1 /*
2 * Copyright 2011-2021 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
4 *
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 */
10
11 #include <openssl/err.h>
12
13 #include "ec_local.h"
14
15 #ifndef OPENSSL_NO_EC2M
16
17 /*-
18 * Calculates and sets the affine coordinates of an EC_POINT from the given
19 * compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
20 * Note that the simple implementation only uses affine coordinates.
21 *
22 * The method is from the following publication:
23 *
24 * Harper, Menezes, Vanstone:
25 * "Public-Key Cryptosystems with Very Small Key Lengths",
26 * EUROCRYPT '92, Springer-Verlag LNCS 658,
27 * published February 1993
28 *
29 * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
30 * the same method, but claim no priority date earlier than July 29, 1994
31 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
32 */
ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x_,int y_bit,BN_CTX * ctx)33 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group,
34 EC_POINT *point,
35 const BIGNUM *x_, int y_bit,
36 BN_CTX *ctx)
37 {
38 BN_CTX *new_ctx = NULL;
39 BIGNUM *tmp, *x, *y, *z;
40 int ret = 0, z0;
41
42 /* clear error queue */
43 ERR_clear_error();
44
45 if (ctx == NULL) {
46 ctx = new_ctx = BN_CTX_new();
47 if (ctx == NULL)
48 return 0;
49 }
50
51 y_bit = (y_bit != 0) ? 1 : 0;
52
53 BN_CTX_start(ctx);
54 tmp = BN_CTX_get(ctx);
55 x = BN_CTX_get(ctx);
56 y = BN_CTX_get(ctx);
57 z = BN_CTX_get(ctx);
58 if (z == NULL)
59 goto err;
60
61 if (!BN_GF2m_mod_arr(x, x_, group->poly))
62 goto err;
63 if (BN_is_zero(x)) {
64 if (!BN_GF2m_mod_sqrt_arr(y, group->b, group->poly, ctx))
65 goto err;
66 } else {
67 if (!group->meth->field_sqr(group, tmp, x, ctx))
68 goto err;
69 if (!group->meth->field_div(group, tmp, group->b, tmp, ctx))
70 goto err;
71 if (!BN_GF2m_add(tmp, group->a, tmp))
72 goto err;
73 if (!BN_GF2m_add(tmp, x, tmp))
74 goto err;
75 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) {
76 unsigned long err = ERR_peek_last_error();
77
78 if (ERR_GET_LIB(err) == ERR_LIB_BN
79 && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) {
80 ERR_clear_error();
81 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES,
82 EC_R_INVALID_COMPRESSED_POINT);
83 } else
84 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES,
85 ERR_R_BN_LIB);
86 goto err;
87 }
88 z0 = (BN_is_odd(z)) ? 1 : 0;
89 if (!group->meth->field_mul(group, y, x, z, ctx))
90 goto err;
91 if (z0 != y_bit) {
92 if (!BN_GF2m_add(y, y, x))
93 goto err;
94 }
95 }
96
97 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
98 goto err;
99
100 ret = 1;
101
102 err:
103 BN_CTX_end(ctx);
104 BN_CTX_free(new_ctx);
105 return ret;
106 }
107
108 /*
109 * Converts an EC_POINT to an octet string. If buf is NULL, the encoded
110 * length will be returned. If the length len of buf is smaller than required
111 * an error will be returned.
112 */
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)113 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point,
114 point_conversion_form_t form,
115 unsigned char *buf, size_t len, BN_CTX *ctx)
116 {
117 size_t ret;
118 BN_CTX *new_ctx = NULL;
119 int used_ctx = 0;
120 BIGNUM *x, *y, *yxi;
121 size_t field_len, i, skip;
122
123 if ((form != POINT_CONVERSION_COMPRESSED)
124 && (form != POINT_CONVERSION_UNCOMPRESSED)
125 && (form != POINT_CONVERSION_HYBRID)) {
126 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
127 goto err;
128 }
129
130 if (EC_POINT_is_at_infinity(group, point)) {
131 /* encodes to a single 0 octet */
132 if (buf != NULL) {
133 if (len < 1) {
134 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
135 return 0;
136 }
137 buf[0] = 0;
138 }
139 return 1;
140 }
141
142 /* ret := required output buffer length */
143 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
144 ret =
145 (form ==
146 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
147
148 /* if 'buf' is NULL, just return required length */
149 if (buf != NULL) {
150 if (len < ret) {
151 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
152 goto err;
153 }
154
155 if (ctx == NULL) {
156 ctx = new_ctx = BN_CTX_new();
157 if (ctx == NULL)
158 return 0;
159 }
160
161 BN_CTX_start(ctx);
162 used_ctx = 1;
163 x = BN_CTX_get(ctx);
164 y = BN_CTX_get(ctx);
165 yxi = BN_CTX_get(ctx);
166 if (yxi == NULL)
167 goto err;
168
169 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
170 goto err;
171
172 buf[0] = form;
173 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) {
174 if (!group->meth->field_div(group, yxi, y, x, ctx))
175 goto err;
176 if (BN_is_odd(yxi))
177 buf[0]++;
178 }
179
180 i = 1;
181
182 skip = field_len - BN_num_bytes(x);
183 if (skip > field_len) {
184 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
185 goto err;
186 }
187 while (skip > 0) {
188 buf[i++] = 0;
189 skip--;
190 }
191 skip = BN_bn2bin(x, buf + i);
192 i += skip;
193 if (i != 1 + field_len) {
194 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
195 goto err;
196 }
197
198 if (form == POINT_CONVERSION_UNCOMPRESSED
199 || form == POINT_CONVERSION_HYBRID) {
200 skip = field_len - BN_num_bytes(y);
201 if (skip > field_len) {
202 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
203 goto err;
204 }
205 while (skip > 0) {
206 buf[i++] = 0;
207 skip--;
208 }
209 skip = BN_bn2bin(y, buf + i);
210 i += skip;
211 }
212
213 if (i != ret) {
214 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
215 goto err;
216 }
217 }
218
219 if (used_ctx)
220 BN_CTX_end(ctx);
221 BN_CTX_free(new_ctx);
222 return ret;
223
224 err:
225 if (used_ctx)
226 BN_CTX_end(ctx);
227 BN_CTX_free(new_ctx);
228 return 0;
229 }
230
231 /*
232 * Converts an octet string representation to an EC_POINT. Note that the
233 * simple implementation only uses affine coordinates.
234 */
ec_GF2m_simple_oct2point(const EC_GROUP * group,EC_POINT * point,const unsigned char * buf,size_t len,BN_CTX * ctx)235 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
236 const unsigned char *buf, size_t len,
237 BN_CTX *ctx)
238 {
239 point_conversion_form_t form;
240 int y_bit, m;
241 BN_CTX *new_ctx = NULL;
242 BIGNUM *x, *y, *yxi;
243 size_t field_len, enc_len;
244 int ret = 0;
245
246 if (len == 0) {
247 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
248 return 0;
249 }
250
251 /*
252 * The first octet is the point converison octet PC, see X9.62, page 4
253 * and section 4.4.2. It must be:
254 * 0x00 for the point at infinity
255 * 0x02 or 0x03 for compressed form
256 * 0x04 for uncompressed form
257 * 0x06 or 0x07 for hybrid form.
258 * For compressed or hybrid forms, we store the last bit of buf[0] as
259 * y_bit and clear it from buf[0] so as to obtain a POINT_CONVERSION_*.
260 * We error if buf[0] contains any but the above values.
261 */
262 y_bit = buf[0] & 1;
263 form = buf[0] & ~1U;
264
265 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
266 && (form != POINT_CONVERSION_UNCOMPRESSED)
267 && (form != POINT_CONVERSION_HYBRID)) {
268 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
269 return 0;
270 }
271 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
272 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
273 return 0;
274 }
275
276 /* The point at infinity is represented by a single zero octet. */
277 if (form == 0) {
278 if (len != 1) {
279 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
280 return 0;
281 }
282
283 return EC_POINT_set_to_infinity(group, point);
284 }
285
286 m = EC_GROUP_get_degree(group);
287 field_len = (m + 7) / 8;
288 enc_len =
289 (form ==
290 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
291
292 if (len != enc_len) {
293 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
294 return 0;
295 }
296
297 if (ctx == NULL) {
298 ctx = new_ctx = BN_CTX_new();
299 if (ctx == NULL)
300 return 0;
301 }
302
303 BN_CTX_start(ctx);
304 x = BN_CTX_get(ctx);
305 y = BN_CTX_get(ctx);
306 yxi = BN_CTX_get(ctx);
307 if (yxi == NULL)
308 goto err;
309
310 if (!BN_bin2bn(buf + 1, field_len, x))
311 goto err;
312 if (BN_num_bits(x) > m) {
313 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
314 goto err;
315 }
316
317 if (form == POINT_CONVERSION_COMPRESSED) {
318 if (!EC_POINT_set_compressed_coordinates(group, point, x, y_bit, ctx))
319 goto err;
320 } else {
321 if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
322 goto err;
323 if (BN_num_bits(y) > m) {
324 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
325 goto err;
326 }
327 if (form == POINT_CONVERSION_HYBRID) {
328 /*
329 * Check that the form in the encoding was set correctly
330 * according to X9.62 4.4.2.a, 4(c), see also first paragraph
331 * of X9.62, 4.4.1.b.
332 */
333 if (BN_is_zero(x)) {
334 if (y_bit != 0) {
335 ECerr(ERR_LIB_EC, EC_R_INVALID_ENCODING);
336 goto err;
337 }
338 } else {
339 if (!group->meth->field_div(group, yxi, y, x, ctx))
340 goto err;
341 if (y_bit != BN_is_odd(yxi)) {
342 ECerr(ERR_LIB_EC, EC_R_INVALID_ENCODING);
343 goto err;
344 }
345 }
346 }
347
348 /*
349 * EC_POINT_set_affine_coordinates is responsible for checking that
350 * the point is on the curve.
351 */
352 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
353 goto err;
354 }
355
356 ret = 1;
357
358 err:
359 BN_CTX_end(ctx);
360 BN_CTX_free(new_ctx);
361 return ret;
362 }
363 #endif
364