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 */ 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 */ 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 */ 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