1 /* 2 * Elliptic curves over GF(p): generic functions 3 * 4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved 5 * SPDX-License-Identifier: Apache-2.0 6 * 7 * Licensed under the Apache License, Version 2.0 (the "License"); you may 8 * not use this file except in compliance with the License. 9 * You may obtain a copy of the License at 10 * 11 * http://www.apache.org/licenses/LICENSE-2.0 12 * 13 * Unless required by applicable law or agreed to in writing, software 14 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT 15 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 * See the License for the specific language governing permissions and 17 * limitations under the License. 18 * 19 * This file is part of mbed TLS (https://tls.mbed.org) 20 */ 21 22 /* 23 * References: 24 * 25 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg 26 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone 27 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf 28 * RFC 4492 for the related TLS structures and constants 29 * 30 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf 31 * 32 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis 33 * for elliptic curve cryptosystems. In : Cryptographic Hardware and 34 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302. 35 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25> 36 * 37 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to 38 * render ECC resistant against Side Channel Attacks. IACR Cryptology 39 * ePrint Archive, 2004, vol. 2004, p. 342. 40 * <http://eprint.iacr.org/2004/342.pdf> 41 */ 42 43 #if !defined(MBEDTLS_CONFIG_FILE) 44 #include "mbedtls/config.h" 45 #else 46 #include MBEDTLS_CONFIG_FILE 47 #endif 48 49 #if defined(MBEDTLS_ECP_C) 50 51 #include "mbedtls/ecp.h" 52 #include "mbedtls/threading.h" 53 54 #include <string.h> 55 56 #if !defined(MBEDTLS_ECP_ALT) 57 58 #if defined(MBEDTLS_PLATFORM_C) 59 #include "mbedtls/platform.h" 60 #else 61 #include <stdlib.h> 62 #include <stdio.h> 63 #define mbedtls_printf printf 64 #define mbedtls_calloc calloc 65 #define mbedtls_free free 66 #endif 67 68 #include "mbedtls/ecp_internal.h" 69 70 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ 71 !defined(inline) && !defined(__cplusplus) 72 #define inline __inline 73 #endif 74 75 /* Implementation that should never be optimized out by the compiler */ 76 static void mbedtls_zeroize( void *v, size_t n ) { 77 volatile unsigned char *p = v; while( n-- ) *p++ = 0; 78 } 79 80 #if defined(MBEDTLS_SELF_TEST) 81 /* 82 * Counts of point addition and doubling, and field multiplications. 83 * Used to test resistance of point multiplication to simple timing attacks. 84 */ 85 static unsigned long add_count, dbl_count, mul_count; 86 #endif 87 88 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \ 89 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 90 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 91 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \ 92 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \ 93 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \ 94 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \ 95 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \ 96 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 97 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 98 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 99 #define ECP_SHORTWEIERSTRASS 100 #endif 101 102 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 103 #define ECP_MONTGOMERY 104 #endif 105 106 /* 107 * Curve types: internal for now, might be exposed later 108 */ 109 typedef enum 110 { 111 ECP_TYPE_NONE = 0, 112 ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */ 113 ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */ 114 } ecp_curve_type; 115 116 /* 117 * List of supported curves: 118 * - internal ID 119 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2) 120 * - size in bits 121 * - readable name 122 * 123 * Curves are listed in order: largest curves first, and for a given size, 124 * fastest curves first. This provides the default order for the SSL module. 125 * 126 * Reminder: update profiles in x509_crt.c when adding a new curves! 127 */ 128 static const mbedtls_ecp_curve_info ecp_supported_curves[] = 129 { 130 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 131 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" }, 132 #endif 133 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 134 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" }, 135 #endif 136 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 137 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" }, 138 #endif 139 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 140 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" }, 141 #endif 142 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 143 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" }, 144 #endif 145 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 146 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" }, 147 #endif 148 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 149 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" }, 150 #endif 151 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 152 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" }, 153 #endif 154 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 155 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" }, 156 #endif 157 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 158 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" }, 159 #endif 160 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 161 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" }, 162 #endif 163 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL }, 164 }; 165 166 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \ 167 sizeof( ecp_supported_curves[0] ) 168 169 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES]; 170 171 /* 172 * List of supported curves and associated info 173 */ 174 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void ) 175 { 176 return( ecp_supported_curves ); 177 } 178 179 /* 180 * List of supported curves, group ID only 181 */ 182 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void ) 183 { 184 static int init_done = 0; 185 186 if( ! init_done ) 187 { 188 size_t i = 0; 189 const mbedtls_ecp_curve_info *curve_info; 190 191 for( curve_info = mbedtls_ecp_curve_list(); 192 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 193 curve_info++ ) 194 { 195 ecp_supported_grp_id[i++] = curve_info->grp_id; 196 } 197 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE; 198 199 init_done = 1; 200 } 201 202 return( ecp_supported_grp_id ); 203 } 204 205 /* 206 * Get the curve info for the internal identifier 207 */ 208 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id ) 209 { 210 const mbedtls_ecp_curve_info *curve_info; 211 212 for( curve_info = mbedtls_ecp_curve_list(); 213 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 214 curve_info++ ) 215 { 216 if( curve_info->grp_id == grp_id ) 217 return( curve_info ); 218 } 219 220 return( NULL ); 221 } 222 223 /* 224 * Get the curve info from the TLS identifier 225 */ 226 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id ) 227 { 228 const mbedtls_ecp_curve_info *curve_info; 229 230 for( curve_info = mbedtls_ecp_curve_list(); 231 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 232 curve_info++ ) 233 { 234 if( curve_info->tls_id == tls_id ) 235 return( curve_info ); 236 } 237 238 return( NULL ); 239 } 240 241 /* 242 * Get the curve info from the name 243 */ 244 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name ) 245 { 246 const mbedtls_ecp_curve_info *curve_info; 247 248 for( curve_info = mbedtls_ecp_curve_list(); 249 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 250 curve_info++ ) 251 { 252 if( strcmp( curve_info->name, name ) == 0 ) 253 return( curve_info ); 254 } 255 256 return( NULL ); 257 } 258 259 /* 260 * Get the type of a curve 261 */ 262 static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp ) 263 { 264 if( grp->G.X.p == NULL ) 265 return( ECP_TYPE_NONE ); 266 267 if( grp->G.Y.p == NULL ) 268 return( ECP_TYPE_MONTGOMERY ); 269 else 270 return( ECP_TYPE_SHORT_WEIERSTRASS ); 271 } 272 273 /* 274 * Initialize (the components of) a point 275 */ 276 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ) 277 { 278 if( pt == NULL ) 279 return; 280 281 mbedtls_mpi_init( &pt->X ); 282 mbedtls_mpi_init( &pt->Y ); 283 mbedtls_mpi_init( &pt->Z ); 284 } 285 286 /* 287 * Initialize (the components of) a group 288 */ 289 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp ) 290 { 291 if( grp == NULL ) 292 return; 293 294 memset( grp, 0, sizeof( mbedtls_ecp_group ) ); 295 } 296 297 /* 298 * Initialize (the components of) a key pair 299 */ 300 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ) 301 { 302 if( key == NULL ) 303 return; 304 305 mbedtls_ecp_group_init( &key->grp ); 306 mbedtls_mpi_init( &key->d ); 307 mbedtls_ecp_point_init( &key->Q ); 308 } 309 310 /* 311 * Unallocate (the components of) a point 312 */ 313 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt ) 314 { 315 if( pt == NULL ) 316 return; 317 318 mbedtls_mpi_free( &( pt->X ) ); 319 mbedtls_mpi_free( &( pt->Y ) ); 320 mbedtls_mpi_free( &( pt->Z ) ); 321 } 322 323 /* 324 * Unallocate (the components of) a group 325 */ 326 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp ) 327 { 328 size_t i; 329 330 if( grp == NULL ) 331 return; 332 333 if( grp->h != 1 ) 334 { 335 mbedtls_mpi_free( &grp->P ); 336 mbedtls_mpi_free( &grp->A ); 337 mbedtls_mpi_free( &grp->B ); 338 mbedtls_ecp_point_free( &grp->G ); 339 mbedtls_mpi_free( &grp->N ); 340 } 341 342 if( grp->T != NULL ) 343 { 344 for( i = 0; i < grp->T_size; i++ ) 345 mbedtls_ecp_point_free( &grp->T[i] ); 346 mbedtls_free( grp->T ); 347 } 348 349 mbedtls_zeroize( grp, sizeof( mbedtls_ecp_group ) ); 350 } 351 352 /* 353 * Unallocate (the components of) a key pair 354 */ 355 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key ) 356 { 357 if( key == NULL ) 358 return; 359 360 mbedtls_ecp_group_free( &key->grp ); 361 mbedtls_mpi_free( &key->d ); 362 mbedtls_ecp_point_free( &key->Q ); 363 } 364 365 /* 366 * Copy the contents of a point 367 */ 368 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ) 369 { 370 int ret; 371 372 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) ); 373 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) ); 374 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) ); 375 376 cleanup: 377 return( ret ); 378 } 379 380 /* 381 * Copy the contents of a group object 382 */ 383 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src ) 384 { 385 return mbedtls_ecp_group_load( dst, src->id ); 386 } 387 388 /* 389 * Set point to zero 390 */ 391 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt ) 392 { 393 int ret; 394 395 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) ); 396 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) ); 397 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) ); 398 399 cleanup: 400 return( ret ); 401 } 402 403 /* 404 * Tell if a point is zero 405 */ 406 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt ) 407 { 408 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 ); 409 } 410 411 /* 412 * Compare two points lazyly 413 */ 414 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P, 415 const mbedtls_ecp_point *Q ) 416 { 417 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 && 418 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 && 419 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 ) 420 { 421 return( 0 ); 422 } 423 424 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 425 } 426 427 /* 428 * Import a non-zero point from ASCII strings 429 */ 430 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix, 431 const char *x, const char *y ) 432 { 433 int ret; 434 435 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) ); 436 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) ); 437 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) ); 438 439 cleanup: 440 return( ret ); 441 } 442 443 /* 444 * Export a point into unsigned binary data (SEC1 2.3.3) 445 */ 446 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P, 447 int format, size_t *olen, 448 unsigned char *buf, size_t buflen ) 449 { 450 int ret = 0; 451 size_t plen; 452 453 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED && 454 format != MBEDTLS_ECP_PF_COMPRESSED ) 455 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 456 457 /* 458 * Common case: P == 0 459 */ 460 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 ) 461 { 462 if( buflen < 1 ) 463 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); 464 465 buf[0] = 0x00; 466 *olen = 1; 467 468 return( 0 ); 469 } 470 471 plen = mbedtls_mpi_size( &grp->P ); 472 473 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED ) 474 { 475 *olen = 2 * plen + 1; 476 477 if( buflen < *olen ) 478 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); 479 480 buf[0] = 0x04; 481 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) ); 482 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) ); 483 } 484 else if( format == MBEDTLS_ECP_PF_COMPRESSED ) 485 { 486 *olen = plen + 1; 487 488 if( buflen < *olen ) 489 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); 490 491 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 ); 492 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) ); 493 } 494 495 cleanup: 496 return( ret ); 497 } 498 499 /* 500 * Import a point from unsigned binary data (SEC1 2.3.4) 501 */ 502 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, 503 const unsigned char *buf, size_t ilen ) 504 { 505 int ret; 506 size_t plen; 507 508 if( ilen < 1 ) 509 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 510 511 if( buf[0] == 0x00 ) 512 { 513 if( ilen == 1 ) 514 return( mbedtls_ecp_set_zero( pt ) ); 515 else 516 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 517 } 518 519 plen = mbedtls_mpi_size( &grp->P ); 520 521 if( buf[0] != 0x04 ) 522 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); 523 524 if( ilen != 2 * plen + 1 ) 525 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 526 527 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) ); 528 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) ); 529 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); 530 531 cleanup: 532 return( ret ); 533 } 534 535 /* 536 * Import a point from a TLS ECPoint record (RFC 4492) 537 * struct { 538 * opaque point <1..2^8-1>; 539 * } ECPoint; 540 */ 541 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, 542 const unsigned char **buf, size_t buf_len ) 543 { 544 unsigned char data_len; 545 const unsigned char *buf_start; 546 547 /* 548 * We must have at least two bytes (1 for length, at least one for data) 549 */ 550 if( buf_len < 2 ) 551 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 552 553 data_len = *(*buf)++; 554 if( data_len < 1 || data_len > buf_len - 1 ) 555 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 556 557 /* 558 * Save buffer start for read_binary and update buf 559 */ 560 buf_start = *buf; 561 *buf += data_len; 562 563 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ); 564 } 565 566 /* 567 * Export a point as a TLS ECPoint record (RFC 4492) 568 * struct { 569 * opaque point <1..2^8-1>; 570 * } ECPoint; 571 */ 572 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt, 573 int format, size_t *olen, 574 unsigned char *buf, size_t blen ) 575 { 576 int ret; 577 578 /* 579 * buffer length must be at least one, for our length byte 580 */ 581 if( blen < 1 ) 582 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 583 584 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format, 585 olen, buf + 1, blen - 1) ) != 0 ) 586 return( ret ); 587 588 /* 589 * write length to the first byte and update total length 590 */ 591 buf[0] = (unsigned char) *olen; 592 ++*olen; 593 594 return( 0 ); 595 } 596 597 /* 598 * Set a group from an ECParameters record (RFC 4492) 599 */ 600 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len ) 601 { 602 uint16_t tls_id; 603 const mbedtls_ecp_curve_info *curve_info; 604 605 /* 606 * We expect at least three bytes (see below) 607 */ 608 if( len < 3 ) 609 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 610 611 /* 612 * First byte is curve_type; only named_curve is handled 613 */ 614 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE ) 615 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 616 617 /* 618 * Next two bytes are the namedcurve value 619 */ 620 tls_id = *(*buf)++; 621 tls_id <<= 8; 622 tls_id |= *(*buf)++; 623 624 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL ) 625 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); 626 627 return mbedtls_ecp_group_load( grp, curve_info->grp_id ); 628 } 629 630 /* 631 * Write the ECParameters record corresponding to a group (RFC 4492) 632 */ 633 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen, 634 unsigned char *buf, size_t blen ) 635 { 636 const mbedtls_ecp_curve_info *curve_info; 637 638 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL ) 639 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 640 641 /* 642 * We are going to write 3 bytes (see below) 643 */ 644 *olen = 3; 645 if( blen < *olen ) 646 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); 647 648 /* 649 * First byte is curve_type, always named_curve 650 */ 651 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE; 652 653 /* 654 * Next two bytes are the namedcurve value 655 */ 656 buf[0] = curve_info->tls_id >> 8; 657 buf[1] = curve_info->tls_id & 0xFF; 658 659 return( 0 ); 660 } 661 662 /* 663 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi. 664 * See the documentation of struct mbedtls_ecp_group. 665 * 666 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf. 667 */ 668 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp ) 669 { 670 int ret; 671 672 if( grp->modp == NULL ) 673 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) ); 674 675 /* N->s < 0 is a much faster test, which fails only if N is 0 */ 676 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) || 677 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits ) 678 { 679 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 680 } 681 682 MBEDTLS_MPI_CHK( grp->modp( N ) ); 683 684 /* N->s < 0 is a much faster test, which fails only if N is 0 */ 685 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) 686 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) ); 687 688 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 ) 689 /* we known P, N and the result are positive */ 690 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) ); 691 692 cleanup: 693 return( ret ); 694 } 695 696 /* 697 * Fast mod-p functions expect their argument to be in the 0..p^2 range. 698 * 699 * In order to guarantee that, we need to ensure that operands of 700 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will 701 * bring the result back to this range. 702 * 703 * The following macros are shortcuts for doing that. 704 */ 705 706 /* 707 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi 708 */ 709 #if defined(MBEDTLS_SELF_TEST) 710 #define INC_MUL_COUNT mul_count++; 711 #else 712 #define INC_MUL_COUNT 713 #endif 714 715 #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \ 716 while( 0 ) 717 718 /* 719 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi 720 * N->s < 0 is a very fast test, which fails only if N is 0 721 */ 722 #define MOD_SUB( N ) \ 723 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \ 724 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) ) 725 726 /* 727 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int. 728 * We known P, N and the result are positive, so sub_abs is correct, and 729 * a bit faster. 730 */ 731 #define MOD_ADD( N ) \ 732 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \ 733 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) ) 734 735 #if defined(ECP_SHORTWEIERSTRASS) 736 /* 737 * For curves in short Weierstrass form, we do all the internal operations in 738 * Jacobian coordinates. 739 * 740 * For multiplication, we'll use a comb method with coutermeasueres against 741 * SPA, hence timing attacks. 742 */ 743 744 /* 745 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1) 746 * Cost: 1N := 1I + 3M + 1S 747 */ 748 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt ) 749 { 750 int ret; 751 mbedtls_mpi Zi, ZZi; 752 753 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 ) 754 return( 0 ); 755 756 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) 757 if ( mbedtls_internal_ecp_grp_capable( grp ) ) 758 { 759 return mbedtls_internal_ecp_normalize_jac( grp, pt ); 760 } 761 #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */ 762 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi ); 763 764 /* 765 * X = X / Z^2 mod p 766 */ 767 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) ); 768 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi ); 769 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X ); 770 771 /* 772 * Y = Y / Z^3 mod p 773 */ 774 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y ); 775 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y ); 776 777 /* 778 * Z = 1 779 */ 780 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); 781 782 cleanup: 783 784 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi ); 785 786 return( ret ); 787 } 788 789 /* 790 * Normalize jacobian coordinates of an array of (pointers to) points, 791 * using Montgomery's trick to perform only one inversion mod P. 792 * (See for example Cohen's "A Course in Computational Algebraic Number 793 * Theory", Algorithm 10.3.4.) 794 * 795 * Warning: fails (returning an error) if one of the points is zero! 796 * This should never happen, see choice of w in ecp_mul_comb(). 797 * 798 * Cost: 1N(t) := 1I + (6t - 3)M + 1S 799 */ 800 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp, 801 mbedtls_ecp_point *T[], size_t t_len ) 802 { 803 int ret; 804 size_t i; 805 mbedtls_mpi *c, u, Zi, ZZi; 806 807 if( t_len < 2 ) 808 return( ecp_normalize_jac( grp, *T ) ); 809 810 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) 811 if ( mbedtls_internal_ecp_grp_capable( grp ) ) 812 { 813 return mbedtls_internal_ecp_normalize_jac_many(grp, T, t_len); 814 } 815 #endif 816 817 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL ) 818 return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); 819 820 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi ); 821 822 /* 823 * c[i] = Z_0 * ... * Z_i 824 */ 825 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) ); 826 for( i = 1; i < t_len; i++ ) 827 { 828 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) ); 829 MOD_MUL( c[i] ); 830 } 831 832 /* 833 * u = 1 / (Z_0 * ... * Z_n) mod P 834 */ 835 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) ); 836 837 for( i = t_len - 1; ; i-- ) 838 { 839 /* 840 * Zi = 1 / Z_i mod p 841 * u = 1 / (Z_0 * ... * Z_i) mod P 842 */ 843 if( i == 0 ) { 844 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) ); 845 } 846 else 847 { 848 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi ); 849 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u ); 850 } 851 852 /* 853 * proceed as in normalize() 854 */ 855 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi ); 856 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X ); 857 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y ); 858 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y ); 859 860 /* 861 * Post-precessing: reclaim some memory by shrinking coordinates 862 * - not storing Z (always 1) 863 * - shrinking other coordinates, but still keeping the same number of 864 * limbs as P, as otherwise it will too likely be regrown too fast. 865 */ 866 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) ); 867 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) ); 868 mbedtls_mpi_free( &T[i]->Z ); 869 870 if( i == 0 ) 871 break; 872 } 873 874 cleanup: 875 876 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi ); 877 for( i = 0; i < t_len; i++ ) 878 mbedtls_mpi_free( &c[i] ); 879 mbedtls_free( c ); 880 881 return( ret ); 882 } 883 884 /* 885 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak. 886 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid 887 */ 888 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp, 889 mbedtls_ecp_point *Q, 890 unsigned char inv ) 891 { 892 int ret; 893 unsigned char nonzero; 894 mbedtls_mpi mQY; 895 896 mbedtls_mpi_init( &mQY ); 897 898 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */ 899 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) ); 900 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0; 901 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) ); 902 903 cleanup: 904 mbedtls_mpi_free( &mQY ); 905 906 return( ret ); 907 } 908 909 /* 910 * Point doubling R = 2 P, Jacobian coordinates 911 * 912 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 . 913 * 914 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR 915 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring. 916 * 917 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }. 918 * 919 * Cost: 1D := 3M + 4S (A == 0) 920 * 4M + 4S (A == -3) 921 * 3M + 6S + 1a otherwise 922 */ 923 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 924 const mbedtls_ecp_point *P ) 925 { 926 int ret; 927 mbedtls_mpi M, S, T, U; 928 929 #if defined(MBEDTLS_SELF_TEST) 930 dbl_count++; 931 #endif 932 933 #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) 934 if ( mbedtls_internal_ecp_grp_capable( grp ) ) 935 { 936 return mbedtls_internal_ecp_double_jac( grp, R, P ); 937 } 938 #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */ 939 940 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U ); 941 942 /* Special case for A = -3 */ 943 if( grp->A.p == NULL ) 944 { 945 /* M = 3(X + Z^2)(X - Z^2) */ 946 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S ); 947 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T ); 948 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U ); 949 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S ); 950 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M ); 951 } 952 else 953 { 954 /* M = 3.X^2 */ 955 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S ); 956 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M ); 957 958 /* Optimize away for "koblitz" curves with A = 0 */ 959 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 ) 960 { 961 /* M += A.Z^4 */ 962 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S ); 963 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T ); 964 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S ); 965 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M ); 966 } 967 } 968 969 /* S = 4.X.Y^2 */ 970 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T ); 971 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T ); 972 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S ); 973 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S ); 974 975 /* U = 8.Y^4 */ 976 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U ); 977 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U ); 978 979 /* T = M^2 - 2.S */ 980 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T ); 981 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T ); 982 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T ); 983 984 /* S = M(S - T) - U */ 985 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S ); 986 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S ); 987 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S ); 988 989 /* U = 2.Y.Z */ 990 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U ); 991 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U ); 992 993 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) ); 994 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) ); 995 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) ); 996 997 cleanup: 998 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U ); 999 1000 return( ret ); 1001 } 1002 1003 /* 1004 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22) 1005 * 1006 * The coordinates of Q must be normalized (= affine), 1007 * but those of P don't need to. R is not normalized. 1008 * 1009 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q. 1010 * None of these cases can happen as intermediate step in ecp_mul_comb(): 1011 * - at each step, P, Q and R are multiples of the base point, the factor 1012 * being less than its order, so none of them is zero; 1013 * - Q is an odd multiple of the base point, P an even multiple, 1014 * due to the choice of precomputed points in the modified comb method. 1015 * So branches for these cases do not leak secret information. 1016 * 1017 * We accept Q->Z being unset (saving memory in tables) as meaning 1. 1018 * 1019 * Cost: 1A := 8M + 3S 1020 */ 1021 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1022 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ) 1023 { 1024 int ret; 1025 mbedtls_mpi T1, T2, T3, T4, X, Y, Z; 1026 1027 #if defined(MBEDTLS_SELF_TEST) 1028 add_count++; 1029 #endif 1030 1031 #if defined(MBEDTLS_ECP_ADD_MIXED_ALT) 1032 if ( mbedtls_internal_ecp_grp_capable( grp ) ) 1033 { 1034 return mbedtls_internal_ecp_add_mixed( grp, R, P, Q ); 1035 } 1036 #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */ 1037 1038 /* 1039 * Trivial cases: P == 0 or Q == 0 (case 1) 1040 */ 1041 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 ) 1042 return( mbedtls_ecp_copy( R, Q ) ); 1043 1044 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 ) 1045 return( mbedtls_ecp_copy( R, P ) ); 1046 1047 /* 1048 * Make sure Q coordinates are normalized 1049 */ 1050 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 ) 1051 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1052 1053 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 ); 1054 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); 1055 1056 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 ); 1057 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 ); 1058 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 ); 1059 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 ); 1060 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 ); 1061 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 ); 1062 1063 /* Special cases (2) and (3) */ 1064 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 ) 1065 { 1066 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 ) 1067 { 1068 ret = ecp_double_jac( grp, R, P ); 1069 goto cleanup; 1070 } 1071 else 1072 { 1073 ret = mbedtls_ecp_set_zero( R ); 1074 goto cleanup; 1075 } 1076 } 1077 1078 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z ); 1079 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 ); 1080 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 ); 1081 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 ); 1082 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 ); 1083 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X ); 1084 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X ); 1085 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X ); 1086 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 ); 1087 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 ); 1088 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 ); 1089 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y ); 1090 1091 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) ); 1092 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) ); 1093 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) ); 1094 1095 cleanup: 1096 1097 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 ); 1098 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); 1099 1100 return( ret ); 1101 } 1102 1103 /* 1104 * Randomize jacobian coordinates: 1105 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l 1106 * This is sort of the reverse operation of ecp_normalize_jac(). 1107 * 1108 * This countermeasure was first suggested in [2]. 1109 */ 1110 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, 1111 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) 1112 { 1113 int ret; 1114 mbedtls_mpi l, ll; 1115 size_t p_size; 1116 int count = 0; 1117 1118 #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) 1119 if ( mbedtls_internal_ecp_grp_capable( grp ) ) 1120 { 1121 return mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng ); 1122 } 1123 #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */ 1124 1125 p_size = ( grp->pbits + 7 ) / 8; 1126 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll ); 1127 1128 /* Generate l such that 1 < l < p */ 1129 do 1130 { 1131 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) ); 1132 1133 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 ) 1134 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) ); 1135 1136 if( count++ > 10 ) 1137 return( MBEDTLS_ERR_ECP_RANDOM_FAILED ); 1138 } 1139 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 ); 1140 1141 /* Z = l * Z */ 1142 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z ); 1143 1144 /* X = l^2 * X */ 1145 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll ); 1146 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X ); 1147 1148 /* Y = l^3 * Y */ 1149 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll ); 1150 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y ); 1151 1152 cleanup: 1153 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll ); 1154 1155 return( ret ); 1156 } 1157 1158 /* 1159 * Check and define parameters used by the comb method (see below for details) 1160 */ 1161 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7 1162 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds" 1163 #endif 1164 1165 /* d = ceil( n / w ) */ 1166 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2 1167 1168 /* number of precomputed points */ 1169 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) ) 1170 1171 /* 1172 * Compute the representation of m that will be used with our comb method. 1173 * 1174 * The basic comb method is described in GECC 3.44 for example. We use a 1175 * modified version that provides resistance to SPA by avoiding zero 1176 * digits in the representation as in [3]. We modify the method further by 1177 * requiring that all K_i be odd, which has the small cost that our 1178 * representation uses one more K_i, due to carries. 1179 * 1180 * Also, for the sake of compactness, only the seven low-order bits of x[i] 1181 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in 1182 * the paper): it is set if and only if if s_i == -1; 1183 * 1184 * Calling conventions: 1185 * - x is an array of size d + 1 1186 * - w is the size, ie number of teeth, of the comb, and must be between 1187 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE) 1188 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d 1189 * (the result will be incorrect if these assumptions are not satisfied) 1190 */ 1191 static void ecp_comb_fixed( unsigned char x[], size_t d, 1192 unsigned char w, const mbedtls_mpi *m ) 1193 { 1194 size_t i, j; 1195 unsigned char c, cc, adjust; 1196 1197 memset( x, 0, d+1 ); 1198 1199 /* First get the classical comb values (except for x_d = 0) */ 1200 for( i = 0; i < d; i++ ) 1201 for( j = 0; j < w; j++ ) 1202 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j; 1203 1204 /* Now make sure x_1 .. x_d are odd */ 1205 c = 0; 1206 for( i = 1; i <= d; i++ ) 1207 { 1208 /* Add carry and update it */ 1209 cc = x[i] & c; 1210 x[i] = x[i] ^ c; 1211 c = cc; 1212 1213 /* Adjust if needed, avoiding branches */ 1214 adjust = 1 - ( x[i] & 0x01 ); 1215 c |= x[i] & ( x[i-1] * adjust ); 1216 x[i] = x[i] ^ ( x[i-1] * adjust ); 1217 x[i-1] |= adjust << 7; 1218 } 1219 } 1220 1221 /* 1222 * Precompute points for the comb method 1223 * 1224 * If i = i_{w-1} ... i_1 is the binary representation of i, then 1225 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P 1226 * 1227 * T must be able to hold 2^{w - 1} elements 1228 * 1229 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1) 1230 */ 1231 static int ecp_precompute_comb( const mbedtls_ecp_group *grp, 1232 mbedtls_ecp_point T[], const mbedtls_ecp_point *P, 1233 unsigned char w, size_t d ) 1234 { 1235 int ret; 1236 unsigned char i, k; 1237 size_t j; 1238 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1]; 1239 1240 /* 1241 * Set T[0] = P and 1242 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value) 1243 */ 1244 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) ); 1245 1246 k = 0; 1247 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 ) 1248 { 1249 cur = T + i; 1250 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) ); 1251 for( j = 0; j < d; j++ ) 1252 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) ); 1253 1254 TT[k++] = cur; 1255 } 1256 1257 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) ); 1258 1259 /* 1260 * Compute the remaining ones using the minimal number of additions 1261 * Be careful to update T[2^l] only after using it! 1262 */ 1263 k = 0; 1264 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 ) 1265 { 1266 j = i; 1267 while( j-- ) 1268 { 1269 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) ); 1270 TT[k++] = &T[i + j]; 1271 } 1272 } 1273 1274 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) ); 1275 1276 cleanup: 1277 1278 return( ret ); 1279 } 1280 1281 /* 1282 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ] 1283 */ 1284 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1285 const mbedtls_ecp_point T[], unsigned char t_len, 1286 unsigned char i ) 1287 { 1288 int ret; 1289 unsigned char ii, j; 1290 1291 /* Ignore the "sign" bit and scale down */ 1292 ii = ( i & 0x7Fu ) >> 1; 1293 1294 /* Read the whole table to thwart cache-based timing attacks */ 1295 for( j = 0; j < t_len; j++ ) 1296 { 1297 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) ); 1298 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) ); 1299 } 1300 1301 /* Safely invert result if i is "negative" */ 1302 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) ); 1303 1304 cleanup: 1305 return( ret ); 1306 } 1307 1308 /* 1309 * Core multiplication algorithm for the (modified) comb method. 1310 * This part is actually common with the basic comb method (GECC 3.44) 1311 * 1312 * Cost: d A + d D + 1 R 1313 */ 1314 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1315 const mbedtls_ecp_point T[], unsigned char t_len, 1316 const unsigned char x[], size_t d, 1317 int (*f_rng)(void *, unsigned char *, size_t), 1318 void *p_rng ) 1319 { 1320 int ret; 1321 mbedtls_ecp_point Txi; 1322 size_t i; 1323 1324 mbedtls_ecp_point_init( &Txi ); 1325 1326 /* Start with a non-zero point and randomize its coordinates */ 1327 i = d; 1328 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) ); 1329 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) ); 1330 if( f_rng != 0 ) 1331 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) ); 1332 1333 while( i-- != 0 ) 1334 { 1335 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) ); 1336 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) ); 1337 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) ); 1338 } 1339 1340 cleanup: 1341 1342 mbedtls_ecp_point_free( &Txi ); 1343 1344 return( ret ); 1345 } 1346 1347 /* 1348 * Multiplication using the comb method, 1349 * for curves in short Weierstrass form 1350 */ 1351 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1352 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1353 int (*f_rng)(void *, unsigned char *, size_t), 1354 void *p_rng ) 1355 { 1356 int ret; 1357 unsigned char w, m_is_odd, p_eq_g, pre_len, i; 1358 size_t d; 1359 unsigned char k[COMB_MAX_D + 1]; 1360 mbedtls_ecp_point *T; 1361 mbedtls_mpi M, mm; 1362 1363 mbedtls_mpi_init( &M ); 1364 mbedtls_mpi_init( &mm ); 1365 1366 /* we need N to be odd to trnaform m in an odd number, check now */ 1367 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 ) 1368 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1369 1370 /* 1371 * Minimize the number of multiplications, that is minimize 1372 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w ) 1373 * (see costs of the various parts, with 1S = 1M) 1374 */ 1375 w = grp->nbits >= 384 ? 5 : 4; 1376 1377 /* 1378 * If P == G, pre-compute a bit more, since this may be re-used later. 1379 * Just adding one avoids upping the cost of the first mul too much, 1380 * and the memory cost too. 1381 */ 1382 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 1383 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 && 1384 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 ); 1385 if( p_eq_g ) 1386 w++; 1387 #else 1388 p_eq_g = 0; 1389 #endif 1390 1391 /* 1392 * Make sure w is within bounds. 1393 * (The last test is useful only for very small curves in the test suite.) 1394 */ 1395 if( w > MBEDTLS_ECP_WINDOW_SIZE ) 1396 w = MBEDTLS_ECP_WINDOW_SIZE; 1397 if( w >= grp->nbits ) 1398 w = 2; 1399 1400 /* Other sizes that depend on w */ 1401 pre_len = 1U << ( w - 1 ); 1402 d = ( grp->nbits + w - 1 ) / w; 1403 1404 /* 1405 * Prepare precomputed points: if P == G we want to 1406 * use grp->T if already initialized, or initialize it. 1407 */ 1408 T = p_eq_g ? grp->T : NULL; 1409 1410 if( T == NULL ) 1411 { 1412 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) ); 1413 if( T == NULL ) 1414 { 1415 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED; 1416 goto cleanup; 1417 } 1418 1419 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) ); 1420 1421 if( p_eq_g ) 1422 { 1423 grp->T = T; 1424 grp->T_size = pre_len; 1425 } 1426 } 1427 1428 /* 1429 * Make sure M is odd (M = m or M = N - m, since N is odd) 1430 * using the fact that m * P = - (N - m) * P 1431 */ 1432 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 ); 1433 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) ); 1434 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) ); 1435 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) ); 1436 1437 /* 1438 * Go for comb multiplication, R = M * P 1439 */ 1440 ecp_comb_fixed( k, d, w, &M ); 1441 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) ); 1442 1443 /* 1444 * Now get m * P from M * P and normalize it 1445 */ 1446 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) ); 1447 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) ); 1448 1449 cleanup: 1450 1451 if( T != NULL && ! p_eq_g ) 1452 { 1453 for( i = 0; i < pre_len; i++ ) 1454 mbedtls_ecp_point_free( &T[i] ); 1455 mbedtls_free( T ); 1456 } 1457 1458 mbedtls_mpi_free( &M ); 1459 mbedtls_mpi_free( &mm ); 1460 1461 if( ret != 0 ) 1462 mbedtls_ecp_point_free( R ); 1463 1464 return( ret ); 1465 } 1466 1467 #endif /* ECP_SHORTWEIERSTRASS */ 1468 1469 #if defined(ECP_MONTGOMERY) 1470 /* 1471 * For Montgomery curves, we do all the internal arithmetic in projective 1472 * coordinates. Import/export of points uses only the x coordinates, which is 1473 * internaly represented as X / Z. 1474 * 1475 * For scalar multiplication, we'll use a Montgomery ladder. 1476 */ 1477 1478 /* 1479 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1 1480 * Cost: 1M + 1I 1481 */ 1482 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P ) 1483 { 1484 int ret; 1485 1486 #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) 1487 if ( mbedtls_internal_ecp_grp_capable( grp ) ) 1488 { 1489 return mbedtls_internal_ecp_normalize_mxz( grp, P ); 1490 } 1491 #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */ 1492 1493 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) ); 1494 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X ); 1495 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) ); 1496 1497 cleanup: 1498 return( ret ); 1499 } 1500 1501 /* 1502 * Randomize projective x/z coordinates: 1503 * (X, Z) -> (l X, l Z) for random l 1504 * This is sort of the reverse operation of ecp_normalize_mxz(). 1505 * 1506 * This countermeasure was first suggested in [2]. 1507 * Cost: 2M 1508 */ 1509 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P, 1510 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) 1511 { 1512 int ret; 1513 mbedtls_mpi l; 1514 size_t p_size; 1515 int count = 0; 1516 1517 #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) 1518 if ( mbedtls_internal_ecp_grp_capable( grp ) ) 1519 { 1520 return mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng ); 1521 } 1522 #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */ 1523 1524 p_size = ( grp->pbits + 7 ) / 8; 1525 mbedtls_mpi_init( &l ); 1526 1527 /* Generate l such that 1 < l < p */ 1528 do 1529 { 1530 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) ); 1531 1532 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 ) 1533 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) ); 1534 1535 if( count++ > 10 ) 1536 return( MBEDTLS_ERR_ECP_RANDOM_FAILED ); 1537 } 1538 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 ); 1539 1540 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X ); 1541 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z ); 1542 1543 cleanup: 1544 mbedtls_mpi_free( &l ); 1545 1546 return( ret ); 1547 } 1548 1549 /* 1550 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q), 1551 * for Montgomery curves in x/z coordinates. 1552 * 1553 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3 1554 * with 1555 * d = X1 1556 * P = (X2, Z2) 1557 * Q = (X3, Z3) 1558 * R = (X4, Z4) 1559 * S = (X5, Z5) 1560 * and eliminating temporary variables tO, ..., t4. 1561 * 1562 * Cost: 5M + 4S 1563 */ 1564 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp, 1565 mbedtls_ecp_point *R, mbedtls_ecp_point *S, 1566 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q, 1567 const mbedtls_mpi *d ) 1568 { 1569 int ret; 1570 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB; 1571 1572 #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) 1573 if ( mbedtls_internal_ecp_grp_capable( grp ) ) 1574 { 1575 return mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d ); 1576 } 1577 #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */ 1578 1579 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B ); 1580 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C ); 1581 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB ); 1582 1583 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A ); 1584 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA ); 1585 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B ); 1586 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB ); 1587 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E ); 1588 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C ); 1589 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D ); 1590 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA ); 1591 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB ); 1592 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X ); 1593 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X ); 1594 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z ); 1595 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z ); 1596 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z ); 1597 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X ); 1598 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z ); 1599 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z ); 1600 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z ); 1601 1602 cleanup: 1603 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B ); 1604 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C ); 1605 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB ); 1606 1607 return( ret ); 1608 } 1609 1610 /* 1611 * Multiplication with Montgomery ladder in x/z coordinates, 1612 * for curves in Montgomery form 1613 */ 1614 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1615 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1616 int (*f_rng)(void *, unsigned char *, size_t), 1617 void *p_rng ) 1618 { 1619 int ret; 1620 size_t i; 1621 unsigned char b; 1622 mbedtls_ecp_point RP; 1623 mbedtls_mpi PX; 1624 1625 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX ); 1626 1627 /* Save PX and read from P before writing to R, in case P == R */ 1628 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) ); 1629 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) ); 1630 1631 /* Set R to zero in modified x/z coordinates */ 1632 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) ); 1633 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) ); 1634 mbedtls_mpi_free( &R->Y ); 1635 1636 /* RP.X might be sligtly larger than P, so reduce it */ 1637 MOD_ADD( RP.X ); 1638 1639 /* Randomize coordinates of the starting point */ 1640 if( f_rng != NULL ) 1641 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) ); 1642 1643 /* Loop invariant: R = result so far, RP = R + P */ 1644 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */ 1645 while( i-- > 0 ) 1646 { 1647 b = mbedtls_mpi_get_bit( m, i ); 1648 /* 1649 * if (b) R = 2R + P else R = 2R, 1650 * which is: 1651 * if (b) double_add( RP, R, RP, R ) 1652 * else double_add( R, RP, R, RP ) 1653 * but using safe conditional swaps to avoid leaks 1654 */ 1655 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) ); 1656 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) ); 1657 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) ); 1658 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) ); 1659 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) ); 1660 } 1661 1662 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) ); 1663 1664 cleanup: 1665 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX ); 1666 1667 return( ret ); 1668 } 1669 1670 #endif /* ECP_MONTGOMERY */ 1671 1672 /* 1673 * Multiplication R = m * P 1674 */ 1675 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1676 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1677 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) 1678 { 1679 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 1680 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 1681 char is_grp_capable = 0; 1682 #endif 1683 1684 /* Common sanity checks */ 1685 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 ) 1686 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1687 1688 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 || 1689 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 ) 1690 return( ret ); 1691 1692 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 1693 if ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) 1694 { 1695 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) ); 1696 } 1697 1698 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 1699 #if defined(ECP_MONTGOMERY) 1700 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) 1701 ret = ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ); 1702 1703 #endif 1704 #if defined(ECP_SHORTWEIERSTRASS) 1705 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS ) 1706 ret = ecp_mul_comb( grp, R, m, P, f_rng, p_rng ); 1707 1708 #endif 1709 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 1710 cleanup: 1711 1712 if ( is_grp_capable ) 1713 { 1714 mbedtls_internal_ecp_free( grp ); 1715 } 1716 1717 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 1718 return( ret ); 1719 } 1720 1721 #if defined(ECP_SHORTWEIERSTRASS) 1722 /* 1723 * Check that an affine point is valid as a public key, 1724 * short weierstrass curves (SEC1 3.2.3.1) 1725 */ 1726 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ) 1727 { 1728 int ret; 1729 mbedtls_mpi YY, RHS; 1730 1731 /* pt coordinates must be normalized for our checks */ 1732 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 || 1733 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 || 1734 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 || 1735 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 ) 1736 return( MBEDTLS_ERR_ECP_INVALID_KEY ); 1737 1738 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS ); 1739 1740 /* 1741 * YY = Y^2 1742 * RHS = X (X^2 + A) + B = X^3 + A X + B 1743 */ 1744 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY ); 1745 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS ); 1746 1747 /* Special case for A = -3 */ 1748 if( grp->A.p == NULL ) 1749 { 1750 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS ); 1751 } 1752 else 1753 { 1754 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS ); 1755 } 1756 1757 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS ); 1758 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS ); 1759 1760 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 ) 1761 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 1762 1763 cleanup: 1764 1765 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS ); 1766 1767 return( ret ); 1768 } 1769 #endif /* ECP_SHORTWEIERSTRASS */ 1770 1771 /* 1772 * R = m * P with shortcuts for m == 1 and m == -1 1773 * NOT constant-time - ONLY for short Weierstrass! 1774 */ 1775 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp, 1776 mbedtls_ecp_point *R, 1777 const mbedtls_mpi *m, 1778 const mbedtls_ecp_point *P ) 1779 { 1780 int ret; 1781 1782 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 ) 1783 { 1784 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) ); 1785 } 1786 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 ) 1787 { 1788 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) ); 1789 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 ) 1790 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) ); 1791 } 1792 else 1793 { 1794 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) ); 1795 } 1796 1797 cleanup: 1798 return( ret ); 1799 } 1800 1801 /* 1802 * Linear combination 1803 * NOT constant-time 1804 */ 1805 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1806 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1807 const mbedtls_mpi *n, const mbedtls_ecp_point *Q ) 1808 { 1809 int ret; 1810 mbedtls_ecp_point mP; 1811 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 1812 char is_grp_capable = 0; 1813 #endif 1814 1815 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS ) 1816 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); 1817 1818 mbedtls_ecp_point_init( &mP ); 1819 1820 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) ); 1821 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) ); 1822 1823 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 1824 if ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) 1825 { 1826 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) ); 1827 } 1828 1829 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 1830 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) ); 1831 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) ); 1832 1833 cleanup: 1834 1835 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 1836 if ( is_grp_capable ) 1837 { 1838 mbedtls_internal_ecp_free( grp ); 1839 } 1840 1841 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 1842 mbedtls_ecp_point_free( &mP ); 1843 1844 return( ret ); 1845 } 1846 1847 1848 #if defined(ECP_MONTGOMERY) 1849 /* 1850 * Check validity of a public key for Montgomery curves with x-only schemes 1851 */ 1852 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ) 1853 { 1854 /* [Curve25519 p. 5] Just check X is the correct number of bytes */ 1855 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 ) 1856 return( MBEDTLS_ERR_ECP_INVALID_KEY ); 1857 1858 return( 0 ); 1859 } 1860 #endif /* ECP_MONTGOMERY */ 1861 1862 /* 1863 * Check that a point is valid as a public key 1864 */ 1865 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ) 1866 { 1867 /* Must use affine coordinates */ 1868 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 ) 1869 return( MBEDTLS_ERR_ECP_INVALID_KEY ); 1870 1871 #if defined(ECP_MONTGOMERY) 1872 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) 1873 return( ecp_check_pubkey_mx( grp, pt ) ); 1874 #endif 1875 #if defined(ECP_SHORTWEIERSTRASS) 1876 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS ) 1877 return( ecp_check_pubkey_sw( grp, pt ) ); 1878 #endif 1879 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1880 } 1881 1882 /* 1883 * Check that an mbedtls_mpi is valid as a private key 1884 */ 1885 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d ) 1886 { 1887 #if defined(ECP_MONTGOMERY) 1888 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) 1889 { 1890 /* see [Curve25519] page 5 */ 1891 if( mbedtls_mpi_get_bit( d, 0 ) != 0 || 1892 mbedtls_mpi_get_bit( d, 1 ) != 0 || 1893 mbedtls_mpi_get_bit( d, 2 ) != 0 || 1894 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */ 1895 return( MBEDTLS_ERR_ECP_INVALID_KEY ); 1896 else 1897 return( 0 ); 1898 } 1899 #endif /* ECP_MONTGOMERY */ 1900 #if defined(ECP_SHORTWEIERSTRASS) 1901 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS ) 1902 { 1903 /* see SEC1 3.2 */ 1904 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 || 1905 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 ) 1906 return( MBEDTLS_ERR_ECP_INVALID_KEY ); 1907 else 1908 return( 0 ); 1909 } 1910 #endif /* ECP_SHORTWEIERSTRASS */ 1911 1912 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1913 } 1914 1915 /* 1916 * Generate a keypair with configurable base point 1917 */ 1918 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp, 1919 const mbedtls_ecp_point *G, 1920 mbedtls_mpi *d, mbedtls_ecp_point *Q, 1921 int (*f_rng)(void *, unsigned char *, size_t), 1922 void *p_rng ) 1923 { 1924 int ret; 1925 size_t n_size = ( grp->nbits + 7 ) / 8; 1926 1927 #if defined(ECP_MONTGOMERY) 1928 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) 1929 { 1930 /* [M225] page 5 */ 1931 size_t b; 1932 1933 do { 1934 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) ); 1935 } while( mbedtls_mpi_bitlen( d ) == 0); 1936 1937 /* Make sure the most significant bit is nbits */ 1938 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */ 1939 if( b > grp->nbits ) 1940 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) ); 1941 else 1942 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) ); 1943 1944 /* Make sure the last three bits are unset */ 1945 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) ); 1946 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) ); 1947 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) ); 1948 } 1949 else 1950 #endif /* ECP_MONTGOMERY */ 1951 #if defined(ECP_SHORTWEIERSTRASS) 1952 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS ) 1953 { 1954 /* SEC1 3.2.1: Generate d such that 1 <= n < N */ 1955 int count = 0; 1956 unsigned char rnd[MBEDTLS_ECP_MAX_BYTES]; 1957 1958 /* 1959 * Match the procedure given in RFC 6979 (deterministic ECDSA): 1960 * - use the same byte ordering; 1961 * - keep the leftmost nbits bits of the generated octet string; 1962 * - try until result is in the desired range. 1963 * This also avoids any biais, which is especially important for ECDSA. 1964 */ 1965 do 1966 { 1967 MBEDTLS_MPI_CHK( f_rng( p_rng, rnd, n_size ) ); 1968 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( d, rnd, n_size ) ); 1969 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) ); 1970 1971 /* 1972 * Each try has at worst a probability 1/2 of failing (the msb has 1973 * a probability 1/2 of being 0, and then the result will be < N), 1974 * so after 30 tries failure probability is a most 2**(-30). 1975 * 1976 * For most curves, 1 try is enough with overwhelming probability, 1977 * since N starts with a lot of 1s in binary, but some curves 1978 * such as secp224k1 are actually very close to the worst case. 1979 */ 1980 if( ++count > 30 ) 1981 return( MBEDTLS_ERR_ECP_RANDOM_FAILED ); 1982 } 1983 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 || 1984 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 ); 1985 } 1986 else 1987 #endif /* ECP_SHORTWEIERSTRASS */ 1988 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1989 1990 cleanup: 1991 if( ret != 0 ) 1992 return( ret ); 1993 1994 return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) ); 1995 } 1996 1997 /* 1998 * Generate key pair, wrapper for conventional base point 1999 */ 2000 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, 2001 mbedtls_mpi *d, mbedtls_ecp_point *Q, 2002 int (*f_rng)(void *, unsigned char *, size_t), 2003 void *p_rng ) 2004 { 2005 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) ); 2006 } 2007 2008 /* 2009 * Generate a keypair, prettier wrapper 2010 */ 2011 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 2012 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) 2013 { 2014 int ret; 2015 2016 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 ) 2017 return( ret ); 2018 2019 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) ); 2020 } 2021 2022 /* 2023 * Check a public-private key pair 2024 */ 2025 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv ) 2026 { 2027 int ret; 2028 mbedtls_ecp_point Q; 2029 mbedtls_ecp_group grp; 2030 2031 if( pub->grp.id == MBEDTLS_ECP_DP_NONE || 2032 pub->grp.id != prv->grp.id || 2033 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) || 2034 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) || 2035 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) ) 2036 { 2037 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 2038 } 2039 2040 mbedtls_ecp_point_init( &Q ); 2041 mbedtls_ecp_group_init( &grp ); 2042 2043 /* mbedtls_ecp_mul() needs a non-const group... */ 2044 mbedtls_ecp_group_copy( &grp, &prv->grp ); 2045 2046 /* Also checks d is valid */ 2047 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) ); 2048 2049 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) || 2050 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) || 2051 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) ) 2052 { 2053 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2054 goto cleanup; 2055 } 2056 2057 cleanup: 2058 mbedtls_ecp_point_free( &Q ); 2059 mbedtls_ecp_group_free( &grp ); 2060 2061 return( ret ); 2062 } 2063 2064 #if defined(MBEDTLS_SELF_TEST) 2065 2066 /* 2067 * Checkup routine 2068 */ 2069 int mbedtls_ecp_self_test( int verbose ) 2070 { 2071 int ret; 2072 size_t i; 2073 mbedtls_ecp_group grp; 2074 mbedtls_ecp_point R, P; 2075 mbedtls_mpi m; 2076 unsigned long add_c_prev, dbl_c_prev, mul_c_prev; 2077 /* exponents especially adapted for secp192r1 */ 2078 const char *exponents[] = 2079 { 2080 "000000000000000000000000000000000000000000000001", /* one */ 2081 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */ 2082 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */ 2083 "400000000000000000000000000000000000000000000000", /* one and zeros */ 2084 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */ 2085 "555555555555555555555555555555555555555555555555", /* 101010... */ 2086 }; 2087 2088 mbedtls_ecp_group_init( &grp ); 2089 mbedtls_ecp_point_init( &R ); 2090 mbedtls_ecp_point_init( &P ); 2091 mbedtls_mpi_init( &m ); 2092 2093 /* Use secp192r1 if available, or any available curve */ 2094 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 2095 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) ); 2096 #else 2097 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) ); 2098 #endif 2099 2100 if( verbose != 0 ) 2101 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " ); 2102 2103 /* Do a dummy multiplication first to trigger precomputation */ 2104 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) ); 2105 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) ); 2106 2107 add_count = 0; 2108 dbl_count = 0; 2109 mul_count = 0; 2110 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) ); 2111 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) ); 2112 2113 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ ) 2114 { 2115 add_c_prev = add_count; 2116 dbl_c_prev = dbl_count; 2117 mul_c_prev = mul_count; 2118 add_count = 0; 2119 dbl_count = 0; 2120 mul_count = 0; 2121 2122 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) ); 2123 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) ); 2124 2125 if( add_count != add_c_prev || 2126 dbl_count != dbl_c_prev || 2127 mul_count != mul_c_prev ) 2128 { 2129 if( verbose != 0 ) 2130 mbedtls_printf( "failed (%u)\n", (unsigned int) i ); 2131 2132 ret = 1; 2133 goto cleanup; 2134 } 2135 } 2136 2137 if( verbose != 0 ) 2138 mbedtls_printf( "passed\n" ); 2139 2140 if( verbose != 0 ) 2141 mbedtls_printf( " ECP test #2 (constant op_count, other point): " ); 2142 /* We computed P = 2G last time, use it */ 2143 2144 add_count = 0; 2145 dbl_count = 0; 2146 mul_count = 0; 2147 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) ); 2148 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) ); 2149 2150 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ ) 2151 { 2152 add_c_prev = add_count; 2153 dbl_c_prev = dbl_count; 2154 mul_c_prev = mul_count; 2155 add_count = 0; 2156 dbl_count = 0; 2157 mul_count = 0; 2158 2159 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) ); 2160 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) ); 2161 2162 if( add_count != add_c_prev || 2163 dbl_count != dbl_c_prev || 2164 mul_count != mul_c_prev ) 2165 { 2166 if( verbose != 0 ) 2167 mbedtls_printf( "failed (%u)\n", (unsigned int) i ); 2168 2169 ret = 1; 2170 goto cleanup; 2171 } 2172 } 2173 2174 if( verbose != 0 ) 2175 mbedtls_printf( "passed\n" ); 2176 2177 cleanup: 2178 2179 if( ret < 0 && verbose != 0 ) 2180 mbedtls_printf( "Unexpected error, return code = %08X\n", ret ); 2181 2182 mbedtls_ecp_group_free( &grp ); 2183 mbedtls_ecp_point_free( &R ); 2184 mbedtls_ecp_point_free( &P ); 2185 mbedtls_mpi_free( &m ); 2186 2187 if( verbose != 0 ) 2188 mbedtls_printf( "\n" ); 2189 2190 return( ret ); 2191 } 2192 2193 #endif /* MBEDTLS_SELF_TEST */ 2194 2195 #endif /* !MBEDTLS_ECP_ALT */ 2196 2197 #endif /* MBEDTLS_ECP_C */ 2198