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1 /* Originally written by Bodo Moeller 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 
73 #include "internal.h"
74 
75 
ec_GFp_simple_point2oct(const EC_GROUP * group,const EC_RAW_POINT * point,point_conversion_form_t form,uint8_t * buf,size_t len)76 static size_t ec_GFp_simple_point2oct(const EC_GROUP *group,
77                                       const EC_RAW_POINT *point,
78                                       point_conversion_form_t form,
79                                       uint8_t *buf, size_t len) {
80   if (form != POINT_CONVERSION_COMPRESSED &&
81       form != POINT_CONVERSION_UNCOMPRESSED) {
82     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FORM);
83     return 0;
84   }
85 
86   if (ec_GFp_simple_is_at_infinity(group, point)) {
87     OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
88     return 0;
89   }
90 
91   const size_t field_len = BN_num_bytes(&group->field);
92   size_t output_len = 1 /* type byte */ + field_len;
93   if (form == POINT_CONVERSION_UNCOMPRESSED) {
94     // Uncompressed points have a second coordinate.
95     output_len += field_len;
96   }
97 
98   // if 'buf' is NULL, just return required length
99   if (buf != NULL) {
100     if (len < output_len) {
101       OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
102       return 0;
103     }
104 
105     uint8_t y_buf[EC_MAX_BYTES];
106     size_t field_len_out;
107     if (!ec_point_get_affine_coordinate_bytes(
108             group, buf + 1 /* x */,
109             form == POINT_CONVERSION_COMPRESSED ? y_buf : buf + 1 + field_len,
110             &field_len_out, field_len, point)) {
111       return 0;
112     }
113 
114     if (field_len_out != field_len) {
115       OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
116       return 0;
117     }
118 
119     if (form == POINT_CONVERSION_COMPRESSED) {
120       buf[0] = form + (y_buf[field_len - 1] & 1);
121     } else {
122       buf[0] = form;
123     }
124   }
125 
126   return output_len;
127 }
128 
ec_GFp_simple_oct2point(const EC_GROUP * group,EC_POINT * point,const uint8_t * buf,size_t len,BN_CTX * ctx)129 static int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
130                                    const uint8_t *buf, size_t len,
131                                    BN_CTX *ctx) {
132   BN_CTX *new_ctx = NULL;
133   int ret = 0, used_ctx = 0;
134 
135   if (len == 0) {
136     OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
137     goto err;
138   }
139 
140   point_conversion_form_t form = buf[0];
141   const int y_bit = form & 1;
142   form = form & ~1U;
143   if ((form != POINT_CONVERSION_COMPRESSED &&
144        form != POINT_CONVERSION_UNCOMPRESSED) ||
145       (form == POINT_CONVERSION_UNCOMPRESSED && y_bit)) {
146     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
147     goto err;
148   }
149 
150   const size_t field_len = BN_num_bytes(&group->field);
151   size_t enc_len = 1 /* type byte */ + field_len;
152   if (form == POINT_CONVERSION_UNCOMPRESSED) {
153     // Uncompressed points have a second coordinate.
154     enc_len += field_len;
155   }
156 
157   if (len != enc_len) {
158     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
159     goto err;
160   }
161 
162   if (ctx == NULL) {
163     ctx = new_ctx = BN_CTX_new();
164     if (ctx == NULL) {
165       goto err;
166     }
167   }
168 
169   BN_CTX_start(ctx);
170   used_ctx = 1;
171   BIGNUM *x = BN_CTX_get(ctx);
172   BIGNUM *y = BN_CTX_get(ctx);
173   if (x == NULL || y == NULL) {
174     goto err;
175   }
176 
177   if (!BN_bin2bn(buf + 1, field_len, x)) {
178     goto err;
179   }
180   if (BN_ucmp(x, &group->field) >= 0) {
181     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
182     goto err;
183   }
184 
185   if (form == POINT_CONVERSION_COMPRESSED) {
186     if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) {
187       goto err;
188     }
189   } else {
190     if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) {
191       goto err;
192     }
193     if (BN_ucmp(y, &group->field) >= 0) {
194       OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
195       goto err;
196     }
197 
198     if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
199       goto err;
200     }
201   }
202 
203   ret = 1;
204 
205 err:
206   if (used_ctx) {
207     BN_CTX_end(ctx);
208   }
209   BN_CTX_free(new_ctx);
210   return ret;
211 }
212 
EC_POINT_oct2point(const EC_GROUP * group,EC_POINT * point,const uint8_t * buf,size_t len,BN_CTX * ctx)213 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point,
214                        const uint8_t *buf, size_t len, BN_CTX *ctx) {
215   if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
216     OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
217     return 0;
218   }
219   return ec_GFp_simple_oct2point(group, point, buf, len, ctx);
220 }
221 
EC_POINT_point2oct(const EC_GROUP * group,const EC_POINT * point,point_conversion_form_t form,uint8_t * buf,size_t len,BN_CTX * ctx)222 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point,
223                           point_conversion_form_t form, uint8_t *buf,
224                           size_t len, BN_CTX *ctx) {
225   if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
226     OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
227     return 0;
228   }
229   return ec_GFp_simple_point2oct(group, &point->raw, form, buf, len);
230 }
231 
EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,int y_bit,BN_CTX * ctx)232 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
233                                             EC_POINT *point, const BIGNUM *x,
234                                             int y_bit, BN_CTX *ctx) {
235   if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
236     OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
237     return 0;
238   }
239 
240   if (BN_is_negative(x) || BN_cmp(x, &group->field) >= 0) {
241     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
242     return 0;
243   }
244 
245   BN_CTX *new_ctx = NULL;
246   int ret = 0;
247 
248   ERR_clear_error();
249 
250   if (ctx == NULL) {
251     ctx = new_ctx = BN_CTX_new();
252     if (ctx == NULL) {
253       return 0;
254     }
255   }
256 
257   y_bit = (y_bit != 0);
258 
259   BN_CTX_start(ctx);
260   BIGNUM *tmp1 = BN_CTX_get(ctx);
261   BIGNUM *tmp2 = BN_CTX_get(ctx);
262   BIGNUM *a = BN_CTX_get(ctx);
263   BIGNUM *b = BN_CTX_get(ctx);
264   BIGNUM *y = BN_CTX_get(ctx);
265   if (y == NULL ||
266       !EC_GROUP_get_curve_GFp(group, NULL, a, b, ctx)) {
267     goto err;
268   }
269 
270   // Recover y.  We have a Weierstrass equation
271   //     y^2 = x^3 + a*x + b,
272   // so  y  is one of the square roots of  x^3 + a*x + b.
273 
274   // tmp1 := x^3
275   if (!BN_mod_sqr(tmp2, x, &group->field, ctx) ||
276       !BN_mod_mul(tmp1, tmp2, x, &group->field, ctx)) {
277     goto err;
278   }
279 
280   // tmp1 := tmp1 + a*x
281   if (group->a_is_minus3) {
282     if (!bn_mod_lshift1_consttime(tmp2, x, &group->field, ctx) ||
283         !bn_mod_add_consttime(tmp2, tmp2, x, &group->field, ctx) ||
284         !bn_mod_sub_consttime(tmp1, tmp1, tmp2, &group->field, ctx)) {
285       goto err;
286     }
287   } else {
288     if (!BN_mod_mul(tmp2, a, x, &group->field, ctx) ||
289         !bn_mod_add_consttime(tmp1, tmp1, tmp2, &group->field, ctx)) {
290       goto err;
291     }
292   }
293 
294   // tmp1 := tmp1 + b
295   if (!bn_mod_add_consttime(tmp1, tmp1, b, &group->field, ctx)) {
296     goto err;
297   }
298 
299   if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) {
300     unsigned long err = ERR_peek_last_error();
301 
302     if (ERR_GET_LIB(err) == ERR_LIB_BN &&
303         ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) {
304       ERR_clear_error();
305       OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
306     } else {
307       OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
308     }
309     goto err;
310   }
311 
312   if (y_bit != BN_is_odd(y)) {
313     if (BN_is_zero(y)) {
314       OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSION_BIT);
315       goto err;
316     }
317     if (!BN_usub(y, &group->field, y)) {
318       goto err;
319     }
320   }
321   if (y_bit != BN_is_odd(y)) {
322     OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
323     goto err;
324   }
325 
326   if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
327     goto err;
328   }
329 
330   ret = 1;
331 
332 err:
333   BN_CTX_end(ctx);
334   BN_CTX_free(new_ctx);
335   return ret;
336 }
337