-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille *
- * Distributed under the MIT software license, see the accompanying *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
+/*****************************************************************************
+ * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra, Jonas Nick *
+ * Distributed under the MIT software license, see the accompanying *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php. *
+ *****************************************************************************/
-#ifndef _SECP256K1_ECMULT_IMPL_H_
-#define _SECP256K1_ECMULT_IMPL_H_
+#ifndef SECP256K1_ECMULT_IMPL_H
+#define SECP256K1_ECMULT_IMPL_H
+#include <string.h>
+#include <stdint.h>
+
+#include "util.h"
#include "group.h"
#include "scalar.h"
#include "ecmult.h"
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/* We need to lower these values for exhaustive tests because
+ * the tables cannot have infinities in them (this breaks the
+ * affine-isomorphism stuff which tracks z-ratios) */
+# if EXHAUSTIVE_TEST_ORDER > 128
+# define WINDOW_A 5
+# define WINDOW_G 8
+# elif EXHAUSTIVE_TEST_ORDER > 8
+# define WINDOW_A 4
+# define WINDOW_G 4
+# else
+# define WINDOW_A 2
+# define WINDOW_G 2
+# endif
+#else
/* optimal for 128-bit and 256-bit exponents. */
-#define WINDOW_A 5
+# define WINDOW_A 5
+/** Larger values for ECMULT_WINDOW_SIZE result in possibly better
+ * performance at the cost of an exponentially larger precomputed
+ * table. The exact table size is
+ * (1 << (WINDOW_G - 2)) * sizeof(secp256k1_ge_storage) bytes,
+ * where sizeof(secp256k1_ge_storage) is typically 64 bytes but can
+ * be larger due to platform-specific padding and alignment.
+ * If the endomorphism optimization is enabled (USE_ENDOMORMPHSIM)
+ * two tables of this size are used instead of only one.
+ */
+# define WINDOW_G ECMULT_WINDOW_SIZE
+#endif
+
+/* Noone will ever need more than a window size of 24. The code might
+ * be correct for larger values of ECMULT_WINDOW_SIZE but this is not
+ * not tested.
+ *
+ * The following limitations are known, and there are probably more:
+ * If WINDOW_G > 27 and size_t has 32 bits, then the code is incorrect
+ * because the size of the memory object that we allocate (in bytes)
+ * will not fit in a size_t.
+ * If WINDOW_G > 31 and int has 32 bits, then the code is incorrect
+ * because certain expressions will overflow.
+ */
+#if ECMULT_WINDOW_SIZE < 2 || ECMULT_WINDOW_SIZE > 24
+# error Set ECMULT_WINDOW_SIZE to an integer in range [2..24].
+#endif
+
+#ifdef USE_ENDOMORPHISM
+ #define WNAF_BITS 128
+#else
+ #define WNAF_BITS 256
+#endif
+#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))
+
+/* The number of objects allocated on the scratch space for ecmult_multi algorithms */
+#define PIPPENGER_SCRATCH_OBJECTS 6
+#define STRAUSS_SCRATCH_OBJECTS 6
+
+#define PIPPENGER_MAX_BUCKET_WINDOW 12
+
+/* Minimum number of points for which pippenger_wnaf is faster than strauss wnaf */
+#ifdef USE_ENDOMORPHISM
+ #define ECMULT_PIPPENGER_THRESHOLD 88
+#else
+ #define ECMULT_PIPPENGER_THRESHOLD 160
+#endif
-/** larger numbers may result in slightly better performance, at the cost of
- exponentially larger precomputed tables. */
#ifdef USE_ENDOMORPHISM
-/** Two tables for window size 15: 1.375 MiB. */
-#define WINDOW_G 15
+ #define ECMULT_MAX_POINTS_PER_BATCH 5000000
#else
-/** One table for window size 16: 1.375 MiB. */
-#define WINDOW_G 16
+ #define ECMULT_MAX_POINTS_PER_BATCH 10000000
#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.
+/** 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_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;
+
+ 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_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.
+ * - 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_table_precomp_gej_var(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) {
- pre[0] = *a;
- secp256k1_gej_t d; secp256k1_gej_double_var(&d, &pre[0]);
- for (int i=1; i<(1 << (w-2)); i++)
- secp256k1_gej_add_var(&pre[i], &d, &pre[i-1]);
+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_var(secp256k1_ge_t *pre, const secp256k1_gej_t *a, int w) {
- const int table_size = 1 << (w-2);
- secp256k1_gej_t *prej = checked_malloc(sizeof(secp256k1_gej_t) * table_size);
- prej[0] = *a;
- secp256k1_gej_t d; secp256k1_gej_double_var(&d, a);
- for (int i=1; i<table_size; i++) {
- secp256k1_gej_add_var(&prej[i], &d, &prej[i-1]);
+static void secp256k1_ecmult_odd_multiples_table_storage_var(const int n, secp256k1_ge_storage *pre, const secp256k1_gej *a) {
+ secp256k1_gej d;
+ secp256k1_ge d_ge, p_ge;
+ secp256k1_gej pj;
+ secp256k1_fe zi;
+ secp256k1_fe zr;
+ secp256k1_fe dx_over_dz_squared;
+ int i;
+
+ VERIFY_CHECK(!a->infinity);
+
+ secp256k1_gej_double_var(&d, a, NULL);
+
+ /* First, we perform all the additions in an isomorphic curve obtained by multiplying
+ * all `z` coordinates by 1/`d.z`. In these coordinates `d` is affine so we can use
+ * `secp256k1_gej_add_ge_var` to perform the additions. For each addition, we store
+ * the resulting y-coordinate and the z-ratio, since we only have enough memory to
+ * store two field elements. These are sufficient to efficiently undo the isomorphism
+ * and recompute all the `x`s.
+ */
+ d_ge.x = d.x;
+ d_ge.y = d.y;
+ d_ge.infinity = 0;
+
+ secp256k1_ge_set_gej_zinv(&p_ge, a, &d.z);
+ pj.x = p_ge.x;
+ pj.y = p_ge.y;
+ pj.z = a->z;
+ pj.infinity = 0;
+
+ for (i = 0; i < (n - 1); i++) {
+ secp256k1_fe_normalize_var(&pj.y);
+ secp256k1_fe_to_storage(&pre[i].y, &pj.y);
+ secp256k1_gej_add_ge_var(&pj, &pj, &d_ge, &zr);
+ secp256k1_fe_normalize_var(&zr);
+ secp256k1_fe_to_storage(&pre[i].x, &zr);
}
- secp256k1_ge_set_all_gej_var(table_size, pre, prej);
- free(prej);
-}
-/** The number of entries a table with precomputed multiples needs to have. */
-#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
+ /* Invert d.z in the same batch, preserving pj.z so we can extract 1/d.z */
+ secp256k1_fe_mul(&zi, &pj.z, &d.z);
+ secp256k1_fe_inv_var(&zi, &zi);
+
+ /* Directly set `pre[n - 1]` to `pj`, saving the inverted z-coordinate so
+ * that we can combine it with the saved z-ratios to compute the other zs
+ * without any more inversions. */
+ secp256k1_ge_set_gej_zinv(&p_ge, &pj, &zi);
+ secp256k1_ge_to_storage(&pre[n - 1], &p_ge);
+
+ /* Compute the actual x-coordinate of D, which will be needed below. */
+ secp256k1_fe_mul(&d.z, &zi, &pj.z); /* d.z = 1/d.z */
+ secp256k1_fe_sqr(&dx_over_dz_squared, &d.z);
+ secp256k1_fe_mul(&dx_over_dz_squared, &dx_over_dz_squared, &d.x);
+
+ /* Going into the second loop, we have set `pre[n-1]` to its final affine
+ * form, but still need to set `pre[i]` for `i` in 0 through `n-2`. We
+ * have `zi = (p.z * d.z)^-1`, where
+ *
+ * `p.z` is the z-coordinate of the point on the isomorphic curve
+ * which was ultimately assigned to `pre[n-1]`.
+ * `d.z` is the multiplier that must be applied to all z-coordinates
+ * to move from our isomorphic curve back to secp256k1; so the
+ * product `p.z * d.z` is the z-coordinate of the secp256k1
+ * point assigned to `pre[n-1]`.
+ *
+ * All subsequent inverse-z-coordinates can be obtained by multiplying this
+ * factor by successive z-ratios, which is much more efficient than directly
+ * computing each one.
+ *
+ * Importantly, these inverse-zs will be coordinates of points on secp256k1,
+ * while our other stored values come from computations on the isomorphic
+ * curve. So in the below loop, we will take care not to actually use `zi`
+ * or any derived values until we're back on secp256k1.
+ */
+ i = n - 1;
+ while (i > 0) {
+ secp256k1_fe zi2, zi3;
+ const secp256k1_fe *rzr;
+ i--;
+
+ secp256k1_ge_from_storage(&p_ge, &pre[i]);
+
+ /* For each remaining point, we extract the z-ratio from the stored
+ * x-coordinate, compute its z^-1 from that, and compute the full
+ * point from that. */
+ rzr = &p_ge.x;
+ secp256k1_fe_mul(&zi, &zi, rzr);
+ secp256k1_fe_sqr(&zi2, &zi);
+ secp256k1_fe_mul(&zi3, &zi2, &zi);
+ /* To compute the actual x-coordinate, we use the stored z ratio and
+ * y-coordinate, which we obtained from `secp256k1_gej_add_ge_var`
+ * in the loop above, as well as the inverse of the square of its
+ * z-coordinate. We store the latter in the `zi2` variable, which is
+ * computed iteratively starting from the overall Z inverse then
+ * multiplying by each z-ratio in turn.
+ *
+ * Denoting the z-ratio as `rzr`, we observe that it is equal to `h`
+ * from the inside of the above `gej_add_ge_var` call. This satisfies
+ *
+ * rzr = d_x * z^2 - x * d_z^2
+ *
+ * where (`d_x`, `d_z`) are Jacobian coordinates of `D` and `(x, z)`
+ * are Jacobian coordinates of our desired point -- except both are on
+ * the isomorphic curve that we were using when we called `gej_add_ge_var`.
+ * To get back to secp256k1, we must multiply both `z`s by `d_z`, or
+ * equivalently divide both `x`s by `d_z^2`. Our equation then becomes
+ *
+ * rzr = d_x * z^2 / d_z^2 - x
+ *
+ * (The left-hand-side, being a ratio of z-coordinates, is unaffected
+ * by the isomorphism.)
+ *
+ * Rearranging to solve for `x`, we have
+ *
+ * x = d_x * z^2 / d_z^2 - rzr
+ *
+ * But what we actually want is the affine coordinate `X = x/z^2`,
+ * which will satisfy
+ *
+ * X = d_x / d_z^2 - rzr / z^2
+ * = dx_over_dz_squared - rzr * zi2
+ */
+ secp256k1_fe_mul(&p_ge.x, rzr, &zi2);
+ secp256k1_fe_negate(&p_ge.x, &p_ge.x, 1);
+ secp256k1_fe_add(&p_ge.x, &dx_over_dz_squared);
+ /* y is stored_y/z^3, as we expect */
+ secp256k1_fe_mul(&p_ge.y, &p_ge.y, &zi3);
+ /* Store */
+ secp256k1_ge_to_storage(&pre[i], &p_ge);
+ }
+}
/** The following two macro retrieves a particular odd multiple from a table
* of precomputed multiples. */
-#define ECMULT_TABLE_GET(r,pre,n,w,neg) 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) \
+ if ((n) > 0) { \
*(r) = (pre)[((n)-1)/2]; \
- else \
- (neg)((r), &(pre)[(-(n)-1)/2]); \
+ } else { \
+ *(r) = (pre)[(-(n)-1)/2]; \
+ secp256k1_fe_negate(&((r)->y), &((r)->y), 1); \
+ } \
} while(0)
-#define ECMULT_TABLE_GET_GEJ(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_gej_neg)
-#define ECMULT_TABLE_GET_GE(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_ge_neg)
+#define ECMULT_TABLE_GET_GE_STORAGE(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) { \
+ secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
+ } else { \
+ secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
+ secp256k1_fe_negate(&((r)->y), &((r)->y), 1); \
+ } \
+} while(0)
-typedef struct {
- /* For accelerating the computation of a*P + b*G: */
- secp256k1_ge_t pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; /* odd multiples of the generator */
+static const size_t SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE =
+ ROUND_TO_ALIGN(sizeof((*((secp256k1_ecmult_context*) NULL)->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G))
#ifdef USE_ENDOMORPHISM
- secp256k1_ge_t pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; /* odd multiples of 2^128*generator */
+ + ROUND_TO_ALIGN(sizeof((*((secp256k1_ecmult_context*) NULL)->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G))
#endif
-} secp256k1_ecmult_consts_t;
+ ;
-static const secp256k1_ecmult_consts_t *secp256k1_ecmult_consts = NULL;
+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_start(void) {
- if (secp256k1_ecmult_consts != NULL)
- return;
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, void **prealloc) {
+ secp256k1_gej gj;
+ void* const base = *prealloc;
+ size_t const prealloc_size = SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE;
- /* Allocate the precomputation table. */
- secp256k1_ecmult_consts_t *ret = (secp256k1_ecmult_consts_t*)checked_malloc(sizeof(secp256k1_ecmult_consts_t));
+ if (ctx->pre_g != NULL) {
+ return;
+ }
/* get the generator */
- secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
+ secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
-#ifdef USE_ENDOMORPHISM
- /* calculate 2^128*generator */
- secp256k1_gej_t g_128j = gj;
- for (int i=0; i<128; i++)
- secp256k1_gej_double_var(&g_128j, &g_128j);
-#endif
+ {
+ size_t size = sizeof((*ctx->pre_g)[0]) * ((size_t)ECMULT_TABLE_SIZE(WINDOW_G));
+ /* check for overflow */
+ VERIFY_CHECK(size / sizeof((*ctx->pre_g)[0]) == ((size_t)ECMULT_TABLE_SIZE(WINDOW_G)));
+ ctx->pre_g = (secp256k1_ge_storage (*)[])manual_alloc(prealloc, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G), base, prealloc_size);
+ }
/* precompute the tables with odd multiples */
- secp256k1_ecmult_table_precomp_ge_var(ret->pre_g, &gj, WINDOW_G);
+ secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj);
+
#ifdef USE_ENDOMORPHISM
- secp256k1_ecmult_table_precomp_ge_var(ret->pre_g_128, &g_128j, WINDOW_G);
+ {
+ secp256k1_gej g_128j;
+ int i;
+
+ size_t size = sizeof((*ctx->pre_g_128)[0]) * ((size_t) ECMULT_TABLE_SIZE(WINDOW_G));
+ /* check for overflow */
+ VERIFY_CHECK(size / sizeof((*ctx->pre_g_128)[0]) == ((size_t)ECMULT_TABLE_SIZE(WINDOW_G)));
+ ctx->pre_g_128 = (secp256k1_ge_storage (*)[])manual_alloc(prealloc, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G), base, prealloc_size);
+
+ /* calculate 2^128*generator */
+ g_128j = gj;
+ for (i = 0; i < 128; i++) {
+ secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
+ }
+ secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j);
+ }
#endif
+}
- /* Set the global pointer to the precomputation table. */
- secp256k1_ecmult_consts = ret;
+static void secp256k1_ecmult_context_finalize_memcpy(secp256k1_ecmult_context *dst, const secp256k1_ecmult_context *src) {
+ if (src->pre_g != NULL) {
+ /* We cast to void* first to suppress a -Wcast-align warning. */
+ dst->pre_g = (secp256k1_ge_storage (*)[])(void*)((unsigned char*)dst + ((unsigned char*)(src->pre_g) - (unsigned char*)src));
+ }
+#ifdef USE_ENDOMORPHISM
+ if (src->pre_g_128 != NULL) {
+ dst->pre_g_128 = (secp256k1_ge_storage (*)[])(void*)((unsigned char*)dst + ((unsigned char*)(src->pre_g_128) - (unsigned char*)src));
+ }
+#endif
}
-static void secp256k1_ecmult_stop(void) {
- if (secp256k1_ecmult_consts == NULL)
- return;
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
+ return ctx->pre_g != NULL;
+}
- secp256k1_ecmult_consts_t *c = (secp256k1_ecmult_consts_t*)secp256k1_ecmult_consts;
- secp256k1_ecmult_consts = NULL;
- free(c);
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
+ secp256k1_ecmult_context_init(ctx);
}
/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
* - 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;
-
+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;
}
- int set_bits = 0;
- int bit = 0;
- while (bit < 256) {
- if (secp256k1_scalar_get_bits(&s, bit, 1) == 0) {
+ while (bit < len) {
+ int now;
+ int word;
+ if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
bit++;
continue;
}
- while (set_bits < bit) {
- wnaf[set_bits++] = 0;
- }
- int now = w;
- if (bit + now > 256) {
- now = 256 - bit;
- }
- int 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;
+
+ now = w;
+ 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(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng) {
- const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
+struct secp256k1_strauss_point_state {
+#ifdef USE_ENDOMORPHISM
+ secp256k1_scalar na_1, na_lam;
+ int wnaf_na_1[130];
+ int wnaf_na_lam[130];
+ int bits_na_1;
+ int bits_na_lam;
+#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_scalar_t na_1, 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_var(&na_1, &na_lam, na);
+ secp256k1_ge* pre_a_lam;
+#endif
+ struct secp256k1_strauss_point_state* ps;
+};
- /* build wnaf representation for na_1 and na_lam. */
- int wnaf_na_1[130]; int bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, &na_1, WINDOW_A);
- int wnaf_na_lam[130]; int bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
- VERIFY_CHECK(bits_na_1 <= 130);
- VERIFY_CHECK(bits_na_lam <= 130);
- int bits = bits_na_1;
- if (bits_na_lam > bits) bits = bits_na_lam;
+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
- /* build wnaf representation for na. */
- int wnaf_na[256]; int bits_na = secp256k1_ecmult_wnaf(wnaf_na, na, WINDOW_A);
- int bits = bits_na;
+ int wnaf_ng[256];
+ int bits_ng = 0;
#endif
+ int i;
+ int bits = 0;
+ int np;
+ int no = 0;
- /* calculate odd multiples of a */
- secp256k1_gej_t pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
- secp256k1_ecmult_table_precomp_gej_var(pre_a, a, WINDOW_A);
-
+ 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
- secp256k1_gej_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
- for (int i=0; i<ECMULT_TABLE_SIZE(WINDOW_A); i++)
- secp256k1_gej_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+ /* 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]);
- /* Splitted G factors. */
- secp256k1_scalar_t ng_1, ng_128;
+ /* 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. */
+ 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;
+ }
- /* 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);
+ /* 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.
+ */
+ 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);
+ }
- /* Build wnaf representation for ng_1 and ng_128 */
- int wnaf_ng_1[129]; int bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, &ng_1, WINDOW_G);
- int wnaf_ng_128[129]; int bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, &ng_128, WINDOW_G);
- if (bits_ng_1 > bits) bits = bits_ng_1;
- if (bits_ng_128 > bits) bits = bits_ng_128;
+#ifdef USE_ENDOMORPHISM
+ 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]);
+ }
+ }
+
+ 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;
+ }
+ }
#else
- int wnaf_ng[257]; int bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 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
secp256k1_gej_set_infinity(r);
- secp256k1_gej_t tmpj;
- secp256k1_ge_t tmpa;
- for (int i=bits-1; i>=0; i--) {
- secp256k1_gej_double_var(r, r);
+ for (i = bits - 1; i >= 0; i--) {
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_GEJ(&tmpj, pre_a, n, WINDOW_A);
- secp256k1_gej_add_var(r, r, &tmpj);
- }
- 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);
+ 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(&tmpa, c->pre_g, n, WINDOW_G);
- secp256k1_gej_add_ge_var(r, r, &tmpa);
+ ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
+ secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
- ECMULT_TABLE_GET_GE(&tmpa, c->pre_g_128, n, WINDOW_G);
- secp256k1_gej_add_ge_var(r, r, &tmpa);
+ ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
+ 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);
+ 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(&tmpa, c->pre_g, n, WINDOW_G);
- secp256k1_gej_add_ge_var(r, r, &tmpa);
+ ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
+ secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+ }
+#endif
+ }
+
+ if (!r->infinity) {
+ secp256k1_fe_mul(&r->z, &r->z, &Z);
+ }
+}
+
+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 size_t secp256k1_strauss_scratch_size(size_t n_points) {
+#ifdef USE_ENDOMORPHISM
+ static const size_t point_size = (2 * sizeof(secp256k1_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * 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_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar);
+#endif
+ return n_points*point_size;
+}
+
+static int secp256k1_ecmult_strauss_batch(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_points, size_t cb_offset) {
+ secp256k1_gej* points;
+ secp256k1_scalar* scalars;
+ struct secp256k1_strauss_state state;
+ size_t i;
+
+ secp256k1_gej_set_infinity(r);
+ if (inp_g_sc == NULL && n_points == 0) {
+ return 1;
+ }
+
+ if (!secp256k1_scratch_allocate_frame(scratch, secp256k1_strauss_scratch_size(n_points), STRAUSS_SCRATCH_OBJECTS)) {
+ return 0;
+ }
+ points = (secp256k1_gej*)secp256k1_scratch_alloc(scratch, n_points * sizeof(secp256k1_gej));
+ scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(scratch, n_points * sizeof(secp256k1_scalar));
+ state.prej = (secp256k1_gej*)secp256k1_scratch_alloc(scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_gej));
+ state.zr = (secp256k1_fe*)secp256k1_scratch_alloc(scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe));
+#ifdef USE_ENDOMORPHISM
+ state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(scratch, n_points * 2 * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
+ state.pre_a_lam = state.pre_a + n_points * ECMULT_TABLE_SIZE(WINDOW_A);
+#else
+ state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
+#endif
+ state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(scratch, n_points * sizeof(struct secp256k1_strauss_point_state));
+
+ for (i = 0; i < n_points; i++) {
+ secp256k1_ge point;
+ if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) {
+ secp256k1_scratch_deallocate_frame(scratch);
+ return 0;
+ }
+ secp256k1_gej_set_ge(&points[i], &point);
+ }
+ secp256k1_ecmult_strauss_wnaf(ctx, &state, r, n_points, points, scalars, inp_g_sc);
+ secp256k1_scratch_deallocate_frame(scratch);
+ return 1;
+}
+
+/* Wrapper for secp256k1_ecmult_multi_func interface */
+static int secp256k1_ecmult_strauss_batch_single(const secp256k1_ecmult_context *actx, 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_strauss_batch(actx, scratch, r, inp_g_sc, cb, cbdata, n, 0);
+}
+
+static size_t secp256k1_strauss_max_points(secp256k1_scratch *scratch) {
+ return secp256k1_scratch_max_allocation(scratch, STRAUSS_SCRATCH_OBJECTS) / secp256k1_strauss_scratch_size(1);
+}
+
+/** Convert a number to WNAF notation.
+ * The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
+ * It has the following guarantees:
+ * - each wnaf[i] is either 0 or an odd integer between -(1 << w) and (1 << w)
+ * - the number of words set is always WNAF_SIZE(w)
+ * - the returned skew is 0 or 1
+ */
+static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) {
+ int skew = 0;
+ int pos;
+ int max_pos;
+ int last_w;
+ const secp256k1_scalar *work = s;
+
+ if (secp256k1_scalar_is_zero(s)) {
+ for (pos = 0; pos < WNAF_SIZE(w); pos++) {
+ wnaf[pos] = 0;
+ }
+ return 0;
+ }
+
+ if (secp256k1_scalar_is_even(s)) {
+ skew = 1;
+ }
+
+ wnaf[0] = secp256k1_scalar_get_bits_var(work, 0, w) + skew;
+ /* Compute last window size. Relevant when window size doesn't divide the
+ * number of bits in the scalar */
+ last_w = WNAF_BITS - (WNAF_SIZE(w) - 1) * w;
+
+ /* Store the position of the first nonzero word in max_pos to allow
+ * skipping leading zeros when calculating the wnaf. */
+ for (pos = WNAF_SIZE(w) - 1; pos > 0; pos--) {
+ int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
+ if(val != 0) {
+ break;
+ }
+ wnaf[pos] = 0;
+ }
+ max_pos = pos;
+ pos = 1;
+
+ while (pos <= max_pos) {
+ int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
+ if ((val & 1) == 0) {
+ wnaf[pos - 1] -= (1 << w);
+ wnaf[pos] = (val + 1);
+ } else {
+ wnaf[pos] = val;
+ }
+ /* Set a coefficient to zero if it is 1 or -1 and the proceeding digit
+ * is strictly negative or strictly positive respectively. Only change
+ * coefficients at previous positions because above code assumes that
+ * wnaf[pos - 1] is odd.
+ */
+ if (pos >= 2 && ((wnaf[pos - 1] == 1 && wnaf[pos - 2] < 0) || (wnaf[pos - 1] == -1 && wnaf[pos - 2] > 0))) {
+ if (wnaf[pos - 1] == 1) {
+ wnaf[pos - 2] += 1 << w;
+ } else {
+ wnaf[pos - 2] -= 1 << w;
+ }
+ wnaf[pos - 1] = 0;
+ }
+ ++pos;
+ }
+
+ return skew;
+}
+
+struct secp256k1_pippenger_point_state {
+ int skew_na;
+ size_t input_pos;
+};
+
+struct secp256k1_pippenger_state {
+ int *wnaf_na;
+ struct secp256k1_pippenger_point_state* ps;
+};
+
+/*
+ * pippenger_wnaf computes the result of a multi-point multiplication as
+ * follows: The scalars are brought into wnaf with n_wnaf elements each. Then
+ * for every i < n_wnaf, first each point is added to a "bucket" corresponding
+ * to the point's wnaf[i]. Second, the buckets are added together such that
+ * r += 1*bucket[0] + 3*bucket[1] + 5*bucket[2] + ...
+ */
+static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_window, struct secp256k1_pippenger_state *state, secp256k1_gej *r, const secp256k1_scalar *sc, const secp256k1_ge *pt, size_t num) {
+ size_t n_wnaf = WNAF_SIZE(bucket_window+1);
+ size_t np;
+ size_t no = 0;
+ int i;
+ int j;
+
+ for (np = 0; np < num; ++np) {
+ if (secp256k1_scalar_is_zero(&sc[np]) || secp256k1_ge_is_infinity(&pt[np])) {
+ continue;
+ }
+ state->ps[no].input_pos = np;
+ state->ps[no].skew_na = secp256k1_wnaf_fixed(&state->wnaf_na[no*n_wnaf], &sc[np], bucket_window+1);
+ no++;
+ }
+ secp256k1_gej_set_infinity(r);
+
+ if (no == 0) {
+ return 1;
+ }
+
+ for (i = n_wnaf - 1; i >= 0; i--) {
+ secp256k1_gej running_sum;
+
+ for(j = 0; j < ECMULT_TABLE_SIZE(bucket_window+2); j++) {
+ secp256k1_gej_set_infinity(&buckets[j]);
+ }
+
+ for (np = 0; np < no; ++np) {
+ int n = state->wnaf_na[np*n_wnaf + i];
+ struct secp256k1_pippenger_point_state point_state = state->ps[np];
+ secp256k1_ge tmp;
+ int idx;
+
+ if (i == 0) {
+ /* correct for wnaf skew */
+ int skew = point_state.skew_na;
+ if (skew) {
+ secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]);
+ secp256k1_gej_add_ge_var(&buckets[0], &buckets[0], &tmp, NULL);
+ }
+ }
+ if (n > 0) {
+ idx = (n - 1)/2;
+ secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &pt[point_state.input_pos], NULL);
+ } else if (n < 0) {
+ idx = -(n + 1)/2;
+ secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]);
+ secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &tmp, NULL);
+ }
+ }
+
+ for(j = 0; j < bucket_window; j++) {
+ secp256k1_gej_double_var(r, r, NULL);
+ }
+
+ secp256k1_gej_set_infinity(&running_sum);
+ /* Accumulate the sum: bucket[0] + 3*bucket[1] + 5*bucket[2] + 7*bucket[3] + ...
+ * = bucket[0] + bucket[1] + bucket[2] + bucket[3] + ...
+ * + 2 * (bucket[1] + 2*bucket[2] + 3*bucket[3] + ...)
+ * using an intermediate running sum:
+ * running_sum = bucket[0] + bucket[1] + bucket[2] + ...
+ *
+ * The doubling is done implicitly by deferring the final window doubling (of 'r').
+ */
+ for(j = ECMULT_TABLE_SIZE(bucket_window+2) - 1; j > 0; j--) {
+ secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[j], NULL);
+ secp256k1_gej_add_var(r, r, &running_sum, NULL);
+ }
+
+ secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[0], NULL);
+ secp256k1_gej_double_var(r, r, NULL);
+ secp256k1_gej_add_var(r, r, &running_sum, NULL);
+ }
+ return 1;
+}
+
+/**
+ * Returns optimal bucket_window (number of bits of a scalar represented by a
+ * set of buckets) for a given number of points.
+ */
+static int secp256k1_pippenger_bucket_window(size_t n) {
+#ifdef USE_ENDOMORPHISM
+ if (n <= 1) {
+ return 1;
+ } else if (n <= 4) {
+ return 2;
+ } else if (n <= 20) {
+ return 3;
+ } else if (n <= 57) {
+ return 4;
+ } else if (n <= 136) {
+ return 5;
+ } else if (n <= 235) {
+ return 6;
+ } else if (n <= 1260) {
+ return 7;
+ } else if (n <= 4420) {
+ return 9;
+ } else if (n <= 7880) {
+ return 10;
+ } else if (n <= 16050) {
+ return 11;
+ } else {
+ return PIPPENGER_MAX_BUCKET_WINDOW;
+ }
+#else
+ if (n <= 1) {
+ return 1;
+ } else if (n <= 11) {
+ return 2;
+ } else if (n <= 45) {
+ return 3;
+ } else if (n <= 100) {
+ return 4;
+ } else if (n <= 275) {
+ return 5;
+ } else if (n <= 625) {
+ return 6;
+ } else if (n <= 1850) {
+ return 7;
+ } else if (n <= 3400) {
+ return 8;
+ } else if (n <= 9630) {
+ return 9;
+ } else if (n <= 17900) {
+ return 10;
+ } else if (n <= 32800) {
+ return 11;
+ } else {
+ return PIPPENGER_MAX_BUCKET_WINDOW;
+ }
+#endif
+}
+
+/**
+ * Returns the maximum optimal number of points for a bucket_window.
+ */
+static size_t secp256k1_pippenger_bucket_window_inv(int bucket_window) {
+ switch(bucket_window) {
+#ifdef USE_ENDOMORPHISM
+ case 1: return 1;
+ case 2: return 4;
+ case 3: return 20;
+ case 4: return 57;
+ case 5: return 136;
+ case 6: return 235;
+ case 7: return 1260;
+ case 8: return 1260;
+ case 9: return 4420;
+ case 10: return 7880;
+ case 11: return 16050;
+ case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX;
+#else
+ case 1: return 1;
+ case 2: return 11;
+ case 3: return 45;
+ case 4: return 100;
+ case 5: return 275;
+ case 6: return 625;
+ case 7: return 1850;
+ case 8: return 3400;
+ case 9: return 9630;
+ case 10: return 17900;
+ case 11: return 32800;
+ case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX;
+#endif
+ }
+ return 0;
+}
+
+
+#ifdef USE_ENDOMORPHISM
+SECP256K1_INLINE static void secp256k1_ecmult_endo_split(secp256k1_scalar *s1, secp256k1_scalar *s2, secp256k1_ge *p1, secp256k1_ge *p2) {
+ secp256k1_scalar tmp = *s1;
+ secp256k1_scalar_split_lambda(s1, s2, &tmp);
+ secp256k1_ge_mul_lambda(p2, p1);
+
+ if (secp256k1_scalar_is_high(s1)) {
+ secp256k1_scalar_negate(s1, s1);
+ secp256k1_ge_neg(p1, p1);
+ }
+ if (secp256k1_scalar_is_high(s2)) {
+ secp256k1_scalar_negate(s2, s2);
+ secp256k1_ge_neg(p2, p2);
+ }
+}
+#endif
+
+/**
+ * Returns the scratch size required for a given number of points (excluding
+ * base point G) without considering alignment.
+ */
+static size_t secp256k1_pippenger_scratch_size(size_t n_points, int bucket_window) {
+#ifdef USE_ENDOMORPHISM
+ size_t entries = 2*n_points + 2;
+#else
+ size_t entries = n_points + 1;
+#endif
+ size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int);
+ return (sizeof(secp256k1_gej) << bucket_window) + sizeof(struct secp256k1_pippenger_state) + entries * entry_size;
+}
+
+static int secp256k1_ecmult_pippenger_batch(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_points, size_t cb_offset) {
+ /* Use 2(n+1) with the endomorphism, n+1 without, when calculating batch
+ * sizes. The reason for +1 is that we add the G scalar to the list of
+ * other scalars. */
+#ifdef USE_ENDOMORPHISM
+ size_t entries = 2*n_points + 2;
+#else
+ size_t entries = n_points + 1;
+#endif
+ secp256k1_ge *points;
+ secp256k1_scalar *scalars;
+ secp256k1_gej *buckets;
+ struct secp256k1_pippenger_state *state_space;
+ size_t idx = 0;
+ size_t point_idx = 0;
+ int i, j;
+ int bucket_window;
+
+ (void)ctx;
+ secp256k1_gej_set_infinity(r);
+ if (inp_g_sc == NULL && n_points == 0) {
+ return 1;
+ }
+
+ bucket_window = secp256k1_pippenger_bucket_window(n_points);
+ if (!secp256k1_scratch_allocate_frame(scratch, secp256k1_pippenger_scratch_size(n_points, bucket_window), PIPPENGER_SCRATCH_OBJECTS)) {
+ return 0;
+ }
+ points = (secp256k1_ge *) secp256k1_scratch_alloc(scratch, entries * sizeof(*points));
+ scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(scratch, entries * sizeof(*scalars));
+ state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(scratch, sizeof(*state_space));
+ state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(scratch, entries * sizeof(*state_space->ps));
+ state_space->wnaf_na = (int *) secp256k1_scratch_alloc(scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int));
+ buckets = (secp256k1_gej *) secp256k1_scratch_alloc(scratch, sizeof(*buckets) << bucket_window);
+
+ if (inp_g_sc != NULL) {
+ scalars[0] = *inp_g_sc;
+ points[0] = secp256k1_ge_const_g;
+ idx++;
+#ifdef USE_ENDOMORPHISM
+ secp256k1_ecmult_endo_split(&scalars[0], &scalars[1], &points[0], &points[1]);
+ idx++;
+#endif
+ }
+
+ while (point_idx < n_points) {
+ if (!cb(&scalars[idx], &points[idx], point_idx + cb_offset, cbdata)) {
+ secp256k1_scratch_deallocate_frame(scratch);
+ return 0;
}
+ idx++;
+#ifdef USE_ENDOMORPHISM
+ secp256k1_ecmult_endo_split(&scalars[idx - 1], &scalars[idx], &points[idx - 1], &points[idx]);
+ idx++;
#endif
+ point_idx++;
}
+
+ secp256k1_ecmult_pippenger_wnaf(buckets, bucket_window, state_space, r, scalars, points, idx);
+
+ /* Clear data */
+ for(i = 0; (size_t)i < idx; i++) {
+ secp256k1_scalar_clear(&scalars[i]);
+ state_space->ps[i].skew_na = 0;
+ for(j = 0; j < WNAF_SIZE(bucket_window+1); j++) {
+ state_space->wnaf_na[i * WNAF_SIZE(bucket_window+1) + j] = 0;
+ }
+ }
+ for(i = 0; i < 1<<bucket_window; i++) {
+ secp256k1_gej_clear(&buckets[i]);
+ }
+ secp256k1_scratch_deallocate_frame(scratch);
+ return 1;
+}
+
+/* Wrapper for secp256k1_ecmult_multi_func interface */
+static int secp256k1_ecmult_pippenger_batch_single(const secp256k1_ecmult_context *actx, 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_pippenger_batch(actx, scratch, r, inp_g_sc, cb, cbdata, n, 0);
}
+/**
+ * Returns the maximum number of points in addition to G that can be used with
+ * a given scratch space. The function ensures that fewer points may also be
+ * used.
+ */
+static size_t secp256k1_pippenger_max_points(secp256k1_scratch *scratch) {
+ size_t max_alloc = secp256k1_scratch_max_allocation(scratch, PIPPENGER_SCRATCH_OBJECTS);
+ int bucket_window;
+ size_t res = 0;
+
+ for (bucket_window = 1; bucket_window <= PIPPENGER_MAX_BUCKET_WINDOW; bucket_window++) {
+ size_t n_points;
+ size_t max_points = secp256k1_pippenger_bucket_window_inv(bucket_window);
+ size_t space_for_points;
+ size_t space_overhead;
+ size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int);
+
+#ifdef USE_ENDOMORPHISM
+ entry_size = 2*entry_size;
#endif
+ space_overhead = (sizeof(secp256k1_gej) << bucket_window) + entry_size + sizeof(struct secp256k1_pippenger_state);
+ if (space_overhead > max_alloc) {
+ break;
+ }
+ space_for_points = max_alloc - space_overhead;
+
+ n_points = space_for_points/entry_size;
+ n_points = n_points > max_points ? max_points : n_points;
+ if (n_points > res) {
+ res = n_points;
+ }
+ if (n_points < max_points) {
+ /* A larger bucket_window may support even more points. But if we
+ * would choose that then the caller couldn't safely use any number
+ * smaller than what this function returns */
+ break;
+ }
+ }
+ return res;
+}
+
+/* Computes ecmult_multi by simply multiplying and adding each point. Does not
+ * require a scratch space */
+static int secp256k1_ecmult_multi_simple_var(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points) {
+ size_t point_idx;
+ secp256k1_scalar szero;
+ secp256k1_gej tmpj;
+
+ secp256k1_scalar_set_int(&szero, 0);
+ secp256k1_gej_set_infinity(r);
+ secp256k1_gej_set_infinity(&tmpj);
+ /* r = inp_g_sc*G */
+ secp256k1_ecmult(ctx, r, &tmpj, &szero, inp_g_sc);
+ for (point_idx = 0; point_idx < n_points; point_idx++) {
+ secp256k1_ge point;
+ secp256k1_gej pointj;
+ secp256k1_scalar scalar;
+ if (!cb(&scalar, &point, point_idx, cbdata)) {
+ return 0;
+ }
+ /* r += scalar*point */
+ secp256k1_gej_set_ge(&pointj, &point);
+ secp256k1_ecmult(ctx, &tmpj, &pointj, &scalar, NULL);
+ secp256k1_gej_add_var(r, r, &tmpj, NULL);
+ }
+ return 1;
+}
+
+/* Compute the number of batches and the batch size given the maximum batch size and the
+ * total number of points */
+static int secp256k1_ecmult_multi_batch_size_helper(size_t *n_batches, size_t *n_batch_points, size_t max_n_batch_points, size_t n) {
+ if (max_n_batch_points == 0) {
+ return 0;
+ }
+ if (max_n_batch_points > ECMULT_MAX_POINTS_PER_BATCH) {
+ max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH;
+ }
+ if (n == 0) {
+ *n_batches = 0;
+ *n_batch_points = 0;
+ return 1;
+ }
+ /* Compute ceil(n/max_n_batch_points) and ceil(n/n_batches) */
+ *n_batches = 1 + (n - 1) / max_n_batch_points;
+ *n_batch_points = 1 + (n - 1) / *n_batches;
+ return 1;
+}
+
+typedef int (*secp256k1_ecmult_multi_func)(const secp256k1_ecmult_context*, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t);
+static int secp256k1_ecmult_multi_var(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) {
+ size_t i;
+
+ int (*f)(const secp256k1_ecmult_context*, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t, size_t);
+ size_t n_batches;
+ size_t n_batch_points;
+
+ secp256k1_gej_set_infinity(r);
+ if (inp_g_sc == NULL && n == 0) {
+ return 1;
+ } else if (n == 0) {
+ secp256k1_scalar szero;
+ secp256k1_scalar_set_int(&szero, 0);
+ secp256k1_ecmult(ctx, r, r, &szero, inp_g_sc);
+ return 1;
+ }
+ if (scratch == NULL) {
+ return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
+ }
+
+ /* Compute the batch sizes for Pippenger's algorithm given a scratch space. If it's greater than
+ * a threshold use Pippenger's algorithm. Otherwise use Strauss' algorithm.
+ * As a first step check if there's enough space for Pippenger's algo (which requires less space
+ * than Strauss' algo) and if not, use the simple algorithm. */
+ if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_pippenger_max_points(scratch), n)) {
+ return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
+ }
+ if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) {
+ f = secp256k1_ecmult_pippenger_batch;
+ } else {
+ if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_strauss_max_points(scratch), n)) {
+ return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
+ }
+ f = secp256k1_ecmult_strauss_batch;
+ }
+ for(i = 0; i < n_batches; i++) {
+ size_t nbp = n < n_batch_points ? n : n_batch_points;
+ size_t offset = n_batch_points*i;
+ secp256k1_gej tmp;
+ if (!f(ctx, scratch, &tmp, i == 0 ? inp_g_sc : NULL, cb, cbdata, nbp, offset)) {
+ return 0;
+ }
+ secp256k1_gej_add_var(r, r, &tmp, NULL);
+ n -= nbp;
+ }
+ return 1;
+}
+
+#endif /* SECP256K1_ECMULT_IMPL_H */
projects / secp256k1.git / blobdiff