1 /* $OpenBSD: ec2_oct.c,v 1.16 2021/05/03 14:42:45 tb Exp $ */
2 /* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
4 *
5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7 * to the OpenSSL project.
8 *
9 * The ECC Code is licensed pursuant to the OpenSSL open source
10 * license provided below.
11 *
12 * The software is originally written by Sheueling Chang Shantz and
13 * Douglas Stebila of Sun Microsystems Laboratories.
14 *
15 */
16 /* ====================================================================
17 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
18 *
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
21 * are met:
22 *
23 * 1. Redistributions of source code must retain the above copyright
24 * notice, this list of conditions and the following disclaimer.
25 *
26 * 2. Redistributions in binary form must reproduce the above copyright
27 * notice, this list of conditions and the following disclaimer in
28 * the documentation and/or other materials provided with the
29 * distribution.
30 *
31 * 3. All advertising materials mentioning features or use of this
32 * software must display the following acknowledgment:
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
35 *
36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
37 * endorse or promote products derived from this software without
38 * prior written permission. For written permission, please contact
39 * openssl-core@openssl.org.
40 *
41 * 5. Products derived from this software may not be called "OpenSSL"
42 * nor may "OpenSSL" appear in their names without prior written
43 * permission of the OpenSSL Project.
44 *
45 * 6. Redistributions of any form whatsoever must retain the following
46 * acknowledgment:
47 * "This product includes software developed by the OpenSSL Project
48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
49 *
50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
61 * OF THE POSSIBILITY OF SUCH DAMAGE.
62 * ====================================================================
63 *
64 * This product includes cryptographic software written by Eric Young
65 * (eay@cryptsoft.com). This product includes software written by Tim
66 * Hudson (tjh@cryptsoft.com).
67 *
68 */
69
70 #include <openssl/opensslconf.h>
71
72 #include <openssl/err.h>
73
74 #include "ec_lcl.h"
75
76 #ifndef OPENSSL_NO_EC2M
77
78 /* Calculates and sets the affine coordinates of an EC_POINT from the given
79 * compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
80 * Note that the simple implementation only uses affine coordinates.
81 *
82 * The method is from the following publication:
83 *
84 * Harper, Menezes, Vanstone:
85 * "Public-Key Cryptosystems with Very Small Key Lengths",
86 * EUROCRYPT '92, Springer-Verlag LNCS 658,
87 * published February 1993
88 *
89 * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
90 * the same method, but claim no priority date earlier than July 29, 1994
91 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
92 */
93 int
ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x_,int y_bit,BN_CTX * ctx)94 ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
95 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
96 {
97 BN_CTX *new_ctx = NULL;
98 BIGNUM *tmp, *x, *y, *z;
99 int ret = 0, z0;
100
101 /* clear error queue */
102 ERR_clear_error();
103
104 if (ctx == NULL) {
105 ctx = new_ctx = BN_CTX_new();
106 if (ctx == NULL)
107 return 0;
108 }
109 y_bit = (y_bit != 0) ? 1 : 0;
110
111 BN_CTX_start(ctx);
112 if ((tmp = BN_CTX_get(ctx)) == NULL)
113 goto err;
114 if ((x = BN_CTX_get(ctx)) == NULL)
115 goto err;
116 if ((y = BN_CTX_get(ctx)) == NULL)
117 goto err;
118 if ((z = BN_CTX_get(ctx)) == NULL)
119 goto err;
120
121 if (!BN_GF2m_mod_arr(x, x_, group->poly))
122 goto err;
123 if (BN_is_zero(x)) {
124 if (y_bit != 0) {
125 ECerror(EC_R_INVALID_COMPRESSED_POINT);
126 goto err;
127 }
128 if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx))
129 goto err;
130 } else {
131 if (!group->meth->field_sqr(group, tmp, x, ctx))
132 goto err;
133 if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx))
134 goto err;
135 if (!BN_GF2m_add(tmp, &group->a, tmp))
136 goto err;
137 if (!BN_GF2m_add(tmp, x, tmp))
138 goto err;
139 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) {
140 unsigned long err = ERR_peek_last_error();
141
142 if (ERR_GET_LIB(err) == ERR_LIB_BN &&
143 ERR_GET_REASON(err) == BN_R_NO_SOLUTION) {
144 ERR_clear_error();
145 ECerror(EC_R_INVALID_COMPRESSED_POINT);
146 } else
147 ECerror(ERR_R_BN_LIB);
148 goto err;
149 }
150 z0 = (BN_is_odd(z)) ? 1 : 0;
151 if (!group->meth->field_mul(group, y, x, z, ctx))
152 goto err;
153 if (z0 != y_bit) {
154 if (!BN_GF2m_add(y, y, x))
155 goto err;
156 }
157 }
158
159 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
160 goto err;
161
162 ret = 1;
163
164 err:
165 BN_CTX_end(ctx);
166 BN_CTX_free(new_ctx);
167 return ret;
168 }
169
170
171 /* Converts an EC_POINT to an octet string.
172 * If buf is NULL, the encoded length will be returned.
173 * If the length len of buf is smaller than required an error will be returned.
174 */
175 size_t
ec_GF2m_simple_point2oct(const EC_GROUP * group,const EC_POINT * point,point_conversion_form_t form,unsigned char * buf,size_t len,BN_CTX * ctx)176 ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point,
177 point_conversion_form_t form,
178 unsigned char *buf, size_t len, BN_CTX * ctx)
179 {
180 size_t ret;
181 BN_CTX *new_ctx = NULL;
182 int used_ctx = 0;
183 BIGNUM *x, *y, *yxi;
184 size_t field_len, i, skip;
185
186 if ((form != POINT_CONVERSION_COMPRESSED)
187 && (form != POINT_CONVERSION_UNCOMPRESSED)
188 && (form != POINT_CONVERSION_HYBRID)) {
189 ECerror(EC_R_INVALID_FORM);
190 goto err;
191 }
192 if (EC_POINT_is_at_infinity(group, point) > 0) {
193 /* encodes to a single 0 octet */
194 if (buf != NULL) {
195 if (len < 1) {
196 ECerror(EC_R_BUFFER_TOO_SMALL);
197 return 0;
198 }
199 buf[0] = 0;
200 }
201 return 1;
202 }
203 /* ret := required output buffer length */
204 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
205 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len :
206 1 + 2 * field_len;
207
208 /* if 'buf' is NULL, just return required length */
209 if (buf != NULL) {
210 if (len < ret) {
211 ECerror(EC_R_BUFFER_TOO_SMALL);
212 goto err;
213 }
214 if (ctx == NULL) {
215 ctx = new_ctx = BN_CTX_new();
216 if (ctx == NULL)
217 return 0;
218 }
219 BN_CTX_start(ctx);
220 used_ctx = 1;
221 if ((x = BN_CTX_get(ctx)) == NULL)
222 goto err;
223 if ((y = BN_CTX_get(ctx)) == NULL)
224 goto err;
225 if ((yxi = BN_CTX_get(ctx)) == NULL)
226 goto err;
227
228 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
229 goto err;
230
231 buf[0] = form;
232 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) {
233 if (!group->meth->field_div(group, yxi, y, x, ctx))
234 goto err;
235 if (BN_is_odd(yxi))
236 buf[0]++;
237 }
238 i = 1;
239
240 skip = field_len - BN_num_bytes(x);
241 if (skip > field_len) {
242 ECerror(ERR_R_INTERNAL_ERROR);
243 goto err;
244 }
245 while (skip > 0) {
246 buf[i++] = 0;
247 skip--;
248 }
249 skip = BN_bn2bin(x, buf + i);
250 i += skip;
251 if (i != 1 + field_len) {
252 ECerror(ERR_R_INTERNAL_ERROR);
253 goto err;
254 }
255 if (form == POINT_CONVERSION_UNCOMPRESSED ||
256 form == POINT_CONVERSION_HYBRID) {
257 skip = field_len - BN_num_bytes(y);
258 if (skip > field_len) {
259 ECerror(ERR_R_INTERNAL_ERROR);
260 goto err;
261 }
262 while (skip > 0) {
263 buf[i++] = 0;
264 skip--;
265 }
266 skip = BN_bn2bin(y, buf + i);
267 i += skip;
268 }
269 if (i != ret) {
270 ECerror(ERR_R_INTERNAL_ERROR);
271 goto err;
272 }
273 }
274 if (used_ctx)
275 BN_CTX_end(ctx);
276 BN_CTX_free(new_ctx);
277 return ret;
278
279 err:
280 if (used_ctx)
281 BN_CTX_end(ctx);
282 BN_CTX_free(new_ctx);
283 return 0;
284 }
285
286
287 /*
288 * Converts an octet string representation to an EC_POINT.
289 * Note that the simple implementation only uses affine coordinates.
290 */
291 int
ec_GF2m_simple_oct2point(const EC_GROUP * group,EC_POINT * point,const unsigned char * buf,size_t len,BN_CTX * ctx)292 ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
293 const unsigned char *buf, size_t len, BN_CTX *ctx)
294 {
295 point_conversion_form_t form;
296 int y_bit;
297 BN_CTX *new_ctx = NULL;
298 BIGNUM *x, *y, *yxi;
299 size_t field_len, enc_len;
300 int ret = 0;
301
302 if (len == 0) {
303 ECerror(EC_R_BUFFER_TOO_SMALL);
304 return 0;
305 }
306
307 /*
308 * The first octet is the point conversion octet PC, see X9.62, page 4
309 * and section 4.4.2. It must be:
310 * 0x00 for the point at infinity
311 * 0x02 or 0x03 for compressed form
312 * 0x04 for uncompressed form
313 * 0x06 or 0x07 for hybrid form.
314 * For compressed or hybrid forms, we store the last bit of buf[0] as
315 * y_bit and clear it from buf[0] so as to obtain a POINT_CONVERSION_*.
316 * We error if buf[0] contains any but the above values.
317 */
318 y_bit = buf[0] & 1;
319 form = buf[0] & ~1U;
320
321 if (form != 0 && form != POINT_CONVERSION_COMPRESSED &&
322 form != POINT_CONVERSION_UNCOMPRESSED &&
323 form != POINT_CONVERSION_HYBRID) {
324 ECerror(EC_R_INVALID_ENCODING);
325 return 0;
326 }
327 if (form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) {
328 if (y_bit != 0) {
329 ECerror(EC_R_INVALID_ENCODING);
330 return 0;
331 }
332 }
333
334 /* The point at infinity is represented by a single zero octet. */
335 if (form == 0) {
336 if (len != 1) {
337 ECerror(EC_R_INVALID_ENCODING);
338 return 0;
339 }
340 return EC_POINT_set_to_infinity(group, point);
341 }
342
343 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
344 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len :
345 1 + 2 * field_len;
346
347 if (len != enc_len) {
348 ECerror(EC_R_INVALID_ENCODING);
349 return 0;
350 }
351
352 if (ctx == NULL) {
353 ctx = new_ctx = BN_CTX_new();
354 if (ctx == NULL)
355 return 0;
356 }
357 BN_CTX_start(ctx);
358 if ((x = BN_CTX_get(ctx)) == NULL)
359 goto err;
360 if ((y = BN_CTX_get(ctx)) == NULL)
361 goto err;
362 if ((yxi = BN_CTX_get(ctx)) == NULL)
363 goto err;
364
365 if (!BN_bin2bn(buf + 1, field_len, x))
366 goto err;
367 if (BN_ucmp(x, &group->field) >= 0) {
368 ECerror(EC_R_INVALID_ENCODING);
369 goto err;
370 }
371 if (form == POINT_CONVERSION_COMPRESSED) {
372 /*
373 * EC_POINT_set_compressed_coordinates checks that the
374 * point is on the curve as required by X9.62.
375 */
376 if (!EC_POINT_set_compressed_coordinates(group, point, x, y_bit, ctx))
377 goto err;
378 } else {
379 if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
380 goto err;
381 if (BN_ucmp(y, &group->field) >= 0) {
382 ECerror(EC_R_INVALID_ENCODING);
383 goto err;
384 }
385 if (form == POINT_CONVERSION_HYBRID) {
386 /*
387 * Check that the form in the encoding was set
388 * correctly according to X9.62 4.4.2.a, 4(c),
389 * see also first paragraph of X9.62 4.4.1.b.
390 */
391 if (BN_is_zero(x)) {
392 if (y_bit != 0) {
393 ECerror(EC_R_INVALID_ENCODING);
394 goto err;
395 }
396 } else {
397 if (!group->meth->field_div(group, yxi, y, x,
398 ctx))
399 goto err;
400 if (y_bit != BN_is_odd(yxi)) {
401 ECerror(EC_R_INVALID_ENCODING);
402 goto err;
403 }
404 }
405 }
406 /*
407 * EC_POINT_set_affine_coordinates checks that the
408 * point is on the curve as required by X9.62.
409 */
410 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
411 goto err;
412 }
413
414 ret = 1;
415
416 err:
417 BN_CTX_end(ctx);
418 BN_CTX_free(new_ctx);
419 return ret;
420 }
421 #endif
422