/* * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved. * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved * * Licensed under the Apache License 2.0 (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy * in the file LICENSE in the source distribution or at * https://www.openssl.org/source/license.html */ #include #include #include "internal/cryptlib.h" #include "internal/bn_int.h" #include "ec_lcl.h" #include "internal/refcount.h" /* * This file implements the wNAF-based interleaving multi-exponentiation method * Formerly at: * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp * You might now find it here: * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13 * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf * For multiplication with precomputation, we use wNAF splitting, formerly at: * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp */ /* structure for precomputed multiples of the generator */ struct ec_pre_comp_st { const EC_GROUP *group; /* parent EC_GROUP object */ size_t blocksize; /* block size for wNAF splitting */ size_t numblocks; /* max. number of blocks for which we have * precomputation */ size_t w; /* window size */ EC_POINT **points; /* array with pre-calculated multiples of * generator: 'num' pointers to EC_POINT * objects followed by a NULL */ size_t num; /* numblocks * 2^(w-1) */ CRYPTO_REF_COUNT references; CRYPTO_RWLOCK *lock; }; static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) { EC_PRE_COMP *ret = NULL; if (!group) return NULL; ret = OPENSSL_zalloc(sizeof(*ret)); if (ret == NULL) { ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; } ret->group = group; ret->blocksize = 8; /* default */ ret->w = 4; /* default */ ret->references = 1; ret->lock = CRYPTO_THREAD_lock_new(); if (ret->lock == NULL) { ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); OPENSSL_free(ret); return NULL; } return ret; } EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre) { int i; if (pre != NULL) CRYPTO_UP_REF(&pre->references, &i, pre->lock); return pre; } void EC_ec_pre_comp_free(EC_PRE_COMP *pre) { int i; if (pre == NULL) return; CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); REF_PRINT_COUNT("EC_ec", pre); if (i > 0) return; REF_ASSERT_ISNT(i < 0); if (pre->points != NULL) { EC_POINT **pts; for (pts = pre->points; *pts != NULL; pts++) EC_POINT_free(*pts); OPENSSL_free(pre->points); } CRYPTO_THREAD_lock_free(pre->lock); OPENSSL_free(pre); } #define EC_POINT_BN_set_flags(P, flags) do { \ BN_set_flags((P)->X, (flags)); \ BN_set_flags((P)->Y, (flags)); \ BN_set_flags((P)->Z, (flags)); \ } while(0) /*- * This functions computes a single point multiplication over the EC group, * using, at a high level, a Montgomery ladder with conditional swaps, with * various timing attack defenses. * * It performs either a fixed point multiplication * (scalar * generator) * when point is NULL, or a variable point multiplication * (scalar * point) * when point is not NULL. * * `scalar` cannot be NULL and should be in the range [0,n) otherwise all * constant time bets are off (where n is the cardinality of the EC group). * * This function expects `group->order` and `group->cardinality` to be well * defined and non-zero: it fails with an error code otherwise. * * NB: This says nothing about the constant-timeness of the ladder step * implementation (i.e., the default implementation is based on EC_POINT_add and * EC_POINT_dbl, which of course are not constant time themselves) or the * underlying multiprecision arithmetic. * * The product is stored in `r`. * * This is an internal function: callers are in charge of ensuring that the * input parameters `group`, `r`, `scalar` and `ctx` are not NULL. * * Returns 1 on success, 0 otherwise. */ int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx) { int i, cardinality_bits, group_top, kbit, pbit, Z_is_one; EC_POINT *p = NULL; EC_POINT *s = NULL; BIGNUM *k = NULL; BIGNUM *lambda = NULL; BIGNUM *cardinality = NULL; int ret = 0; /* early exit if the input point is the point at infinity */ if (point != NULL && EC_POINT_is_at_infinity(group, point)) return EC_POINT_set_to_infinity(group, r); if (BN_is_zero(group->order)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_ORDER); return 0; } if (BN_is_zero(group->cofactor)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_COFACTOR); return 0; } BN_CTX_start(ctx); if (((p = EC_POINT_new(group)) == NULL) || ((s = EC_POINT_new(group)) == NULL)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE); goto err; } if (point == NULL) { if (!EC_POINT_copy(p, group->generator)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); goto err; } } else { if (!EC_POINT_copy(p, point)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); goto err; } } EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME); EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME); EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME); cardinality = BN_CTX_get(ctx); lambda = BN_CTX_get(ctx); k = BN_CTX_get(ctx); if (k == NULL) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE); goto err; } if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); goto err; } /* * Group cardinalities are often on a word boundary. * So when we pad the scalar, some timing diff might * pop if it needs to be expanded due to carries. * So expand ahead of time. */ cardinality_bits = BN_num_bits(cardinality); group_top = bn_get_top(cardinality); if ((bn_wexpand(k, group_top + 2) == NULL) || (bn_wexpand(lambda, group_top + 2) == NULL)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); goto err; } if (!BN_copy(k, scalar)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); goto err; } BN_set_flags(k, BN_FLG_CONSTTIME); if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) { /*- * this is an unusual input, and we don't guarantee * constant-timeness */ if (!BN_nnmod(k, k, cardinality, ctx)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); goto err; } } if (!BN_add(lambda, k, cardinality)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); goto err; } BN_set_flags(lambda, BN_FLG_CONSTTIME); if (!BN_add(k, lambda, cardinality)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); goto err; } /* * lambda := scalar + cardinality * k := scalar + 2*cardinality */ kbit = BN_is_bit_set(lambda, cardinality_bits); BN_consttime_swap(kbit, k, lambda, group_top + 2); group_top = bn_get_top(group->field); if ((bn_wexpand(s->X, group_top) == NULL) || (bn_wexpand(s->Y, group_top) == NULL) || (bn_wexpand(s->Z, group_top) == NULL) || (bn_wexpand(r->X, group_top) == NULL) || (bn_wexpand(r->Y, group_top) == NULL) || (bn_wexpand(r->Z, group_top) == NULL) || (bn_wexpand(p->X, group_top) == NULL) || (bn_wexpand(p->Y, group_top) == NULL) || (bn_wexpand(p->Z, group_top) == NULL)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); goto err; } /*- * Apply coordinate blinding for EC_POINT. * * The underlying EC_METHOD can optionally implement this function: * ec_point_blind_coordinates() returns 0 in case of errors or 1 on * success or if coordinate blinding is not implemented for this * group. */ if (!ec_point_blind_coordinates(group, p, ctx)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_POINT_COORDINATES_BLIND_FAILURE); goto err; } /* Initialize the Montgomery ladder */ if (!ec_point_ladder_pre(group, r, s, p, ctx)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_PRE_FAILURE); goto err; } /* top bit is a 1, in a fixed pos */ pbit = 1; #define EC_POINT_CSWAP(c, a, b, w, t) do { \ BN_consttime_swap(c, (a)->X, (b)->X, w); \ BN_consttime_swap(c, (a)->Y, (b)->Y, w); \ BN_consttime_swap(c, (a)->Z, (b)->Z, w); \ t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ (a)->Z_is_one ^= (t); \ (b)->Z_is_one ^= (t); \ } while(0) /*- * The ladder step, with branches, is * * k[i] == 0: S = add(R, S), R = dbl(R) * k[i] == 1: R = add(S, R), S = dbl(S) * * Swapping R, S conditionally on k[i] leaves you with state * * k[i] == 0: T, U = R, S * k[i] == 1: T, U = S, R * * Then perform the ECC ops. * * U = add(T, U) * T = dbl(T) * * Which leaves you with state * * k[i] == 0: U = add(R, S), T = dbl(R) * k[i] == 1: U = add(S, R), T = dbl(S) * * Swapping T, U conditionally on k[i] leaves you with state * * k[i] == 0: R, S = T, U * k[i] == 1: R, S = U, T * * Which leaves you with state * * k[i] == 0: S = add(R, S), R = dbl(R) * k[i] == 1: R = add(S, R), S = dbl(S) * * So we get the same logic, but instead of a branch it's a * conditional swap, followed by ECC ops, then another conditional swap. * * Optimization: The end of iteration i and start of i-1 looks like * * ... * CSWAP(k[i], R, S) * ECC * CSWAP(k[i], R, S) * (next iteration) * CSWAP(k[i-1], R, S) * ECC * CSWAP(k[i-1], R, S) * ... * * So instead of two contiguous swaps, you can merge the condition * bits and do a single swap. * * k[i] k[i-1] Outcome * 0 0 No Swap * 0 1 Swap * 1 0 Swap * 1 1 No Swap * * This is XOR. pbit tracks the previous bit of k. */ for (i = cardinality_bits - 1; i >= 0; i--) { kbit = BN_is_bit_set(k, i) ^ pbit; EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); /* Perform a single step of the Montgomery ladder */ if (!ec_point_ladder_step(group, r, s, p, ctx)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_STEP_FAILURE); goto err; } /* * pbit logic merges this cswap with that of the * next iteration */ pbit ^= kbit; } /* one final cswap to move the right value into r */ EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); #undef EC_POINT_CSWAP /* Finalize ladder (and recover full point coordinates) */ if (!ec_point_ladder_post(group, r, s, p, ctx)) { ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_POST_FAILURE); goto err; } ret = 1; err: EC_POINT_free(p); EC_POINT_clear_free(s); BN_CTX_end(ctx); return ret; } #undef EC_POINT_BN_set_flags /* * TODO: table should be optimised for the wNAF-based implementation, * sometimes smaller windows will give better performance (thus the * boundaries should be increased) */ #define EC_window_bits_for_scalar_size(b) \ ((size_t) \ ((b) >= 2000 ? 6 : \ (b) >= 800 ? 5 : \ (b) >= 300 ? 4 : \ (b) >= 70 ? 3 : \ (b) >= 20 ? 2 : \ 1)) /*- * Compute * \sum scalars[i]*points[i], * also including * scalar*generator * in the addition if scalar != NULL */ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) { const EC_POINT *generator = NULL; EC_POINT *tmp = NULL; size_t totalnum; size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ size_t pre_points_per_block = 0; size_t i, j; int k; int r_is_inverted = 0; int r_is_at_infinity = 1; size_t *wsize = NULL; /* individual window sizes */ signed char **wNAF = NULL; /* individual wNAFs */ size_t *wNAF_len = NULL; size_t max_len = 0; size_t num_val; EC_POINT **val = NULL; /* precomputation */ EC_POINT **v; EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or * 'pre_comp->points' */ const EC_PRE_COMP *pre_comp = NULL; int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be * treated like other scalars, i.e. * precomputation is not available */ int ret = 0; if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) { /*- * Handle the common cases where the scalar is secret, enforcing a * scalar multiplication implementation based on a Montgomery ladder, * with various timing attack defenses. */ if ((scalar != group->order) && (scalar != NULL) && (num == 0)) { /*- * In this case we want to compute scalar * GeneratorPoint: this * codepath is reached most prominently by (ephemeral) key * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup, * ECDH keygen/first half), where the scalar is always secret. This * is why we ignore if BN_FLG_CONSTTIME is actually set and we * always call the ladder version. */ return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx); } if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) { /*- * In this case we want to compute scalar * VariablePoint: this * codepath is reached most prominently by the second half of ECDH, * where the secret scalar is multiplied by the peer's public point. * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is * actually set and we always call the ladder version. */ return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx); } } if (scalar != NULL) { generator = EC_GROUP_get0_generator(group); if (generator == NULL) { ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); goto err; } /* look if we can use precomputed multiples of generator */ pre_comp = group->pre_comp.ec; if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) { blocksize = pre_comp->blocksize; /* * determine maximum number of blocks that wNAF splitting may * yield (NB: maximum wNAF length is bit length plus one) */ numblocks = (BN_num_bits(scalar) / blocksize) + 1; /* * we cannot use more blocks than we have precomputation for */ if (numblocks > pre_comp->numblocks) numblocks = pre_comp->numblocks; pre_points_per_block = (size_t)1 << (pre_comp->w - 1); /* check that pre_comp looks sane */ if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; } } else { /* can't use precomputation */ pre_comp = NULL; numblocks = 1; num_scalar = 1; /* treat 'scalar' like 'num'-th element of * 'scalars' */ } } totalnum = num + numblocks; wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0])); wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0])); /* include space for pivot */ wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0])); val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0])); /* Ensure wNAF is initialised in case we end up going to err */ if (wNAF != NULL) wNAF[0] = NULL; /* preliminary pivot */ if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); goto err; } /* * num_val will be the total number of temporarily precomputed points */ num_val = 0; for (i = 0; i < num + num_scalar; i++) { size_t bits; bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); wsize[i] = EC_window_bits_for_scalar_size(bits); num_val += (size_t)1 << (wsize[i] - 1); wNAF[i + 1] = NULL; /* make sure we always have a pivot */ wNAF[i] = bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]); if (wNAF[i] == NULL) goto err; if (wNAF_len[i] > max_len) max_len = wNAF_len[i]; } if (numblocks) { /* we go here iff scalar != NULL */ if (pre_comp == NULL) { if (num_scalar != 1) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; } /* we have already generated a wNAF for 'scalar' */ } else { signed char *tmp_wNAF = NULL; size_t tmp_len = 0; if (num_scalar != 0) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; } /* * use the window size for which we have precomputation */ wsize[num] = pre_comp->w; tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); if (!tmp_wNAF) goto err; if (tmp_len <= max_len) { /* * One of the other wNAFs is at least as long as the wNAF * belonging to the generator, so wNAF splitting will not buy * us anything. */ numblocks = 1; totalnum = num + 1; /* don't use wNAF splitting */ wNAF[num] = tmp_wNAF; wNAF[num + 1] = NULL; wNAF_len[num] = tmp_len; /* * pre_comp->points starts with the points that we need here: */ val_sub[num] = pre_comp->points; } else { /* * don't include tmp_wNAF directly into wNAF array - use wNAF * splitting and include the blocks */ signed char *pp; EC_POINT **tmp_points; if (tmp_len < numblocks * blocksize) { /* * possibly we can do with fewer blocks than estimated */ numblocks = (tmp_len + blocksize - 1) / blocksize; if (numblocks > pre_comp->numblocks) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); OPENSSL_free(tmp_wNAF); goto err; } totalnum = num + numblocks; } /* split wNAF in 'numblocks' parts */ pp = tmp_wNAF; tmp_points = pre_comp->points; for (i = num; i < totalnum; i++) { if (i < totalnum - 1) { wNAF_len[i] = blocksize; if (tmp_len < blocksize) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); OPENSSL_free(tmp_wNAF); goto err; } tmp_len -= blocksize; } else /* * last block gets whatever is left (this could be * more or less than 'blocksize'!) */ wNAF_len[i] = tmp_len; wNAF[i + 1] = NULL; wNAF[i] = OPENSSL_malloc(wNAF_len[i]); if (wNAF[i] == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); OPENSSL_free(tmp_wNAF); goto err; } memcpy(wNAF[i], pp, wNAF_len[i]); if (wNAF_len[i] > max_len) max_len = wNAF_len[i]; if (*tmp_points == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); OPENSSL_free(tmp_wNAF); goto err; } val_sub[i] = tmp_points; tmp_points += pre_points_per_block; pp += blocksize; } OPENSSL_free(tmp_wNAF); } } } /* * All points we precompute now go into a single array 'val'. * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a * subarray of 'pre_comp->points' if we already have precomputation. */ val = OPENSSL_malloc((num_val + 1) * sizeof(val[0])); if (val == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); goto err; } val[num_val] = NULL; /* pivot element */ /* allocate points for precomputation */ v = val; for (i = 0; i < num + num_scalar; i++) { val_sub[i] = v; for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { *v = EC_POINT_new(group); if (*v == NULL) goto err; v++; } } if (!(v == val + num_val)) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; } if ((tmp = EC_POINT_new(group)) == NULL) goto err; /*- * prepare precomputed values: * val_sub[i][0] := points[i] * val_sub[i][1] := 3 * points[i] * val_sub[i][2] := 5 * points[i] * ... */ for (i = 0; i < num + num_scalar; i++) { if (i < num) { if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; } else { if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; } if (wsize[i] > 1) { if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { if (!EC_POINT_add (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; } } } if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err; r_is_at_infinity = 1; for (k = max_len - 1; k >= 0; k--) { if (!r_is_at_infinity) { if (!EC_POINT_dbl(group, r, r, ctx)) goto err; } for (i = 0; i < totalnum; i++) { if (wNAF_len[i] > (size_t)k) { int digit = wNAF[i][k]; int is_neg; if (digit) { is_neg = digit < 0; if (is_neg) digit = -digit; if (is_neg != r_is_inverted) { if (!r_is_at_infinity) { if (!EC_POINT_invert(group, r, ctx)) goto err; } r_is_inverted = !r_is_inverted; } /* digit > 0 */ if (r_is_at_infinity) { if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; r_is_at_infinity = 0; } else { if (!EC_POINT_add (group, r, r, val_sub[i][digit >> 1], ctx)) goto err; } } } } } if (r_is_at_infinity) { if (!EC_POINT_set_to_infinity(group, r)) goto err; } else { if (r_is_inverted) if (!EC_POINT_invert(group, r, ctx)) goto err; } ret = 1; err: EC_POINT_free(tmp); OPENSSL_free(wsize); OPENSSL_free(wNAF_len); if (wNAF != NULL) { signed char **w; for (w = wNAF; *w != NULL; w++) OPENSSL_free(*w); OPENSSL_free(wNAF); } if (val != NULL) { for (v = val; *v != NULL; v++) EC_POINT_clear_free(*v); OPENSSL_free(val); } OPENSSL_free(val_sub); return ret; } /*- * ec_wNAF_precompute_mult() * creates an EC_PRE_COMP object with preprecomputed multiples of the generator * for use with wNAF splitting as implemented in ec_wNAF_mul(). * * 'pre_comp->points' is an array of multiples of the generator * of the following form: * points[0] = generator; * points[1] = 3 * generator; * ... * points[2^(w-1)-1] = (2^(w-1)-1) * generator; * points[2^(w-1)] = 2^blocksize * generator; * points[2^(w-1)+1] = 3 * 2^blocksize * generator; * ... * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator * ... * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator * points[2^(w-1)*numblocks] = NULL */ int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) { const EC_POINT *generator; EC_POINT *tmp_point = NULL, *base = NULL, **var; const BIGNUM *order; size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; EC_POINT **points = NULL; EC_PRE_COMP *pre_comp; int ret = 0; #ifndef FIPS_MODE BN_CTX *new_ctx = NULL; #endif /* if there is an old EC_PRE_COMP object, throw it away */ EC_pre_comp_free(group); if ((pre_comp = ec_pre_comp_new(group)) == NULL) return 0; generator = EC_GROUP_get0_generator(group); if (generator == NULL) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); goto err; } #ifndef FIPS_MODE if (ctx == NULL) ctx = new_ctx = BN_CTX_new(); #endif if (ctx == NULL) goto err; BN_CTX_start(ctx); order = EC_GROUP_get0_order(group); if (order == NULL) goto err; if (BN_is_zero(order)) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); goto err; } bits = BN_num_bits(order); /* * The following parameters mean we precompute (approximately) one point * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other * bit lengths, other parameter combinations might provide better * efficiency. */ blocksize = 8; w = 4; if (EC_window_bits_for_scalar_size(bits) > w) { /* let's not make the window too small ... */ w = EC_window_bits_for_scalar_size(bits); } numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks * to use for wNAF * splitting */ pre_points_per_block = (size_t)1 << (w - 1); num = pre_points_per_block * numblocks; /* number of points to compute * and store */ points = OPENSSL_malloc(sizeof(*points) * (num + 1)); if (points == NULL) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; } var = points; var[num] = NULL; /* pivot */ for (i = 0; i < num; i++) { if ((var[i] = EC_POINT_new(group)) == NULL) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; } } if ((tmp_point = EC_POINT_new(group)) == NULL || (base = EC_POINT_new(group)) == NULL) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; } if (!EC_POINT_copy(base, generator)) goto err; /* do the precomputation */ for (i = 0; i < numblocks; i++) { size_t j; if (!EC_POINT_dbl(group, tmp_point, base, ctx)) goto err; if (!EC_POINT_copy(*var++, base)) goto err; for (j = 1; j < pre_points_per_block; j++, var++) { /* * calculate odd multiples of the current base point */ if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) goto err; } if (i < numblocks - 1) { /* * get the next base (multiply current one by 2^blocksize) */ size_t k; if (blocksize <= 2) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); goto err; } if (!EC_POINT_dbl(group, base, tmp_point, ctx)) goto err; for (k = 2; k < blocksize; k++) { if (!EC_POINT_dbl(group, base, base, ctx)) goto err; } } } if (!EC_POINTs_make_affine(group, num, points, ctx)) goto err; pre_comp->group = group; pre_comp->blocksize = blocksize; pre_comp->numblocks = numblocks; pre_comp->w = w; pre_comp->points = points; points = NULL; pre_comp->num = num; SETPRECOMP(group, ec, pre_comp); pre_comp = NULL; ret = 1; err: BN_CTX_end(ctx); #ifndef FIPS_MODE BN_CTX_free(new_ctx); #endif EC_ec_pre_comp_free(pre_comp); if (points) { EC_POINT **p; for (p = points; *p != NULL; p++) EC_POINT_free(*p); OPENSSL_free(points); } EC_POINT_free(tmp_point); EC_POINT_free(base); return ret; } int ec_wNAF_have_precompute_mult(const EC_GROUP *group) { return HAVEPRECOMP(group, ec); }