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Generalize Strauss to support multiple points
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API by Andrew Poelstra.
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@sipa @jonasnick
sipa authored and jonasnick committed Dec 7, 2017
1 parent 548de42 commit 8c1c831
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Showing 4 changed files with 216 additions and 56 deletions.
9 changes: 8 additions & 1 deletion src/ecmult.h
View file
@@ -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.*
**********************************************************************/
Expand All @@ -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: */
Expand All @@ -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 */
254 changes: 199 additions & 55 deletions src/ecmult_impl.h
View file
@@ -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.*
**********************************************************************/
Expand Down Expand Up @@ -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);

/* 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;
}
/* 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. */
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
Expand All @@ -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

Expand All @@ -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);
Expand All @@ -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);
Expand All @@ -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 */
3 changes: 3 additions & 0 deletions src/group.h
View file
Expand Up @@ -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);

Expand Down
6 changes: 6 additions & 0 deletions src/group_impl.h
View file
Expand Up @@ -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);
Expand Down

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