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