crypto/ec/ec2_mult.c

   1 /* crypto/ec/ec2_mult.c */
   2 /* ====================================================================
   3  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
   4  *
   5  * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
   6  * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
   7  * to the OpenSSL project.
   8  *
   9  * The ECC Code is licensed pursuant to the OpenSSL open source
  10  * license provided below.
  11  *
  12  * In addition, Sun covenants to all licensees who provide a reciprocal
  13  * covenant with respect to their own patents if any, not to sue under
  14  * current and future patent claims necessarily infringed by the making,
  15  * using, practicing, selling, offering for sale and/or otherwise
  16  * disposing of the ECC Code as delivered hereunder (or portions thereof),
  17  * provided that such covenant shall not apply:
  18  *  1) for code that a licensee deletes from the ECC Code;
  19  *  2) separates from the ECC Code; or
  20  *  3) for infringements caused by:
  21  *       i) the modification of the ECC Code or
  22  *      ii) the combination of the ECC Code with other software or
  23  *          devices where such combination causes the infringement.
  24  *
  25  * The software is originally written by Sheueling Chang Shantz and
  26  * Douglas Stebila of Sun Microsystems Laboratories.
  27  *
  28  */
  29 /* ====================================================================
  30  * Copyright (c) 1998-2002 The OpenSSL Project.  All rights reserved.
  31  *
  32  * Redistribution and use in source and binary forms, with or without
  33  * modification, are permitted provided that the following conditions
  34  * are met:
  35  *
  36  * 1. Redistributions of source code must retain the above copyright
  37  *    notice, this list of conditions and the following disclaimer.
  38  *
  39  * 2. Redistributions in binary form must reproduce the above copyright
  40  *    notice, this list of conditions and the following disclaimer in
  41  *    the documentation and/or other materials provided with the
  42  *    distribution.
  43  *
  44  * 3. All advertising materials mentioning features or use of this
  45  *    software must display the following acknowledgment:
  46  *    "This product includes software developed by the OpenSSL Project
  47  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  48  *
  49  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  50  *    endorse or promote products derived from this software without
  51  *    prior written permission. For written permission, please contact
  52  *    openssl-core@openssl.org.
  53  *
  54  * 5. Products derived from this software may not be called "OpenSSL"
  55  *    nor may "OpenSSL" appear in their names without prior written
  56  *    permission of the OpenSSL Project.
  57  *
  58  * 6. Redistributions of any form whatsoever must retain the following
  59  *    acknowledgment:
  60  *    "This product includes software developed by the OpenSSL Project
  61  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  62  *
  63  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  64  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  65  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  66  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  67  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  68  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  69  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  70  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  71  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  72  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  73  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  74  * OF THE POSSIBILITY OF SUCH DAMAGE.
  75  * ====================================================================
  76  *
  77  * This product includes cryptographic software written by Eric Young
  78  * (eay@cryptsoft.com).  This product includes software written by Tim
  79  * Hudson (tjh@cryptsoft.com).
  80  *
  81  */
  82
  83 #include <openssl/err.h>
  84
  85 #include "ec_lcl.h"
  86
  87
  88 /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
  89  * coordinates.
  90  * Uses algorithm Mdouble in appendix of
  91  *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
  92  *     GF(2^m) without precomputation".
  93  * modified to not require precomputation of c=b^{2^{m-1}}.
  94  */
  95 static int Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
  96         {
  97         BIGNUM *t1;
  98         int ret = 0;
  99
 100         /* Since Mdouble is static we can guarantee that ctx != NULL. */
 101         BN_CTX_start(ctx);
 102         t1 = BN_CTX_get(ctx);
 103         if (t1 == NULL) goto err;
 104
 105         if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
 106         if (!group->meth->field_sqr(group, t1, z, ctx)) goto err;
 107         if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err;
 108         if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
 109         if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err;
 110         if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err;
 111         if (!BN_GF2m_add(x, x, t1)) goto err;
 112
 113         ret = 1;
 114
 115  err:
 116         BN_CTX_end(ctx);
 117         return ret;
 118         }
 119
 120 /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
 121  * projective coordinates.
 122  * Uses algorithm Madd in appendix of
 123  *     Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 124  *     GF(2^m) without precomputation".
 125  */
 126 static int Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1,
 127         const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
 128         {
 129         BIGNUM *t1, *t2;
 130         int ret = 0;
 131
 132         /* Since Madd is static we can guarantee that ctx != NULL. */
 133         BN_CTX_start(ctx);
 134         t1 = BN_CTX_get(ctx);
 135         t2 = BN_CTX_get(ctx);
 136         if (t2 == NULL) goto err;
 137
 138         if (!BN_copy(t1, x)) goto err;
 139         if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err;
 140         if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err;
 141         if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err;
 142         if (!BN_GF2m_add(z1, z1, x1)) goto err;
 143         if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err;
 144         if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err;
 145         if (!BN_GF2m_add(x1, x1, t2)) goto err;
 146
 147         ret = 1;
 148
 149  err:
 150         BN_CTX_end(ctx);
 151         return ret;
 152         }
 153
 154 /* Compute the affine coordinates x2, y2=z2 for the point (x1/z1) and (x2/x2) in
 155  * Montgomery projective coordinates.
 156  * Uses algorithm Mxy in appendix of
 157  *     Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 158  *     GF(2^m) without precomputation".
 159  * Returns:
 160  *     0 on error
 161  *     1 if return value should be the point at infinity
 162  *     2 otherwise
 163  */
 164 static int Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1,
 165         BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
 166         {
 167         BIGNUM *t3, *t4, *t5;
 168         int ret = 0;
 169
 170         if (BN_is_zero(z1))
 171                 {
 172                 if (!BN_zero(x2)) return 0;
 173                 if (!BN_zero(z2)) return 0;
 174                 return 1;
 175                 }
 176
 177         if (BN_is_zero(z2))
 178                 {
 179                 if (!BN_copy(x2, x)) return 0;
 180                 if (!BN_GF2m_add(z2, x, y)) return 0;
 181                 return 2;
 182                 }
 183
 184         /* Since Mxy is static we can guarantee that ctx != NULL. */
 185         BN_CTX_start(ctx);
 186         t3 = BN_CTX_get(ctx);
 187         t4 = BN_CTX_get(ctx);
 188         t5 = BN_CTX_get(ctx);
 189         if (t5 == NULL) goto err;
 190
 191         if (!BN_one(t5)) goto err;
 192
 193         if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err;
 194
 195         if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err;
 196         if (!BN_GF2m_add(z1, z1, x1)) goto err;
 197         if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err;
 198         if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err;
 199         if (!BN_GF2m_add(z2, z2, x2)) goto err;
 200
 201         if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err;
 202         if (!group->meth->field_sqr(group, t4, x, ctx)) goto err;
 203         if (!BN_GF2m_add(t4, t4, y)) goto err;
 204         if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err;
 205         if (!BN_GF2m_add(t4, t4, z2)) goto err;
 206
 207         if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err;
 208         if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err;
 209         if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err;
 210         if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err;
 211         if (!BN_GF2m_add(z2, x2, x)) goto err;
 212
 213         if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err;
 214         if (!BN_GF2m_add(z2, z2, y)) goto err;
 215
 216         ret = 2;
 217
 218  err:
 219         BN_CTX_end(ctx);
 220         return ret;
 221         }
 222
 223 /* Computes scalar*point and stores the result in r.
 224  * point can not equal r.
 225  * Uses algorithm 2P of
 226  *     Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 227  *     GF(2^m) without precomputation".
 228  */
 229 static int point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 230         const EC_POINT *point, BN_CTX *ctx)
 231         {
 232         BIGNUM *x1, *x2, *z1, *z2;
 233         int ret = 0, i, j;
 234         BN_ULONG mask;
 235
 236         if (r == point)
 237                 {
 238                 ECerr(EC_F_EC_POINT_MUL, EC_R_INVALID_ARGUMENT);
 239                 return 0;
 240                 }
 241
 242         /* if result should be point at infinity */
 243         if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
 244                 EC_POINT_is_at_infinity(group, point))
 245                 {
 246                 return EC_POINT_set_to_infinity(group, r);
 247                 }
 248
 249         /* only support affine coordinates */
 250         if (!point->Z_is_one) return 0;
 251
 252         /* Since point_multiply is static we can guarantee that ctx != NULL. */
 253         BN_CTX_start(ctx);
 254         x1 = BN_CTX_get(ctx);
 255         z1 = BN_CTX_get(ctx);
 256         if (z1 == NULL) goto err;
 257
 258         x2 = &r->X;
 259         z2 = &r->Y;
 260
 261         if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */
 262         if (!BN_one(z1)) goto err; /* z1 = 1 */
 263         if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */
 264         if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err;
 265         if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */
 266
 267         /* find top most bit and go one past it */
 268         i = scalar->top - 1; j = BN_BITS2 - 1;
 269         mask = BN_TBIT;
 270         while (!(scalar->d[i] & mask)) { mask >>= 1; j--; }
 271         mask >>= 1; j--;
 272         /* if top most bit was at word break, go to next word */
 273         if (!mask)
 274                 {
 275                 i--; j = BN_BITS2 - 1;
 276                 mask = BN_TBIT;
 277                 }
 278
 279         for (; i >= 0; i--)
 280                 {
 281                 for (; j >= 0; j--)
 282                         {
 283                         if (scalar->d[i] & mask)
 284                                 {
 285                                 if (!Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err;
 286                                 if (!Mdouble(group, x2, z2, ctx)) goto err;
 287                                 }
 288                         else
 289                                 {
 290                                 if (!Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err;
 291                                 if (!Mdouble(group, x1, z1, ctx)) goto err;
 292                                 }
 293                         mask >>= 1;
 294                         }
 295                 j = BN_BITS2 - 1;
 296                 mask = BN_TBIT;
 297                 }
 298
 299         /* convert out of "projective" coordinates */
 300         i = Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
 301         if (i == 0) goto err;
 302         else if (i == 1)
 303                 {
 304                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
 305                 }
 306         else
 307                 {
 308                 if (!BN_one(&r->Z)) goto err;
 309                 r->Z_is_one = 1;
 310                 }
 311
 312         /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
 313         r->X.neg = 0;
 314         r->Y.neg = 0;
 315
 316         ret = 1;
 317
 318  err:
 319         BN_CTX_end(ctx);
 320         return ret;
 321         }
 322
 323
 324 /* Computes the sum
 325  *     scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
 326  * gracefully ignoring NULL scalar values.
 327  */
 328 int ec_GF2m_mont_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 329         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
 330         {
 331         BN_CTX *new_ctx = NULL;
 332         int ret = 0, i;
 333         EC_POINT *p=NULL;
 334
 335         if (ctx == NULL)
 336                 {
 337                 ctx = new_ctx = BN_CTX_new();
 338                 if (ctx == NULL)
 339                         return 0;
 340                 }
 341
 342         /* This implementation is more efficient than the wNAF implementation for 2
 343          * or fewer points.  Use the ec_wNAF_mul implementation 3 or more points.
 344          */
 345         if ((scalar && (num > 1)) || (num > 2))
 346                 {
 347                 ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
 348                 goto err;
 349                 }
 350
 351         if ((p = EC_POINT_new(group)) == NULL) goto err;
 352
 353         if (!EC_POINT_set_to_infinity(group, r)) goto err;
 354
 355         if (scalar)
 356                 {
 357                 if (!point_multiply(group, p, scalar, group->generator, ctx)) goto err;
 358                 if (scalar->neg) if (!group->meth->invert(group, p, ctx)) goto err;
 359                 if (!group->meth->add(group, r, r, p, ctx)) goto err;
 360                 }
 361
 362         for (i = 0; i < num; i++)
 363                 {
 364                 if (!point_multiply(group, p, scalars[i], points[i], ctx)) goto err;
 365                 if (scalars[i]->neg) if (!group->meth->invert(group, p, ctx)) goto err;
 366                 if (!group->meth->add(group, r, r, p, ctx)) goto err;
 367                 }
 368
 369         ret = 1;
 370
 371   err:
 372         if (p) EC_POINT_free(p);
 373         if (new_ctx != NULL)
 374                 BN_CTX_free(new_ctx);
 375         return ret;
 376         }
 377
 378
 379 /* Precomputation for point multiplication. */
 380 int ec_GF2m_mont_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 381         {
 382         /* There is no precomputation to do for Montgomery scalar multiplication but
 383          * since this implementation falls back to the wNAF multiplication for more than
 384          * two points, call the wNAF implementation's precompute.
 385          */
 386         return ec_wNAF_precompute_mult(group, ctx);
 387         }