| /* |
| * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. |
| * |
| * Licensed under the OpenSSL license (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 |
| */ |
| |
| /* ==================================================================== |
| * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. |
| * Portions of this software developed by SUN MICROSYSTEMS, INC., |
| * and contributed to the OpenSSL project. |
| */ |
| |
| #include <string.h> |
| #include <openssl/err.h> |
| |
| #include "internal/cryptlib.h" |
| #include "internal/bn_int.h" |
| #include "ec_lcl.h" |
| |
| /* |
| * This file implements the wNAF-based interleaving multi-exponentiation method |
| * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>); |
| * for multiplication with precomputation, we use wNAF splitting |
| * (<URL: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); |
| } |
| |
| /* |
| * 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 = 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]); |
| 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 != 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: |
| 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; |
| 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; |
| |
| /* 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; |
| } |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| 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: |
| if (ctx != NULL) |
| BN_CTX_end(ctx); |
| BN_CTX_free(new_ctx); |
| 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); |
| } |
