/* crypto/ec/ec_mult.c */ /* * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project. */ /* ==================================================================== * Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * Portions of this software developed by SUN MICROSYSTEMS, INC., * and contributed to the OpenSSL project. */ #include #include #include "internal/bn_int.h" #include "ec_lcl.h" /* * This file implements the wNAF-based interleaving multi-exponentation method * (); * for multiplication with precomputation, we use wNAF splitting * (). */ /* structure for precomputed multiples of the generator */ typedef 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) */ int references; } EC_PRE_COMP; /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */ static void *ec_pre_comp_dup(void *); static void ec_pre_comp_free(void *); static void ec_pre_comp_clear_free(void *); 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) { 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; return ret; } static void *ec_pre_comp_dup(void *src_) { EC_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; } static void ec_pre_comp_free(void *pre_) { int i; EC_PRE_COMP *pre = pre_; if (!pre) return; i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); if (i > 0) return; if (pre->points) { EC_POINT **p; for (p = pre->points; *p != NULL; p++) EC_POINT_free(*p); OPENSSL_free(pre->points); } OPENSSL_free(pre); } static void ec_pre_comp_clear_free(void *pre_) { int i; EC_PRE_COMP *pre = pre_; if (!pre) return; i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); if (i > 0) return; if (pre->points) { EC_POINT **p; for (p = pre->points; *p != NULL; p++) { EC_POINT_clear_free(*p); OPENSSL_cleanse(p, sizeof(*p)); } OPENSSL_free(pre->points); } OPENSSL_clear_free(pre, sizeof(*pre)); } /* * 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) { BN_CTX *new_ctx = NULL; 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 (group->meth != r->meth) { ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; } if ((scalar == NULL) && (num == 0)) { return EC_POINT_set_to_infinity(group, r); } for (i = 0; i < num; i++) { if (group->meth != points[i]->meth) { ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; } } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; } 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 = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); 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]); wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space * for pivot */ val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); /* Ensure wNAF is initialised in case we end up going to err */ if (wNAF) wNAF[0] = NULL; /* preliminary pivot */ if (!wsize || !wNAF_len || !wNAF || !val_sub) { 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; if (tmp_len > max_len) max_len = 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); 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); 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: BN_CTX_free(new_ctx); 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; BN_CTX *new_ctx = NULL; 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; /* if there is an old EC_PRE_COMP object, throw it away */ EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); 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; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; } BN_CTX_start(ctx); order = BN_CTX_get(ctx); if (order == NULL) goto err; if (!EC_GROUP_get_order(group, order, ctx)) 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) { 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; if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free)) goto err; pre_comp = NULL; ret = 1; err: if (ctx != NULL) BN_CTX_end(ctx); BN_CTX_free(new_ctx); 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) { if (EC_EX_DATA_get_data (group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL) return 1; else return 0; }