1/*
2 * Copyright 2011-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
4 *
5 * Licensed under the Apache License 2.0 (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 */
33int 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 BIGNUM *tmp, *x, *y, *z;
39 int ret = 0, z0;
40#ifndef FIPS_MODE
41 BN_CTX *new_ctx = NULL;
42
43 /* clear error queue */
44 ERR_clear_error();
45
46 if (ctx == NULL) {
47 ctx = new_ctx = BN_CTX_new();
48 if (ctx == NULL)
49 return 0;
50 }
51#endif
52
53 y_bit = (y_bit != 0) ? 1 : 0;
54
55 BN_CTX_start(ctx);
56 tmp = BN_CTX_get(ctx);
57 x = BN_CTX_get(ctx);
58 y = BN_CTX_get(ctx);
59 z = BN_CTX_get(ctx);
60 if (z == NULL)
61 goto err;
62
63 if (!BN_GF2m_mod_arr(x, x_, group->poly))
64 goto err;
65 if (BN_is_zero(x)) {
66 if (!BN_GF2m_mod_sqrt_arr(y, group->b, group->poly, ctx))
67 goto err;
68 } else {
69 if (!group->meth->field_sqr(group, tmp, x, ctx))
70 goto err;
71 if (!group->meth->field_div(group, tmp, group->b, tmp, ctx))
72 goto err;
73 if (!BN_GF2m_add(tmp, group->a, tmp))
74 goto err;
75 if (!BN_GF2m_add(tmp, x, tmp))
76 goto err;
77 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) {
78#ifndef FIPS_MODE
79 unsigned long err = ERR_peek_last_error();
80
81 if (ERR_GET_LIB(err) == ERR_LIB_BN
82 && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) {
83 ERR_clear_error();
84 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES,
85 EC_R_INVALID_COMPRESSED_POINT);
86 } else
87#endif
88 {
89 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES,
90 ERR_R_BN_LIB);
91 }
92 goto err;
93 }
94 z0 = (BN_is_odd(z)) ? 1 : 0;
95 if (!group->meth->field_mul(group, y, x, z, ctx))
96 goto err;
97 if (z0 != y_bit) {
98 if (!BN_GF2m_add(y, y, x))
99 goto err;
100 }
101 }
102
103 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
104 goto err;
105
106 ret = 1;
107
108 err:
109 BN_CTX_end(ctx);
110#ifndef FIPS_MODE
111 BN_CTX_free(new_ctx);
112#endif
113 return ret;
114}
115
116/*
117 * Converts an EC_POINT to an octet string. If buf is NULL, the encoded
118 * length will be returned. If the length len of buf is smaller than required
119 * an error will be returned.
120 */
121size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point,
122 point_conversion_form_t form,
123 unsigned char *buf, size_t len, BN_CTX *ctx)
124{
125 size_t ret;
126 int used_ctx = 0;
127 BIGNUM *x, *y, *yxi;
128 size_t field_len, i, skip;
129#ifndef FIPS_MODE
130 BN_CTX *new_ctx = NULL;
131#endif
132
133 if ((form != POINT_CONVERSION_COMPRESSED)
134 && (form != POINT_CONVERSION_UNCOMPRESSED)
135 && (form != POINT_CONVERSION_HYBRID)) {
136 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
137 goto err;
138 }
139
140 if (EC_POINT_is_at_infinity(group, point)) {
141 /* encodes to a single 0 octet */
142 if (buf != NULL) {
143 if (len < 1) {
144 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
145 return 0;
146 }
147 buf[0] = 0;
148 }
149 return 1;
150 }
151
152 /* ret := required output buffer length */
153 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
154 ret =
155 (form ==
156 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
157
158 /* if 'buf' is NULL, just return required length */
159 if (buf != NULL) {
160 if (len < ret) {
161 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
162 goto err;
163 }
164
165#ifndef FIPS_MODE
166 if (ctx == NULL) {
167 ctx = new_ctx = BN_CTX_new();
168 if (ctx == NULL)
169 return 0;
170 }
171#endif
172
173 BN_CTX_start(ctx);
174 used_ctx = 1;
175 x = BN_CTX_get(ctx);
176 y = BN_CTX_get(ctx);
177 yxi = BN_CTX_get(ctx);
178 if (yxi == NULL)
179 goto err;
180
181 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
182 goto err;
183
184 buf[0] = form;
185 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) {
186 if (!group->meth->field_div(group, yxi, y, x, ctx))
187 goto err;
188 if (BN_is_odd(yxi))
189 buf[0]++;
190 }
191
192 i = 1;
193
194 skip = field_len - BN_num_bytes(x);
195 if (skip > field_len) {
196 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
197 goto err;
198 }
199 while (skip > 0) {
200 buf[i++] = 0;
201 skip--;
202 }
203 skip = BN_bn2bin(x, buf + i);
204 i += skip;
205 if (i != 1 + field_len) {
206 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
207 goto err;
208 }
209
210 if (form == POINT_CONVERSION_UNCOMPRESSED
211 || form == POINT_CONVERSION_HYBRID) {
212 skip = field_len - BN_num_bytes(y);
213 if (skip > field_len) {
214 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
215 goto err;
216 }
217 while (skip > 0) {
218 buf[i++] = 0;
219 skip--;
220 }
221 skip = BN_bn2bin(y, buf + i);
222 i += skip;
223 }
224
225 if (i != ret) {
226 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
227 goto err;
228 }
229 }
230
231 if (used_ctx)
232 BN_CTX_end(ctx);
233#ifndef FIPS_MODE
234 BN_CTX_free(new_ctx);
235#endif
236 return ret;
237
238 err:
239 if (used_ctx)
240 BN_CTX_end(ctx);
241#ifndef FIPS_MODE
242 BN_CTX_free(new_ctx);
243#endif
244 return 0;
245}
246
247/*
248 * Converts an octet string representation to an EC_POINT. Note that the
249 * simple implementation only uses affine coordinates.
250 */
251int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
252 const unsigned char *buf, size_t len,
253 BN_CTX *ctx)
254{
255 point_conversion_form_t form;
256 int y_bit, m;
257 BIGNUM *x, *y, *yxi;
258 size_t field_len, enc_len;
259 int ret = 0;
260#ifndef FIPS_MODE
261 BN_CTX *new_ctx = NULL;
262#endif
263
264 if (len == 0) {
265 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
266 return 0;
267 }
268 form = buf[0];
269 y_bit = form & 1;
270 form = form & ~1U;
271 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
272 && (form != POINT_CONVERSION_UNCOMPRESSED)
273 && (form != POINT_CONVERSION_HYBRID)) {
274 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
275 return 0;
276 }
277 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
278 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
279 return 0;
280 }
281
282 if (form == 0) {
283 if (len != 1) {
284 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
285 return 0;
286 }
287
288 return EC_POINT_set_to_infinity(group, point);
289 }
290
291 m = EC_GROUP_get_degree(group);
292 field_len = (m + 7) / 8;
293 enc_len =
294 (form ==
295 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
296
297 if (len != enc_len) {
298 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
299 return 0;
300 }
301
302#ifndef FIPS_MODE
303 if (ctx == NULL) {
304 ctx = new_ctx = BN_CTX_new();
305 if (ctx == NULL)
306 return 0;
307 }
308#endif
309
310 BN_CTX_start(ctx);
311 x = BN_CTX_get(ctx);
312 y = BN_CTX_get(ctx);
313 yxi = BN_CTX_get(ctx);
314 if (yxi == NULL)
315 goto err;
316
317 if (!BN_bin2bn(buf + 1, field_len, x))
318 goto err;
319 if (BN_num_bits(x) > m) {
320 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
321 goto err;
322 }
323
324 if (form == POINT_CONVERSION_COMPRESSED) {
325 if (!EC_POINT_set_compressed_coordinates(group, point, x, y_bit, ctx))
326 goto err;
327 } else {
328 if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
329 goto err;
330 if (BN_num_bits(y) > m) {
331 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
332 goto err;
333 }
334 if (form == POINT_CONVERSION_HYBRID) {
335 if (!group->meth->field_div(group, yxi, y, x, ctx))
336 goto err;
337 if (y_bit != BN_is_odd(yxi)) {
338 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
339 goto err;
340 }
341 }
342
343 /*
344 * EC_POINT_set_affine_coordinates is responsible for checking that
345 * the point is on the curve.
346 */
347 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
348 goto err;
349 }
350
351 ret = 1;
352
353 err:
354 BN_CTX_end(ctx);
355#ifndef FIPS_MODE
356 BN_CTX_free(new_ctx);
357#endif
358 return ret;
359}
360#endif
361