1/* Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
2 * ====================================================================
3 * Copyright (c) 1998-2005 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 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
57 *
58 * Portions of the attached software ("Contribution") are developed by
59 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
60 *
61 * The Contribution is licensed pursuant to the OpenSSL open source
62 * license provided above.
63 *
64 * The elliptic curve binary polynomial software is originally written by
65 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
66 * Laboratories. */
67
68#include <openssl/ec.h>
69
70#include <openssl/bn.h>
71#include <openssl/err.h>
72#include <openssl/mem.h>
73
74#include "../bn/internal.h"
75#include "../delocate.h"
76#include "internal.h"
77
78
79int ec_GFp_mont_group_init(EC_GROUP *group) {
80  int ok;
81
82  ok = ec_GFp_simple_group_init(group);
83  group->mont = NULL;
84  return ok;
85}
86
87void ec_GFp_mont_group_finish(EC_GROUP *group) {
88  BN_MONT_CTX_free(group->mont);
89  group->mont = NULL;
90  ec_GFp_simple_group_finish(group);
91}
92
93int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p,
94                                const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
95  BN_CTX *new_ctx = NULL;
96  int ret = 0;
97
98  BN_MONT_CTX_free(group->mont);
99  group->mont = NULL;
100
101  if (ctx == NULL) {
102    ctx = new_ctx = BN_CTX_new();
103    if (ctx == NULL) {
104      return 0;
105    }
106  }
107
108  group->mont = BN_MONT_CTX_new_for_modulus(p, ctx);
109  if (group->mont == NULL) {
110    OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
111    goto err;
112  }
113
114  ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
115
116  if (!ret) {
117    BN_MONT_CTX_free(group->mont);
118    group->mont = NULL;
119  }
120
121err:
122  BN_CTX_free(new_ctx);
123  return ret;
124}
125
126int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
127                          const BIGNUM *b, BN_CTX *ctx) {
128  if (group->mont == NULL) {
129    OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
130    return 0;
131  }
132
133  return BN_mod_mul_montgomery(r, a, b, group->mont, ctx);
134}
135
136int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
137                          BN_CTX *ctx) {
138  if (group->mont == NULL) {
139    OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
140    return 0;
141  }
142
143  return BN_mod_mul_montgomery(r, a, a, group->mont, ctx);
144}
145
146int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
147                             BN_CTX *ctx) {
148  if (group->mont == NULL) {
149    OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
150    return 0;
151  }
152
153  return BN_to_montgomery(r, a, group->mont, ctx);
154}
155
156int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
157                             BN_CTX *ctx) {
158  if (group->mont == NULL) {
159    OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
160    return 0;
161  }
162
163  return BN_from_montgomery(r, a, group->mont, ctx);
164}
165
166static int ec_GFp_mont_point_get_affine_coordinates(const EC_GROUP *group,
167                                                    const EC_POINT *point,
168                                                    BIGNUM *x, BIGNUM *y,
169                                                    BN_CTX *ctx) {
170  if (EC_POINT_is_at_infinity(group, point)) {
171    OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
172    return 0;
173  }
174
175  BN_CTX *new_ctx = NULL;
176  if (ctx == NULL) {
177    ctx = new_ctx = BN_CTX_new();
178    if (ctx == NULL) {
179      return 0;
180    }
181  }
182
183  int ret = 0;
184
185  BN_CTX_start(ctx);
186
187  if (BN_cmp(&point->Z, &group->one) == 0) {
188    // |point| is already affine.
189    if (x != NULL && !BN_from_montgomery(x, &point->X, group->mont, ctx)) {
190      goto err;
191    }
192    if (y != NULL && !BN_from_montgomery(y, &point->Y, group->mont, ctx)) {
193      goto err;
194    }
195  } else {
196    // transform  (X, Y, Z)  into  (x, y) := (X/Z^2, Y/Z^3)
197
198    BIGNUM *Z_1 = BN_CTX_get(ctx);
199    BIGNUM *Z_2 = BN_CTX_get(ctx);
200    BIGNUM *Z_3 = BN_CTX_get(ctx);
201    if (Z_1 == NULL ||
202        Z_2 == NULL ||
203        Z_3 == NULL) {
204      goto err;
205    }
206
207    // The straightforward way to calculate the inverse of a Montgomery-encoded
208    // value where the result is Montgomery-encoded is:
209    //
210    //    |BN_from_montgomery| + invert + |BN_to_montgomery|.
211    //
212    // This is equivalent, but more efficient, because |BN_from_montgomery|
213    // is more efficient (at least in theory) than |BN_to_montgomery|, since it
214    // doesn't have to do the multiplication before the reduction.
215    //
216    // Use Fermat's Little Theorem instead of |BN_mod_inverse_odd| since this
217    // inversion may be done as the final step of private key operations.
218    // Unfortunately, this is suboptimal for ECDSA verification.
219    if (!BN_from_montgomery(Z_1, &point->Z, group->mont, ctx) ||
220        !BN_from_montgomery(Z_1, Z_1, group->mont, ctx) ||
221        !bn_mod_inverse_prime(Z_1, Z_1, &group->field, ctx, group->mont)) {
222      goto err;
223    }
224
225    if (!BN_mod_mul_montgomery(Z_2, Z_1, Z_1, group->mont, ctx)) {
226      goto err;
227    }
228
229    // Instead of using |BN_from_montgomery| to convert the |x| coordinate
230    // and then calling |BN_from_montgomery| again to convert the |y|
231    // coordinate below, convert the common factor |Z_2| once now, saving one
232    // reduction.
233    if (!BN_from_montgomery(Z_2, Z_2, group->mont, ctx)) {
234      goto err;
235    }
236
237    if (x != NULL) {
238      if (!BN_mod_mul_montgomery(x, &point->X, Z_2, group->mont, ctx)) {
239        goto err;
240      }
241    }
242
243    if (y != NULL) {
244      if (!BN_mod_mul_montgomery(Z_3, Z_2, Z_1, group->mont, ctx) ||
245          !BN_mod_mul_montgomery(y, &point->Y, Z_3, group->mont, ctx)) {
246        goto err;
247      }
248    }
249  }
250
251  ret = 1;
252
253err:
254  BN_CTX_end(ctx);
255  BN_CTX_free(new_ctx);
256  return ret;
257}
258
259DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_mont_method) {
260  out->group_init = ec_GFp_mont_group_init;
261  out->group_finish = ec_GFp_mont_group_finish;
262  out->group_set_curve = ec_GFp_mont_group_set_curve;
263  out->point_get_affine_coordinates = ec_GFp_mont_point_get_affine_coordinates;
264  out->mul = ec_wNAF_mul /* XXX: Not constant time. */;
265  out->mul_public = ec_wNAF_mul;
266  out->field_mul = ec_GFp_mont_field_mul;
267  out->field_sqr = ec_GFp_mont_field_sqr;
268  out->field_encode = ec_GFp_mont_field_encode;
269  out->field_decode = ec_GFp_mont_field_decode;
270}
271