r, r, &acc, NULL); + } + first = 0; + out_pos = 0; + } + } + return 1; +} + +static int secp256k1_ecmult_multi(const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { + return secp256k1_ecmult_multi_split_strauss_wnaf(ctx, scratch, r, inp_g_sc, cb, cbdata, n); +} + #endif /* SECP256K1_ECMULT_IMPL_H */ diff --git a/src/group.h b/src/group.h index ea1302d..3947ea2 100644 --- a/src/group.h +++ b/src/group.h @@ -79,6 +79,9 @@ static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej * stored in globalz. */ static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr); +/** Set a group element (affine) equal to the point at infinity. */ +static void secp256k1_ge_set_infinity(secp256k1_ge *r); + /** Set a group element (jacobian) equal to the point at infinity. */ static void secp256k1_gej_set_infinity(secp256k1_gej *r); diff --git a/src/group_impl.h b/src/group_impl.h index b31b6c1..b1ace87 100644 --- a/src/group_impl.h +++ b/src/group_impl.h @@ -200,6 +200,12 @@ static void secp256k1_gej_set_infinity(secp256k1_gej *r) { secp256k1_fe_clear(&r->z); } +static void secp256k1_ge_set_infinity(secp256k1_ge *r) { + r->infinity = 1; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); +} + static void secp256k1_gej_clear(secp256k1_gej *r) { r->infinity = 0; secp256k1_fe_clear(&r->x);