[331] | 1 | /*
|
---|
| 2 | * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved.
|
---|
| 3 | *
|
---|
| 4 | * Licensed under the OpenSSL license (the "License"). You may not use
|
---|
| 5 | * this file except in compliance with the License. You can obtain a copy
|
---|
| 6 | * in the file LICENSE in the source distribution or at
|
---|
| 7 | * https://www.openssl.org/source/license.html
|
---|
| 8 | */
|
---|
| 9 |
|
---|
| 10 | /* ====================================================================
|
---|
| 11 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
|
---|
| 12 | * Portions of this software developed by SUN MICROSYSTEMS, INC.,
|
---|
| 13 | * and contributed to the OpenSSL project.
|
---|
| 14 | */
|
---|
| 15 |
|
---|
| 16 | #include <openssl/err.h>
|
---|
| 17 | #include <openssl/symhacks.h>
|
---|
| 18 |
|
---|
| 19 | #include "ec_lcl.h"
|
---|
| 20 |
|
---|
| 21 | int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group,
|
---|
| 22 | EC_POINT *point,
|
---|
| 23 | const BIGNUM *x_, int y_bit,
|
---|
| 24 | BN_CTX *ctx)
|
---|
| 25 | {
|
---|
| 26 | BN_CTX *new_ctx = NULL;
|
---|
| 27 | BIGNUM *tmp1, *tmp2, *x, *y;
|
---|
| 28 | int ret = 0;
|
---|
| 29 |
|
---|
| 30 | /* clear error queue */
|
---|
| 31 | ERR_clear_error();
|
---|
| 32 |
|
---|
| 33 | if (ctx == NULL) {
|
---|
| 34 | ctx = new_ctx = BN_CTX_new();
|
---|
| 35 | if (ctx == NULL)
|
---|
| 36 | return 0;
|
---|
| 37 | }
|
---|
| 38 |
|
---|
| 39 | y_bit = (y_bit != 0);
|
---|
| 40 |
|
---|
| 41 | BN_CTX_start(ctx);
|
---|
| 42 | tmp1 = BN_CTX_get(ctx);
|
---|
| 43 | tmp2 = BN_CTX_get(ctx);
|
---|
| 44 | x = BN_CTX_get(ctx);
|
---|
| 45 | y = BN_CTX_get(ctx);
|
---|
| 46 | if (y == NULL)
|
---|
| 47 | goto err;
|
---|
| 48 |
|
---|
| 49 | /*-
|
---|
| 50 | * Recover y. We have a Weierstrass equation
|
---|
| 51 | * y^2 = x^3 + a*x + b,
|
---|
| 52 | * so y is one of the square roots of x^3 + a*x + b.
|
---|
| 53 | */
|
---|
| 54 |
|
---|
| 55 | /* tmp1 := x^3 */
|
---|
| 56 | if (!BN_nnmod(x, x_, group->field, ctx))
|
---|
| 57 | goto err;
|
---|
| 58 | if (group->meth->field_decode == 0) {
|
---|
| 59 | /* field_{sqr,mul} work on standard representation */
|
---|
| 60 | if (!group->meth->field_sqr(group, tmp2, x_, ctx))
|
---|
| 61 | goto err;
|
---|
| 62 | if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx))
|
---|
| 63 | goto err;
|
---|
| 64 | } else {
|
---|
| 65 | if (!BN_mod_sqr(tmp2, x_, group->field, ctx))
|
---|
| 66 | goto err;
|
---|
| 67 | if (!BN_mod_mul(tmp1, tmp2, x_, group->field, ctx))
|
---|
| 68 | goto err;
|
---|
| 69 | }
|
---|
| 70 |
|
---|
| 71 | /* tmp1 := tmp1 + a*x */
|
---|
| 72 | if (group->a_is_minus3) {
|
---|
| 73 | if (!BN_mod_lshift1_quick(tmp2, x, group->field))
|
---|
| 74 | goto err;
|
---|
| 75 | if (!BN_mod_add_quick(tmp2, tmp2, x, group->field))
|
---|
| 76 | goto err;
|
---|
| 77 | if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, group->field))
|
---|
| 78 | goto err;
|
---|
| 79 | } else {
|
---|
| 80 | if (group->meth->field_decode) {
|
---|
| 81 | if (!group->meth->field_decode(group, tmp2, group->a, ctx))
|
---|
| 82 | goto err;
|
---|
| 83 | if (!BN_mod_mul(tmp2, tmp2, x, group->field, ctx))
|
---|
| 84 | goto err;
|
---|
| 85 | } else {
|
---|
| 86 | /* field_mul works on standard representation */
|
---|
| 87 | if (!group->meth->field_mul(group, tmp2, group->a, x, ctx))
|
---|
| 88 | goto err;
|
---|
| 89 | }
|
---|
| 90 |
|
---|
| 91 | if (!BN_mod_add_quick(tmp1, tmp1, tmp2, group->field))
|
---|
| 92 | goto err;
|
---|
| 93 | }
|
---|
| 94 |
|
---|
| 95 | /* tmp1 := tmp1 + b */
|
---|
| 96 | if (group->meth->field_decode) {
|
---|
| 97 | if (!group->meth->field_decode(group, tmp2, group->b, ctx))
|
---|
| 98 | goto err;
|
---|
| 99 | if (!BN_mod_add_quick(tmp1, tmp1, tmp2, group->field))
|
---|
| 100 | goto err;
|
---|
| 101 | } else {
|
---|
| 102 | if (!BN_mod_add_quick(tmp1, tmp1, group->b, group->field))
|
---|
| 103 | goto err;
|
---|
| 104 | }
|
---|
| 105 |
|
---|
| 106 | if (!BN_mod_sqrt(y, tmp1, group->field, ctx)) {
|
---|
| 107 | unsigned long err = ERR_peek_last_error();
|
---|
| 108 |
|
---|
| 109 | if (ERR_GET_LIB(err) == ERR_LIB_BN
|
---|
| 110 | && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) {
|
---|
| 111 | ERR_clear_error();
|
---|
| 112 | ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
|
---|
| 113 | EC_R_INVALID_COMPRESSED_POINT);
|
---|
| 114 | } else
|
---|
| 115 | ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
|
---|
| 116 | ERR_R_BN_LIB);
|
---|
| 117 | goto err;
|
---|
| 118 | }
|
---|
| 119 |
|
---|
| 120 | if (y_bit != BN_is_odd(y)) {
|
---|
| 121 | if (BN_is_zero(y)) {
|
---|
| 122 | int kron;
|
---|
| 123 |
|
---|
| 124 | kron = BN_kronecker(x, group->field, ctx);
|
---|
| 125 | if (kron == -2)
|
---|
| 126 | goto err;
|
---|
| 127 |
|
---|
| 128 | if (kron == 1)
|
---|
| 129 | ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
|
---|
| 130 | EC_R_INVALID_COMPRESSION_BIT);
|
---|
| 131 | else
|
---|
| 132 | /*
|
---|
| 133 | * BN_mod_sqrt() should have cought this error (not a square)
|
---|
| 134 | */
|
---|
| 135 | ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
|
---|
| 136 | EC_R_INVALID_COMPRESSED_POINT);
|
---|
| 137 | goto err;
|
---|
| 138 | }
|
---|
| 139 | if (!BN_usub(y, group->field, y))
|
---|
| 140 | goto err;
|
---|
| 141 | }
|
---|
| 142 | if (y_bit != BN_is_odd(y)) {
|
---|
| 143 | ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
|
---|
| 144 | ERR_R_INTERNAL_ERROR);
|
---|
| 145 | goto err;
|
---|
| 146 | }
|
---|
| 147 |
|
---|
| 148 | if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
|
---|
| 149 | goto err;
|
---|
| 150 |
|
---|
| 151 | ret = 1;
|
---|
| 152 |
|
---|
| 153 | err:
|
---|
| 154 | BN_CTX_end(ctx);
|
---|
| 155 | BN_CTX_free(new_ctx);
|
---|
| 156 | return ret;
|
---|
| 157 | }
|
---|
| 158 |
|
---|
| 159 | size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point,
|
---|
| 160 | point_conversion_form_t form,
|
---|
| 161 | unsigned char *buf, size_t len, BN_CTX *ctx)
|
---|
| 162 | {
|
---|
| 163 | size_t ret;
|
---|
| 164 | BN_CTX *new_ctx = NULL;
|
---|
| 165 | int used_ctx = 0;
|
---|
| 166 | BIGNUM *x, *y;
|
---|
| 167 | size_t field_len, i, skip;
|
---|
| 168 |
|
---|
| 169 | if ((form != POINT_CONVERSION_COMPRESSED)
|
---|
| 170 | && (form != POINT_CONVERSION_UNCOMPRESSED)
|
---|
| 171 | && (form != POINT_CONVERSION_HYBRID)) {
|
---|
| 172 | ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
|
---|
| 173 | goto err;
|
---|
| 174 | }
|
---|
| 175 |
|
---|
| 176 | if (EC_POINT_is_at_infinity(group, point)) {
|
---|
| 177 | /* encodes to a single 0 octet */
|
---|
| 178 | if (buf != NULL) {
|
---|
| 179 | if (len < 1) {
|
---|
| 180 | ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
|
---|
| 181 | return 0;
|
---|
| 182 | }
|
---|
| 183 | buf[0] = 0;
|
---|
| 184 | }
|
---|
| 185 | return 1;
|
---|
| 186 | }
|
---|
| 187 |
|
---|
| 188 | /* ret := required output buffer length */
|
---|
| 189 | field_len = BN_num_bytes(group->field);
|
---|
| 190 | ret =
|
---|
| 191 | (form ==
|
---|
| 192 | POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
|
---|
| 193 |
|
---|
| 194 | /* if 'buf' is NULL, just return required length */
|
---|
| 195 | if (buf != NULL) {
|
---|
| 196 | if (len < ret) {
|
---|
| 197 | ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
|
---|
| 198 | goto err;
|
---|
| 199 | }
|
---|
| 200 |
|
---|
| 201 | if (ctx == NULL) {
|
---|
| 202 | ctx = new_ctx = BN_CTX_new();
|
---|
| 203 | if (ctx == NULL)
|
---|
| 204 | return 0;
|
---|
| 205 | }
|
---|
| 206 |
|
---|
| 207 | BN_CTX_start(ctx);
|
---|
| 208 | used_ctx = 1;
|
---|
| 209 | x = BN_CTX_get(ctx);
|
---|
| 210 | y = BN_CTX_get(ctx);
|
---|
| 211 | if (y == NULL)
|
---|
| 212 | goto err;
|
---|
| 213 |
|
---|
| 214 | if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
|
---|
| 215 | goto err;
|
---|
| 216 |
|
---|
| 217 | if ((form == POINT_CONVERSION_COMPRESSED
|
---|
| 218 | || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
|
---|
| 219 | buf[0] = form + 1;
|
---|
| 220 | else
|
---|
| 221 | buf[0] = form;
|
---|
| 222 |
|
---|
| 223 | i = 1;
|
---|
| 224 |
|
---|
| 225 | skip = field_len - BN_num_bytes(x);
|
---|
| 226 | if (skip > field_len) {
|
---|
| 227 | ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
|
---|
| 228 | goto err;
|
---|
| 229 | }
|
---|
| 230 | while (skip > 0) {
|
---|
| 231 | buf[i++] = 0;
|
---|
| 232 | skip--;
|
---|
| 233 | }
|
---|
| 234 | skip = BN_bn2bin(x, buf + i);
|
---|
| 235 | i += skip;
|
---|
| 236 | if (i != 1 + field_len) {
|
---|
| 237 | ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
|
---|
| 238 | goto err;
|
---|
| 239 | }
|
---|
| 240 |
|
---|
| 241 | if (form == POINT_CONVERSION_UNCOMPRESSED
|
---|
| 242 | || form == POINT_CONVERSION_HYBRID) {
|
---|
| 243 | skip = field_len - BN_num_bytes(y);
|
---|
| 244 | if (skip > field_len) {
|
---|
| 245 | ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
|
---|
| 246 | goto err;
|
---|
| 247 | }
|
---|
| 248 | while (skip > 0) {
|
---|
| 249 | buf[i++] = 0;
|
---|
| 250 | skip--;
|
---|
| 251 | }
|
---|
| 252 | skip = BN_bn2bin(y, buf + i);
|
---|
| 253 | i += skip;
|
---|
| 254 | }
|
---|
| 255 |
|
---|
| 256 | if (i != ret) {
|
---|
| 257 | ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
|
---|
| 258 | goto err;
|
---|
| 259 | }
|
---|
| 260 | }
|
---|
| 261 |
|
---|
| 262 | if (used_ctx)
|
---|
| 263 | BN_CTX_end(ctx);
|
---|
| 264 | BN_CTX_free(new_ctx);
|
---|
| 265 | return ret;
|
---|
| 266 |
|
---|
| 267 | err:
|
---|
| 268 | if (used_ctx)
|
---|
| 269 | BN_CTX_end(ctx);
|
---|
| 270 | BN_CTX_free(new_ctx);
|
---|
| 271 | return 0;
|
---|
| 272 | }
|
---|
| 273 |
|
---|
| 274 | int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
|
---|
| 275 | const unsigned char *buf, size_t len, BN_CTX *ctx)
|
---|
| 276 | {
|
---|
| 277 | point_conversion_form_t form;
|
---|
| 278 | int y_bit;
|
---|
| 279 | BN_CTX *new_ctx = NULL;
|
---|
| 280 | BIGNUM *x, *y;
|
---|
| 281 | size_t field_len, enc_len;
|
---|
| 282 | int ret = 0;
|
---|
| 283 |
|
---|
| 284 | if (len == 0) {
|
---|
| 285 | ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
|
---|
| 286 | return 0;
|
---|
| 287 | }
|
---|
| 288 | form = buf[0];
|
---|
| 289 | y_bit = form & 1;
|
---|
| 290 | form = form & ~1U;
|
---|
| 291 | if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
|
---|
| 292 | && (form != POINT_CONVERSION_UNCOMPRESSED)
|
---|
| 293 | && (form != POINT_CONVERSION_HYBRID)) {
|
---|
| 294 | ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
---|
| 295 | return 0;
|
---|
| 296 | }
|
---|
| 297 | if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
|
---|
| 298 | ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
---|
| 299 | return 0;
|
---|
| 300 | }
|
---|
| 301 |
|
---|
| 302 | if (form == 0) {
|
---|
| 303 | if (len != 1) {
|
---|
| 304 | ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
---|
| 305 | return 0;
|
---|
| 306 | }
|
---|
| 307 |
|
---|
| 308 | return EC_POINT_set_to_infinity(group, point);
|
---|
| 309 | }
|
---|
| 310 |
|
---|
| 311 | field_len = BN_num_bytes(group->field);
|
---|
| 312 | enc_len =
|
---|
| 313 | (form ==
|
---|
| 314 | POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
|
---|
| 315 |
|
---|
| 316 | if (len != enc_len) {
|
---|
| 317 | ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
---|
| 318 | return 0;
|
---|
| 319 | }
|
---|
| 320 |
|
---|
| 321 | if (ctx == NULL) {
|
---|
| 322 | ctx = new_ctx = BN_CTX_new();
|
---|
| 323 | if (ctx == NULL)
|
---|
| 324 | return 0;
|
---|
| 325 | }
|
---|
| 326 |
|
---|
| 327 | BN_CTX_start(ctx);
|
---|
| 328 | x = BN_CTX_get(ctx);
|
---|
| 329 | y = BN_CTX_get(ctx);
|
---|
| 330 | if (y == NULL)
|
---|
| 331 | goto err;
|
---|
| 332 |
|
---|
| 333 | if (!BN_bin2bn(buf + 1, field_len, x))
|
---|
| 334 | goto err;
|
---|
| 335 | if (BN_ucmp(x, group->field) >= 0) {
|
---|
| 336 | ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
---|
| 337 | goto err;
|
---|
| 338 | }
|
---|
| 339 |
|
---|
| 340 | if (form == POINT_CONVERSION_COMPRESSED) {
|
---|
| 341 | if (!EC_POINT_set_compressed_coordinates_GFp
|
---|
| 342 | (group, point, x, y_bit, ctx))
|
---|
| 343 | goto err;
|
---|
| 344 | } else {
|
---|
| 345 | if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
|
---|
| 346 | goto err;
|
---|
| 347 | if (BN_ucmp(y, group->field) >= 0) {
|
---|
| 348 | ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
---|
| 349 | goto err;
|
---|
| 350 | }
|
---|
| 351 | if (form == POINT_CONVERSION_HYBRID) {
|
---|
| 352 | if (y_bit != BN_is_odd(y)) {
|
---|
| 353 | ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
---|
| 354 | goto err;
|
---|
| 355 | }
|
---|
| 356 | }
|
---|
| 357 |
|
---|
| 358 | /*
|
---|
| 359 | * EC_POINT_set_affine_coordinates_GFp is responsible for checking that
|
---|
| 360 | * the point is on the curve.
|
---|
| 361 | */
|
---|
| 362 | if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
|
---|
| 363 | goto err;
|
---|
| 364 | }
|
---|
| 365 |
|
---|
| 366 | ret = 1;
|
---|
| 367 |
|
---|
| 368 | err:
|
---|
| 369 | BN_CTX_end(ctx);
|
---|
| 370 | BN_CTX_free(new_ctx);
|
---|
| 371 | return ret;
|
---|
| 372 | }
|
---|