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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_POINT * point,point_conversion_form_t form,uint8_t * buf,size_t len,BN_CTX * ctx)76 static size_t ec_GFp_simple_point2oct(const EC_GROUP *group,
77                                       const EC_POINT *point,
78                                       point_conversion_form_t form,
79                                       uint8_t *buf, size_t len, BN_CTX *ctx) {
80   size_t ret = 0;
81   BN_CTX *new_ctx = NULL;
82   int used_ctx = 0;
83 
84   if ((form != POINT_CONVERSION_COMPRESSED) &&
85       (form != POINT_CONVERSION_UNCOMPRESSED)) {
86     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FORM);
87     goto err;
88   }
89 
90   if (EC_POINT_is_at_infinity(group, point)) {
91     OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
92     goto err;
93   }
94 
95   const size_t field_len = BN_num_bytes(&group->field);
96   size_t output_len = 1 /* type byte */ + field_len;
97   if (form == POINT_CONVERSION_UNCOMPRESSED) {
98     // Uncompressed points have a second coordinate.
99     output_len += field_len;
100   }
101 
102   // if 'buf' is NULL, just return required length
103   if (buf != NULL) {
104     if (len < output_len) {
105       OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
106       goto err;
107     }
108 
109     if (ctx == NULL) {
110       ctx = new_ctx = BN_CTX_new();
111       if (ctx == NULL) {
112         goto err;
113       }
114     }
115 
116     BN_CTX_start(ctx);
117     used_ctx = 1;
118     BIGNUM *x = BN_CTX_get(ctx);
119     BIGNUM *y = BN_CTX_get(ctx);
120     if (y == NULL) {
121       goto err;
122     }
123 
124     if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) {
125       goto err;
126     }
127 
128     if ((form == POINT_CONVERSION_COMPRESSED) &&
129         BN_is_odd(y)) {
130       buf[0] = form + 1;
131     } else {
132       buf[0] = form;
133     }
134     size_t i = 1;
135 
136     if (!BN_bn2bin_padded(buf + i, field_len, x)) {
137       OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
138       goto err;
139     }
140     i += field_len;
141 
142     if (form == POINT_CONVERSION_UNCOMPRESSED) {
143       if (!BN_bn2bin_padded(buf + i, field_len, y)) {
144         OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
145         goto err;
146       }
147       i += field_len;
148     }
149 
150     if (i != output_len) {
151       OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
152       goto err;
153     }
154   }
155 
156   ret = output_len;
157 
158 err:
159   if (used_ctx) {
160     BN_CTX_end(ctx);
161   }
162   BN_CTX_free(new_ctx);
163   return ret;
164 }
165 
ec_GFp_simple_oct2point(const EC_GROUP * group,EC_POINT * point,const uint8_t * buf,size_t len,BN_CTX * ctx)166 static int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
167                                    const uint8_t *buf, size_t len,
168                                    BN_CTX *ctx) {
169   BN_CTX *new_ctx = NULL;
170   int ret = 0, used_ctx = 0;
171 
172   if (len == 0) {
173     OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
174     goto err;
175   }
176 
177   point_conversion_form_t form = buf[0];
178   const int y_bit = form & 1;
179   form = form & ~1U;
180   if ((form != POINT_CONVERSION_COMPRESSED &&
181        form != POINT_CONVERSION_UNCOMPRESSED) ||
182       (form == POINT_CONVERSION_UNCOMPRESSED && y_bit)) {
183     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
184     goto err;
185   }
186 
187   const size_t field_len = BN_num_bytes(&group->field);
188   size_t enc_len = 1 /* type byte */ + field_len;
189   if (form == POINT_CONVERSION_UNCOMPRESSED) {
190     // Uncompressed points have a second coordinate.
191     enc_len += field_len;
192   }
193 
194   if (len != enc_len) {
195     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
196     goto err;
197   }
198 
199   if (ctx == NULL) {
200     ctx = new_ctx = BN_CTX_new();
201     if (ctx == NULL) {
202       goto err;
203     }
204   }
205 
206   BN_CTX_start(ctx);
207   used_ctx = 1;
208   BIGNUM *x = BN_CTX_get(ctx);
209   BIGNUM *y = BN_CTX_get(ctx);
210   if (x == NULL || y == NULL) {
211     goto err;
212   }
213 
214   if (!BN_bin2bn(buf + 1, field_len, x)) {
215     goto err;
216   }
217   if (BN_ucmp(x, &group->field) >= 0) {
218     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
219     goto err;
220   }
221 
222   if (form == POINT_CONVERSION_COMPRESSED) {
223     if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) {
224       goto err;
225     }
226   } else {
227     if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) {
228       goto err;
229     }
230     if (BN_ucmp(y, &group->field) >= 0) {
231       OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
232       goto err;
233     }
234 
235     if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
236       goto err;
237     }
238   }
239 
240   ret = 1;
241 
242 err:
243   if (used_ctx) {
244     BN_CTX_end(ctx);
245   }
246   BN_CTX_free(new_ctx);
247   return ret;
248 }
249 
EC_POINT_oct2point(const EC_GROUP * group,EC_POINT * point,const uint8_t * buf,size_t len,BN_CTX * ctx)250 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point,
251                        const uint8_t *buf, size_t len, BN_CTX *ctx) {
252   if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
253     OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
254     return 0;
255   }
256   return ec_GFp_simple_oct2point(group, point, buf, len, ctx);
257 }
258 
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)259 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point,
260                           point_conversion_form_t form, uint8_t *buf,
261                           size_t len, BN_CTX *ctx) {
262   if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
263     OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
264     return 0;
265   }
266   return ec_GFp_simple_point2oct(group, point, form, buf, len, ctx);
267 }
268 
EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,int y_bit,BN_CTX * ctx)269 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
270                                             EC_POINT *point, const BIGNUM *x,
271                                             int y_bit, BN_CTX *ctx) {
272   if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
273     OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
274     return 0;
275   }
276 
277   if (BN_is_negative(x) || BN_cmp(x, &group->field) >= 0) {
278     OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
279     return 0;
280   }
281 
282   BN_CTX *new_ctx = NULL;
283   int ret = 0;
284 
285   ERR_clear_error();
286 
287   if (ctx == NULL) {
288     ctx = new_ctx = BN_CTX_new();
289     if (ctx == NULL) {
290       return 0;
291     }
292   }
293 
294   y_bit = (y_bit != 0);
295 
296   BN_CTX_start(ctx);
297   BIGNUM *tmp1 = BN_CTX_get(ctx);
298   BIGNUM *tmp2 = BN_CTX_get(ctx);
299   BIGNUM *a = BN_CTX_get(ctx);
300   BIGNUM *b = BN_CTX_get(ctx);
301   BIGNUM *y = BN_CTX_get(ctx);
302   if (y == NULL ||
303       !EC_GROUP_get_curve_GFp(group, NULL, a, b, ctx)) {
304     goto err;
305   }
306 
307   // Recover y.  We have a Weierstrass equation
308   //     y^2 = x^3 + a*x + b,
309   // so  y  is one of the square roots of  x^3 + a*x + b.
310 
311   // tmp1 := x^3
312   if (!BN_mod_sqr(tmp2, x, &group->field, ctx) ||
313       !BN_mod_mul(tmp1, tmp2, x, &group->field, ctx)) {
314     goto err;
315   }
316 
317   // tmp1 := tmp1 + a*x
318   if (group->a_is_minus3) {
319     if (!BN_mod_lshift1_quick(tmp2, x, &group->field) ||
320         !BN_mod_add_quick(tmp2, tmp2, x, &group->field) ||
321         !BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) {
322       goto err;
323     }
324   } else {
325     if (!BN_mod_mul(tmp2, a, x, &group->field, ctx) ||
326         !BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) {
327       goto err;
328     }
329   }
330 
331   // tmp1 := tmp1 + b
332   if (!BN_mod_add_quick(tmp1, tmp1, b, &group->field)) {
333     goto err;
334   }
335 
336   if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) {
337     unsigned long err = ERR_peek_last_error();
338 
339     if (ERR_GET_LIB(err) == ERR_LIB_BN &&
340         ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) {
341       ERR_clear_error();
342       OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
343     } else {
344       OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
345     }
346     goto err;
347   }
348 
349   if (y_bit != BN_is_odd(y)) {
350     if (BN_is_zero(y)) {
351       OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSION_BIT);
352       goto err;
353     }
354     if (!BN_usub(y, &group->field, y)) {
355       goto err;
356     }
357   }
358   if (y_bit != BN_is_odd(y)) {
359     OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
360     goto err;
361   }
362 
363   if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
364     goto err;
365   }
366 
367   ret = 1;
368 
369 err:
370   BN_CTX_end(ctx);
371   BN_CTX_free(new_ctx);
372   return ret;
373 }
374