crypto/ec/ec_mult.c

   1 /* crypto/ec/ec_mult.c */
   2 /* ====================================================================
   3  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  *
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  *
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in
  14  *    the documentation and/or other materials provided with the
  15  *    distribution.
  16  *
  17  * 3. All advertising materials mentioning features or use of this
  18  *    software must display the following acknowledgment:
  19  *    "This product includes software developed by the OpenSSL Project
  20  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  21  *
  22  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  23  *    endorse or promote products derived from this software without
  24  *    prior written permission. For written permission, please contact
  25  *    openssl-core@openssl.org.
  26  *
  27  * 5. Products derived from this software may not be called "OpenSSL"
  28  *    nor may "OpenSSL" appear in their names without prior written
  29  *    permission of the OpenSSL Project.
  30  *
  31  * 6. Redistributions of any form whatsoever must retain the following
  32  *    acknowledgment:
  33  *    "This product includes software developed by the OpenSSL Project
  34  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  35  *
  36  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  37  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  38  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  39  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  40  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  41  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  42  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  43  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  44  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  45  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  46  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  47  * OF THE POSSIBILITY OF SUCH DAMAGE.
  48  * ====================================================================
  49  *
  50  * This product includes cryptographic software written by Eric Young
  51  * (eay@cryptsoft.com).  This product includes software written by Tim
  52  * Hudson (tjh@cryptsoft.com).
  53  *
  54  */
  55
  56 #include <openssl/err.h>
  57
  58 #include "ec_lcl.h"
  59
  60
  61 /* TODO: width-m NAFs */
  62
  63 /* TODO: optional Lim-Lee precomputation for the generator */
  64
  65
  66 /* this is just BN_window_bits_for_exponent_size from bn_lcl.h for now;
  67  * the table should be updated for EC */ /* TODO */
  68 #define EC_window_bits_for_scalar_size(b) \
  69                 ((b) > 671 ? 6 : \
  70                  (b) > 239 ? 5 : \
  71                  (b) >  79 ? 4 : \
  72                  (b) >  23 ? 3 : 1)
  73
  74 /* Compute
  75  *      \sum scalar[i]*points[i]
  76  * where
  77  *      scalar*generator
  78  * is included in the addition if scalar != NULL
  79  */
  80 int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, BIGNUM *scalar,
  81         size_t num, EC_POINT *points[], BIGNUM *scalars[], BN_CTX *ctx)
  82         {
  83         BN_CTX *new_ctx = NULL;
  84         EC_POINT *generator = NULL;
  85         EC_POINT *tmp = NULL;
  86         size_t totalnum;
  87         size_t i, j;
  88         int k, t;
  89         int r_is_at_infinity = 1;
  90         size_t max_bits = 0;
  91         size_t *wsize = NULL; /* individual window sizes */
  92         unsigned long *wbits = NULL; /* individual window contents */
  93         int *wpos = NULL; /* position of bottom bit of current individual windows
  94                            * (wpos[i] is valid if wbits[i] != 0) */
  95         size_t num_val;
  96         EC_POINT **val = NULL; /* precomputation */
  97         EC_POINT **v;
  98         EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */
  99         int ret = 0;
 100
 101         if (scalar != NULL)
 102                 {
 103                 generator = EC_GROUP_get0_generator(group);
 104                 if (generator == NULL)
 105                         {
 106                         ECerr(EC_F_EC_POINTS_MUL, EC_R_NO_GENERATOR_SET);
 107                         return 0;
 108                         }
 109                 }
 110
 111         for (i = 0; i < num; i++)
 112                 {
 113                 if (group->meth != points[i]->meth)
 114                         {
 115                         ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 116                         return 0;
 117                         }
 118                 }
 119
 120         totalnum = num + (scalar != NULL);
 121
 122         wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
 123         wbits = OPENSSL_malloc(totalnum * sizeof wbits[0]);
 124         wpos = OPENSSL_malloc(totalnum * sizeof wpos[0]);
 125         if (wsize == NULL || wbits == NULL || wpos == NULL) goto err;
 126
 127         /* num_val := total number of points to precompute */
 128         num_val = 0;
 129         for (i = 0; i < totalnum; i++)
 130                 {
 131                 size_t bits;
 132
 133                 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 134                 wsize[i] = EC_window_bits_for_scalar_size(bits);
 135                 num_val += 1 << (wsize[i] - 1);
 136                 if (bits > max_bits)
 137                         max_bits = bits;
 138                 wbits[i] = 0;
 139                 wpos[i] = 0;
 140                 }
 141
 142         /* all precomputed points go into a single array 'val',
 143          * 'val_sub[i]' is a pointer to the subarray for the i-th point */
 144         val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
 145         if (val == NULL) goto err;
 146         val[num_val] = NULL; /* pivot element */
 147
 148         val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
 149         if (val_sub == NULL) goto err;
 150
 151         /* allocate points for precomputation */
 152         v = val;
 153         for (i = 0; i < totalnum; i++)
 154                 {
 155                 val_sub[i] = v;
 156                 for (j = 0; j < (1 << (wsize[i] - 1)); j++)
 157                         {
 158                         *v = EC_POINT_new(group);
 159                         if (*v == NULL) goto err;
 160                         v++;
 161                         }
 162                 }
 163         if (!(v == val + num_val))
 164                 {
 165                 ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR);
 166                 goto err;
 167                 }
 168
 169         if (ctx == NULL)
 170                 {
 171                 ctx = new_ctx = BN_CTX_new();
 172                 if (ctx == NULL)
 173                         goto err;
 174                 }
 175
 176         tmp = EC_POINT_new(group);
 177         if (tmp == NULL) goto err;
 178
 179         /* prepare precomputed values:
 180          *    val_sub[i][0] :=     points[i]
 181          *    val_sub[i][1] := 3 * points[i]
 182          *    val_sub[i][2] := 5 * points[i]
 183          *    ...
 184          */
 185         for (i = 0; i < totalnum; i++)
 186                 {
 187                 if (i < num)
 188                         {
 189                         if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
 190                         }
 191                 else
 192                         {
 193                         if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
 194                         }
 195
 196                 if (wsize[i] > 1)
 197                         {
 198                         if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
 199                         for (j = 1; j < (1 << (wsize[i] - 1)); j++)
 200                                 {
 201                                 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
 202                                 }
 203                         }
 204                 }
 205
 206 #if 1 /* optional, maybe we should only do this if total_num > 1 */
 207         if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err;
 208 #endif
 209
 210         r_is_at_infinity = 1;
 211
 212         for (k = max_bits - 1; k >= 0; k--)
 213                 {
 214                 if (!r_is_at_infinity)
 215                         {
 216                         if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
 217                         }
 218
 219                 for (i = 0; i < totalnum; i++)
 220                         {
 221                         if (wbits[i] == 0)
 222                                 {
 223                                 BIGNUM *s;
 224
 225                                 s = i < num ? scalars[i] : scalar;
 226
 227                                 if (BN_is_bit_set(s, k))
 228                                         {
 229                                         /* look at bits  k - wsize[i] + 1 .. k  for this window */
 230                                         t = k - wsize[i] + 1;
 231                                         while (!BN_is_bit_set(s, t)) /* BN_is_bit_set is false for t < 0 */
 232                                                 t++;
 233                                         wpos[i] = t;
 234                                         wbits[i] = 1;
 235                                         for (t = k - 1; t >= wpos[i]; t--)
 236                                                 {
 237                                                 wbits[i] <<= 1;
 238                                                 if (BN_is_bit_set(s, t))
 239                                                         wbits[i]++;
 240                                                 }
 241                                         /* now wbits[i] is the odd bit pattern at bits wpos[i] .. k */
 242                                         }
 243                                 }
 244
 245                         if ((wbits[i] != 0) && (wpos[i] == k))
 246                                 {
 247                                 if (r_is_at_infinity)
 248                                         {
 249                                         if (!EC_POINT_copy(r, val_sub[i][wbits[i] >> 1])) goto err;
 250                                         r_is_at_infinity = 0;
 251                                         }
 252                                 else
 253                                         {
 254                                         if (!EC_POINT_add(group, r, r, val_sub[i][wbits[i] >> 1], ctx)) goto err;
 255                                         }
 256                                 wbits[i] = 0;
 257                                 }
 258                         }
 259                 }
 260
 261         if (r_is_at_infinity)
 262                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
 263
 264         ret = 1;
 265
 266  err:
 267         if (new_ctx != NULL)
 268                 BN_CTX_free(new_ctx);
 269         if (tmp != NULL)
 270                 EC_POINT_free(tmp);
 271         if (wsize != NULL)
 272                 OPENSSL_free(wsize);
 273         if (wbits != NULL)
 274                 OPENSSL_free(wbits);
 275         if (wpos != NULL)
 276                 OPENSSL_free(wpos);
 277         if (val != NULL)
 278                 {
 279                 for (v = val; *v != NULL; v++)
 280                         EC_POINT_clear_free(*v);
 281
 282                 OPENSSL_free(val);
 283                 }
 284         if (val_sub != NULL)
 285                 {
 286                 OPENSSL_free(val_sub);
 287                 }
 288         return ret;
 289         }