2 * Copyright 2011-2022 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
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
12 * ECDSA low level APIs are deprecated for public use, but still ok for
15 #include "internal/deprecated.h"
17 #include <openssl/err.h>
21 #ifndef OPENSSL_NO_EC2M
24 * Calculates and sets the affine coordinates of an EC_POINT from the given
25 * compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
26 * Note that the simple implementation only uses affine coordinates.
28 * The method is from the following publication:
30 * Harper, Menezes, Vanstone:
31 * "Public-Key Cryptosystems with Very Small Key Lengths",
32 * EUROCRYPT '92, Springer-Verlag LNCS 658,
33 * published February 1993
35 * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
36 * the same method, but claim no priority date earlier than July 29, 1994
37 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
39 int ossl_ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group,
41 const BIGNUM *x_, int y_bit,
44 BIGNUM *tmp, *x, *y, *z;
47 BN_CTX *new_ctx = NULL;
50 ctx = new_ctx = BN_CTX_new();
56 y_bit = (y_bit != 0) ? 1 : 0;
59 tmp = BN_CTX_get(ctx);
66 if (!BN_GF2m_mod_arr(x, x_, group->poly))
69 if (!BN_GF2m_mod_sqrt_arr(y, group->b, group->poly, ctx))
72 if (!group->meth->field_sqr(group, tmp, x, ctx))
74 if (!group->meth->field_div(group, tmp, group->b, tmp, ctx))
76 if (!BN_GF2m_add(tmp, group->a, tmp))
78 if (!BN_GF2m_add(tmp, x, tmp))
81 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) {
83 unsigned long err = ERR_peek_last_error();
85 if (ERR_GET_LIB(err) == ERR_LIB_BN
86 && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) {
88 ERR_raise(ERR_LIB_EC, EC_R_INVALID_COMPRESSED_POINT);
92 ERR_clear_last_mark();
93 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
97 ERR_clear_last_mark();
98 z0 = (BN_is_odd(z)) ? 1 : 0;
99 if (!group->meth->field_mul(group, y, x, z, ctx))
102 if (!BN_GF2m_add(y, y, x))
107 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
115 BN_CTX_free(new_ctx);
121 * Converts an EC_POINT to an octet string. If buf is NULL, the encoded
122 * length will be returned. If the length len of buf is smaller than required
123 * an error will be returned.
125 size_t ossl_ec_GF2m_simple_point2oct(const EC_GROUP *group,
126 const EC_POINT *point,
127 point_conversion_form_t form,
128 unsigned char *buf, size_t len, BN_CTX *ctx)
133 size_t field_len, i, skip;
135 BN_CTX *new_ctx = NULL;
138 if ((form != POINT_CONVERSION_COMPRESSED)
139 && (form != POINT_CONVERSION_UNCOMPRESSED)
140 && (form != POINT_CONVERSION_HYBRID)) {
141 ERR_raise(ERR_LIB_EC, EC_R_INVALID_FORM);
145 if (EC_POINT_is_at_infinity(group, point)) {
146 /* encodes to a single 0 octet */
149 ERR_raise(ERR_LIB_EC, EC_R_BUFFER_TOO_SMALL);
157 /* ret := required output buffer length */
158 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
161 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
163 /* if 'buf' is NULL, just return required length */
166 ERR_raise(ERR_LIB_EC, EC_R_BUFFER_TOO_SMALL);
172 ctx = new_ctx = BN_CTX_new();
182 yxi = BN_CTX_get(ctx);
186 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
190 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) {
191 if (!group->meth->field_div(group, yxi, y, x, ctx))
199 skip = field_len - BN_num_bytes(x);
200 if (skip > field_len) {
201 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
208 skip = BN_bn2bin(x, buf + i);
210 if (i != 1 + field_len) {
211 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
215 if (form == POINT_CONVERSION_UNCOMPRESSED
216 || form == POINT_CONVERSION_HYBRID) {
217 skip = field_len - BN_num_bytes(y);
218 if (skip > field_len) {
219 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
226 skip = BN_bn2bin(y, buf + i);
231 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
239 BN_CTX_free(new_ctx);
247 BN_CTX_free(new_ctx);
253 * Converts an octet string representation to an EC_POINT. Note that the
254 * simple implementation only uses affine coordinates.
256 int ossl_ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
257 const unsigned char *buf, size_t len,
260 point_conversion_form_t form;
263 size_t field_len, enc_len;
266 BN_CTX *new_ctx = NULL;
270 ERR_raise(ERR_LIB_EC, EC_R_BUFFER_TOO_SMALL);
275 * The first octet is the point conversion octet PC, see X9.62, page 4
276 * and section 4.4.2. It must be:
277 * 0x00 for the point at infinity
278 * 0x02 or 0x03 for compressed form
279 * 0x04 for uncompressed form
280 * 0x06 or 0x07 for hybrid form.
281 * For compressed or hybrid forms, we store the last bit of buf[0] as
282 * y_bit and clear it from buf[0] so as to obtain a POINT_CONVERSION_*.
283 * We error if buf[0] contains any but the above values.
288 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
289 && (form != POINT_CONVERSION_UNCOMPRESSED)
290 && (form != POINT_CONVERSION_HYBRID)) {
291 ERR_raise(ERR_LIB_EC, EC_R_INVALID_ENCODING);
294 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
295 ERR_raise(ERR_LIB_EC, EC_R_INVALID_ENCODING);
299 /* The point at infinity is represented by a single zero octet. */
302 ERR_raise(ERR_LIB_EC, EC_R_INVALID_ENCODING);
306 return EC_POINT_set_to_infinity(group, point);
309 m = EC_GROUP_get_degree(group);
310 field_len = (m + 7) / 8;
313 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
315 if (len != enc_len) {
316 ERR_raise(ERR_LIB_EC, EC_R_INVALID_ENCODING);
322 ctx = new_ctx = BN_CTX_new();
331 yxi = BN_CTX_get(ctx);
335 if (!BN_bin2bn(buf + 1, field_len, x))
337 if (BN_num_bits(x) > m) {
338 ERR_raise(ERR_LIB_EC, EC_R_INVALID_ENCODING);
342 if (form == POINT_CONVERSION_COMPRESSED) {
343 if (!EC_POINT_set_compressed_coordinates(group, point, x, y_bit, ctx))
346 if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
348 if (BN_num_bits(y) > m) {
349 ERR_raise(ERR_LIB_EC, EC_R_INVALID_ENCODING);
352 if (form == POINT_CONVERSION_HYBRID) {
354 * Check that the form in the encoding was set correctly
355 * according to X9.62 4.4.2.a, 4(c), see also first paragraph
360 ERR_raise(ERR_LIB_EC, EC_R_INVALID_ENCODING);
364 if (!group->meth->field_div(group, yxi, y, x, ctx))
366 if (y_bit != BN_is_odd(yxi)) {
367 ERR_raise(ERR_LIB_EC, EC_R_INVALID_ENCODING);
374 * EC_POINT_set_affine_coordinates is responsible for checking that
375 * the point is on the curve.
377 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
386 BN_CTX_free(new_ctx);