release/src/router/openssl/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  * The software is originally written by Sheueling Chang Shantz and
  13  * Douglas Stebila of Sun Microsystems Laboratories.
  14  *
  15  */
  16 /* ====================================================================
  17  * Copyright (c) 1998-2003 The OpenSSL Project.  All rights reserved.
  18  *
  19  * Redistribution and use in source and binary forms, with or without
  20  * modification, are permitted provided that the following conditions
  21  * are met:
  22  *
  23  * 1. Redistributions of source code must retain the above copyright
  24  *    notice, this list of conditions and the following disclaimer.
  25  *
  26  * 2. Redistributions in binary form must reproduce the above copyright
  27  *    notice, this list of conditions and the following disclaimer in
  28  *    the documentation and/or other materials provided with the
  29  *    distribution.
  30  *
  31  * 3. All advertising materials mentioning features or use of this
  32  *    software must display the following acknowledgment:
  33  *    "This product includes software developed by the OpenSSL Project
  34  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  35  *
  36  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  37  *    endorse or promote products derived from this software without
  38  *    prior written permission. For written permission, please contact
  39  *    openssl-core@openssl.org.
  40  *
  41  * 5. Products derived from this software may not be called "OpenSSL"
  42  *    nor may "OpenSSL" appear in their names without prior written
  43  *    permission of the OpenSSL Project.
  44  *
  45  * 6. Redistributions of any form whatsoever must retain the following
  46  *    acknowledgment:
  47  *    "This product includes software developed by the OpenSSL Project
  48  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  49  *
  50  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  51  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  52  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  53  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  54  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  55  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  56  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  57  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  58  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  59  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  60  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  61  * OF THE POSSIBILITY OF SUCH DAMAGE.
  62  * ====================================================================
  63  *
  64  * This product includes cryptographic software written by Eric Young
  65  * (eay@cryptsoft.com).  This product includes software written by Tim
  66  * Hudson (tjh@cryptsoft.com).
  67  *
  68  */
  69
  70 #include <openssl/err.h>
  71
  72 #include "ec_lcl.h"
  73
  74 #ifndef OPENSSL_NO_EC2M
  75
  76 /*-
  77  * Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
  78  * coordinates.
  79  * Uses algorithm Mdouble in appendix of
  80  *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
  81  *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  82  * modified to not require precomputation of c=b^{2^{m-1}}.
  83  */
  84 static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
  85                         BN_CTX *ctx)
  86 {
  87     BIGNUM *t1;
  88     int ret = 0;
  89
  90     /* Since Mdouble is static we can guarantee that ctx != NULL. */
  91     BN_CTX_start(ctx);
  92     t1 = BN_CTX_get(ctx);
  93     if (t1 == NULL)
  94         goto err;
  95
  96     if (!group->meth->field_sqr(group, x, x, ctx))
  97         goto err;
  98     if (!group->meth->field_sqr(group, t1, z, ctx))
  99         goto err;
 100     if (!group->meth->field_mul(group, z, x, t1, ctx))
 101         goto err;
 102     if (!group->meth->field_sqr(group, x, x, ctx))
 103         goto err;
 104     if (!group->meth->field_sqr(group, t1, t1, ctx))
 105         goto err;
 106     if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
 107         goto err;
 108     if (!BN_GF2m_add(x, x, t1))
 109         goto err;
 110
 111     ret = 1;
 112
 113  err:
 114     BN_CTX_end(ctx);
 115     return ret;
 116 }
 117
 118 /*-
 119  * Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
 120  * projective coordinates.
 121  * Uses algorithm Madd in appendix of
 122  *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 123  *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
 124  */
 125 static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1,
 126                      BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2,
 127                      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)
 137         goto err;
 138
 139     if (!BN_copy(t1, x))
 140         goto err;
 141     if (!group->meth->field_mul(group, x1, x1, z2, ctx))
 142         goto err;
 143     if (!group->meth->field_mul(group, z1, z1, x2, ctx))
 144         goto err;
 145     if (!group->meth->field_mul(group, t2, x1, z1, ctx))
 146         goto err;
 147     if (!BN_GF2m_add(z1, z1, x1))
 148         goto err;
 149     if (!group->meth->field_sqr(group, z1, z1, ctx))
 150         goto err;
 151     if (!group->meth->field_mul(group, x1, z1, t1, ctx))
 152         goto err;
 153     if (!BN_GF2m_add(x1, x1, t2))
 154         goto err;
 155
 156     ret = 1;
 157
 158  err:
 159     BN_CTX_end(ctx);
 160     return ret;
 161 }
 162
 163 /*-
 164  * Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
 165  * using Montgomery point multiplication algorithm Mxy() in appendix of
 166  *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 167  *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
 168  * Returns:
 169  *     0 on error
 170  *     1 if return value should be the point at infinity
 171  *     2 otherwise
 172  */
 173 static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y,
 174                     BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2,
 175                     BN_CTX *ctx)
 176 {
 177     BIGNUM *t3, *t4, *t5;
 178     int ret = 0;
 179
 180     if (BN_is_zero(z1)) {
 181         BN_zero(x2);
 182         BN_zero(z2);
 183         return 1;
 184     }
 185
 186     if (BN_is_zero(z2)) {
 187         if (!BN_copy(x2, x))
 188             return 0;
 189         if (!BN_GF2m_add(z2, x, y))
 190             return 0;
 191         return 2;
 192     }
 193
 194     /* Since Mxy is static we can guarantee that ctx != NULL. */
 195     BN_CTX_start(ctx);
 196     t3 = BN_CTX_get(ctx);
 197     t4 = BN_CTX_get(ctx);
 198     t5 = BN_CTX_get(ctx);
 199     if (t5 == NULL)
 200         goto err;
 201
 202     if (!BN_one(t5))
 203         goto err;
 204
 205     if (!group->meth->field_mul(group, t3, z1, z2, ctx))
 206         goto err;
 207
 208     if (!group->meth->field_mul(group, z1, z1, x, ctx))
 209         goto err;
 210     if (!BN_GF2m_add(z1, z1, x1))
 211         goto err;
 212     if (!group->meth->field_mul(group, z2, z2, x, ctx))
 213         goto err;
 214     if (!group->meth->field_mul(group, x1, z2, x1, ctx))
 215         goto err;
 216     if (!BN_GF2m_add(z2, z2, x2))
 217         goto err;
 218
 219     if (!group->meth->field_mul(group, z2, z2, z1, ctx))
 220         goto err;
 221     if (!group->meth->field_sqr(group, t4, x, ctx))
 222         goto err;
 223     if (!BN_GF2m_add(t4, t4, y))
 224         goto err;
 225     if (!group->meth->field_mul(group, t4, t4, t3, ctx))
 226         goto err;
 227     if (!BN_GF2m_add(t4, t4, z2))
 228         goto err;
 229
 230     if (!group->meth->field_mul(group, t3, t3, x, ctx))
 231         goto err;
 232     if (!group->meth->field_div(group, t3, t5, t3, ctx))
 233         goto err;
 234     if (!group->meth->field_mul(group, t4, t3, t4, ctx))
 235         goto err;
 236     if (!group->meth->field_mul(group, x2, x1, t3, ctx))
 237         goto err;
 238     if (!BN_GF2m_add(z2, x2, x))
 239         goto err;
 240
 241     if (!group->meth->field_mul(group, z2, z2, t4, ctx))
 242         goto err;
 243     if (!BN_GF2m_add(z2, z2, y))
 244         goto err;
 245
 246     ret = 2;
 247
 248  err:
 249     BN_CTX_end(ctx);
 250     return ret;
 251 }
 252
 253 /*-
 254  * Computes scalar*point and stores the result in r.
 255  * point can not equal r.
 256  * Uses a modified algorithm 2P of
 257  *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 258  *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
 259  *
 260  * To protect against side-channel attack the function uses constant time swap,
 261  * avoiding conditional branches.
 262  */
 263 static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group,
 264                                              EC_POINT *r,
 265                                              const BIGNUM *scalar,
 266                                              const EC_POINT *point,
 267                                              BN_CTX *ctx)
 268 {
 269     BIGNUM *x1, *x2, *z1, *z2;
 270     int ret = 0, i;
 271     BN_ULONG mask, word;
 272
 273     if (r == point) {
 274         ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
 275         return 0;
 276     }
 277
 278     /* if result should be point at infinity */
 279     if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
 280         EC_POINT_is_at_infinity(group, point)) {
 281         return EC_POINT_set_to_infinity(group, r);
 282     }
 283
 284     /* only support affine coordinates */
 285     if (!point->Z_is_one)
 286         return 0;
 287
 288     /*
 289      * Since point_multiply is static we can guarantee that ctx != NULL.
 290      */
 291     BN_CTX_start(ctx);
 292     x1 = BN_CTX_get(ctx);
 293     z1 = BN_CTX_get(ctx);
 294     if (z1 == NULL)
 295         goto err;
 296
 297     x2 = &r->X;
 298     z2 = &r->Y;
 299
 300     bn_wexpand(x1, group->field.top);
 301     bn_wexpand(z1, group->field.top);
 302     bn_wexpand(x2, group->field.top);
 303     bn_wexpand(z2, group->field.top);
 304
 305     if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
 306         goto err;               /* x1 = x */
 307     if (!BN_one(z1))
 308         goto err;               /* z1 = 1 */
 309     if (!group->meth->field_sqr(group, z2, x1, ctx))
 310         goto err;               /* z2 = x1^2 = x^2 */
 311     if (!group->meth->field_sqr(group, x2, z2, ctx))
 312         goto err;
 313     if (!BN_GF2m_add(x2, x2, &group->b))
 314         goto err;               /* x2 = x^4 + b */
 315
 316     /* find top most bit and go one past it */
 317     i = scalar->top - 1;
 318     mask = BN_TBIT;
 319     word = scalar->d[i];
 320     while (!(word & mask))
 321         mask >>= 1;
 322     mask >>= 1;
 323     /* if top most bit was at word break, go to next word */
 324     if (!mask) {
 325         i--;
 326         mask = BN_TBIT;
 327     }
 328
 329     for (; i >= 0; i--) {
 330         word = scalar->d[i];
 331         while (mask) {
 332             BN_consttime_swap(word & mask, x1, x2, group->field.top);
 333             BN_consttime_swap(word & mask, z1, z2, group->field.top);
 334             if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
 335                 goto err;
 336             if (!gf2m_Mdouble(group, x1, z1, ctx))
 337                 goto err;
 338             BN_consttime_swap(word & mask, x1, x2, group->field.top);
 339             BN_consttime_swap(word & mask, z1, z2, group->field.top);
 340             mask >>= 1;
 341         }
 342         mask = BN_TBIT;
 343     }
 344
 345     /* convert out of "projective" coordinates */
 346     i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
 347     if (i == 0)
 348         goto err;
 349     else if (i == 1) {
 350         if (!EC_POINT_set_to_infinity(group, r))
 351             goto err;
 352     } else {
 353         if (!BN_one(&r->Z))
 354             goto err;
 355         r->Z_is_one = 1;
 356     }
 357
 358     /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
 359     BN_set_negative(&r->X, 0);
 360     BN_set_negative(&r->Y, 0);
 361
 362     ret = 1;
 363
 364  err:
 365     BN_CTX_end(ctx);
 366     return ret;
 367 }
 368
 369 /*-
 370  * Computes the sum
 371  *     scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
 372  * gracefully ignoring NULL scalar values.
 373  */
 374 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
 375                        const BIGNUM *scalar, size_t num,
 376                        const EC_POINT *points[], const BIGNUM *scalars[],
 377                        BN_CTX *ctx)
 378 {
 379     BN_CTX *new_ctx = NULL;
 380     int ret = 0;
 381     size_t i;
 382     EC_POINT *p = NULL;
 383     EC_POINT *acc = NULL;
 384
 385     if (ctx == NULL) {
 386         ctx = new_ctx = BN_CTX_new();
 387         if (ctx == NULL)
 388             return 0;
 389     }
 390
 391     /*
 392      * This implementation is more efficient than the wNAF implementation for
 393      * 2 or fewer points.  Use the ec_wNAF_mul implementation for 3 or more
 394      * points, or if we can perform a fast multiplication based on
 395      * precomputation.
 396      */
 397     if ((scalar && (num > 1)) || (num > 2)
 398         || (num == 0 && EC_GROUP_have_precompute_mult(group))) {
 399         ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
 400         goto err;
 401     }
 402
 403     if ((p = EC_POINT_new(group)) == NULL)
 404         goto err;
 405     if ((acc = EC_POINT_new(group)) == NULL)
 406         goto err;
 407
 408     if (!EC_POINT_set_to_infinity(group, acc))
 409         goto err;
 410
 411     if (scalar) {
 412         if (!ec_GF2m_montgomery_point_multiply
 413             (group, p, scalar, group->generator, ctx))
 414             goto err;
 415         if (BN_is_negative(scalar))
 416             if (!group->meth->invert(group, p, ctx))
 417                 goto err;
 418         if (!group->meth->add(group, acc, acc, p, ctx))
 419             goto err;
 420     }
 421
 422     for (i = 0; i < num; i++) {
 423         if (!ec_GF2m_montgomery_point_multiply
 424             (group, p, scalars[i], points[i], ctx))
 425             goto err;
 426         if (BN_is_negative(scalars[i]))
 427             if (!group->meth->invert(group, p, ctx))
 428                 goto err;
 429         if (!group->meth->add(group, acc, acc, p, ctx))
 430             goto err;
 431     }
 432
 433     if (!EC_POINT_copy(r, acc))
 434         goto err;
 435
 436     ret = 1;
 437
 438  err:
 439     if (p)
 440         EC_POINT_free(p);
 441     if (acc)
 442         EC_POINT_free(acc);
 443     if (new_ctx != NULL)
 444         BN_CTX_free(new_ctx);
 445     return ret;
 446 }
 447
 448 /*
 449  * Precomputation for point multiplication: fall back to wNAF methods because
 450  * ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
 451  */
 452
 453 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 454 {
 455     return ec_wNAF_precompute_mult(group, ctx);
 456 }
 457
 458 int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
 459 {
 460     return ec_wNAF_have_precompute_mult(group);
 461 }
 462
 463 #endif