1 /* 2 * Elliptic curves over GF(p): generic functions 3 * 4 * Copyright The Mbed TLS Contributors 5 * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later 6 */ 7 8 /* 9 * References: 10 * 11 * SEC1 https://www.secg.org/sec1-v2.pdf 12 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone 13 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf 14 * RFC 4492 for the related TLS structures and constants 15 * - https://www.rfc-editor.org/rfc/rfc4492 16 * RFC 7748 for the Curve448 and Curve25519 curve definitions 17 * - https://www.rfc-editor.org/rfc/rfc7748 18 * 19 * [Curve25519] https://cr.yp.to/ecdh/curve25519-20060209.pdf 20 * 21 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis 22 * for elliptic curve cryptosystems. In : Cryptographic Hardware and 23 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302. 24 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25> 25 * 26 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to 27 * render ECC resistant against Side Channel Attacks. IACR Cryptology 28 * ePrint Archive, 2004, vol. 2004, p. 342. 29 * <http://eprint.iacr.org/2004/342.pdf> 30 */ 31 32 #include "common.h" 33 34 /** 35 * \brief Function level alternative implementation. 36 * 37 * The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to 38 * replace certain functions in this module. The alternative implementations are 39 * typically hardware accelerators and need to activate the hardware before the 40 * computation starts and deactivate it after it finishes. The 41 * mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve 42 * this purpose. 43 * 44 * To preserve the correct functionality the following conditions must hold: 45 * 46 * - The alternative implementation must be activated by 47 * mbedtls_internal_ecp_init() before any of the replaceable functions is 48 * called. 49 * - mbedtls_internal_ecp_free() must \b only be called when the alternative 50 * implementation is activated. 51 * - mbedtls_internal_ecp_init() must \b not be called when the alternative 52 * implementation is activated. 53 * - Public functions must not return while the alternative implementation is 54 * activated. 55 * - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and 56 * before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) ) 57 * \endcode ensures that the alternative implementation supports the current 58 * group. 59 */ 60 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 61 #endif 62 63 #if defined(MBEDTLS_ECP_LIGHT) 64 65 #include "mbedtls/ecp.h" 66 #include "mbedtls/threading.h" 67 #include "mbedtls/platform_util.h" 68 #include "mbedtls/error.h" 69 70 #include "bn_mul.h" 71 #include "bignum_internal.h" 72 #include "ecp_invasive.h" 73 74 #include <string.h> 75 76 #if !defined(MBEDTLS_ECP_ALT) 77 78 #include "mbedtls/platform.h" 79 80 #include "ecp_internal_alt.h" 81 82 #if defined(MBEDTLS_SELF_TEST) 83 /* 84 * Counts of point addition and doubling, and field multiplications. 85 * Used to test resistance of point multiplication to simple timing attacks. 86 */ 87 #if defined(MBEDTLS_ECP_C) 88 static unsigned long add_count, dbl_count; 89 #endif /* MBEDTLS_ECP_C */ 90 static unsigned long mul_count; 91 #endif 92 93 #if defined(MBEDTLS_ECP_RESTARTABLE) 94 /* 95 * Maximum number of "basic operations" to be done in a row. 96 * 97 * Default value 0 means that ECC operations will not yield. 98 * Note that regardless of the value of ecp_max_ops, always at 99 * least one step is performed before yielding. 100 * 101 * Setting ecp_max_ops=1 can be suitable for testing purposes 102 * as it will interrupt computation at all possible points. 103 */ 104 static unsigned ecp_max_ops = 0; 105 106 /* 107 * Set ecp_max_ops 108 */ 109 void mbedtls_ecp_set_max_ops(unsigned max_ops) 110 { 111 ecp_max_ops = max_ops; 112 } 113 114 /* 115 * Check if restart is enabled 116 */ 117 int mbedtls_ecp_restart_is_enabled(void) 118 { 119 return ecp_max_ops != 0; 120 } 121 122 /* 123 * Restart sub-context for ecp_mul_comb() 124 */ 125 struct mbedtls_ecp_restart_mul { 126 mbedtls_ecp_point R; /* current intermediate result */ 127 size_t i; /* current index in various loops, 0 outside */ 128 mbedtls_ecp_point *T; /* table for precomputed points */ 129 unsigned char T_size; /* number of points in table T */ 130 enum { /* what were we doing last time we returned? */ 131 ecp_rsm_init = 0, /* nothing so far, dummy initial state */ 132 ecp_rsm_pre_dbl, /* precompute 2^n multiples */ 133 ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */ 134 ecp_rsm_pre_add, /* precompute remaining points by adding */ 135 ecp_rsm_pre_norm_add, /* normalize all precomputed points */ 136 ecp_rsm_comb_core, /* ecp_mul_comb_core() */ 137 ecp_rsm_final_norm, /* do the final normalization */ 138 } state; 139 }; 140 141 /* 142 * Init restart_mul sub-context 143 */ 144 static void ecp_restart_rsm_init(mbedtls_ecp_restart_mul_ctx *ctx) 145 { 146 mbedtls_ecp_point_init(&ctx->R); 147 ctx->i = 0; 148 ctx->T = NULL; 149 ctx->T_size = 0; 150 ctx->state = ecp_rsm_init; 151 } 152 153 /* 154 * Free the components of a restart_mul sub-context 155 */ 156 static void ecp_restart_rsm_free(mbedtls_ecp_restart_mul_ctx *ctx) 157 { 158 unsigned char i; 159 160 if (ctx == NULL) { 161 return; 162 } 163 164 mbedtls_ecp_point_free(&ctx->R); 165 166 if (ctx->T != NULL) { 167 for (i = 0; i < ctx->T_size; i++) { 168 mbedtls_ecp_point_free(ctx->T + i); 169 } 170 mbedtls_free(ctx->T); 171 } 172 173 ecp_restart_rsm_init(ctx); 174 } 175 176 /* 177 * Restart context for ecp_muladd() 178 */ 179 struct mbedtls_ecp_restart_muladd { 180 mbedtls_ecp_point mP; /* mP value */ 181 mbedtls_ecp_point R; /* R intermediate result */ 182 enum { /* what should we do next? */ 183 ecp_rsma_mul1 = 0, /* first multiplication */ 184 ecp_rsma_mul2, /* second multiplication */ 185 ecp_rsma_add, /* addition */ 186 ecp_rsma_norm, /* normalization */ 187 } state; 188 }; 189 190 /* 191 * Init restart_muladd sub-context 192 */ 193 static void ecp_restart_ma_init(mbedtls_ecp_restart_muladd_ctx *ctx) 194 { 195 mbedtls_ecp_point_init(&ctx->mP); 196 mbedtls_ecp_point_init(&ctx->R); 197 ctx->state = ecp_rsma_mul1; 198 } 199 200 /* 201 * Free the components of a restart_muladd sub-context 202 */ 203 static void ecp_restart_ma_free(mbedtls_ecp_restart_muladd_ctx *ctx) 204 { 205 if (ctx == NULL) { 206 return; 207 } 208 209 mbedtls_ecp_point_free(&ctx->mP); 210 mbedtls_ecp_point_free(&ctx->R); 211 212 ecp_restart_ma_init(ctx); 213 } 214 215 /* 216 * Initialize a restart context 217 */ 218 void mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx *ctx) 219 { 220 ctx->ops_done = 0; 221 ctx->depth = 0; 222 ctx->rsm = NULL; 223 ctx->ma = NULL; 224 } 225 226 /* 227 * Free the components of a restart context 228 */ 229 void mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx *ctx) 230 { 231 if (ctx == NULL) { 232 return; 233 } 234 235 ecp_restart_rsm_free(ctx->rsm); 236 mbedtls_free(ctx->rsm); 237 238 ecp_restart_ma_free(ctx->ma); 239 mbedtls_free(ctx->ma); 240 241 mbedtls_ecp_restart_init(ctx); 242 } 243 244 /* 245 * Check if we can do the next step 246 */ 247 int mbedtls_ecp_check_budget(const mbedtls_ecp_group *grp, 248 mbedtls_ecp_restart_ctx *rs_ctx, 249 unsigned ops) 250 { 251 if (rs_ctx != NULL && ecp_max_ops != 0) { 252 /* scale depending on curve size: the chosen reference is 256-bit, 253 * and multiplication is quadratic. Round to the closest integer. */ 254 if (grp->pbits >= 512) { 255 ops *= 4; 256 } else if (grp->pbits >= 384) { 257 ops *= 2; 258 } 259 260 /* Avoid infinite loops: always allow first step. 261 * Because of that, however, it's not generally true 262 * that ops_done <= ecp_max_ops, so the check 263 * ops_done > ecp_max_ops below is mandatory. */ 264 if ((rs_ctx->ops_done != 0) && 265 (rs_ctx->ops_done > ecp_max_ops || 266 ops > ecp_max_ops - rs_ctx->ops_done)) { 267 return MBEDTLS_ERR_ECP_IN_PROGRESS; 268 } 269 270 /* update running count */ 271 rs_ctx->ops_done += ops; 272 } 273 274 return 0; 275 } 276 277 /* Call this when entering a function that needs its own sub-context */ 278 #define ECP_RS_ENTER(SUB) do { \ 279 /* reset ops count for this call if top-level */ \ 280 if (rs_ctx != NULL && rs_ctx->depth++ == 0) \ 281 rs_ctx->ops_done = 0; \ 282 \ 283 /* set up our own sub-context if needed */ \ 284 if (mbedtls_ecp_restart_is_enabled() && \ 285 rs_ctx != NULL && rs_ctx->SUB == NULL) \ 286 { \ 287 rs_ctx->SUB = mbedtls_calloc(1, sizeof(*rs_ctx->SUB)); \ 288 if (rs_ctx->SUB == NULL) \ 289 return MBEDTLS_ERR_ECP_ALLOC_FAILED; \ 290 \ 291 ecp_restart_## SUB ##_init(rs_ctx->SUB); \ 292 } \ 293 } while (0) 294 295 /* Call this when leaving a function that needs its own sub-context */ 296 #define ECP_RS_LEAVE(SUB) do { \ 297 /* clear our sub-context when not in progress (done or error) */ \ 298 if (rs_ctx != NULL && rs_ctx->SUB != NULL && \ 299 ret != MBEDTLS_ERR_ECP_IN_PROGRESS) \ 300 { \ 301 ecp_restart_## SUB ##_free(rs_ctx->SUB); \ 302 mbedtls_free(rs_ctx->SUB); \ 303 rs_ctx->SUB = NULL; \ 304 } \ 305 \ 306 if (rs_ctx != NULL) \ 307 rs_ctx->depth--; \ 308 } while (0) 309 310 #else /* MBEDTLS_ECP_RESTARTABLE */ 311 312 #define ECP_RS_ENTER(sub) (void) rs_ctx; 313 #define ECP_RS_LEAVE(sub) (void) rs_ctx; 314 315 #endif /* MBEDTLS_ECP_RESTARTABLE */ 316 317 #if defined(MBEDTLS_ECP_C) 318 static void mpi_init_many(mbedtls_mpi *arr, size_t size) 319 { 320 while (size--) { 321 mbedtls_mpi_init(arr++); 322 } 323 } 324 325 static void mpi_free_many(mbedtls_mpi *arr, size_t size) 326 { 327 while (size--) { 328 mbedtls_mpi_free(arr++); 329 } 330 } 331 #endif /* MBEDTLS_ECP_C */ 332 333 /* 334 * List of supported curves: 335 * - internal ID 336 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7) 337 * - size in bits 338 * - readable name 339 * 340 * Curves are listed in order: largest curves first, and for a given size, 341 * fastest curves first. 342 * 343 * Reminder: update profiles in x509_crt.c and ssl_tls.c when adding a new curve! 344 */ 345 static const mbedtls_ecp_curve_info ecp_supported_curves[] = 346 { 347 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 348 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" }, 349 #endif 350 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 351 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" }, 352 #endif 353 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 354 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" }, 355 #endif 356 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 357 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" }, 358 #endif 359 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 360 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" }, 361 #endif 362 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 363 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" }, 364 #endif 365 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 366 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" }, 367 #endif 368 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 369 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" }, 370 #endif 371 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 372 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" }, 373 #endif 374 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 375 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" }, 376 #endif 377 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 378 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" }, 379 #endif 380 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 381 { MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" }, 382 #endif 383 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 384 { MBEDTLS_ECP_DP_CURVE448, 30, 448, "x448" }, 385 #endif 386 #if defined(MBEDTLS_ECP_DP_SM2_ENABLED) 387 /* https://tools.ietf.org/id/draft-yang-tls-tls13-sm-suites-05.html */ 388 { MBEDTLS_ECP_DP_SM2, 41, 256, "sm2" }, 389 #endif 390 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL }, 391 }; 392 393 #define ECP_NB_CURVES sizeof(ecp_supported_curves) / \ 394 sizeof(ecp_supported_curves[0]) 395 396 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES]; 397 398 /* 399 * List of supported curves and associated info 400 */ 401 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list(void) 402 { 403 return ecp_supported_curves; 404 } 405 406 /* 407 * List of supported curves, group ID only 408 */ 409 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list(void) 410 { 411 static int init_done = 0; 412 413 if (!init_done) { 414 size_t i = 0; 415 const mbedtls_ecp_curve_info *curve_info; 416 417 for (curve_info = mbedtls_ecp_curve_list(); 418 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 419 curve_info++) { 420 ecp_supported_grp_id[i++] = curve_info->grp_id; 421 } 422 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE; 423 424 init_done = 1; 425 } 426 427 return ecp_supported_grp_id; 428 } 429 430 /* 431 * Get the curve info for the internal identifier 432 */ 433 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id) 434 { 435 const mbedtls_ecp_curve_info *curve_info; 436 437 for (curve_info = mbedtls_ecp_curve_list(); 438 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 439 curve_info++) { 440 if (curve_info->grp_id == grp_id) { 441 return curve_info; 442 } 443 } 444 445 return NULL; 446 } 447 448 /* 449 * Get the curve info from the TLS identifier 450 */ 451 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id) 452 { 453 const mbedtls_ecp_curve_info *curve_info; 454 455 for (curve_info = mbedtls_ecp_curve_list(); 456 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 457 curve_info++) { 458 if (curve_info->tls_id == tls_id) { 459 return curve_info; 460 } 461 } 462 463 return NULL; 464 } 465 466 /* 467 * Get the curve info from the name 468 */ 469 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name(const char *name) 470 { 471 const mbedtls_ecp_curve_info *curve_info; 472 473 if (name == NULL) { 474 return NULL; 475 } 476 477 for (curve_info = mbedtls_ecp_curve_list(); 478 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 479 curve_info++) { 480 if (strcmp(curve_info->name, name) == 0) { 481 return curve_info; 482 } 483 } 484 485 return NULL; 486 } 487 488 /* 489 * Get the type of a curve 490 */ 491 mbedtls_ecp_curve_type mbedtls_ecp_get_type(const mbedtls_ecp_group *grp) 492 { 493 if (grp->G.X.p == NULL) { 494 return MBEDTLS_ECP_TYPE_NONE; 495 } 496 497 if (grp->G.Y.p == NULL) { 498 return MBEDTLS_ECP_TYPE_MONTGOMERY; 499 } else { 500 return MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS; 501 } 502 } 503 504 /* 505 * Initialize (the components of) a point 506 */ 507 void mbedtls_ecp_point_init(mbedtls_ecp_point *pt) 508 { 509 mbedtls_mpi_init(&pt->X); 510 mbedtls_mpi_init(&pt->Y); 511 mbedtls_mpi_init(&pt->Z); 512 } 513 514 /* 515 * Initialize (the components of) a group 516 */ 517 void mbedtls_ecp_group_init(mbedtls_ecp_group *grp) 518 { 519 grp->id = MBEDTLS_ECP_DP_NONE; 520 mbedtls_mpi_init(&grp->P); 521 mbedtls_mpi_init(&grp->A); 522 mbedtls_mpi_init(&grp->B); 523 mbedtls_ecp_point_init(&grp->G); 524 mbedtls_mpi_init(&grp->N); 525 grp->pbits = 0; 526 grp->nbits = 0; 527 grp->h = 0; 528 grp->modp = NULL; 529 grp->t_pre = NULL; 530 grp->t_post = NULL; 531 grp->t_data = NULL; 532 grp->T = NULL; 533 grp->T_size = 0; 534 } 535 536 /* 537 * Initialize (the components of) a key pair 538 */ 539 void mbedtls_ecp_keypair_init(mbedtls_ecp_keypair *key) 540 { 541 mbedtls_ecp_group_init(&key->grp); 542 mbedtls_mpi_init(&key->d); 543 mbedtls_ecp_point_init(&key->Q); 544 } 545 546 /* 547 * Unallocate (the components of) a point 548 */ 549 void mbedtls_ecp_point_free(mbedtls_ecp_point *pt) 550 { 551 if (pt == NULL) { 552 return; 553 } 554 555 mbedtls_mpi_free(&(pt->X)); 556 mbedtls_mpi_free(&(pt->Y)); 557 mbedtls_mpi_free(&(pt->Z)); 558 } 559 560 /* 561 * Check that the comb table (grp->T) is static initialized. 562 */ 563 static int ecp_group_is_static_comb_table(const mbedtls_ecp_group *grp) 564 { 565 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 566 return grp->T != NULL && grp->T_size == 0; 567 #else 568 (void) grp; 569 return 0; 570 #endif 571 } 572 573 /* 574 * Unallocate (the components of) a group 575 */ 576 void mbedtls_ecp_group_free(mbedtls_ecp_group *grp) 577 { 578 size_t i; 579 580 if (grp == NULL) { 581 return; 582 } 583 584 if (grp->h != 1) { 585 mbedtls_mpi_free(&grp->A); 586 mbedtls_mpi_free(&grp->B); 587 mbedtls_ecp_point_free(&grp->G); 588 589 #if !defined(MBEDTLS_ECP_WITH_MPI_UINT) 590 mbedtls_mpi_free(&grp->N); 591 mbedtls_mpi_free(&grp->P); 592 #endif 593 } 594 595 if (!ecp_group_is_static_comb_table(grp) && grp->T != NULL) { 596 for (i = 0; i < grp->T_size; i++) { 597 mbedtls_ecp_point_free(&grp->T[i]); 598 } 599 mbedtls_free(grp->T); 600 } 601 602 mbedtls_platform_zeroize(grp, sizeof(mbedtls_ecp_group)); 603 } 604 605 /* 606 * Unallocate (the components of) a key pair 607 */ 608 void mbedtls_ecp_keypair_free(mbedtls_ecp_keypair *key) 609 { 610 if (key == NULL) { 611 return; 612 } 613 614 mbedtls_ecp_group_free(&key->grp); 615 mbedtls_mpi_free(&key->d); 616 mbedtls_ecp_point_free(&key->Q); 617 } 618 619 /* 620 * Copy the contents of a point 621 */ 622 int mbedtls_ecp_copy(mbedtls_ecp_point *P, const mbedtls_ecp_point *Q) 623 { 624 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 625 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->X, &Q->X)); 626 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Y, &Q->Y)); 627 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Z, &Q->Z)); 628 629 cleanup: 630 return ret; 631 } 632 633 /* 634 * Copy the contents of a group object 635 */ 636 int mbedtls_ecp_group_copy(mbedtls_ecp_group *dst, const mbedtls_ecp_group *src) 637 { 638 return mbedtls_ecp_group_load(dst, src->id); 639 } 640 641 /* 642 * Set point to zero 643 */ 644 int mbedtls_ecp_set_zero(mbedtls_ecp_point *pt) 645 { 646 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 647 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->X, 1)); 648 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Y, 1)); 649 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 0)); 650 651 cleanup: 652 return ret; 653 } 654 655 /* 656 * Tell if a point is zero 657 */ 658 int mbedtls_ecp_is_zero(mbedtls_ecp_point *pt) 659 { 660 return mbedtls_mpi_cmp_int(&pt->Z, 0) == 0; 661 } 662 663 /* 664 * Compare two points lazily 665 */ 666 int mbedtls_ecp_point_cmp(const mbedtls_ecp_point *P, 667 const mbedtls_ecp_point *Q) 668 { 669 if (mbedtls_mpi_cmp_mpi(&P->X, &Q->X) == 0 && 670 mbedtls_mpi_cmp_mpi(&P->Y, &Q->Y) == 0 && 671 mbedtls_mpi_cmp_mpi(&P->Z, &Q->Z) == 0) { 672 return 0; 673 } 674 675 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 676 } 677 678 /* 679 * Import a non-zero point from ASCII strings 680 */ 681 int mbedtls_ecp_point_read_string(mbedtls_ecp_point *P, int radix, 682 const char *x, const char *y) 683 { 684 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 685 MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->X, radix, x)); 686 MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->Y, radix, y)); 687 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&P->Z, 1)); 688 689 cleanup: 690 return ret; 691 } 692 693 /* 694 * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748) 695 */ 696 int mbedtls_ecp_point_write_binary(const mbedtls_ecp_group *grp, 697 const mbedtls_ecp_point *P, 698 int format, size_t *olen, 699 unsigned char *buf, size_t buflen) 700 { 701 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 702 size_t plen; 703 if (format != MBEDTLS_ECP_PF_UNCOMPRESSED && 704 format != MBEDTLS_ECP_PF_COMPRESSED) { 705 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 706 } 707 708 plen = mbedtls_mpi_size(&grp->P); 709 710 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 711 (void) format; /* Montgomery curves always use the same point format */ 712 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 713 *olen = plen; 714 if (buflen < *olen) { 715 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 716 } 717 718 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&P->X, buf, plen)); 719 } 720 #endif 721 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 722 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 723 /* 724 * Common case: P == 0 725 */ 726 if (mbedtls_mpi_cmp_int(&P->Z, 0) == 0) { 727 if (buflen < 1) { 728 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 729 } 730 731 buf[0] = 0x00; 732 *olen = 1; 733 734 return 0; 735 } 736 737 if (format == MBEDTLS_ECP_PF_UNCOMPRESSED) { 738 *olen = 2 * plen + 1; 739 740 if (buflen < *olen) { 741 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 742 } 743 744 buf[0] = 0x04; 745 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen)); 746 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->Y, buf + 1 + plen, plen)); 747 } else if (format == MBEDTLS_ECP_PF_COMPRESSED) { 748 *olen = plen + 1; 749 750 if (buflen < *olen) { 751 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 752 } 753 754 buf[0] = 0x02 + mbedtls_mpi_get_bit(&P->Y, 0); 755 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen)); 756 } 757 } 758 #endif 759 760 cleanup: 761 return ret; 762 } 763 764 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 765 static int mbedtls_ecp_sw_derive_y(const mbedtls_ecp_group *grp, 766 const mbedtls_mpi *X, 767 mbedtls_mpi *Y, 768 int parity_bit); 769 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 770 771 /* 772 * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748) 773 */ 774 int mbedtls_ecp_point_read_binary(const mbedtls_ecp_group *grp, 775 mbedtls_ecp_point *pt, 776 const unsigned char *buf, size_t ilen) 777 { 778 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 779 size_t plen; 780 if (ilen < 1) { 781 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 782 } 783 784 plen = mbedtls_mpi_size(&grp->P); 785 786 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 787 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 788 if (plen != ilen) { 789 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 790 } 791 792 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&pt->X, buf, plen)); 793 mbedtls_mpi_free(&pt->Y); 794 795 if (grp->id == MBEDTLS_ECP_DP_CURVE25519) { 796 /* Set most significant bit to 0 as prescribed in RFC7748 §5 */ 797 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&pt->X, plen * 8 - 1, 0)); 798 } 799 800 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1)); 801 } 802 #endif 803 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 804 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 805 if (buf[0] == 0x00) { 806 if (ilen == 1) { 807 return mbedtls_ecp_set_zero(pt); 808 } else { 809 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 810 } 811 } 812 813 if (ilen < 1 + plen) { 814 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 815 } 816 817 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->X, buf + 1, plen)); 818 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1)); 819 820 if (buf[0] == 0x04) { 821 /* format == MBEDTLS_ECP_PF_UNCOMPRESSED */ 822 if (ilen != 1 + plen * 2) { 823 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 824 } 825 return mbedtls_mpi_read_binary(&pt->Y, buf + 1 + plen, plen); 826 } else if (buf[0] == 0x02 || buf[0] == 0x03) { 827 /* format == MBEDTLS_ECP_PF_COMPRESSED */ 828 if (ilen != 1 + plen) { 829 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 830 } 831 return mbedtls_ecp_sw_derive_y(grp, &pt->X, &pt->Y, 832 (buf[0] & 1)); 833 } else { 834 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 835 } 836 } 837 #endif 838 839 cleanup: 840 return ret; 841 } 842 843 /* 844 * Import a point from a TLS ECPoint record (RFC 4492) 845 * struct { 846 * opaque point <1..2^8-1>; 847 * } ECPoint; 848 */ 849 int mbedtls_ecp_tls_read_point(const mbedtls_ecp_group *grp, 850 mbedtls_ecp_point *pt, 851 const unsigned char **buf, size_t buf_len) 852 { 853 unsigned char data_len; 854 const unsigned char *buf_start; 855 /* 856 * We must have at least two bytes (1 for length, at least one for data) 857 */ 858 if (buf_len < 2) { 859 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 860 } 861 862 data_len = *(*buf)++; 863 if (data_len < 1 || data_len > buf_len - 1) { 864 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 865 } 866 867 /* 868 * Save buffer start for read_binary and update buf 869 */ 870 buf_start = *buf; 871 *buf += data_len; 872 873 return mbedtls_ecp_point_read_binary(grp, pt, buf_start, data_len); 874 } 875 876 /* 877 * Export a point as a TLS ECPoint record (RFC 4492) 878 * struct { 879 * opaque point <1..2^8-1>; 880 * } ECPoint; 881 */ 882 int mbedtls_ecp_tls_write_point(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt, 883 int format, size_t *olen, 884 unsigned char *buf, size_t blen) 885 { 886 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 887 if (format != MBEDTLS_ECP_PF_UNCOMPRESSED && 888 format != MBEDTLS_ECP_PF_COMPRESSED) { 889 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 890 } 891 892 /* 893 * buffer length must be at least one, for our length byte 894 */ 895 if (blen < 1) { 896 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 897 } 898 899 if ((ret = mbedtls_ecp_point_write_binary(grp, pt, format, 900 olen, buf + 1, blen - 1)) != 0) { 901 return ret; 902 } 903 904 /* 905 * write length to the first byte and update total length 906 */ 907 buf[0] = (unsigned char) *olen; 908 ++*olen; 909 910 return 0; 911 } 912 913 /* 914 * Set a group from an ECParameters record (RFC 4492) 915 */ 916 int mbedtls_ecp_tls_read_group(mbedtls_ecp_group *grp, 917 const unsigned char **buf, size_t len) 918 { 919 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 920 mbedtls_ecp_group_id grp_id; 921 if ((ret = mbedtls_ecp_tls_read_group_id(&grp_id, buf, len)) != 0) { 922 return ret; 923 } 924 925 return mbedtls_ecp_group_load(grp, grp_id); 926 } 927 928 /* 929 * Read a group id from an ECParameters record (RFC 4492) and convert it to 930 * mbedtls_ecp_group_id. 931 */ 932 int mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id *grp, 933 const unsigned char **buf, size_t len) 934 { 935 uint16_t tls_id; 936 const mbedtls_ecp_curve_info *curve_info; 937 /* 938 * We expect at least three bytes (see below) 939 */ 940 if (len < 3) { 941 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 942 } 943 944 /* 945 * First byte is curve_type; only named_curve is handled 946 */ 947 if (*(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE) { 948 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 949 } 950 951 /* 952 * Next two bytes are the namedcurve value 953 */ 954 tls_id = MBEDTLS_GET_UINT16_BE(*buf, 0); 955 *buf += 2; 956 957 if ((curve_info = mbedtls_ecp_curve_info_from_tls_id(tls_id)) == NULL) { 958 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 959 } 960 961 *grp = curve_info->grp_id; 962 963 return 0; 964 } 965 966 /* 967 * Write the ECParameters record corresponding to a group (RFC 4492) 968 */ 969 int mbedtls_ecp_tls_write_group(const mbedtls_ecp_group *grp, size_t *olen, 970 unsigned char *buf, size_t blen) 971 { 972 const mbedtls_ecp_curve_info *curve_info; 973 if ((curve_info = mbedtls_ecp_curve_info_from_grp_id(grp->id)) == NULL) { 974 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 975 } 976 977 /* 978 * We are going to write 3 bytes (see below) 979 */ 980 *olen = 3; 981 if (blen < *olen) { 982 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 983 } 984 985 /* 986 * First byte is curve_type, always named_curve 987 */ 988 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE; 989 990 /* 991 * Next two bytes are the namedcurve value 992 */ 993 MBEDTLS_PUT_UINT16_BE(curve_info->tls_id, buf, 0); 994 995 return 0; 996 } 997 998 /* 999 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi. 1000 * See the documentation of struct mbedtls_ecp_group. 1001 * 1002 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf. 1003 */ 1004 static int ecp_modp(mbedtls_mpi *N, const mbedtls_ecp_group *grp) 1005 { 1006 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1007 1008 if (grp->modp == NULL) { 1009 return mbedtls_mpi_mod_mpi(N, N, &grp->P); 1010 } 1011 1012 /* N->s < 0 is a much faster test, which fails only if N is 0 */ 1013 if ((N->s < 0 && mbedtls_mpi_cmp_int(N, 0) != 0) || 1014 mbedtls_mpi_bitlen(N) > 2 * grp->pbits) { 1015 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 1016 } 1017 1018 MBEDTLS_MPI_CHK(grp->modp(N)); 1019 1020 /* N->s < 0 is a much faster test, which fails only if N is 0 */ 1021 while (N->s < 0 && mbedtls_mpi_cmp_int(N, 0) != 0) { 1022 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(N, N, &grp->P)); 1023 } 1024 1025 while (mbedtls_mpi_cmp_mpi(N, &grp->P) >= 0) { 1026 /* we known P, N and the result are positive */ 1027 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(N, N, &grp->P)); 1028 } 1029 1030 cleanup: 1031 return ret; 1032 } 1033 1034 /* 1035 * Fast mod-p functions expect their argument to be in the 0..p^2 range. 1036 * 1037 * In order to guarantee that, we need to ensure that operands of 1038 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will 1039 * bring the result back to this range. 1040 * 1041 * The following macros are shortcuts for doing that. 1042 */ 1043 1044 /* 1045 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi 1046 */ 1047 #if defined(MBEDTLS_SELF_TEST) 1048 #define INC_MUL_COUNT mul_count++; 1049 #else 1050 #define INC_MUL_COUNT 1051 #endif 1052 1053 #define MOD_MUL(N) \ 1054 do \ 1055 { \ 1056 MBEDTLS_MPI_CHK(ecp_modp(&(N), grp)); \ 1057 INC_MUL_COUNT \ 1058 } while (0) 1059 1060 static inline int mbedtls_mpi_mul_mod(const mbedtls_ecp_group *grp, 1061 mbedtls_mpi *X, 1062 const mbedtls_mpi *A, 1063 const mbedtls_mpi *B) 1064 { 1065 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1066 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(X, A, B)); 1067 MOD_MUL(*X); 1068 cleanup: 1069 return ret; 1070 } 1071 1072 /* 1073 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi 1074 * N->s < 0 is a very fast test, which fails only if N is 0 1075 */ 1076 #define MOD_SUB(N) \ 1077 do { \ 1078 while ((N)->s < 0 && mbedtls_mpi_cmp_int((N), 0) != 0) \ 1079 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi((N), (N), &grp->P)); \ 1080 } while (0) 1081 1082 MBEDTLS_MAYBE_UNUSED 1083 static inline int mbedtls_mpi_sub_mod(const mbedtls_ecp_group *grp, 1084 mbedtls_mpi *X, 1085 const mbedtls_mpi *A, 1086 const mbedtls_mpi *B) 1087 { 1088 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1089 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(X, A, B)); 1090 MOD_SUB(X); 1091 cleanup: 1092 return ret; 1093 } 1094 1095 /* 1096 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int. 1097 * We known P, N and the result are positive, so sub_abs is correct, and 1098 * a bit faster. 1099 */ 1100 #define MOD_ADD(N) \ 1101 while (mbedtls_mpi_cmp_mpi((N), &grp->P) >= 0) \ 1102 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs((N), (N), &grp->P)) 1103 1104 static inline int mbedtls_mpi_add_mod(const mbedtls_ecp_group *grp, 1105 mbedtls_mpi *X, 1106 const mbedtls_mpi *A, 1107 const mbedtls_mpi *B) 1108 { 1109 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1110 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, A, B)); 1111 MOD_ADD(X); 1112 cleanup: 1113 return ret; 1114 } 1115 1116 MBEDTLS_MAYBE_UNUSED 1117 static inline int mbedtls_mpi_mul_int_mod(const mbedtls_ecp_group *grp, 1118 mbedtls_mpi *X, 1119 const mbedtls_mpi *A, 1120 mbedtls_mpi_uint c) 1121 { 1122 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1123 1124 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(X, A, c)); 1125 MOD_ADD(X); 1126 cleanup: 1127 return ret; 1128 } 1129 1130 MBEDTLS_MAYBE_UNUSED 1131 static inline int mbedtls_mpi_sub_int_mod(const mbedtls_ecp_group *grp, 1132 mbedtls_mpi *X, 1133 const mbedtls_mpi *A, 1134 mbedtls_mpi_uint c) 1135 { 1136 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1137 1138 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(X, A, c)); 1139 MOD_SUB(X); 1140 cleanup: 1141 return ret; 1142 } 1143 1144 #define MPI_ECP_SUB_INT(X, A, c) \ 1145 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int_mod(grp, X, A, c)) 1146 1147 MBEDTLS_MAYBE_UNUSED 1148 static inline int mbedtls_mpi_shift_l_mod(const mbedtls_ecp_group *grp, 1149 mbedtls_mpi *X, 1150 size_t count) 1151 { 1152 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1153 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(X, count)); 1154 MOD_ADD(X); 1155 cleanup: 1156 return ret; 1157 } 1158 1159 /* 1160 * Macro wrappers around ECP modular arithmetic 1161 * 1162 * Currently, these wrappers are defined via the bignum module. 1163 */ 1164 1165 #define MPI_ECP_ADD(X, A, B) \ 1166 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, X, A, B)) 1167 1168 #define MPI_ECP_SUB(X, A, B) \ 1169 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, X, A, B)) 1170 1171 #define MPI_ECP_MUL(X, A, B) \ 1172 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, X, A, B)) 1173 1174 #define MPI_ECP_SQR(X, A) \ 1175 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, X, A, A)) 1176 1177 #define MPI_ECP_MUL_INT(X, A, c) \ 1178 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int_mod(grp, X, A, c)) 1179 1180 #define MPI_ECP_INV(dst, src) \ 1181 MBEDTLS_MPI_CHK(mbedtls_mpi_gcd_modinv_odd(NULL, (dst), (src), &grp->P)) 1182 1183 #define MPI_ECP_MOV(X, A) \ 1184 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A)) 1185 1186 #define MPI_ECP_SHIFT_L(X, count) \ 1187 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, X, count)) 1188 1189 #define MPI_ECP_LSET(X, c) \ 1190 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, c)) 1191 1192 #define MPI_ECP_CMP_INT(X, c) \ 1193 mbedtls_mpi_cmp_int(X, c) 1194 1195 #define MPI_ECP_CMP(X, Y) \ 1196 mbedtls_mpi_cmp_mpi(X, Y) 1197 1198 /* Needs f_rng, p_rng to be defined. */ 1199 #define MPI_ECP_RAND(X) \ 1200 MBEDTLS_MPI_CHK(mbedtls_mpi_random((X), 2, &grp->P, f_rng, p_rng)) 1201 1202 /* Conditional negation 1203 * Needs grp and a temporary MPI tmp to be defined. */ 1204 #define MPI_ECP_COND_NEG(X, cond) \ 1205 do \ 1206 { \ 1207 unsigned char nonzero = mbedtls_mpi_cmp_int((X), 0) != 0; \ 1208 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&tmp, &grp->P, (X))); \ 1209 MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign((X), &tmp, \ 1210 nonzero & cond)); \ 1211 } while (0) 1212 1213 #define MPI_ECP_NEG(X) MPI_ECP_COND_NEG((X), 1) 1214 1215 #define MPI_ECP_VALID(X) \ 1216 ((X)->p != NULL) 1217 1218 #define MPI_ECP_COND_ASSIGN(X, Y, cond) \ 1219 MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign((X), (Y), (cond))) 1220 1221 #define MPI_ECP_COND_SWAP(X, Y, cond) \ 1222 MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap((X), (Y), (cond))) 1223 1224 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 1225 1226 /* 1227 * Computes the right-hand side of the Short Weierstrass equation 1228 * RHS = X^3 + A X + B 1229 */ 1230 static int ecp_sw_rhs(const mbedtls_ecp_group *grp, 1231 mbedtls_mpi *rhs, 1232 const mbedtls_mpi *X) 1233 { 1234 int ret; 1235 1236 /* Compute X^3 + A X + B as X (X^2 + A) + B */ 1237 MPI_ECP_SQR(rhs, X); 1238 1239 /* Special case for A = -3 */ 1240 if (mbedtls_ecp_group_a_is_minus_3(grp)) { 1241 MPI_ECP_SUB_INT(rhs, rhs, 3); 1242 } else { 1243 MPI_ECP_ADD(rhs, rhs, &grp->A); 1244 } 1245 1246 MPI_ECP_MUL(rhs, rhs, X); 1247 MPI_ECP_ADD(rhs, rhs, &grp->B); 1248 1249 cleanup: 1250 return ret; 1251 } 1252 1253 /* 1254 * Derive Y from X and a parity bit 1255 */ 1256 static int mbedtls_ecp_sw_derive_y(const mbedtls_ecp_group *grp, 1257 const mbedtls_mpi *X, 1258 mbedtls_mpi *Y, 1259 int parity_bit) 1260 { 1261 /* w = y^2 = x^3 + ax + b 1262 * y = sqrt(w) = w^((p+1)/4) mod p (for prime p where p = 3 mod 4) 1263 * 1264 * Note: this method for extracting square root does not validate that w 1265 * was indeed a square so this function will return garbage in Y if X 1266 * does not correspond to a point on the curve. 1267 */ 1268 1269 /* Check prerequisite p = 3 mod 4 */ 1270 if (mbedtls_mpi_get_bit(&grp->P, 0) != 1 || 1271 mbedtls_mpi_get_bit(&grp->P, 1) != 1) { 1272 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1273 } 1274 1275 int ret; 1276 mbedtls_mpi exp; 1277 mbedtls_mpi_init(&exp); 1278 1279 /* use Y to store intermediate result, actually w above */ 1280 MBEDTLS_MPI_CHK(ecp_sw_rhs(grp, Y, X)); 1281 1282 /* w = y^2 */ /* Y contains y^2 intermediate result */ 1283 /* exp = ((p+1)/4) */ 1284 MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&exp, &grp->P, 1)); 1285 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&exp, 2)); 1286 /* sqrt(w) = w^((p+1)/4) mod p (for prime p where p = 3 mod 4) */ 1287 MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(Y, Y /*y^2*/, &exp, &grp->P, NULL)); 1288 1289 /* check parity bit match or else invert Y */ 1290 /* This quick inversion implementation is valid because Y != 0 for all 1291 * Short Weierstrass curves supported by mbedtls, as each supported curve 1292 * has an order that is a large prime, so each supported curve does not 1293 * have any point of order 2, and a point with Y == 0 would be of order 2 */ 1294 if (mbedtls_mpi_get_bit(Y, 0) != parity_bit) { 1295 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(Y, &grp->P, Y)); 1296 } 1297 1298 cleanup: 1299 1300 mbedtls_mpi_free(&exp); 1301 return ret; 1302 } 1303 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 1304 1305 #if defined(MBEDTLS_ECP_C) 1306 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 1307 /* 1308 * For curves in short Weierstrass form, we do all the internal operations in 1309 * Jacobian coordinates. 1310 * 1311 * For multiplication, we'll use a comb method with countermeasures against 1312 * SPA, hence timing attacks. 1313 */ 1314 1315 /* 1316 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1) 1317 * Cost: 1N := 1I + 3M + 1S 1318 */ 1319 static int ecp_normalize_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt) 1320 { 1321 if (MPI_ECP_CMP_INT(&pt->Z, 0) == 0) { 1322 return 0; 1323 } 1324 1325 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) 1326 if (mbedtls_internal_ecp_grp_capable(grp)) { 1327 return mbedtls_internal_ecp_normalize_jac(grp, pt); 1328 } 1329 #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */ 1330 1331 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) 1332 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1333 #else 1334 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1335 mbedtls_mpi T; 1336 mbedtls_mpi_init(&T); 1337 1338 MPI_ECP_INV(&T, &pt->Z); /* T <- 1 / Z */ 1339 MPI_ECP_MUL(&pt->Y, &pt->Y, &T); /* Y' <- Y*T = Y / Z */ 1340 MPI_ECP_SQR(&T, &T); /* T <- T^2 = 1 / Z^2 */ 1341 MPI_ECP_MUL(&pt->X, &pt->X, &T); /* X <- X * T = X / Z^2 */ 1342 MPI_ECP_MUL(&pt->Y, &pt->Y, &T); /* Y'' <- Y' * T = Y / Z^3 */ 1343 1344 MPI_ECP_LSET(&pt->Z, 1); 1345 1346 cleanup: 1347 1348 mbedtls_mpi_free(&T); 1349 1350 return ret; 1351 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */ 1352 } 1353 1354 /* 1355 * Normalize jacobian coordinates of an array of (pointers to) points, 1356 * using Montgomery's trick to perform only one inversion mod P. 1357 * (See for example Cohen's "A Course in Computational Algebraic Number 1358 * Theory", Algorithm 10.3.4.) 1359 * 1360 * Warning: fails (returning an error) if one of the points is zero! 1361 * This should never happen, see choice of w in ecp_mul_comb(). 1362 * 1363 * Cost: 1N(t) := 1I + (6t - 3)M + 1S 1364 */ 1365 static int ecp_normalize_jac_many(const mbedtls_ecp_group *grp, 1366 mbedtls_ecp_point *T[], size_t T_size) 1367 { 1368 if (T_size < 2) { 1369 return ecp_normalize_jac(grp, *T); 1370 } 1371 1372 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) 1373 if (mbedtls_internal_ecp_grp_capable(grp)) { 1374 return mbedtls_internal_ecp_normalize_jac_many(grp, T, T_size); 1375 } 1376 #endif 1377 1378 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) 1379 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1380 #else 1381 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1382 size_t i; 1383 mbedtls_mpi *c, t; 1384 1385 if ((c = mbedtls_calloc(T_size, sizeof(mbedtls_mpi))) == NULL) { 1386 return MBEDTLS_ERR_ECP_ALLOC_FAILED; 1387 } 1388 1389 mbedtls_mpi_init(&t); 1390 1391 mpi_init_many(c, T_size); 1392 /* 1393 * c[i] = Z_0 * ... * Z_i, i = 0,..,n := T_size-1 1394 */ 1395 MPI_ECP_MOV(&c[0], &T[0]->Z); 1396 for (i = 1; i < T_size; i++) { 1397 MPI_ECP_MUL(&c[i], &c[i-1], &T[i]->Z); 1398 } 1399 1400 /* 1401 * c[n] = 1 / (Z_0 * ... * Z_n) mod P 1402 */ 1403 MPI_ECP_INV(&c[T_size-1], &c[T_size-1]); 1404 1405 for (i = T_size - 1;; i--) { 1406 /* At the start of iteration i (note that i decrements), we have 1407 * - c[j] = Z_0 * .... * Z_j for j < i, 1408 * - c[j] = 1 / (Z_0 * .... * Z_j) for j == i, 1409 * 1410 * This is maintained via 1411 * - c[i-1] <- c[i] * Z_i 1412 * 1413 * We also derive 1/Z_i = c[i] * c[i-1] for i>0 and use that 1414 * to do the actual normalization. For i==0, we already have 1415 * c[0] = 1 / Z_0. 1416 */ 1417 1418 if (i > 0) { 1419 /* Compute 1/Z_i and establish invariant for the next iteration. */ 1420 MPI_ECP_MUL(&t, &c[i], &c[i-1]); 1421 MPI_ECP_MUL(&c[i-1], &c[i], &T[i]->Z); 1422 } else { 1423 MPI_ECP_MOV(&t, &c[0]); 1424 } 1425 1426 /* Now t holds 1 / Z_i; normalize as in ecp_normalize_jac() */ 1427 MPI_ECP_MUL(&T[i]->Y, &T[i]->Y, &t); 1428 MPI_ECP_SQR(&t, &t); 1429 MPI_ECP_MUL(&T[i]->X, &T[i]->X, &t); 1430 MPI_ECP_MUL(&T[i]->Y, &T[i]->Y, &t); 1431 1432 /* 1433 * Post-precessing: reclaim some memory by shrinking coordinates 1434 * - not storing Z (always 1) 1435 * - shrinking other coordinates, but still keeping the same number of 1436 * limbs as P, as otherwise it will too likely be regrown too fast. 1437 */ 1438 MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->X, grp->P.n)); 1439 MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->Y, grp->P.n)); 1440 1441 MPI_ECP_LSET(&T[i]->Z, 1); 1442 1443 if (i == 0) { 1444 break; 1445 } 1446 } 1447 1448 cleanup: 1449 1450 mbedtls_mpi_free(&t); 1451 mpi_free_many(c, T_size); 1452 mbedtls_free(c); 1453 1454 return ret; 1455 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */ 1456 } 1457 1458 /* 1459 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak. 1460 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid 1461 */ 1462 static int ecp_safe_invert_jac(const mbedtls_ecp_group *grp, 1463 mbedtls_ecp_point *Q, 1464 unsigned char inv) 1465 { 1466 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1467 mbedtls_mpi tmp; 1468 mbedtls_mpi_init(&tmp); 1469 1470 MPI_ECP_COND_NEG(&Q->Y, inv); 1471 1472 cleanup: 1473 mbedtls_mpi_free(&tmp); 1474 return ret; 1475 } 1476 1477 /* 1478 * Point doubling R = 2 P, Jacobian coordinates 1479 * 1480 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 . 1481 * 1482 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR 1483 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring. 1484 * 1485 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }. 1486 * 1487 * Cost: 1D := 3M + 4S (A == 0) 1488 * 4M + 4S (A == -3) 1489 * 3M + 6S + 1a otherwise 1490 */ 1491 static int ecp_double_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1492 const mbedtls_ecp_point *P, 1493 mbedtls_mpi tmp[4]) 1494 { 1495 #if defined(MBEDTLS_SELF_TEST) 1496 dbl_count++; 1497 #endif 1498 1499 #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) 1500 if (mbedtls_internal_ecp_grp_capable(grp)) { 1501 return mbedtls_internal_ecp_double_jac(grp, R, P); 1502 } 1503 #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */ 1504 1505 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) 1506 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1507 #else 1508 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1509 1510 /* Special case for A = -3 */ 1511 if (mbedtls_ecp_group_a_is_minus_3(grp)) { 1512 /* tmp[0] <- M = 3(X + Z^2)(X - Z^2) */ 1513 MPI_ECP_SQR(&tmp[1], &P->Z); 1514 MPI_ECP_ADD(&tmp[2], &P->X, &tmp[1]); 1515 MPI_ECP_SUB(&tmp[3], &P->X, &tmp[1]); 1516 MPI_ECP_MUL(&tmp[1], &tmp[2], &tmp[3]); 1517 MPI_ECP_MUL_INT(&tmp[0], &tmp[1], 3); 1518 } else { 1519 /* tmp[0] <- M = 3.X^2 + A.Z^4 */ 1520 MPI_ECP_SQR(&tmp[1], &P->X); 1521 MPI_ECP_MUL_INT(&tmp[0], &tmp[1], 3); 1522 1523 /* Optimize away for "koblitz" curves with A = 0 */ 1524 if (MPI_ECP_CMP_INT(&grp->A, 0) != 0) { 1525 /* M += A.Z^4 */ 1526 MPI_ECP_SQR(&tmp[1], &P->Z); 1527 MPI_ECP_SQR(&tmp[2], &tmp[1]); 1528 MPI_ECP_MUL(&tmp[1], &tmp[2], &grp->A); 1529 MPI_ECP_ADD(&tmp[0], &tmp[0], &tmp[1]); 1530 } 1531 } 1532 1533 /* tmp[1] <- S = 4.X.Y^2 */ 1534 MPI_ECP_SQR(&tmp[2], &P->Y); 1535 MPI_ECP_SHIFT_L(&tmp[2], 1); 1536 MPI_ECP_MUL(&tmp[1], &P->X, &tmp[2]); 1537 MPI_ECP_SHIFT_L(&tmp[1], 1); 1538 1539 /* tmp[3] <- U = 8.Y^4 */ 1540 MPI_ECP_SQR(&tmp[3], &tmp[2]); 1541 MPI_ECP_SHIFT_L(&tmp[3], 1); 1542 1543 /* tmp[2] <- T = M^2 - 2.S */ 1544 MPI_ECP_SQR(&tmp[2], &tmp[0]); 1545 MPI_ECP_SUB(&tmp[2], &tmp[2], &tmp[1]); 1546 MPI_ECP_SUB(&tmp[2], &tmp[2], &tmp[1]); 1547 1548 /* tmp[1] <- S = M(S - T) - U */ 1549 MPI_ECP_SUB(&tmp[1], &tmp[1], &tmp[2]); 1550 MPI_ECP_MUL(&tmp[1], &tmp[1], &tmp[0]); 1551 MPI_ECP_SUB(&tmp[1], &tmp[1], &tmp[3]); 1552 1553 /* tmp[3] <- U = 2.Y.Z */ 1554 MPI_ECP_MUL(&tmp[3], &P->Y, &P->Z); 1555 MPI_ECP_SHIFT_L(&tmp[3], 1); 1556 1557 /* Store results */ 1558 MPI_ECP_MOV(&R->X, &tmp[2]); 1559 MPI_ECP_MOV(&R->Y, &tmp[1]); 1560 MPI_ECP_MOV(&R->Z, &tmp[3]); 1561 1562 cleanup: 1563 1564 return ret; 1565 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */ 1566 } 1567 1568 /* 1569 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22) 1570 * 1571 * The coordinates of Q must be normalized (= affine), 1572 * but those of P don't need to. R is not normalized. 1573 * 1574 * P,Q,R may alias, but only at the level of EC points: they must be either 1575 * equal as pointers, or disjoint (including the coordinate data buffers). 1576 * Fine-grained aliasing at the level of coordinates is not supported. 1577 * 1578 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q. 1579 * None of these cases can happen as intermediate step in ecp_mul_comb(): 1580 * - at each step, P, Q and R are multiples of the base point, the factor 1581 * being less than its order, so none of them is zero; 1582 * - Q is an odd multiple of the base point, P an even multiple, 1583 * due to the choice of precomputed points in the modified comb method. 1584 * So branches for these cases do not leak secret information. 1585 * 1586 * Cost: 1A := 8M + 3S 1587 */ 1588 static int ecp_add_mixed(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1589 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q, 1590 mbedtls_mpi tmp[4]) 1591 { 1592 #if defined(MBEDTLS_SELF_TEST) 1593 add_count++; 1594 #endif 1595 1596 #if defined(MBEDTLS_ECP_ADD_MIXED_ALT) 1597 if (mbedtls_internal_ecp_grp_capable(grp)) { 1598 return mbedtls_internal_ecp_add_mixed(grp, R, P, Q); 1599 } 1600 #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */ 1601 1602 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT) 1603 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1604 #else 1605 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1606 1607 /* NOTE: Aliasing between input and output is allowed, so one has to make 1608 * sure that at the point X,Y,Z are written, {P,Q}->{X,Y,Z} are no 1609 * longer read from. */ 1610 mbedtls_mpi * const X = &R->X; 1611 mbedtls_mpi * const Y = &R->Y; 1612 mbedtls_mpi * const Z = &R->Z; 1613 1614 if (!MPI_ECP_VALID(&Q->Z)) { 1615 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 1616 } 1617 1618 /* 1619 * Trivial cases: P == 0 or Q == 0 (case 1) 1620 */ 1621 if (MPI_ECP_CMP_INT(&P->Z, 0) == 0) { 1622 return mbedtls_ecp_copy(R, Q); 1623 } 1624 1625 if (MPI_ECP_CMP_INT(&Q->Z, 0) == 0) { 1626 return mbedtls_ecp_copy(R, P); 1627 } 1628 1629 /* 1630 * Make sure Q coordinates are normalized 1631 */ 1632 if (MPI_ECP_CMP_INT(&Q->Z, 1) != 0) { 1633 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 1634 } 1635 1636 MPI_ECP_SQR(&tmp[0], &P->Z); 1637 MPI_ECP_MUL(&tmp[1], &tmp[0], &P->Z); 1638 MPI_ECP_MUL(&tmp[0], &tmp[0], &Q->X); 1639 MPI_ECP_MUL(&tmp[1], &tmp[1], &Q->Y); 1640 MPI_ECP_SUB(&tmp[0], &tmp[0], &P->X); 1641 MPI_ECP_SUB(&tmp[1], &tmp[1], &P->Y); 1642 1643 /* Special cases (2) and (3) */ 1644 if (MPI_ECP_CMP_INT(&tmp[0], 0) == 0) { 1645 if (MPI_ECP_CMP_INT(&tmp[1], 0) == 0) { 1646 ret = ecp_double_jac(grp, R, P, tmp); 1647 goto cleanup; 1648 } else { 1649 ret = mbedtls_ecp_set_zero(R); 1650 goto cleanup; 1651 } 1652 } 1653 1654 /* {P,Q}->Z no longer used, so OK to write to Z even if there's aliasing. */ 1655 MPI_ECP_MUL(Z, &P->Z, &tmp[0]); 1656 MPI_ECP_SQR(&tmp[2], &tmp[0]); 1657 MPI_ECP_MUL(&tmp[3], &tmp[2], &tmp[0]); 1658 MPI_ECP_MUL(&tmp[2], &tmp[2], &P->X); 1659 1660 MPI_ECP_MOV(&tmp[0], &tmp[2]); 1661 MPI_ECP_SHIFT_L(&tmp[0], 1); 1662 1663 /* {P,Q}->X no longer used, so OK to write to X even if there's aliasing. */ 1664 MPI_ECP_SQR(X, &tmp[1]); 1665 MPI_ECP_SUB(X, X, &tmp[0]); 1666 MPI_ECP_SUB(X, X, &tmp[3]); 1667 MPI_ECP_SUB(&tmp[2], &tmp[2], X); 1668 MPI_ECP_MUL(&tmp[2], &tmp[2], &tmp[1]); 1669 MPI_ECP_MUL(&tmp[3], &tmp[3], &P->Y); 1670 /* {P,Q}->Y no longer used, so OK to write to Y even if there's aliasing. */ 1671 MPI_ECP_SUB(Y, &tmp[2], &tmp[3]); 1672 1673 cleanup: 1674 1675 return ret; 1676 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */ 1677 } 1678 1679 /* 1680 * Randomize jacobian coordinates: 1681 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l 1682 * This is sort of the reverse operation of ecp_normalize_jac(). 1683 * 1684 * This countermeasure was first suggested in [2]. 1685 */ 1686 static int ecp_randomize_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, 1687 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 1688 { 1689 #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) 1690 if (mbedtls_internal_ecp_grp_capable(grp)) { 1691 return mbedtls_internal_ecp_randomize_jac(grp, pt, f_rng, p_rng); 1692 } 1693 #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */ 1694 1695 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) 1696 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1697 #else 1698 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1699 mbedtls_mpi l; 1700 1701 mbedtls_mpi_init(&l); 1702 1703 /* Generate l such that 1 < l < p */ 1704 MPI_ECP_RAND(&l); 1705 1706 /* Z' = l * Z */ 1707 MPI_ECP_MUL(&pt->Z, &pt->Z, &l); 1708 1709 /* Y' = l * Y */ 1710 MPI_ECP_MUL(&pt->Y, &pt->Y, &l); 1711 1712 /* X' = l^2 * X */ 1713 MPI_ECP_SQR(&l, &l); 1714 MPI_ECP_MUL(&pt->X, &pt->X, &l); 1715 1716 /* Y'' = l^2 * Y' = l^3 * Y */ 1717 MPI_ECP_MUL(&pt->Y, &pt->Y, &l); 1718 1719 cleanup: 1720 mbedtls_mpi_free(&l); 1721 1722 if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) { 1723 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; 1724 } 1725 return ret; 1726 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */ 1727 } 1728 1729 /* 1730 * Check and define parameters used by the comb method (see below for details) 1731 */ 1732 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7 1733 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds" 1734 #endif 1735 1736 /* d = ceil( n / w ) */ 1737 #define COMB_MAX_D (MBEDTLS_ECP_MAX_BITS + 1) / 2 1738 1739 /* number of precomputed points */ 1740 #define COMB_MAX_PRE (1 << (MBEDTLS_ECP_WINDOW_SIZE - 1)) 1741 1742 /* 1743 * Compute the representation of m that will be used with our comb method. 1744 * 1745 * The basic comb method is described in GECC 3.44 for example. We use a 1746 * modified version that provides resistance to SPA by avoiding zero 1747 * digits in the representation as in [3]. We modify the method further by 1748 * requiring that all K_i be odd, which has the small cost that our 1749 * representation uses one more K_i, due to carries, but saves on the size of 1750 * the precomputed table. 1751 * 1752 * Summary of the comb method and its modifications: 1753 * 1754 * - The goal is to compute m*P for some w*d-bit integer m. 1755 * 1756 * - The basic comb method splits m into the w-bit integers 1757 * x[0] .. x[d-1] where x[i] consists of the bits in m whose 1758 * index has residue i modulo d, and computes m * P as 1759 * S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where 1760 * S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P. 1761 * 1762 * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by 1763 * .. + 2^{i-1} S[x[i-1]] - 2^i S[x[i]] + 2^{i+1} S[x[i]] + 2^{i+2} S[x[i+2]] .., 1764 * thereby successively converting it into a form where all summands 1765 * are nonzero, at the cost of negative summands. This is the basic idea of [3]. 1766 * 1767 * - More generally, even if x[i+1] != 0, we can first transform the sum as 1768 * .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] .., 1769 * and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]]. 1770 * Performing and iterating this procedure for those x[i] that are even 1771 * (keeping track of carry), we can transform the original sum into one of the form 1772 * S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]] 1773 * with all x'[i] odd. It is therefore only necessary to know S at odd indices, 1774 * which is why we are only computing half of it in the first place in 1775 * ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb. 1776 * 1777 * - For the sake of compactness, only the seven low-order bits of x[i] 1778 * are used to represent its absolute value (K_i in the paper), and the msb 1779 * of x[i] encodes the sign (s_i in the paper): it is set if and only if 1780 * if s_i == -1; 1781 * 1782 * Calling conventions: 1783 * - x is an array of size d + 1 1784 * - w is the size, ie number of teeth, of the comb, and must be between 1785 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE) 1786 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d 1787 * (the result will be incorrect if these assumptions are not satisfied) 1788 */ 1789 static void ecp_comb_recode_core(unsigned char x[], size_t d, 1790 unsigned char w, const mbedtls_mpi *m) 1791 { 1792 size_t i, j; 1793 unsigned char c, cc, adjust; 1794 1795 memset(x, 0, d+1); 1796 1797 /* First get the classical comb values (except for x_d = 0) */ 1798 for (i = 0; i < d; i++) { 1799 for (j = 0; j < w; j++) { 1800 x[i] |= mbedtls_mpi_get_bit(m, i + d * j) << j; 1801 } 1802 } 1803 1804 /* Now make sure x_1 .. x_d are odd */ 1805 c = 0; 1806 for (i = 1; i <= d; i++) { 1807 /* Add carry and update it */ 1808 cc = x[i] & c; 1809 x[i] = x[i] ^ c; 1810 c = cc; 1811 1812 /* Adjust if needed, avoiding branches */ 1813 adjust = 1 - (x[i] & 0x01); 1814 c |= x[i] & (x[i-1] * adjust); 1815 x[i] = x[i] ^ (x[i-1] * adjust); 1816 x[i-1] |= adjust << 7; 1817 } 1818 } 1819 1820 /* 1821 * Precompute points for the adapted comb method 1822 * 1823 * Assumption: T must be able to hold 2^{w - 1} elements. 1824 * 1825 * Operation: If i = i_{w-1} ... i_1 is the binary representation of i, 1826 * sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P. 1827 * 1828 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1) 1829 * 1830 * Note: Even comb values (those where P would be omitted from the 1831 * sum defining T[i] above) are not needed in our adaption 1832 * the comb method. See ecp_comb_recode_core(). 1833 * 1834 * This function currently works in four steps: 1835 * (1) [dbl] Computation of intermediate T[i] for 2-power values of i 1836 * (2) [norm_dbl] Normalization of coordinates of these T[i] 1837 * (3) [add] Computation of all T[i] 1838 * (4) [norm_add] Normalization of all T[i] 1839 * 1840 * Step 1 can be interrupted but not the others; together with the final 1841 * coordinate normalization they are the largest steps done at once, depending 1842 * on the window size. Here are operation counts for P-256: 1843 * 1844 * step (2) (3) (4) 1845 * w = 5 142 165 208 1846 * w = 4 136 77 160 1847 * w = 3 130 33 136 1848 * w = 2 124 11 124 1849 * 1850 * So if ECC operations are blocking for too long even with a low max_ops 1851 * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order 1852 * to minimize maximum blocking time. 1853 */ 1854 static int ecp_precompute_comb(const mbedtls_ecp_group *grp, 1855 mbedtls_ecp_point T[], const mbedtls_ecp_point *P, 1856 unsigned char w, size_t d, 1857 mbedtls_ecp_restart_ctx *rs_ctx) 1858 { 1859 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1860 unsigned char i; 1861 size_t j = 0; 1862 const unsigned char T_size = 1U << (w - 1); 1863 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1] = { NULL }; 1864 1865 mbedtls_mpi tmp[4]; 1866 1867 mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 1868 1869 #if defined(MBEDTLS_ECP_RESTARTABLE) 1870 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1871 if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) { 1872 goto dbl; 1873 } 1874 if (rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl) { 1875 goto norm_dbl; 1876 } 1877 if (rs_ctx->rsm->state == ecp_rsm_pre_add) { 1878 goto add; 1879 } 1880 if (rs_ctx->rsm->state == ecp_rsm_pre_norm_add) { 1881 goto norm_add; 1882 } 1883 } 1884 #else 1885 (void) rs_ctx; 1886 #endif 1887 1888 #if defined(MBEDTLS_ECP_RESTARTABLE) 1889 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1890 rs_ctx->rsm->state = ecp_rsm_pre_dbl; 1891 1892 /* initial state for the loop */ 1893 rs_ctx->rsm->i = 0; 1894 } 1895 1896 dbl: 1897 #endif 1898 /* 1899 * Set T[0] = P and 1900 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value) 1901 */ 1902 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&T[0], P)); 1903 1904 #if defined(MBEDTLS_ECP_RESTARTABLE) 1905 if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) { 1906 j = rs_ctx->rsm->i; 1907 } else 1908 #endif 1909 j = 0; 1910 1911 for (; j < d * (w - 1); j++) { 1912 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL); 1913 1914 i = 1U << (j / d); 1915 cur = T + i; 1916 1917 if (j % d == 0) { 1918 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(cur, T + (i >> 1))); 1919 } 1920 1921 MBEDTLS_MPI_CHK(ecp_double_jac(grp, cur, cur, tmp)); 1922 } 1923 1924 #if defined(MBEDTLS_ECP_RESTARTABLE) 1925 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1926 rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl; 1927 } 1928 1929 norm_dbl: 1930 #endif 1931 /* 1932 * Normalize current elements in T to allow them to be used in 1933 * ecp_add_mixed() below, which requires one normalized input. 1934 * 1935 * As T has holes, use an auxiliary array of pointers to elements in T. 1936 * 1937 */ 1938 j = 0; 1939 for (i = 1; i < T_size; i <<= 1) { 1940 TT[j++] = T + i; 1941 } 1942 1943 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2); 1944 1945 MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j)); 1946 1947 #if defined(MBEDTLS_ECP_RESTARTABLE) 1948 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1949 rs_ctx->rsm->state = ecp_rsm_pre_add; 1950 } 1951 1952 add: 1953 #endif 1954 /* 1955 * Compute the remaining ones using the minimal number of additions 1956 * Be careful to update T[2^l] only after using it! 1957 */ 1958 MBEDTLS_ECP_BUDGET((T_size - 1) * MBEDTLS_ECP_OPS_ADD); 1959 1960 for (i = 1; i < T_size; i <<= 1) { 1961 j = i; 1962 while (j--) { 1963 MBEDTLS_MPI_CHK(ecp_add_mixed(grp, &T[i + j], &T[j], &T[i], tmp)); 1964 } 1965 } 1966 1967 #if defined(MBEDTLS_ECP_RESTARTABLE) 1968 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1969 rs_ctx->rsm->state = ecp_rsm_pre_norm_add; 1970 } 1971 1972 norm_add: 1973 #endif 1974 /* 1975 * Normalize final elements in T. Even though there are no holes now, we 1976 * still need the auxiliary array for homogeneity with the previous 1977 * call. Also, skip T[0] which is already normalised, being a copy of P. 1978 */ 1979 for (j = 0; j + 1 < T_size; j++) { 1980 TT[j] = T + j + 1; 1981 } 1982 1983 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2); 1984 1985 MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j)); 1986 1987 /* Free Z coordinate (=1 after normalization) to save RAM. 1988 * This makes T[i] invalid as mbedtls_ecp_points, but this is OK 1989 * since from this point onwards, they are only accessed indirectly 1990 * via the getter function ecp_select_comb() which does set the 1991 * target's Z coordinate to 1. */ 1992 for (i = 0; i < T_size; i++) { 1993 mbedtls_mpi_free(&T[i].Z); 1994 } 1995 1996 cleanup: 1997 1998 mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 1999 2000 #if defined(MBEDTLS_ECP_RESTARTABLE) 2001 if (rs_ctx != NULL && rs_ctx->rsm != NULL && 2002 ret == MBEDTLS_ERR_ECP_IN_PROGRESS) { 2003 if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) { 2004 rs_ctx->rsm->i = j; 2005 } 2006 } 2007 #endif 2008 2009 return ret; 2010 } 2011 2012 /* 2013 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ] 2014 * 2015 * See ecp_comb_recode_core() for background 2016 */ 2017 static int ecp_select_comb(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2018 const mbedtls_ecp_point T[], unsigned char T_size, 2019 unsigned char i) 2020 { 2021 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2022 unsigned char ii, j; 2023 2024 /* Ignore the "sign" bit and scale down */ 2025 ii = (i & 0x7Fu) >> 1; 2026 2027 /* Read the whole table to thwart cache-based timing attacks */ 2028 for (j = 0; j < T_size; j++) { 2029 MPI_ECP_COND_ASSIGN(&R->X, &T[j].X, j == ii); 2030 MPI_ECP_COND_ASSIGN(&R->Y, &T[j].Y, j == ii); 2031 } 2032 2033 /* Safely invert result if i is "negative" */ 2034 MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, R, i >> 7)); 2035 2036 MPI_ECP_LSET(&R->Z, 1); 2037 2038 cleanup: 2039 return ret; 2040 } 2041 2042 /* 2043 * Core multiplication algorithm for the (modified) comb method. 2044 * This part is actually common with the basic comb method (GECC 3.44) 2045 * 2046 * Cost: d A + d D + 1 R 2047 */ 2048 static int ecp_mul_comb_core(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2049 const mbedtls_ecp_point T[], unsigned char T_size, 2050 const unsigned char x[], size_t d, 2051 int (*f_rng)(void *, unsigned char *, size_t), 2052 void *p_rng, 2053 mbedtls_ecp_restart_ctx *rs_ctx) 2054 { 2055 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2056 mbedtls_ecp_point Txi; 2057 mbedtls_mpi tmp[4]; 2058 size_t i; 2059 2060 mbedtls_ecp_point_init(&Txi); 2061 mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2062 2063 #if !defined(MBEDTLS_ECP_RESTARTABLE) 2064 (void) rs_ctx; 2065 #endif 2066 2067 #if defined(MBEDTLS_ECP_RESTARTABLE) 2068 if (rs_ctx != NULL && rs_ctx->rsm != NULL && 2069 rs_ctx->rsm->state != ecp_rsm_comb_core) { 2070 rs_ctx->rsm->i = 0; 2071 rs_ctx->rsm->state = ecp_rsm_comb_core; 2072 } 2073 2074 /* new 'if' instead of nested for the sake of the 'else' branch */ 2075 if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) { 2076 /* restore current index (R already pointing to rs_ctx->rsm->R) */ 2077 i = rs_ctx->rsm->i; 2078 } else 2079 #endif 2080 { 2081 /* Start with a non-zero point and randomize its coordinates */ 2082 i = d; 2083 MBEDTLS_MPI_CHK(ecp_select_comb(grp, R, T, T_size, x[i])); 2084 if (f_rng != 0) { 2085 MBEDTLS_MPI_CHK(ecp_randomize_jac(grp, R, f_rng, p_rng)); 2086 } 2087 } 2088 2089 while (i != 0) { 2090 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD); 2091 --i; 2092 2093 MBEDTLS_MPI_CHK(ecp_double_jac(grp, R, R, tmp)); 2094 MBEDTLS_MPI_CHK(ecp_select_comb(grp, &Txi, T, T_size, x[i])); 2095 MBEDTLS_MPI_CHK(ecp_add_mixed(grp, R, R, &Txi, tmp)); 2096 } 2097 2098 cleanup: 2099 2100 mbedtls_ecp_point_free(&Txi); 2101 mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2102 2103 #if defined(MBEDTLS_ECP_RESTARTABLE) 2104 if (rs_ctx != NULL && rs_ctx->rsm != NULL && 2105 ret == MBEDTLS_ERR_ECP_IN_PROGRESS) { 2106 rs_ctx->rsm->i = i; 2107 /* no need to save R, already pointing to rs_ctx->rsm->R */ 2108 } 2109 #endif 2110 2111 return ret; 2112 } 2113 2114 /* 2115 * Recode the scalar to get constant-time comb multiplication 2116 * 2117 * As the actual scalar recoding needs an odd scalar as a starting point, 2118 * this wrapper ensures that by replacing m by N - m if necessary, and 2119 * informs the caller that the result of multiplication will be negated. 2120 * 2121 * This works because we only support large prime order for Short Weierstrass 2122 * curves, so N is always odd hence either m or N - m is. 2123 * 2124 * See ecp_comb_recode_core() for background. 2125 */ 2126 static int ecp_comb_recode_scalar(const mbedtls_ecp_group *grp, 2127 const mbedtls_mpi *m, 2128 unsigned char k[COMB_MAX_D + 1], 2129 size_t d, 2130 unsigned char w, 2131 unsigned char *parity_trick) 2132 { 2133 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2134 mbedtls_mpi M, mm; 2135 2136 mbedtls_mpi_init(&M); 2137 mbedtls_mpi_init(&mm); 2138 2139 /* N is always odd (see above), just make extra sure */ 2140 if (mbedtls_mpi_get_bit(&grp->N, 0) != 1) { 2141 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2142 } 2143 2144 /* do we need the parity trick? */ 2145 *parity_trick = (mbedtls_mpi_get_bit(m, 0) == 0); 2146 2147 /* execute parity fix in constant time */ 2148 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&M, m)); 2149 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&mm, &grp->N, m)); 2150 MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&M, &mm, *parity_trick)); 2151 2152 /* actual scalar recoding */ 2153 ecp_comb_recode_core(k, d, w, &M); 2154 2155 cleanup: 2156 mbedtls_mpi_free(&mm); 2157 mbedtls_mpi_free(&M); 2158 2159 return ret; 2160 } 2161 2162 /* 2163 * Perform comb multiplication (for short Weierstrass curves) 2164 * once the auxiliary table has been pre-computed. 2165 * 2166 * Scalar recoding may use a parity trick that makes us compute -m * P, 2167 * if that is the case we'll need to recover m * P at the end. 2168 */ 2169 static int ecp_mul_comb_after_precomp(const mbedtls_ecp_group *grp, 2170 mbedtls_ecp_point *R, 2171 const mbedtls_mpi *m, 2172 const mbedtls_ecp_point *T, 2173 unsigned char T_size, 2174 unsigned char w, 2175 size_t d, 2176 int (*f_rng)(void *, unsigned char *, size_t), 2177 void *p_rng, 2178 mbedtls_ecp_restart_ctx *rs_ctx) 2179 { 2180 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2181 unsigned char parity_trick; 2182 unsigned char k[COMB_MAX_D + 1]; 2183 mbedtls_ecp_point *RR = R; 2184 2185 #if defined(MBEDTLS_ECP_RESTARTABLE) 2186 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 2187 RR = &rs_ctx->rsm->R; 2188 2189 if (rs_ctx->rsm->state == ecp_rsm_final_norm) { 2190 goto final_norm; 2191 } 2192 } 2193 #endif 2194 2195 MBEDTLS_MPI_CHK(ecp_comb_recode_scalar(grp, m, k, d, w, 2196 &parity_trick)); 2197 MBEDTLS_MPI_CHK(ecp_mul_comb_core(grp, RR, T, T_size, k, d, 2198 f_rng, p_rng, rs_ctx)); 2199 MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, RR, parity_trick)); 2200 2201 #if defined(MBEDTLS_ECP_RESTARTABLE) 2202 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 2203 rs_ctx->rsm->state = ecp_rsm_final_norm; 2204 } 2205 2206 final_norm: 2207 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV); 2208 #endif 2209 MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, RR)); 2210 2211 #if defined(MBEDTLS_ECP_RESTARTABLE) 2212 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 2213 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, RR)); 2214 } 2215 #endif 2216 2217 cleanup: 2218 return ret; 2219 } 2220 2221 /* 2222 * Pick window size based on curve size and whether we optimize for base point 2223 */ 2224 static unsigned char ecp_pick_window_size(const mbedtls_ecp_group *grp, 2225 unsigned char p_eq_g) 2226 { 2227 unsigned char w; 2228 2229 /* 2230 * Minimize the number of multiplications, that is minimize 2231 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w ) 2232 * (see costs of the various parts, with 1S = 1M) 2233 */ 2234 w = grp->nbits >= 384 ? 5 : 4; 2235 2236 /* 2237 * If P == G, pre-compute a bit more, since this may be re-used later. 2238 * Just adding one avoids upping the cost of the first mul too much, 2239 * and the memory cost too. 2240 */ 2241 if (p_eq_g) { 2242 w++; 2243 } 2244 2245 /* 2246 * If static comb table may not be used (!p_eq_g) or static comb table does 2247 * not exists, make sure w is within bounds. 2248 * (The last test is useful only for very small curves in the test suite.) 2249 * 2250 * The user reduces MBEDTLS_ECP_WINDOW_SIZE does not changes the size of 2251 * static comb table, because the size of static comb table is fixed when 2252 * it is generated. 2253 */ 2254 #if (MBEDTLS_ECP_WINDOW_SIZE < 6) 2255 if ((!p_eq_g || !ecp_group_is_static_comb_table(grp)) && w > MBEDTLS_ECP_WINDOW_SIZE) { 2256 w = MBEDTLS_ECP_WINDOW_SIZE; 2257 } 2258 #endif 2259 if (w >= grp->nbits) { 2260 w = 2; 2261 } 2262 2263 return w; 2264 } 2265 2266 /* 2267 * Multiplication using the comb method - for curves in short Weierstrass form 2268 * 2269 * This function is mainly responsible for administrative work: 2270 * - managing the restart context if enabled 2271 * - managing the table of precomputed points (passed between the below two 2272 * functions): allocation, computation, ownership transfer, freeing. 2273 * 2274 * It delegates the actual arithmetic work to: 2275 * ecp_precompute_comb() and ecp_mul_comb_with_precomp() 2276 * 2277 * See comments on ecp_comb_recode_core() regarding the computation strategy. 2278 */ 2279 static int ecp_mul_comb(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2280 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2281 int (*f_rng)(void *, unsigned char *, size_t), 2282 void *p_rng, 2283 mbedtls_ecp_restart_ctx *rs_ctx) 2284 { 2285 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2286 unsigned char w, p_eq_g, i; 2287 size_t d; 2288 unsigned char T_size = 0, T_ok = 0; 2289 mbedtls_ecp_point *T = NULL; 2290 2291 ECP_RS_ENTER(rsm); 2292 2293 /* Is P the base point ? */ 2294 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 2295 p_eq_g = (MPI_ECP_CMP(&P->Y, &grp->G.Y) == 0 && 2296 MPI_ECP_CMP(&P->X, &grp->G.X) == 0); 2297 #else 2298 p_eq_g = 0; 2299 #endif 2300 2301 /* Pick window size and deduce related sizes */ 2302 w = ecp_pick_window_size(grp, p_eq_g); 2303 T_size = 1U << (w - 1); 2304 d = (grp->nbits + w - 1) / w; 2305 2306 /* Pre-computed table: do we have it already for the base point? */ 2307 if (p_eq_g && grp->T != NULL) { 2308 /* second pointer to the same table, will be deleted on exit */ 2309 T = grp->T; 2310 T_ok = 1; 2311 } else 2312 #if defined(MBEDTLS_ECP_RESTARTABLE) 2313 /* Pre-computed table: do we have one in progress? complete? */ 2314 if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL) { 2315 /* transfer ownership of T from rsm to local function */ 2316 T = rs_ctx->rsm->T; 2317 rs_ctx->rsm->T = NULL; 2318 rs_ctx->rsm->T_size = 0; 2319 2320 /* This effectively jumps to the call to mul_comb_after_precomp() */ 2321 T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core; 2322 } else 2323 #endif 2324 /* Allocate table if we didn't have any */ 2325 { 2326 T = mbedtls_calloc(T_size, sizeof(mbedtls_ecp_point)); 2327 if (T == NULL) { 2328 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED; 2329 goto cleanup; 2330 } 2331 2332 for (i = 0; i < T_size; i++) { 2333 mbedtls_ecp_point_init(&T[i]); 2334 } 2335 2336 T_ok = 0; 2337 } 2338 2339 /* Compute table (or finish computing it) if not done already */ 2340 if (!T_ok) { 2341 MBEDTLS_MPI_CHK(ecp_precompute_comb(grp, T, P, w, d, rs_ctx)); 2342 2343 if (p_eq_g) { 2344 /* almost transfer ownership of T to the group, but keep a copy of 2345 * the pointer to use for calling the next function more easily */ 2346 grp->T = T; 2347 grp->T_size = T_size; 2348 } 2349 } 2350 2351 /* Actual comb multiplication using precomputed points */ 2352 MBEDTLS_MPI_CHK(ecp_mul_comb_after_precomp(grp, R, m, 2353 T, T_size, w, d, 2354 f_rng, p_rng, rs_ctx)); 2355 2356 cleanup: 2357 2358 /* does T belong to the group? */ 2359 if (T == grp->T) { 2360 T = NULL; 2361 } 2362 2363 /* does T belong to the restart context? */ 2364 #if defined(MBEDTLS_ECP_RESTARTABLE) 2365 if (rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL) { 2366 /* transfer ownership of T from local function to rsm */ 2367 rs_ctx->rsm->T_size = T_size; 2368 rs_ctx->rsm->T = T; 2369 T = NULL; 2370 } 2371 #endif 2372 2373 /* did T belong to us? then let's destroy it! */ 2374 if (T != NULL) { 2375 for (i = 0; i < T_size; i++) { 2376 mbedtls_ecp_point_free(&T[i]); 2377 } 2378 mbedtls_free(T); 2379 } 2380 2381 /* prevent caller from using invalid value */ 2382 int should_free_R = (ret != 0); 2383 #if defined(MBEDTLS_ECP_RESTARTABLE) 2384 /* don't free R while in progress in case R == P */ 2385 if (ret == MBEDTLS_ERR_ECP_IN_PROGRESS) { 2386 should_free_R = 0; 2387 } 2388 #endif 2389 if (should_free_R) { 2390 mbedtls_ecp_point_free(R); 2391 } 2392 2393 ECP_RS_LEAVE(rsm); 2394 2395 return ret; 2396 } 2397 2398 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 2399 2400 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 2401 /* 2402 * For Montgomery curves, we do all the internal arithmetic in projective 2403 * coordinates. Import/export of points uses only the x coordinates, which is 2404 * internally represented as X / Z. 2405 * 2406 * For scalar multiplication, we'll use a Montgomery ladder. 2407 */ 2408 2409 /* 2410 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1 2411 * Cost: 1M + 1I 2412 */ 2413 static int ecp_normalize_mxz(const mbedtls_ecp_group *grp, mbedtls_ecp_point *P) 2414 { 2415 #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) 2416 if (mbedtls_internal_ecp_grp_capable(grp)) { 2417 return mbedtls_internal_ecp_normalize_mxz(grp, P); 2418 } 2419 #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */ 2420 2421 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) 2422 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 2423 #else 2424 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2425 MPI_ECP_INV(&P->Z, &P->Z); 2426 MPI_ECP_MUL(&P->X, &P->X, &P->Z); 2427 MPI_ECP_LSET(&P->Z, 1); 2428 2429 cleanup: 2430 return ret; 2431 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */ 2432 } 2433 2434 /* 2435 * Randomize projective x/z coordinates: 2436 * (X, Z) -> (l X, l Z) for random l 2437 * This is sort of the reverse operation of ecp_normalize_mxz(). 2438 * 2439 * This countermeasure was first suggested in [2]. 2440 * Cost: 2M 2441 */ 2442 static int ecp_randomize_mxz(const mbedtls_ecp_group *grp, mbedtls_ecp_point *P, 2443 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 2444 { 2445 #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) 2446 if (mbedtls_internal_ecp_grp_capable(grp)) { 2447 return mbedtls_internal_ecp_randomize_mxz(grp, P, f_rng, p_rng); 2448 } 2449 #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */ 2450 2451 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) 2452 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 2453 #else 2454 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2455 mbedtls_mpi l; 2456 mbedtls_mpi_init(&l); 2457 2458 /* Generate l such that 1 < l < p */ 2459 MPI_ECP_RAND(&l); 2460 2461 MPI_ECP_MUL(&P->X, &P->X, &l); 2462 MPI_ECP_MUL(&P->Z, &P->Z, &l); 2463 2464 cleanup: 2465 mbedtls_mpi_free(&l); 2466 2467 if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) { 2468 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; 2469 } 2470 return ret; 2471 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */ 2472 } 2473 2474 /* 2475 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q), 2476 * for Montgomery curves in x/z coordinates. 2477 * 2478 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3 2479 * with 2480 * d = X1 2481 * P = (X2, Z2) 2482 * Q = (X3, Z3) 2483 * R = (X4, Z4) 2484 * S = (X5, Z5) 2485 * and eliminating temporary variables tO, ..., t4. 2486 * 2487 * Cost: 5M + 4S 2488 */ 2489 static int ecp_double_add_mxz(const mbedtls_ecp_group *grp, 2490 mbedtls_ecp_point *R, mbedtls_ecp_point *S, 2491 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q, 2492 const mbedtls_mpi *d, 2493 mbedtls_mpi T[4]) 2494 { 2495 #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) 2496 if (mbedtls_internal_ecp_grp_capable(grp)) { 2497 return mbedtls_internal_ecp_double_add_mxz(grp, R, S, P, Q, d); 2498 } 2499 #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */ 2500 2501 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) 2502 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 2503 #else 2504 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2505 2506 MPI_ECP_ADD(&T[0], &P->X, &P->Z); /* Pp := PX + PZ */ 2507 MPI_ECP_SUB(&T[1], &P->X, &P->Z); /* Pm := PX - PZ */ 2508 MPI_ECP_ADD(&T[2], &Q->X, &Q->Z); /* Qp := QX + XZ */ 2509 MPI_ECP_SUB(&T[3], &Q->X, &Q->Z); /* Qm := QX - QZ */ 2510 MPI_ECP_MUL(&T[3], &T[3], &T[0]); /* Qm * Pp */ 2511 MPI_ECP_MUL(&T[2], &T[2], &T[1]); /* Qp * Pm */ 2512 MPI_ECP_SQR(&T[0], &T[0]); /* Pp^2 */ 2513 MPI_ECP_SQR(&T[1], &T[1]); /* Pm^2 */ 2514 MPI_ECP_MUL(&R->X, &T[0], &T[1]); /* Pp^2 * Pm^2 */ 2515 MPI_ECP_SUB(&T[0], &T[0], &T[1]); /* Pp^2 - Pm^2 */ 2516 MPI_ECP_MUL(&R->Z, &grp->A, &T[0]); /* A * (Pp^2 - Pm^2) */ 2517 MPI_ECP_ADD(&R->Z, &T[1], &R->Z); /* [ A * (Pp^2-Pm^2) ] + Pm^2 */ 2518 MPI_ECP_ADD(&S->X, &T[3], &T[2]); /* Qm*Pp + Qp*Pm */ 2519 MPI_ECP_SQR(&S->X, &S->X); /* (Qm*Pp + Qp*Pm)^2 */ 2520 MPI_ECP_SUB(&S->Z, &T[3], &T[2]); /* Qm*Pp - Qp*Pm */ 2521 MPI_ECP_SQR(&S->Z, &S->Z); /* (Qm*Pp - Qp*Pm)^2 */ 2522 MPI_ECP_MUL(&S->Z, d, &S->Z); /* d * ( Qm*Pp - Qp*Pm )^2 */ 2523 MPI_ECP_MUL(&R->Z, &T[0], &R->Z); /* [A*(Pp^2-Pm^2)+Pm^2]*(Pp^2-Pm^2) */ 2524 2525 cleanup: 2526 2527 return ret; 2528 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */ 2529 } 2530 2531 /* 2532 * Multiplication with Montgomery ladder in x/z coordinates, 2533 * for curves in Montgomery form 2534 */ 2535 static int ecp_mul_mxz(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2536 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2537 int (*f_rng)(void *, unsigned char *, size_t), 2538 void *p_rng) 2539 { 2540 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2541 size_t i; 2542 unsigned char b; 2543 mbedtls_ecp_point RP; 2544 mbedtls_mpi PX; 2545 mbedtls_mpi tmp[4]; 2546 mbedtls_ecp_point_init(&RP); mbedtls_mpi_init(&PX); 2547 2548 mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2549 2550 if (f_rng == NULL) { 2551 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2552 } 2553 2554 /* Save PX and read from P before writing to R, in case P == R */ 2555 MPI_ECP_MOV(&PX, &P->X); 2556 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&RP, P)); 2557 2558 /* Set R to zero in modified x/z coordinates */ 2559 MPI_ECP_LSET(&R->X, 1); 2560 MPI_ECP_LSET(&R->Z, 0); 2561 mbedtls_mpi_free(&R->Y); 2562 2563 /* RP.X might be slightly larger than P, so reduce it */ 2564 MOD_ADD(&RP.X); 2565 2566 /* Randomize coordinates of the starting point */ 2567 MBEDTLS_MPI_CHK(ecp_randomize_mxz(grp, &RP, f_rng, p_rng)); 2568 2569 /* Loop invariant: R = result so far, RP = R + P */ 2570 i = grp->nbits + 1; /* one past the (zero-based) required msb for private keys */ 2571 while (i-- > 0) { 2572 b = mbedtls_mpi_get_bit(m, i); 2573 /* 2574 * if (b) R = 2R + P else R = 2R, 2575 * which is: 2576 * if (b) double_add( RP, R, RP, R ) 2577 * else double_add( R, RP, R, RP ) 2578 * but using safe conditional swaps to avoid leaks 2579 */ 2580 MPI_ECP_COND_SWAP(&R->X, &RP.X, b); 2581 MPI_ECP_COND_SWAP(&R->Z, &RP.Z, b); 2582 MBEDTLS_MPI_CHK(ecp_double_add_mxz(grp, R, &RP, R, &RP, &PX, tmp)); 2583 MPI_ECP_COND_SWAP(&R->X, &RP.X, b); 2584 MPI_ECP_COND_SWAP(&R->Z, &RP.Z, b); 2585 } 2586 2587 MBEDTLS_MPI_CHK(ecp_normalize_mxz(grp, R)); 2588 2589 cleanup: 2590 mbedtls_ecp_point_free(&RP); mbedtls_mpi_free(&PX); 2591 2592 mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2593 return ret; 2594 } 2595 2596 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 2597 2598 /* 2599 * Restartable multiplication R = m * P 2600 * 2601 * This internal function can be called without an RNG in case where we know 2602 * the inputs are not sensitive. 2603 */ 2604 static int ecp_mul_restartable_internal(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2605 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2606 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 2607 mbedtls_ecp_restart_ctx *rs_ctx) 2608 { 2609 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2610 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2611 char is_grp_capable = 0; 2612 #endif 2613 2614 #if defined(MBEDTLS_ECP_RESTARTABLE) 2615 /* reset ops count for this call if top-level */ 2616 if (rs_ctx != NULL && rs_ctx->depth++ == 0) { 2617 rs_ctx->ops_done = 0; 2618 } 2619 #else 2620 (void) rs_ctx; 2621 #endif 2622 2623 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2624 if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) { 2625 MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp)); 2626 } 2627 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 2628 2629 int restarting = 0; 2630 #if defined(MBEDTLS_ECP_RESTARTABLE) 2631 restarting = (rs_ctx != NULL && rs_ctx->rsm != NULL); 2632 #endif 2633 /* skip argument check when restarting */ 2634 if (!restarting) { 2635 /* check_privkey is free */ 2636 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_CHK); 2637 2638 /* Common sanity checks */ 2639 MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(grp, m)); 2640 MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); 2641 } 2642 2643 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2644 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 2645 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 2646 MBEDTLS_MPI_CHK(ecp_mul_mxz(grp, R, m, P, f_rng, p_rng)); 2647 } 2648 #endif 2649 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 2650 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 2651 MBEDTLS_MPI_CHK(ecp_mul_comb(grp, R, m, P, f_rng, p_rng, rs_ctx)); 2652 } 2653 #endif 2654 2655 cleanup: 2656 2657 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2658 if (is_grp_capable) { 2659 mbedtls_internal_ecp_free(grp); 2660 } 2661 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 2662 2663 #if defined(MBEDTLS_ECP_RESTARTABLE) 2664 if (rs_ctx != NULL) { 2665 rs_ctx->depth--; 2666 } 2667 #endif 2668 2669 return ret; 2670 } 2671 2672 /* 2673 * Restartable multiplication R = m * P 2674 */ 2675 int mbedtls_ecp_mul_restartable(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2676 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2677 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 2678 mbedtls_ecp_restart_ctx *rs_ctx) 2679 { 2680 if (f_rng == NULL) { 2681 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2682 } 2683 2684 return ecp_mul_restartable_internal(grp, R, m, P, f_rng, p_rng, rs_ctx); 2685 } 2686 2687 /* 2688 * Multiplication R = m * P 2689 */ 2690 int mbedtls_ecp_mul(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2691 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2692 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 2693 { 2694 return mbedtls_ecp_mul_restartable(grp, R, m, P, f_rng, p_rng, NULL); 2695 } 2696 #endif /* MBEDTLS_ECP_C */ 2697 2698 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 2699 /* 2700 * Check that an affine point is valid as a public key, 2701 * short weierstrass curves (SEC1 3.2.3.1) 2702 */ 2703 static int ecp_check_pubkey_sw(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt) 2704 { 2705 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2706 mbedtls_mpi YY, RHS; 2707 2708 /* pt coordinates must be normalized for our checks */ 2709 if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0 || 2710 mbedtls_mpi_cmp_int(&pt->Y, 0) < 0 || 2711 mbedtls_mpi_cmp_mpi(&pt->X, &grp->P) >= 0 || 2712 mbedtls_mpi_cmp_mpi(&pt->Y, &grp->P) >= 0) { 2713 return MBEDTLS_ERR_ECP_INVALID_KEY; 2714 } 2715 2716 mbedtls_mpi_init(&YY); mbedtls_mpi_init(&RHS); 2717 2718 /* 2719 * YY = Y^2 2720 * RHS = X^3 + A X + B 2721 */ 2722 MPI_ECP_SQR(&YY, &pt->Y); 2723 MBEDTLS_MPI_CHK(ecp_sw_rhs(grp, &RHS, &pt->X)); 2724 2725 if (MPI_ECP_CMP(&YY, &RHS) != 0) { 2726 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2727 } 2728 2729 cleanup: 2730 2731 mbedtls_mpi_free(&YY); mbedtls_mpi_free(&RHS); 2732 2733 return ret; 2734 } 2735 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 2736 2737 #if defined(MBEDTLS_ECP_C) 2738 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 2739 /* 2740 * R = m * P with shortcuts for m == 0, m == 1 and m == -1 2741 * NOT constant-time - ONLY for short Weierstrass! 2742 */ 2743 static int mbedtls_ecp_mul_shortcuts(mbedtls_ecp_group *grp, 2744 mbedtls_ecp_point *R, 2745 const mbedtls_mpi *m, 2746 const mbedtls_ecp_point *P, 2747 mbedtls_ecp_restart_ctx *rs_ctx) 2748 { 2749 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2750 mbedtls_mpi tmp; 2751 mbedtls_mpi_init(&tmp); 2752 2753 if (mbedtls_mpi_cmp_int(m, 0) == 0) { 2754 MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); 2755 MBEDTLS_MPI_CHK(mbedtls_ecp_set_zero(R)); 2756 } else if (mbedtls_mpi_cmp_int(m, 1) == 0) { 2757 MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); 2758 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P)); 2759 } else if (mbedtls_mpi_cmp_int(m, -1) == 0) { 2760 MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); 2761 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P)); 2762 MPI_ECP_NEG(&R->Y); 2763 } else { 2764 MBEDTLS_MPI_CHK(ecp_mul_restartable_internal(grp, R, m, P, 2765 NULL, NULL, rs_ctx)); 2766 } 2767 2768 cleanup: 2769 mbedtls_mpi_free(&tmp); 2770 2771 return ret; 2772 } 2773 2774 /* 2775 * Restartable linear combination 2776 * NOT constant-time 2777 */ 2778 int mbedtls_ecp_muladd_restartable( 2779 mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2780 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2781 const mbedtls_mpi *n, const mbedtls_ecp_point *Q, 2782 mbedtls_ecp_restart_ctx *rs_ctx) 2783 { 2784 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2785 mbedtls_ecp_point mP; 2786 mbedtls_ecp_point *pmP = &mP; 2787 mbedtls_ecp_point *pR = R; 2788 mbedtls_mpi tmp[4]; 2789 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2790 char is_grp_capable = 0; 2791 #endif 2792 if (mbedtls_ecp_get_type(grp) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 2793 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 2794 } 2795 2796 mbedtls_ecp_point_init(&mP); 2797 mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2798 2799 ECP_RS_ENTER(ma); 2800 2801 #if defined(MBEDTLS_ECP_RESTARTABLE) 2802 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2803 /* redirect intermediate results to restart context */ 2804 pmP = &rs_ctx->ma->mP; 2805 pR = &rs_ctx->ma->R; 2806 2807 /* jump to next operation */ 2808 if (rs_ctx->ma->state == ecp_rsma_mul2) { 2809 goto mul2; 2810 } 2811 if (rs_ctx->ma->state == ecp_rsma_add) { 2812 goto add; 2813 } 2814 if (rs_ctx->ma->state == ecp_rsma_norm) { 2815 goto norm; 2816 } 2817 } 2818 #endif /* MBEDTLS_ECP_RESTARTABLE */ 2819 2820 MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pmP, m, P, rs_ctx)); 2821 #if defined(MBEDTLS_ECP_RESTARTABLE) 2822 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2823 rs_ctx->ma->state = ecp_rsma_mul2; 2824 } 2825 2826 mul2: 2827 #endif 2828 MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pR, n, Q, rs_ctx)); 2829 2830 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2831 if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) { 2832 MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp)); 2833 } 2834 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 2835 2836 #if defined(MBEDTLS_ECP_RESTARTABLE) 2837 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2838 rs_ctx->ma->state = ecp_rsma_add; 2839 } 2840 2841 add: 2842 #endif 2843 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_ADD); 2844 MBEDTLS_MPI_CHK(ecp_add_mixed(grp, pR, pmP, pR, tmp)); 2845 #if defined(MBEDTLS_ECP_RESTARTABLE) 2846 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2847 rs_ctx->ma->state = ecp_rsma_norm; 2848 } 2849 2850 norm: 2851 #endif 2852 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV); 2853 MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, pR)); 2854 2855 #if defined(MBEDTLS_ECP_RESTARTABLE) 2856 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2857 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, pR)); 2858 } 2859 #endif 2860 2861 cleanup: 2862 2863 mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2864 2865 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2866 if (is_grp_capable) { 2867 mbedtls_internal_ecp_free(grp); 2868 } 2869 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 2870 2871 mbedtls_ecp_point_free(&mP); 2872 2873 ECP_RS_LEAVE(ma); 2874 2875 return ret; 2876 } 2877 2878 /* 2879 * Linear combination 2880 * NOT constant-time 2881 */ 2882 int mbedtls_ecp_muladd(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2883 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2884 const mbedtls_mpi *n, const mbedtls_ecp_point *Q) 2885 { 2886 return mbedtls_ecp_muladd_restartable(grp, R, m, P, n, Q, NULL); 2887 } 2888 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 2889 #endif /* MBEDTLS_ECP_C */ 2890 2891 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 2892 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 2893 #define ECP_MPI_INIT(_p, _n) { .p = (mbedtls_mpi_uint *) (_p), .s = 1, .n = (_n), .use_mempool = 0 } 2894 #define ECP_MPI_INIT_ARRAY(x) \ 2895 ECP_MPI_INIT(x, sizeof(x) / sizeof(mbedtls_mpi_uint)) 2896 /* 2897 * Constants for the two points other than 0, 1, -1 (mod p) in 2898 * https://cr.yp.to/ecdh.html#validate 2899 * See ecp_check_pubkey_x25519(). 2900 */ 2901 static const mbedtls_mpi_uint x25519_bad_point_1[] = { 2902 MBEDTLS_BYTES_TO_T_UINT_8(0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae), 2903 MBEDTLS_BYTES_TO_T_UINT_8(0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a), 2904 MBEDTLS_BYTES_TO_T_UINT_8(0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd), 2905 MBEDTLS_BYTES_TO_T_UINT_8(0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00), 2906 }; 2907 static const mbedtls_mpi_uint x25519_bad_point_2[] = { 2908 MBEDTLS_BYTES_TO_T_UINT_8(0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24), 2909 MBEDTLS_BYTES_TO_T_UINT_8(0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b), 2910 MBEDTLS_BYTES_TO_T_UINT_8(0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86), 2911 MBEDTLS_BYTES_TO_T_UINT_8(0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57), 2912 }; 2913 static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY( 2914 x25519_bad_point_1); 2915 static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY( 2916 x25519_bad_point_2); 2917 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 2918 2919 /* 2920 * Check that the input point is not one of the low-order points. 2921 * This is recommended by the "May the Fourth" paper: 2922 * https://eprint.iacr.org/2017/806.pdf 2923 * Those points are never sent by an honest peer. 2924 */ 2925 static int ecp_check_bad_points_mx(const mbedtls_mpi *X, const mbedtls_mpi *P, 2926 const mbedtls_ecp_group_id grp_id) 2927 { 2928 int ret; 2929 mbedtls_mpi XmP; 2930 2931 mbedtls_mpi_init(&XmP); 2932 2933 /* Reduce X mod P so that we only need to check values less than P. 2934 * We know X < 2^256 so we can proceed by subtraction. */ 2935 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&XmP, X)); 2936 while (mbedtls_mpi_cmp_mpi(&XmP, P) >= 0) { 2937 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&XmP, &XmP, P)); 2938 } 2939 2940 /* Check against the known bad values that are less than P. For Curve448 2941 * these are 0, 1 and -1. For Curve25519 we check the values less than P 2942 * from the following list: https://cr.yp.to/ecdh.html#validate */ 2943 if (mbedtls_mpi_cmp_int(&XmP, 1) <= 0) { /* takes care of 0 and 1 */ 2944 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2945 goto cleanup; 2946 } 2947 2948 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 2949 if (grp_id == MBEDTLS_ECP_DP_CURVE25519) { 2950 if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_1) == 0) { 2951 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2952 goto cleanup; 2953 } 2954 2955 if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_2) == 0) { 2956 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2957 goto cleanup; 2958 } 2959 } 2960 #else 2961 (void) grp_id; 2962 #endif 2963 2964 /* Final check: check if XmP + 1 is P (final because it changes XmP!) */ 2965 MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&XmP, &XmP, 1)); 2966 if (mbedtls_mpi_cmp_mpi(&XmP, P) == 0) { 2967 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2968 goto cleanup; 2969 } 2970 2971 ret = 0; 2972 2973 cleanup: 2974 mbedtls_mpi_free(&XmP); 2975 2976 return ret; 2977 } 2978 2979 /* 2980 * Check validity of a public key for Montgomery curves with x-only schemes 2981 */ 2982 static int ecp_check_pubkey_mx(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt) 2983 { 2984 /* [Curve25519 p. 5] Just check X is the correct number of bytes */ 2985 /* Allow any public value, if it's too big then we'll just reduce it mod p 2986 * (RFC 7748 sec. 5 para. 3). */ 2987 if (mbedtls_mpi_size(&pt->X) > (grp->nbits + 7) / 8) { 2988 return MBEDTLS_ERR_ECP_INVALID_KEY; 2989 } 2990 2991 /* Implicit in all standards (as they don't consider negative numbers): 2992 * X must be non-negative. This is normally ensured by the way it's 2993 * encoded for transmission, but let's be extra sure. */ 2994 if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0) { 2995 return MBEDTLS_ERR_ECP_INVALID_KEY; 2996 } 2997 2998 return ecp_check_bad_points_mx(&pt->X, &grp->P, grp->id); 2999 } 3000 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3001 3002 /* 3003 * Check that a point is valid as a public key 3004 */ 3005 int mbedtls_ecp_check_pubkey(const mbedtls_ecp_group *grp, 3006 const mbedtls_ecp_point *pt) 3007 { 3008 /* Must use affine coordinates */ 3009 if (mbedtls_mpi_cmp_int(&pt->Z, 1) != 0) { 3010 return MBEDTLS_ERR_ECP_INVALID_KEY; 3011 } 3012 3013 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3014 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3015 return ecp_check_pubkey_mx(grp, pt); 3016 } 3017 #endif 3018 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3019 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3020 return ecp_check_pubkey_sw(grp, pt); 3021 } 3022 #endif 3023 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3024 } 3025 3026 /* 3027 * Check that an mbedtls_mpi is valid as a private key 3028 */ 3029 int mbedtls_ecp_check_privkey(const mbedtls_ecp_group *grp, 3030 const mbedtls_mpi *d) 3031 { 3032 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3033 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3034 /* see RFC 7748 sec. 5 para. 5 */ 3035 if (mbedtls_mpi_get_bit(d, 0) != 0 || 3036 mbedtls_mpi_get_bit(d, 1) != 0 || 3037 mbedtls_mpi_bitlen(d) != grp->nbits + 1) { /* mbedtls_mpi_bitlen is one-based! */ 3038 return MBEDTLS_ERR_ECP_INVALID_KEY; 3039 } 3040 3041 /* see [Curve25519] page 5 */ 3042 if (grp->nbits == 254 && mbedtls_mpi_get_bit(d, 2) != 0) { 3043 return MBEDTLS_ERR_ECP_INVALID_KEY; 3044 } 3045 3046 return 0; 3047 } 3048 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3049 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3050 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3051 /* see SEC1 3.2 */ 3052 if (mbedtls_mpi_cmp_int(d, 1) < 0 || 3053 mbedtls_mpi_cmp_mpi(d, &grp->N) >= 0) { 3054 return MBEDTLS_ERR_ECP_INVALID_KEY; 3055 } else { 3056 return 0; 3057 } 3058 } 3059 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3060 3061 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3062 } 3063 3064 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3065 MBEDTLS_STATIC_TESTABLE 3066 int mbedtls_ecp_gen_privkey_mx(size_t high_bit, 3067 mbedtls_mpi *d, 3068 int (*f_rng)(void *, unsigned char *, size_t), 3069 void *p_rng) 3070 { 3071 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3072 size_t n_random_bytes = high_bit / 8 + 1; 3073 3074 /* [Curve25519] page 5 */ 3075 /* Generate a (high_bit+1)-bit random number by generating just enough 3076 * random bytes, then shifting out extra bits from the top (necessary 3077 * when (high_bit+1) is not a multiple of 8). */ 3078 MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(d, n_random_bytes, 3079 f_rng, p_rng)); 3080 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(d, 8 * n_random_bytes - high_bit - 1)); 3081 3082 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, high_bit, 1)); 3083 3084 /* Make sure the last two bits are unset for Curve448, three bits for 3085 Curve25519 */ 3086 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 0, 0)); 3087 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 1, 0)); 3088 if (high_bit == 254) { 3089 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 2, 0)); 3090 } 3091 3092 cleanup: 3093 return ret; 3094 } 3095 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3096 3097 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3098 static int mbedtls_ecp_gen_privkey_sw( 3099 const mbedtls_mpi *N, mbedtls_mpi *d, 3100 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 3101 { 3102 int ret = mbedtls_mpi_random(d, 1, N, f_rng, p_rng); 3103 switch (ret) { 3104 case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: 3105 return MBEDTLS_ERR_ECP_RANDOM_FAILED; 3106 default: 3107 return ret; 3108 } 3109 } 3110 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3111 3112 /* 3113 * Generate a private key 3114 */ 3115 int mbedtls_ecp_gen_privkey(const mbedtls_ecp_group *grp, 3116 mbedtls_mpi *d, 3117 int (*f_rng)(void *, unsigned char *, size_t), 3118 void *p_rng) 3119 { 3120 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3121 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3122 return mbedtls_ecp_gen_privkey_mx(grp->nbits, d, f_rng, p_rng); 3123 } 3124 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3125 3126 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3127 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3128 return mbedtls_ecp_gen_privkey_sw(&grp->N, d, f_rng, p_rng); 3129 } 3130 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3131 3132 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3133 } 3134 3135 #if defined(MBEDTLS_ECP_C) 3136 /* 3137 * Generate a keypair with configurable base point 3138 */ 3139 int mbedtls_ecp_gen_keypair_base(mbedtls_ecp_group *grp, 3140 const mbedtls_ecp_point *G, 3141 mbedtls_mpi *d, mbedtls_ecp_point *Q, 3142 int (*f_rng)(void *, unsigned char *, size_t), 3143 void *p_rng) 3144 { 3145 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3146 MBEDTLS_MPI_CHK(mbedtls_ecp_gen_privkey(grp, d, f_rng, p_rng)); 3147 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, Q, d, G, f_rng, p_rng)); 3148 3149 cleanup: 3150 return ret; 3151 } 3152 3153 /* 3154 * Generate key pair, wrapper for conventional base point 3155 */ 3156 int mbedtls_ecp_gen_keypair(mbedtls_ecp_group *grp, 3157 mbedtls_mpi *d, mbedtls_ecp_point *Q, 3158 int (*f_rng)(void *, unsigned char *, size_t), 3159 void *p_rng) 3160 { 3161 return mbedtls_ecp_gen_keypair_base(grp, &grp->G, d, Q, f_rng, p_rng); 3162 } 3163 3164 /* 3165 * Generate a keypair, prettier wrapper 3166 */ 3167 int mbedtls_ecp_gen_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 3168 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 3169 { 3170 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3171 if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) { 3172 return ret; 3173 } 3174 3175 return mbedtls_ecp_gen_keypair(&key->grp, &key->d, &key->Q, f_rng, p_rng); 3176 } 3177 #endif /* MBEDTLS_ECP_C */ 3178 3179 int mbedtls_ecp_set_public_key(mbedtls_ecp_group_id grp_id, 3180 mbedtls_ecp_keypair *key, 3181 const mbedtls_ecp_point *Q) 3182 { 3183 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3184 3185 if (key->grp.id == MBEDTLS_ECP_DP_NONE) { 3186 /* Group not set yet */ 3187 if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) { 3188 return ret; 3189 } 3190 } else if (key->grp.id != grp_id) { 3191 /* Group mismatch */ 3192 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3193 } 3194 return mbedtls_ecp_copy(&key->Q, Q); 3195 } 3196 3197 3198 #define ECP_CURVE25519_KEY_SIZE 32 3199 #define ECP_CURVE448_KEY_SIZE 56 3200 /* 3201 * Read a private key. 3202 */ 3203 int mbedtls_ecp_read_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 3204 const unsigned char *buf, size_t buflen) 3205 { 3206 int ret = 0; 3207 3208 if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) { 3209 return ret; 3210 } 3211 3212 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 3213 3214 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3215 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3216 /* 3217 * Mask the key as mandated by RFC7748 for Curve25519 and Curve448. 3218 */ 3219 if (grp_id == MBEDTLS_ECP_DP_CURVE25519) { 3220 if (buflen != ECP_CURVE25519_KEY_SIZE) { 3221 return MBEDTLS_ERR_ECP_INVALID_KEY; 3222 } 3223 3224 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&key->d, buf, buflen)); 3225 3226 /* Set the three least significant bits to 0 */ 3227 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 0, 0)); 3228 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 1, 0)); 3229 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 2, 0)); 3230 3231 /* Set the most significant bit to 0 */ 3232 MBEDTLS_MPI_CHK( 3233 mbedtls_mpi_set_bit(&key->d, 3234 ECP_CURVE25519_KEY_SIZE * 8 - 1, 0) 3235 ); 3236 3237 /* Set the second most significant bit to 1 */ 3238 MBEDTLS_MPI_CHK( 3239 mbedtls_mpi_set_bit(&key->d, 3240 ECP_CURVE25519_KEY_SIZE * 8 - 2, 1) 3241 ); 3242 } else if (grp_id == MBEDTLS_ECP_DP_CURVE448) { 3243 if (buflen != ECP_CURVE448_KEY_SIZE) { 3244 return MBEDTLS_ERR_ECP_INVALID_KEY; 3245 } 3246 3247 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&key->d, buf, buflen)); 3248 3249 /* Set the two least significant bits to 0 */ 3250 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 0, 0)); 3251 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 1, 0)); 3252 3253 /* Set the most significant bit to 1 */ 3254 MBEDTLS_MPI_CHK( 3255 mbedtls_mpi_set_bit(&key->d, 3256 ECP_CURVE448_KEY_SIZE * 8 - 1, 1) 3257 ); 3258 } 3259 } 3260 #endif 3261 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3262 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3263 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&key->d, buf, buflen)); 3264 } 3265 #endif 3266 3267 if (ret == 0) { 3268 MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(&key->grp, &key->d)); 3269 } 3270 3271 cleanup: 3272 3273 if (ret != 0) { 3274 mbedtls_mpi_free(&key->d); 3275 } 3276 3277 return ret; 3278 } 3279 3280 /* 3281 * Write a private key. 3282 */ 3283 #if !defined MBEDTLS_DEPRECATED_REMOVED 3284 int mbedtls_ecp_write_key(mbedtls_ecp_keypair *key, 3285 unsigned char *buf, size_t buflen) 3286 { 3287 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3288 3289 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3290 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3291 if (key->grp.id == MBEDTLS_ECP_DP_CURVE25519) { 3292 if (buflen < ECP_CURVE25519_KEY_SIZE) { 3293 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 3294 } 3295 3296 } else if (key->grp.id == MBEDTLS_ECP_DP_CURVE448) { 3297 if (buflen < ECP_CURVE448_KEY_SIZE) { 3298 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 3299 } 3300 } 3301 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&key->d, buf, buflen)); 3302 } 3303 #endif 3304 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3305 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3306 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&key->d, buf, buflen)); 3307 } 3308 3309 #endif 3310 cleanup: 3311 3312 return ret; 3313 } 3314 #endif /* MBEDTLS_DEPRECATED_REMOVED */ 3315 3316 int mbedtls_ecp_write_key_ext(const mbedtls_ecp_keypair *key, 3317 size_t *olen, unsigned char *buf, size_t buflen) 3318 { 3319 size_t len = (key->grp.nbits + 7) / 8; 3320 if (len > buflen) { 3321 /* For robustness, ensure *olen <= buflen even on error. */ 3322 *olen = 0; 3323 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 3324 } 3325 *olen = len; 3326 3327 /* Private key not set */ 3328 if (key->d.n == 0) { 3329 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3330 } 3331 3332 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3333 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3334 return mbedtls_mpi_write_binary_le(&key->d, buf, len); 3335 } 3336 #endif 3337 3338 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3339 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3340 return mbedtls_mpi_write_binary(&key->d, buf, len); 3341 } 3342 #endif 3343 3344 /* Private key set but no recognized curve type? This shouldn't happen. */ 3345 return MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3346 } 3347 3348 /* 3349 * Write a public key. 3350 */ 3351 int mbedtls_ecp_write_public_key(const mbedtls_ecp_keypair *key, 3352 int format, size_t *olen, 3353 unsigned char *buf, size_t buflen) 3354 { 3355 return mbedtls_ecp_point_write_binary(&key->grp, &key->Q, 3356 format, olen, buf, buflen); 3357 } 3358 3359 3360 #if defined(MBEDTLS_ECP_C) 3361 /* 3362 * Check a public-private key pair 3363 */ 3364 int mbedtls_ecp_check_pub_priv( 3365 const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv, 3366 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 3367 { 3368 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3369 mbedtls_ecp_point Q; 3370 mbedtls_ecp_group grp; 3371 if (pub->grp.id == MBEDTLS_ECP_DP_NONE || 3372 pub->grp.id != prv->grp.id || 3373 mbedtls_mpi_cmp_mpi(&pub->Q.X, &prv->Q.X) || 3374 mbedtls_mpi_cmp_mpi(&pub->Q.Y, &prv->Q.Y) || 3375 mbedtls_mpi_cmp_mpi(&pub->Q.Z, &prv->Q.Z)) { 3376 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3377 } 3378 3379 mbedtls_ecp_point_init(&Q); 3380 mbedtls_ecp_group_init(&grp); 3381 3382 /* mbedtls_ecp_mul() needs a non-const group... */ 3383 mbedtls_ecp_group_copy(&grp, &prv->grp); 3384 3385 /* Also checks d is valid */ 3386 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &Q, &prv->d, &prv->grp.G, f_rng, p_rng)); 3387 3388 if (mbedtls_mpi_cmp_mpi(&Q.X, &prv->Q.X) || 3389 mbedtls_mpi_cmp_mpi(&Q.Y, &prv->Q.Y) || 3390 mbedtls_mpi_cmp_mpi(&Q.Z, &prv->Q.Z)) { 3391 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3392 goto cleanup; 3393 } 3394 3395 cleanup: 3396 mbedtls_ecp_point_free(&Q); 3397 mbedtls_ecp_group_free(&grp); 3398 3399 return ret; 3400 } 3401 3402 int mbedtls_ecp_keypair_calc_public(mbedtls_ecp_keypair *key, 3403 int (*f_rng)(void *, unsigned char *, size_t), 3404 void *p_rng) 3405 { 3406 return mbedtls_ecp_mul(&key->grp, &key->Q, &key->d, &key->grp.G, 3407 f_rng, p_rng); 3408 } 3409 #endif /* MBEDTLS_ECP_C */ 3410 3411 mbedtls_ecp_group_id mbedtls_ecp_keypair_get_group_id( 3412 const mbedtls_ecp_keypair *key) 3413 { 3414 return key->grp.id; 3415 } 3416 3417 /* 3418 * Export generic key-pair parameters. 3419 */ 3420 int mbedtls_ecp_export(const mbedtls_ecp_keypair *key, mbedtls_ecp_group *grp, 3421 mbedtls_mpi *d, mbedtls_ecp_point *Q) 3422 { 3423 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3424 3425 if (grp != NULL && (ret = mbedtls_ecp_group_copy(grp, &key->grp)) != 0) { 3426 return ret; 3427 } 3428 3429 if (d != NULL && (ret = mbedtls_mpi_copy(d, &key->d)) != 0) { 3430 return ret; 3431 } 3432 3433 if (Q != NULL && (ret = mbedtls_ecp_copy(Q, &key->Q)) != 0) { 3434 return ret; 3435 } 3436 3437 return 0; 3438 } 3439 3440 #if defined(MBEDTLS_SELF_TEST) 3441 3442 #if defined(MBEDTLS_ECP_C) 3443 /* 3444 * PRNG for test - !!!INSECURE NEVER USE IN PRODUCTION!!! 3445 * 3446 * This is the linear congruential generator from numerical recipes, 3447 * except we only use the low byte as the output. See 3448 * https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use 3449 */ 3450 static int self_test_rng(void *ctx, unsigned char *out, size_t len) 3451 { 3452 static uint32_t state = 42; 3453 3454 (void) ctx; 3455 3456 for (size_t i = 0; i < len; i++) { 3457 state = state * 1664525u + 1013904223u; 3458 out[i] = (unsigned char) state; 3459 } 3460 3461 return 0; 3462 } 3463 3464 /* Adjust the exponent to be a valid private point for the specified curve. 3465 * This is sometimes necessary because we use a single set of exponents 3466 * for all curves but the validity of values depends on the curve. */ 3467 static int self_test_adjust_exponent(const mbedtls_ecp_group *grp, 3468 mbedtls_mpi *m) 3469 { 3470 int ret = 0; 3471 switch (grp->id) { 3472 /* If Curve25519 is available, then that's what we use for the 3473 * Montgomery test, so we don't need the adjustment code. */ 3474 #if !defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 3475 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 3476 case MBEDTLS_ECP_DP_CURVE448: 3477 /* Move highest bit from 254 to N-1. Setting bit N-1 is 3478 * necessary to enforce the highest-bit-set constraint. */ 3479 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, 254, 0)); 3480 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, grp->nbits, 1)); 3481 /* Copy second-highest bit from 253 to N-2. This is not 3482 * necessary but improves the test variety a bit. */ 3483 MBEDTLS_MPI_CHK( 3484 mbedtls_mpi_set_bit(m, grp->nbits - 1, 3485 mbedtls_mpi_get_bit(m, 253))); 3486 break; 3487 #endif 3488 #endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */ 3489 default: 3490 /* Non-Montgomery curves and Curve25519 need no adjustment. */ 3491 (void) grp; 3492 (void) m; 3493 goto cleanup; 3494 } 3495 cleanup: 3496 return ret; 3497 } 3498 3499 /* Calculate R = m.P for each m in exponents. Check that the number of 3500 * basic operations doesn't depend on the value of m. */ 3501 static int self_test_point(int verbose, 3502 mbedtls_ecp_group *grp, 3503 mbedtls_ecp_point *R, 3504 mbedtls_mpi *m, 3505 const mbedtls_ecp_point *P, 3506 const char *const *exponents, 3507 size_t n_exponents) 3508 { 3509 int ret = 0; 3510 size_t i = 0; 3511 unsigned long add_c_prev, dbl_c_prev, mul_c_prev; 3512 add_count = 0; 3513 dbl_count = 0; 3514 mul_count = 0; 3515 3516 MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(m, 16, exponents[0])); 3517 MBEDTLS_MPI_CHK(self_test_adjust_exponent(grp, m)); 3518 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, R, m, P, self_test_rng, NULL)); 3519 3520 for (i = 1; i < n_exponents; i++) { 3521 add_c_prev = add_count; 3522 dbl_c_prev = dbl_count; 3523 mul_c_prev = mul_count; 3524 add_count = 0; 3525 dbl_count = 0; 3526 mul_count = 0; 3527 3528 MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(m, 16, exponents[i])); 3529 MBEDTLS_MPI_CHK(self_test_adjust_exponent(grp, m)); 3530 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, R, m, P, self_test_rng, NULL)); 3531 3532 if (add_count != add_c_prev || 3533 dbl_count != dbl_c_prev || 3534 mul_count != mul_c_prev) { 3535 ret = 1; 3536 break; 3537 } 3538 } 3539 3540 cleanup: 3541 if (verbose != 0) { 3542 if (ret != 0) { 3543 mbedtls_printf("failed (%u)\n", (unsigned int) i); 3544 } else { 3545 mbedtls_printf("passed\n"); 3546 } 3547 } 3548 return ret; 3549 } 3550 #endif /* MBEDTLS_ECP_C */ 3551 3552 /* 3553 * Checkup routine 3554 */ 3555 int mbedtls_ecp_self_test(int verbose) 3556 { 3557 #if defined(MBEDTLS_ECP_C) 3558 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3559 mbedtls_ecp_group grp; 3560 mbedtls_ecp_point R, P; 3561 mbedtls_mpi m; 3562 3563 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3564 /* Exponents especially adapted for secp192k1, which has the lowest 3565 * order n of all supported curves (secp192r1 is in a slightly larger 3566 * field but the order of its base point is slightly smaller). */ 3567 const char *sw_exponents[] = 3568 { 3569 "000000000000000000000000000000000000000000000001", /* one */ 3570 "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */ 3571 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */ 3572 "400000000000000000000000000000000000000000000000", /* one and zeros */ 3573 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */ 3574 "555555555555555555555555555555555555555555555555", /* 101010... */ 3575 }; 3576 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3577 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3578 const char *m_exponents[] = 3579 { 3580 /* Valid private values for Curve25519. In a build with Curve448 3581 * but not Curve25519, they will be adjusted in 3582 * self_test_adjust_exponent(). */ 3583 "4000000000000000000000000000000000000000000000000000000000000000", 3584 "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30", 3585 "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8", 3586 "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460", 3587 "5555555555555555555555555555555555555555555555555555555555555550", 3588 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8", 3589 }; 3590 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3591 3592 mbedtls_ecp_group_init(&grp); 3593 mbedtls_ecp_point_init(&R); 3594 mbedtls_ecp_point_init(&P); 3595 mbedtls_mpi_init(&m); 3596 3597 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3598 /* Use secp192r1 if available, or any available curve */ 3599 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 3600 MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_SECP192R1)); 3601 #else 3602 MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, mbedtls_ecp_curve_list()->grp_id)); 3603 #endif 3604 3605 if (verbose != 0) { 3606 mbedtls_printf(" ECP SW test #1 (constant op_count, base point G): "); 3607 } 3608 /* Do a dummy multiplication first to trigger precomputation */ 3609 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&m, 2)); 3610 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &P, &m, &grp.G, self_test_rng, NULL)); 3611 ret = self_test_point(verbose, 3612 &grp, &R, &m, &grp.G, 3613 sw_exponents, 3614 sizeof(sw_exponents) / sizeof(sw_exponents[0])); 3615 if (ret != 0) { 3616 goto cleanup; 3617 } 3618 3619 if (verbose != 0) { 3620 mbedtls_printf(" ECP SW test #2 (constant op_count, other point): "); 3621 } 3622 /* We computed P = 2G last time, use it */ 3623 ret = self_test_point(verbose, 3624 &grp, &R, &m, &P, 3625 sw_exponents, 3626 sizeof(sw_exponents) / sizeof(sw_exponents[0])); 3627 if (ret != 0) { 3628 goto cleanup; 3629 } 3630 3631 mbedtls_ecp_group_free(&grp); 3632 mbedtls_ecp_point_free(&R); 3633 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3634 3635 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3636 if (verbose != 0) { 3637 mbedtls_printf(" ECP Montgomery test (constant op_count): "); 3638 } 3639 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 3640 MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE25519)); 3641 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 3642 MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE448)); 3643 #else 3644 #error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test" 3645 #endif 3646 ret = self_test_point(verbose, 3647 &grp, &R, &m, &grp.G, 3648 m_exponents, 3649 sizeof(m_exponents) / sizeof(m_exponents[0])); 3650 if (ret != 0) { 3651 goto cleanup; 3652 } 3653 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3654 3655 cleanup: 3656 3657 if (ret < 0 && verbose != 0) { 3658 mbedtls_printf("Unexpected error, return code = %08X\n", (unsigned int) ret); 3659 } 3660 3661 mbedtls_ecp_group_free(&grp); 3662 mbedtls_ecp_point_free(&R); 3663 mbedtls_ecp_point_free(&P); 3664 mbedtls_mpi_free(&m); 3665 3666 if (verbose != 0) { 3667 mbedtls_printf("\n"); 3668 } 3669 3670 return ret; 3671 #else /* MBEDTLS_ECP_C */ 3672 (void) verbose; 3673 return 0; 3674 #endif /* MBEDTLS_ECP_C */ 3675 } 3676 3677 #endif /* MBEDTLS_SELF_TEST */ 3678 3679 #endif /* !MBEDTLS_ECP_ALT */ 3680 3681 #endif /* MBEDTLS_ECP_LIGHT */ 3682