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 "internal.h"
76 
77 
ec_GFp_mont_group_init(EC_GROUP * group)78 int ec_GFp_mont_group_init(EC_GROUP *group) {
79   int ok;
80 
81   ok = ec_GFp_simple_group_init(group);
82   group->mont = NULL;
83   return ok;
84 }
85 
ec_GFp_mont_group_finish(EC_GROUP * group)86 void ec_GFp_mont_group_finish(EC_GROUP *group) {
87   BN_MONT_CTX_free(group->mont);
88   group->mont = NULL;
89   ec_GFp_simple_group_finish(group);
90 }
91 
ec_GFp_mont_group_copy(EC_GROUP * dest,const EC_GROUP * src)92 int ec_GFp_mont_group_copy(EC_GROUP *dest, const EC_GROUP *src) {
93   BN_MONT_CTX_free(dest->mont);
94   dest->mont = NULL;
95 
96   if (!ec_GFp_simple_group_copy(dest, src)) {
97     return 0;
98   }
99 
100   if (src->mont != NULL) {
101     dest->mont = BN_MONT_CTX_new();
102     if (dest->mont == NULL) {
103       return 0;
104     }
105     if (!BN_MONT_CTX_copy(dest->mont, src->mont)) {
106       goto err;
107     }
108   }
109 
110   return 1;
111 
112 err:
113   BN_MONT_CTX_free(dest->mont);
114   dest->mont = NULL;
115   return 0;
116 }
117 
ec_GFp_mont_group_set_curve(EC_GROUP * group,const BIGNUM * p,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)118 int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p,
119                                 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
120   BN_CTX *new_ctx = NULL;
121   BN_MONT_CTX *mont = NULL;
122   int ret = 0;
123 
124   BN_MONT_CTX_free(group->mont);
125   group->mont = NULL;
126 
127   if (ctx == NULL) {
128     ctx = new_ctx = BN_CTX_new();
129     if (ctx == NULL) {
130       return 0;
131     }
132   }
133 
134   mont = BN_MONT_CTX_new();
135   if (mont == NULL) {
136     goto err;
137   }
138   if (!BN_MONT_CTX_set(mont, p, ctx)) {
139     OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
140     goto err;
141   }
142 
143   group->mont = mont;
144   mont = NULL;
145 
146   ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
147 
148   if (!ret) {
149     BN_MONT_CTX_free(group->mont);
150     group->mont = NULL;
151   }
152 
153 err:
154   BN_CTX_free(new_ctx);
155   BN_MONT_CTX_free(mont);
156   return ret;
157 }
158 
ec_GFp_mont_field_mul(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)159 int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
160                           const BIGNUM *b, BN_CTX *ctx) {
161   if (group->mont == NULL) {
162     OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
163     return 0;
164   }
165 
166   return BN_mod_mul_montgomery(r, a, b, group->mont, ctx);
167 }
168 
ec_GFp_mont_field_sqr(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)169 int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
170                           BN_CTX *ctx) {
171   if (group->mont == NULL) {
172     OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
173     return 0;
174   }
175 
176   return BN_mod_mul_montgomery(r, a, a, group->mont, ctx);
177 }
178 
ec_GFp_mont_field_encode(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)179 int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
180                              BN_CTX *ctx) {
181   if (group->mont == NULL) {
182     OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
183     return 0;
184   }
185 
186   return BN_to_montgomery(r, a, group->mont, ctx);
187 }
188 
ec_GFp_mont_field_decode(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)189 int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
190                              BN_CTX *ctx) {
191   if (group->mont == NULL) {
192     OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
193     return 0;
194   }
195 
196   return BN_from_montgomery(r, a, group->mont, ctx);
197 }
198 
ec_GFp_mont_point_get_affine_coordinates(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)199 static int ec_GFp_mont_point_get_affine_coordinates(const EC_GROUP *group,
200                                                     const EC_POINT *point,
201                                                     BIGNUM *x, BIGNUM *y,
202                                                     BN_CTX *ctx) {
203   if (EC_POINT_is_at_infinity(group, point)) {
204     OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
205     return 0;
206   }
207 
208   BN_CTX *new_ctx = NULL;
209   if (ctx == NULL) {
210     ctx = new_ctx = BN_CTX_new();
211     if (ctx == NULL) {
212       return 0;
213     }
214   }
215 
216   int ret = 0;
217 
218   BN_CTX_start(ctx);
219 
220   if (BN_cmp(&point->Z, &group->one) == 0) {
221     /* |point| is already affine. */
222     if (x != NULL && !BN_from_montgomery(x, &point->X, group->mont, ctx)) {
223       goto err;
224     }
225     if (y != NULL && !BN_from_montgomery(y, &point->Y, group->mont, ctx)) {
226       goto err;
227     }
228   } else {
229     /* transform  (X, Y, Z)  into  (x, y) := (X/Z^2, Y/Z^3) */
230 
231     BIGNUM *Z_1 = BN_CTX_get(ctx);
232     BIGNUM *Z_2 = BN_CTX_get(ctx);
233     BIGNUM *Z_3 = BN_CTX_get(ctx);
234     if (Z_1 == NULL ||
235         Z_2 == NULL ||
236         Z_3 == NULL) {
237       goto err;
238     }
239 
240     /* The straightforward way to calculate the inverse of a Montgomery-encoded
241      * value where the result is Montgomery-encoded is:
242      *
243      *    |BN_from_montgomery| + invert + |BN_to_montgomery|.
244      *
245      * This is equivalent, but more efficient, because |BN_from_montgomery|
246      * is more efficient (at least in theory) than |BN_to_montgomery|, since it
247      * doesn't have to do the multiplication before the reduction.
248      *
249      * Use Fermat's Little Theorem instead of |BN_mod_inverse_odd| since this
250      * inversion may be done as the final step of private key operations.
251      * Unfortunately, this is suboptimal for ECDSA verification. */
252     if (!BN_from_montgomery(Z_1, &point->Z, group->mont, ctx) ||
253         !BN_from_montgomery(Z_1, Z_1, group->mont, ctx) ||
254         !bn_mod_inverse_prime(Z_1, Z_1, &group->field, ctx, group->mont)) {
255       goto err;
256     }
257 
258     if (!BN_mod_mul_montgomery(Z_2, Z_1, Z_1, group->mont, ctx)) {
259       goto err;
260     }
261 
262     /* Instead of using |BN_from_montgomery| to convert the |x| coordinate
263      * and then calling |BN_from_montgomery| again to convert the |y|
264      * coordinate below, convert the common factor |Z_2| once now, saving one
265      * reduction. */
266     if (!BN_from_montgomery(Z_2, Z_2, group->mont, ctx)) {
267       goto err;
268     }
269 
270     if (x != NULL) {
271       if (!BN_mod_mul_montgomery(x, &point->X, Z_2, group->mont, ctx)) {
272         goto err;
273       }
274     }
275 
276     if (y != NULL) {
277       if (!BN_mod_mul_montgomery(Z_3, Z_2, Z_1, group->mont, ctx) ||
278           !BN_mod_mul_montgomery(y, &point->Y, Z_3, group->mont, ctx)) {
279         goto err;
280       }
281     }
282   }
283 
284   ret = 1;
285 
286 err:
287   BN_CTX_end(ctx);
288   BN_CTX_free(new_ctx);
289   return ret;
290 }
291 
292 const EC_METHOD EC_GFp_mont_method = {
293     ec_GFp_mont_group_init,
294     ec_GFp_mont_group_finish,
295     ec_GFp_mont_group_copy,
296     ec_GFp_mont_group_set_curve,
297     ec_GFp_mont_point_get_affine_coordinates,
298     ec_wNAF_mul /* XXX: Not constant time. */,
299     ec_GFp_mont_field_mul,
300     ec_GFp_mont_field_sqr,
301     ec_GFp_mont_field_encode,
302     ec_GFp_mont_field_decode,
303 };
304