/****************************************************************************** * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra, Jonas Nick * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php. * ******************************************************************************/ #ifndef SECP256K1_ECMULT_IMPL_H #define SECP256K1_ECMULT_IMPL_H #include #include #include "util.h" #include "group.h" #include "scalar.h" #include "ecmult.h" #include "precomputed_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 # elif EXHAUSTIVE_TEST_ORDER > 8 # define WINDOW_A 4 # else # define WINDOW_A 2 # endif #else /* optimal for 128-bit and 256-bit exponents. */ # 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. * Two tables of this size are used (due to the endomorphism * optimization). */ #endif #define WNAF_BITS 128 #define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w)) #define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w) /* The number of objects allocated on the scratch space for ecmult_multi algorithms */ #define PIPPENGER_SCRATCH_OBJECTS 6 #define STRAUSS_SCRATCH_OBJECTS 5 #define PIPPENGER_MAX_BUCKET_WINDOW 12 /* Minimum number of points for which pippenger_wnaf is faster than strauss wnaf */ #define ECMULT_PIPPENGER_THRESHOLD 88 #define ECMULT_MAX_POINTS_PER_BATCH 5000000 /** Fill a table 'pre_a' with precomputed odd multiples of a. * pre_a will contain [1*a,3*a,...,(2*n-1)*a], so it needs space for n group elements. * zr needs space for n field elements. * * Although pre_a is an array of _ge rather than _gej, it actually represents elements * in Jacobian coordinates with their z coordinates omitted. The omitted z-coordinates * can be recovered using z and zr. Using the notation z(b) to represent the omitted * z coordinate of b: * - z(pre_a[n-1]) = 'z' * - z(pre_a[i-1]) = z(pre_a[i]) / zr[i] for n > i > 0 * * Lastly the zr[0] value, which isn't used above, is set so that: * - a.z = z(pre_a[0]) / zr[0] */ static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_ge *pre_a, secp256k1_fe *zr, secp256k1_fe *z, const secp256k1_gej *a) { secp256k1_gej d, ai; secp256k1_ge d_ge; int i; VERIFY_CHECK(!a->infinity); secp256k1_gej_double_var(&d, a, NULL); /* * Perform the additions using an isomorphic curve Y^2 = X^3 + 7*C^6 where C := d.z. * The isomorphism, phi, maps a secp256k1 point (x, y) to the point (x*C^2, y*C^3) on the other curve. * In Jacobian coordinates phi maps (x, y, z) to (x*C^2, y*C^3, z) or, equivalently to (x, y, z/C). * * phi(x, y, z) = (x*C^2, y*C^3, z) = (x, y, z/C) * d_ge := phi(d) = (d.x, d.y, 1) * ai := phi(a) = (a.x*C^2, a.y*C^3, a.z) * * The group addition functions work correctly on these isomorphic curves. * In particular phi(d) is easy to represent in affine coordinates under this isomorphism. * This lets us use the faster secp256k1_gej_add_ge_var group addition function that we wouldn't be able to use otherwise. */ secp256k1_ge_set_xy(&d_ge, &d.x, &d.y); secp256k1_ge_set_gej_zinv(&pre_a[0], a, &d.z); secp256k1_gej_set_ge(&ai, &pre_a[0]); ai.z = a->z; /* pre_a[0] is the point (a.x*C^2, a.y*C^3, a.z*C) which is equivalent to a. * Set zr[0] to C, which is the ratio between the omitted z(pre_a[0]) value and a.z. */ zr[0] = d.z; for (i = 1; i < n; i++) { secp256k1_gej_add_ge_var(&ai, &ai, &d_ge, &zr[i]); secp256k1_ge_set_xy(&pre_a[i], &ai.x, &ai.y); } /* Multiply the last z-coordinate by C to undo the isomorphism. * Since the z-coordinates of the pre_a values are implied by the zr array of z-coordinate ratios, * undoing the isomorphism here undoes the isomorphism for all pre_a values. */ secp256k1_fe_mul(z, &ai.z, &d.z); } #define SECP256K1_ECMULT_TABLE_VERIFY(n,w) \ VERIFY_CHECK(((n) & 1) == 1); \ VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge(secp256k1_ge *r, const secp256k1_ge *pre, int n, int w) { SECP256K1_ECMULT_TABLE_VERIFY(n,w) if (n > 0) { *r = pre[(n-1)/2]; } else { *r = pre[(-n-1)/2]; secp256k1_fe_negate(&(r->y), &(r->y), 1); } } SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_lambda(secp256k1_ge *r, const secp256k1_ge *pre, const secp256k1_fe *x, int n, int w) { SECP256K1_ECMULT_TABLE_VERIFY(n,w) if (n > 0) { secp256k1_ge_set_xy(r, &x[(n-1)/2], &pre[(n-1)/2].y); } else { secp256k1_ge_set_xy(r, &x[(-n-1)/2], &pre[(-n-1)/2].y); secp256k1_fe_negate(&(r->y), &(r->y), 1); } } SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_storage(secp256k1_ge *r, const secp256k1_ge_storage *pre, int n, int w) { SECP256K1_ECMULT_TABLE_VERIFY(n,w) 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); } } /** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits), * with the following guarantees: * - 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. */ static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) { secp256k1_scalar s; 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])); s = *a; if (secp256k1_scalar_get_bits(&s, 255, 1)) { secp256k1_scalar_negate(&s, &s); sign = -1; } while (bit < len) { int now; int word; if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) { bit++; continue; } 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; } #ifdef VERIFY { int verify_bit = bit; VERIFY_CHECK(carry == 0); while (verify_bit < 256) { VERIFY_CHECK(secp256k1_scalar_get_bits(&s, verify_bit, 1) == 0); verify_bit++; } } #endif return last_set_bit + 1; } struct secp256k1_strauss_point_state { int wnaf_na_1[129]; int wnaf_na_lam[129]; int bits_na_1; int bits_na_lam; }; struct secp256k1_strauss_state { /* aux is used to hold z-ratios, and then used to hold pre_a[i].x * BETA values. */ secp256k1_fe* aux; secp256k1_ge* pre_a; struct secp256k1_strauss_point_state* ps; }; static void secp256k1_ecmult_strauss_wnaf(const struct secp256k1_strauss_state *state, secp256k1_gej *r, size_t num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { secp256k1_ge tmpa; secp256k1_fe Z; /* Split 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; int i; int bits = 0; size_t np; size_t no = 0; secp256k1_fe_set_int(&Z, 1); for (np = 0; np < num; ++np) { secp256k1_gej tmp; secp256k1_scalar na_1, na_lam; if (secp256k1_scalar_is_zero(&na[np]) || secp256k1_gej_is_infinity(&a[np])) { continue; } /* 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[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, 129, &na_1, WINDOW_A); state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 129, &na_lam, WINDOW_A); VERIFY_CHECK(state->ps[no].bits_na_1 <= 129); VERIFY_CHECK(state->ps[no].bits_na_lam <= 129); 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; } /* 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. */ tmp = a[np]; if (no) { #ifdef VERIFY secp256k1_fe_normalize_var(&Z); #endif secp256k1_gej_rescale(&tmp, &Z); } secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->pre_a + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &Z, &tmp); if (no) secp256k1_fe_mul(state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &(a[np].z)); ++no; } /* Bring them to the same Z denominator. */ secp256k1_ge_table_set_globalz(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, state->aux); for (np = 0; np < no; ++np) { for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { secp256k1_fe_mul(&state->aux[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + i].x, &secp256k1_const_beta); } } 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; } } secp256k1_gej_set_infinity(r); for (i = bits - 1; i >= 0; i--) { int n; secp256k1_gej_double_var(r, r, NULL); for (np = 0; np < no; ++np) { if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) { secp256k1_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])) { secp256k1_ecmult_table_get_ge_lambda(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + 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])) { secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g, n, WINDOW_G); secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); } if (i < bits_ng_128 && (n = wnaf_ng_128[i])) { secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g_128, n, WINDOW_G); secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); } } if (!r->infinity) { secp256k1_fe_mul(&r->z, &r->z, &Z); } } static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { secp256k1_fe aux[ECMULT_TABLE_SIZE(WINDOW_A)]; secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; struct secp256k1_strauss_point_state ps[1]; struct secp256k1_strauss_state state; state.aux = aux; state.pre_a = pre_a; state.ps = ps; secp256k1_ecmult_strauss_wnaf(&state, r, 1, a, na, ng); } #if 0 static size_t secp256k1_strauss_scratch_size(size_t n_points) { static const size_t point_size = (sizeof(secp256k1_ge) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar); return n_points*point_size; } static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callback, 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; const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch); secp256k1_gej_set_infinity(r); if (inp_g_sc == NULL && n_points == 0) { return 1; } /* We allocate STRAUSS_SCRATCH_OBJECTS objects on the scratch space. If these * allocations change, make sure to update the STRAUSS_SCRATCH_OBJECTS * constant and strauss_scratch_size accordingly. */ points = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_gej)); scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_scalar)); state.aux = (secp256k1_fe*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe)); state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(struct secp256k1_strauss_point_state)); if (points == NULL || scalars == NULL || state.aux == NULL || state.pre_a == NULL || state.ps == NULL) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } for (i = 0; i < n_points; i++) { secp256k1_ge point; if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } secp256k1_gej_set_ge(&points[i], &point); } secp256k1_ecmult_strauss_wnaf(&state, r, n_points, points, scalars, inp_g_sc); secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 1; } /* Wrapper for secp256k1_ecmult_multi_func interface */ static int secp256k1_ecmult_strauss_batch_single(const secp256k1_callback* error_callback, 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(error_callback, scratch, r, inp_g_sc, cb, cbdata, n, 0); } static size_t secp256k1_strauss_max_points(const secp256k1_callback* error_callback, secp256k1_scratch *scratch) { return secp256k1_scratch_max_allocation(error_callback, 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) { 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; } } /** * 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) { 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; } return 0; } 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); } } /** * 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) { size_t entries = 2*n_points + 2; 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_callback* error_callback, 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) { const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch); /* Use 2(n+1) with the endomorphism, when calculating batch * sizes. The reason for +1 is that we add the G scalar to the list of * other scalars. */ size_t entries = 2*n_points + 2; 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; secp256k1_gej_set_infinity(r); if (inp_g_sc == NULL && n_points == 0) { return 1; } bucket_window = secp256k1_pippenger_bucket_window(n_points); /* We allocate PIPPENGER_SCRATCH_OBJECTS objects on the scratch space. If * these allocations change, make sure to update the * PIPPENGER_SCRATCH_OBJECTS constant and pippenger_scratch_size * accordingly. */ points = (secp256k1_ge *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*points)); scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*scalars)); state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(error_callback, scratch, sizeof(*state_space)); if (points == NULL || scalars == NULL || state_space == NULL) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*state_space->ps)); state_space->wnaf_na = (int *) secp256k1_scratch_alloc(error_callback, scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int)); buckets = (secp256k1_gej *) secp256k1_scratch_alloc(error_callback, scratch, (1<ps == NULL || state_space->wnaf_na == NULL || buckets == NULL) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } if (inp_g_sc != NULL) { scalars[0] = *inp_g_sc; points[0] = secp256k1_ge_const_g; idx++; secp256k1_ecmult_endo_split(&scalars[0], &scalars[1], &points[0], &points[1]); idx++; } while (point_idx < n_points) { if (!cb(&scalars[idx], &points[idx], point_idx + cb_offset, cbdata)) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } idx++; secp256k1_ecmult_endo_split(&scalars[idx - 1], &scalars[idx], &points[idx - 1], &points[idx]); idx++; 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< 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(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(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(&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_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t); static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, 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_callback* error_callback, 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(r, r, &szero, inp_g_sc); return 1; } if (scratch == NULL) { return secp256k1_ecmult_multi_simple_var(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(error_callback, scratch), n)) { return secp256k1_ecmult_multi_simple_var(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(error_callback, scratch), n)) { return secp256k1_ecmult_multi_simple_var(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(error_callback, 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 #endif /* SECP256K1_ECMULT_IMPL_H */