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 "ecp_invasive.h" 72 73 #include <string.h> 74 75 #if !defined(MBEDTLS_ECP_ALT) 76 77 #include "mbedtls/platform.h" 78 79 #include "ecp_internal_alt.h" 80 81 #if defined(MBEDTLS_SELF_TEST) 82 /* 83 * Counts of point addition and doubling, and field multiplications. 84 * Used to test resistance of point multiplication to simple timing attacks. 85 */ 86 #if defined(MBEDTLS_ECP_C) 87 static unsigned long add_count, dbl_count; 88 #endif /* MBEDTLS_ECP_C */ 89 static unsigned long mul_count; 90 #endif 91 92 #if defined(MBEDTLS_ECP_RESTARTABLE) 93 /* 94 * Maximum number of "basic operations" to be done in a row. 95 * 96 * Default value 0 means that ECC operations will not yield. 97 * Note that regardless of the value of ecp_max_ops, always at 98 * least one step is performed before yielding. 99 * 100 * Setting ecp_max_ops=1 can be suitable for testing purposes 101 * as it will interrupt computation at all possible points. 102 */ 103 static unsigned ecp_max_ops = 0; 104 105 /* 106 * Set ecp_max_ops 107 */ 108 void mbedtls_ecp_set_max_ops(unsigned max_ops) 109 { 110 ecp_max_ops = max_ops; 111 } 112 113 /* 114 * Check if restart is enabled 115 */ 116 int mbedtls_ecp_restart_is_enabled(void) 117 { 118 return ecp_max_ops != 0; 119 } 120 121 /* 122 * Restart sub-context for ecp_mul_comb() 123 */ 124 struct mbedtls_ecp_restart_mul { 125 mbedtls_ecp_point R; /* current intermediate result */ 126 size_t i; /* current index in various loops, 0 outside */ 127 mbedtls_ecp_point *T; /* table for precomputed points */ 128 unsigned char T_size; /* number of points in table T */ 129 enum { /* what were we doing last time we returned? */ 130 ecp_rsm_init = 0, /* nothing so far, dummy initial state */ 131 ecp_rsm_pre_dbl, /* precompute 2^n multiples */ 132 ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */ 133 ecp_rsm_pre_add, /* precompute remaining points by adding */ 134 ecp_rsm_pre_norm_add, /* normalize all precomputed points */ 135 ecp_rsm_comb_core, /* ecp_mul_comb_core() */ 136 ecp_rsm_final_norm, /* do the final normalization */ 137 } state; 138 }; 139 140 /* 141 * Init restart_mul sub-context 142 */ 143 static void ecp_restart_rsm_init(mbedtls_ecp_restart_mul_ctx *ctx) 144 { 145 mbedtls_ecp_point_init(&ctx->R); 146 ctx->i = 0; 147 ctx->T = NULL; 148 ctx->T_size = 0; 149 ctx->state = ecp_rsm_init; 150 } 151 152 /* 153 * Free the components of a restart_mul sub-context 154 */ 155 static void ecp_restart_rsm_free(mbedtls_ecp_restart_mul_ctx *ctx) 156 { 157 unsigned char i; 158 159 if (ctx == NULL) { 160 return; 161 } 162 163 mbedtls_ecp_point_free(&ctx->R); 164 165 if (ctx->T != NULL) { 166 for (i = 0; i < ctx->T_size; i++) { 167 mbedtls_ecp_point_free(ctx->T + i); 168 } 169 mbedtls_free(ctx->T); 170 } 171 172 ecp_restart_rsm_init(ctx); 173 } 174 175 /* 176 * Restart context for ecp_muladd() 177 */ 178 struct mbedtls_ecp_restart_muladd { 179 mbedtls_ecp_point mP; /* mP value */ 180 mbedtls_ecp_point R; /* R intermediate result */ 181 enum { /* what should we do next? */ 182 ecp_rsma_mul1 = 0, /* first multiplication */ 183 ecp_rsma_mul2, /* second multiplication */ 184 ecp_rsma_add, /* addition */ 185 ecp_rsma_norm, /* normalization */ 186 } state; 187 }; 188 189 /* 190 * Init restart_muladd sub-context 191 */ 192 static void ecp_restart_ma_init(mbedtls_ecp_restart_muladd_ctx *ctx) 193 { 194 mbedtls_ecp_point_init(&ctx->mP); 195 mbedtls_ecp_point_init(&ctx->R); 196 ctx->state = ecp_rsma_mul1; 197 } 198 199 /* 200 * Free the components of a restart_muladd sub-context 201 */ 202 static void ecp_restart_ma_free(mbedtls_ecp_restart_muladd_ctx *ctx) 203 { 204 if (ctx == NULL) { 205 return; 206 } 207 208 mbedtls_ecp_point_free(&ctx->mP); 209 mbedtls_ecp_point_free(&ctx->R); 210 211 ecp_restart_ma_init(ctx); 212 } 213 214 /* 215 * Initialize a restart context 216 */ 217 void mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx *ctx) 218 { 219 ctx->ops_done = 0; 220 ctx->depth = 0; 221 ctx->rsm = NULL; 222 ctx->ma = NULL; 223 } 224 225 /* 226 * Free the components of a restart context 227 */ 228 void mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx *ctx) 229 { 230 if (ctx == NULL) { 231 return; 232 } 233 234 ecp_restart_rsm_free(ctx->rsm); 235 mbedtls_free(ctx->rsm); 236 237 ecp_restart_ma_free(ctx->ma); 238 mbedtls_free(ctx->ma); 239 240 mbedtls_ecp_restart_init(ctx); 241 } 242 243 /* 244 * Check if we can do the next step 245 */ 246 int mbedtls_ecp_check_budget(const mbedtls_ecp_group *grp, 247 mbedtls_ecp_restart_ctx *rs_ctx, 248 unsigned ops) 249 { 250 if (rs_ctx != NULL && ecp_max_ops != 0) { 251 /* scale depending on curve size: the chosen reference is 256-bit, 252 * and multiplication is quadratic. Round to the closest integer. */ 253 if (grp->pbits >= 512) { 254 ops *= 4; 255 } else if (grp->pbits >= 384) { 256 ops *= 2; 257 } 258 259 /* Avoid infinite loops: always allow first step. 260 * Because of that, however, it's not generally true 261 * that ops_done <= ecp_max_ops, so the check 262 * ops_done > ecp_max_ops below is mandatory. */ 263 if ((rs_ctx->ops_done != 0) && 264 (rs_ctx->ops_done > ecp_max_ops || 265 ops > ecp_max_ops - rs_ctx->ops_done)) { 266 return MBEDTLS_ERR_ECP_IN_PROGRESS; 267 } 268 269 /* update running count */ 270 rs_ctx->ops_done += ops; 271 } 272 273 return 0; 274 } 275 276 /* Call this when entering a function that needs its own sub-context */ 277 #define ECP_RS_ENTER(SUB) do { \ 278 /* reset ops count for this call if top-level */ \ 279 if (rs_ctx != NULL && rs_ctx->depth++ == 0) \ 280 rs_ctx->ops_done = 0; \ 281 \ 282 /* set up our own sub-context if needed */ \ 283 if (mbedtls_ecp_restart_is_enabled() && \ 284 rs_ctx != NULL && rs_ctx->SUB == NULL) \ 285 { \ 286 rs_ctx->SUB = mbedtls_calloc(1, sizeof(*rs_ctx->SUB)); \ 287 if (rs_ctx->SUB == NULL) \ 288 return MBEDTLS_ERR_ECP_ALLOC_FAILED; \ 289 \ 290 ecp_restart_## SUB ##_init(rs_ctx->SUB); \ 291 } \ 292 } while (0) 293 294 /* Call this when leaving a function that needs its own sub-context */ 295 #define ECP_RS_LEAVE(SUB) do { \ 296 /* clear our sub-context when not in progress (done or error) */ \ 297 if (rs_ctx != NULL && rs_ctx->SUB != NULL && \ 298 ret != MBEDTLS_ERR_ECP_IN_PROGRESS) \ 299 { \ 300 ecp_restart_## SUB ##_free(rs_ctx->SUB); \ 301 mbedtls_free(rs_ctx->SUB); \ 302 rs_ctx->SUB = NULL; \ 303 } \ 304 \ 305 if (rs_ctx != NULL) \ 306 rs_ctx->depth--; \ 307 } while (0) 308 309 #else /* MBEDTLS_ECP_RESTARTABLE */ 310 311 #define ECP_RS_ENTER(sub) (void) rs_ctx; 312 #define ECP_RS_LEAVE(sub) (void) rs_ctx; 313 314 #endif /* MBEDTLS_ECP_RESTARTABLE */ 315 316 #if defined(MBEDTLS_ECP_C) 317 static void mpi_init_many(mbedtls_mpi *arr, size_t size) 318 { 319 while (size--) { 320 mbedtls_mpi_init(arr++); 321 } 322 } 323 324 static void mpi_free_many(mbedtls_mpi *arr, size_t size) 325 { 326 while (size--) { 327 mbedtls_mpi_free(arr++); 328 } 329 } 330 #endif /* MBEDTLS_ECP_C */ 331 332 /* 333 * List of supported curves: 334 * - internal ID 335 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7) 336 * - size in bits 337 * - readable name 338 * 339 * Curves are listed in order: largest curves first, and for a given size, 340 * fastest curves first. 341 * 342 * Reminder: update profiles in x509_crt.c and ssl_tls.c when adding a new curve! 343 */ 344 static const mbedtls_ecp_curve_info ecp_supported_curves[] = 345 { 346 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 347 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" }, 348 #endif 349 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 350 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" }, 351 #endif 352 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 353 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" }, 354 #endif 355 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 356 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" }, 357 #endif 358 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 359 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" }, 360 #endif 361 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 362 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" }, 363 #endif 364 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 365 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" }, 366 #endif 367 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 368 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" }, 369 #endif 370 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 371 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" }, 372 #endif 373 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 374 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" }, 375 #endif 376 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 377 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" }, 378 #endif 379 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 380 { MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" }, 381 #endif 382 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 383 { MBEDTLS_ECP_DP_CURVE448, 30, 448, "x448" }, 384 #endif 385 #if defined(MBEDTLS_ECP_DP_SM2_ENABLED) 386 /* https://tools.ietf.org/id/draft-yang-tls-tls13-sm-suites-05.html */ 387 { MBEDTLS_ECP_DP_SM2, 41, 256, "sm2" }, 388 #endif 389 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL }, 390 }; 391 392 #define ECP_NB_CURVES sizeof(ecp_supported_curves) / \ 393 sizeof(ecp_supported_curves[0]) 394 395 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES]; 396 397 /* 398 * List of supported curves and associated info 399 */ 400 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list(void) 401 { 402 return ecp_supported_curves; 403 } 404 405 /* 406 * List of supported curves, group ID only 407 */ 408 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list(void) 409 { 410 static int init_done = 0; 411 412 if (!init_done) { 413 size_t i = 0; 414 const mbedtls_ecp_curve_info *curve_info; 415 416 for (curve_info = mbedtls_ecp_curve_list(); 417 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 418 curve_info++) { 419 ecp_supported_grp_id[i++] = curve_info->grp_id; 420 } 421 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE; 422 423 init_done = 1; 424 } 425 426 return ecp_supported_grp_id; 427 } 428 429 /* 430 * Get the curve info for the internal identifier 431 */ 432 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id) 433 { 434 const mbedtls_ecp_curve_info *curve_info; 435 436 for (curve_info = mbedtls_ecp_curve_list(); 437 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 438 curve_info++) { 439 if (curve_info->grp_id == grp_id) { 440 return curve_info; 441 } 442 } 443 444 return NULL; 445 } 446 447 /* 448 * Get the curve info from the TLS identifier 449 */ 450 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id) 451 { 452 const mbedtls_ecp_curve_info *curve_info; 453 454 for (curve_info = mbedtls_ecp_curve_list(); 455 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 456 curve_info++) { 457 if (curve_info->tls_id == tls_id) { 458 return curve_info; 459 } 460 } 461 462 return NULL; 463 } 464 465 /* 466 * Get the curve info from the name 467 */ 468 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name(const char *name) 469 { 470 const mbedtls_ecp_curve_info *curve_info; 471 472 if (name == NULL) { 473 return NULL; 474 } 475 476 for (curve_info = mbedtls_ecp_curve_list(); 477 curve_info->grp_id != MBEDTLS_ECP_DP_NONE; 478 curve_info++) { 479 if (strcmp(curve_info->name, name) == 0) { 480 return curve_info; 481 } 482 } 483 484 return NULL; 485 } 486 487 /* 488 * Get the type of a curve 489 */ 490 mbedtls_ecp_curve_type mbedtls_ecp_get_type(const mbedtls_ecp_group *grp) 491 { 492 if (grp->G.X.p == NULL) { 493 return MBEDTLS_ECP_TYPE_NONE; 494 } 495 496 if (grp->G.Y.p == NULL) { 497 return MBEDTLS_ECP_TYPE_MONTGOMERY; 498 } else { 499 return MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS; 500 } 501 } 502 503 /* 504 * Initialize (the components of) a point 505 */ 506 void mbedtls_ecp_point_init(mbedtls_ecp_point *pt) 507 { 508 mbedtls_mpi_init(&pt->X); 509 mbedtls_mpi_init(&pt->Y); 510 mbedtls_mpi_init(&pt->Z); 511 } 512 513 /* 514 * Initialize (the components of) a group 515 */ 516 void mbedtls_ecp_group_init(mbedtls_ecp_group *grp) 517 { 518 grp->id = MBEDTLS_ECP_DP_NONE; 519 mbedtls_mpi_init(&grp->P); 520 mbedtls_mpi_init(&grp->A); 521 mbedtls_mpi_init(&grp->B); 522 mbedtls_ecp_point_init(&grp->G); 523 mbedtls_mpi_init(&grp->N); 524 grp->pbits = 0; 525 grp->nbits = 0; 526 grp->h = 0; 527 grp->modp = NULL; 528 grp->t_pre = NULL; 529 grp->t_post = NULL; 530 grp->t_data = NULL; 531 grp->T = NULL; 532 grp->T_size = 0; 533 } 534 535 /* 536 * Initialize (the components of) a key pair 537 */ 538 void mbedtls_ecp_keypair_init(mbedtls_ecp_keypair *key) 539 { 540 mbedtls_ecp_group_init(&key->grp); 541 mbedtls_mpi_init(&key->d); 542 mbedtls_ecp_point_init(&key->Q); 543 } 544 545 /* 546 * Unallocate (the components of) a point 547 */ 548 void mbedtls_ecp_point_free(mbedtls_ecp_point *pt) 549 { 550 if (pt == NULL) { 551 return; 552 } 553 554 mbedtls_mpi_free(&(pt->X)); 555 mbedtls_mpi_free(&(pt->Y)); 556 mbedtls_mpi_free(&(pt->Z)); 557 } 558 559 /* 560 * Check that the comb table (grp->T) is static initialized. 561 */ 562 static int ecp_group_is_static_comb_table(const mbedtls_ecp_group *grp) 563 { 564 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 565 return grp->T != NULL && grp->T_size == 0; 566 #else 567 (void) grp; 568 return 0; 569 #endif 570 } 571 572 /* 573 * Unallocate (the components of) a group 574 */ 575 void mbedtls_ecp_group_free(mbedtls_ecp_group *grp) 576 { 577 size_t i; 578 579 if (grp == NULL) { 580 return; 581 } 582 583 if (grp->h != 1) { 584 mbedtls_mpi_free(&grp->A); 585 mbedtls_mpi_free(&grp->B); 586 mbedtls_ecp_point_free(&grp->G); 587 588 #if !defined(MBEDTLS_ECP_WITH_MPI_UINT) 589 mbedtls_mpi_free(&grp->N); 590 mbedtls_mpi_free(&grp->P); 591 #endif 592 } 593 594 if (!ecp_group_is_static_comb_table(grp) && grp->T != NULL) { 595 for (i = 0; i < grp->T_size; i++) { 596 mbedtls_ecp_point_free(&grp->T[i]); 597 } 598 mbedtls_free(grp->T); 599 } 600 601 mbedtls_platform_zeroize(grp, sizeof(mbedtls_ecp_group)); 602 } 603 604 /* 605 * Unallocate (the components of) a key pair 606 */ 607 void mbedtls_ecp_keypair_free(mbedtls_ecp_keypair *key) 608 { 609 if (key == NULL) { 610 return; 611 } 612 613 mbedtls_ecp_group_free(&key->grp); 614 mbedtls_mpi_free(&key->d); 615 mbedtls_ecp_point_free(&key->Q); 616 } 617 618 /* 619 * Copy the contents of a point 620 */ 621 int mbedtls_ecp_copy(mbedtls_ecp_point *P, const mbedtls_ecp_point *Q) 622 { 623 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 624 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->X, &Q->X)); 625 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Y, &Q->Y)); 626 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Z, &Q->Z)); 627 628 cleanup: 629 return ret; 630 } 631 632 /* 633 * Copy the contents of a group object 634 */ 635 int mbedtls_ecp_group_copy(mbedtls_ecp_group *dst, const mbedtls_ecp_group *src) 636 { 637 return mbedtls_ecp_group_load(dst, src->id); 638 } 639 640 /* 641 * Set point to zero 642 */ 643 int mbedtls_ecp_set_zero(mbedtls_ecp_point *pt) 644 { 645 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 646 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->X, 1)); 647 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Y, 1)); 648 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 0)); 649 650 cleanup: 651 return ret; 652 } 653 654 /* 655 * Tell if a point is zero 656 */ 657 int mbedtls_ecp_is_zero(mbedtls_ecp_point *pt) 658 { 659 return mbedtls_mpi_cmp_int(&pt->Z, 0) == 0; 660 } 661 662 /* 663 * Compare two points lazily 664 */ 665 int mbedtls_ecp_point_cmp(const mbedtls_ecp_point *P, 666 const mbedtls_ecp_point *Q) 667 { 668 if (mbedtls_mpi_cmp_mpi(&P->X, &Q->X) == 0 && 669 mbedtls_mpi_cmp_mpi(&P->Y, &Q->Y) == 0 && 670 mbedtls_mpi_cmp_mpi(&P->Z, &Q->Z) == 0) { 671 return 0; 672 } 673 674 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 675 } 676 677 /* 678 * Import a non-zero point from ASCII strings 679 */ 680 int mbedtls_ecp_point_read_string(mbedtls_ecp_point *P, int radix, 681 const char *x, const char *y) 682 { 683 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 684 MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->X, radix, x)); 685 MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->Y, radix, y)); 686 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&P->Z, 1)); 687 688 cleanup: 689 return ret; 690 } 691 692 /* 693 * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748) 694 */ 695 int mbedtls_ecp_point_write_binary(const mbedtls_ecp_group *grp, 696 const mbedtls_ecp_point *P, 697 int format, size_t *olen, 698 unsigned char *buf, size_t buflen) 699 { 700 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 701 size_t plen; 702 if (format != MBEDTLS_ECP_PF_UNCOMPRESSED && 703 format != MBEDTLS_ECP_PF_COMPRESSED) { 704 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 705 } 706 707 plen = mbedtls_mpi_size(&grp->P); 708 709 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 710 (void) format; /* Montgomery curves always use the same point format */ 711 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 712 *olen = plen; 713 if (buflen < *olen) { 714 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 715 } 716 717 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&P->X, buf, plen)); 718 } 719 #endif 720 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 721 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 722 /* 723 * Common case: P == 0 724 */ 725 if (mbedtls_mpi_cmp_int(&P->Z, 0) == 0) { 726 if (buflen < 1) { 727 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 728 } 729 730 buf[0] = 0x00; 731 *olen = 1; 732 733 return 0; 734 } 735 736 if (format == MBEDTLS_ECP_PF_UNCOMPRESSED) { 737 *olen = 2 * plen + 1; 738 739 if (buflen < *olen) { 740 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 741 } 742 743 buf[0] = 0x04; 744 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen)); 745 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->Y, buf + 1 + plen, plen)); 746 } else if (format == MBEDTLS_ECP_PF_COMPRESSED) { 747 *olen = plen + 1; 748 749 if (buflen < *olen) { 750 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 751 } 752 753 buf[0] = 0x02 + mbedtls_mpi_get_bit(&P->Y, 0); 754 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen)); 755 } 756 } 757 #endif 758 759 cleanup: 760 return ret; 761 } 762 763 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 764 static int mbedtls_ecp_sw_derive_y(const mbedtls_ecp_group *grp, 765 const mbedtls_mpi *X, 766 mbedtls_mpi *Y, 767 int parity_bit); 768 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 769 770 /* 771 * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748) 772 */ 773 int mbedtls_ecp_point_read_binary(const mbedtls_ecp_group *grp, 774 mbedtls_ecp_point *pt, 775 const unsigned char *buf, size_t ilen) 776 { 777 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 778 size_t plen; 779 if (ilen < 1) { 780 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 781 } 782 783 plen = mbedtls_mpi_size(&grp->P); 784 785 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 786 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 787 if (plen != ilen) { 788 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 789 } 790 791 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&pt->X, buf, plen)); 792 mbedtls_mpi_free(&pt->Y); 793 794 if (grp->id == MBEDTLS_ECP_DP_CURVE25519) { 795 /* Set most significant bit to 0 as prescribed in RFC7748 §5 */ 796 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&pt->X, plen * 8 - 1, 0)); 797 } 798 799 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1)); 800 } 801 #endif 802 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 803 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 804 if (buf[0] == 0x00) { 805 if (ilen == 1) { 806 return mbedtls_ecp_set_zero(pt); 807 } else { 808 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 809 } 810 } 811 812 if (ilen < 1 + plen) { 813 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 814 } 815 816 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->X, buf + 1, plen)); 817 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1)); 818 819 if (buf[0] == 0x04) { 820 /* format == MBEDTLS_ECP_PF_UNCOMPRESSED */ 821 if (ilen != 1 + plen * 2) { 822 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 823 } 824 return mbedtls_mpi_read_binary(&pt->Y, buf + 1 + plen, plen); 825 } else if (buf[0] == 0x02 || buf[0] == 0x03) { 826 /* format == MBEDTLS_ECP_PF_COMPRESSED */ 827 if (ilen != 1 + plen) { 828 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 829 } 830 return mbedtls_ecp_sw_derive_y(grp, &pt->X, &pt->Y, 831 (buf[0] & 1)); 832 } else { 833 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 834 } 835 } 836 #endif 837 838 cleanup: 839 return ret; 840 } 841 842 /* 843 * Import a point from a TLS ECPoint record (RFC 4492) 844 * struct { 845 * opaque point <1..2^8-1>; 846 * } ECPoint; 847 */ 848 int mbedtls_ecp_tls_read_point(const mbedtls_ecp_group *grp, 849 mbedtls_ecp_point *pt, 850 const unsigned char **buf, size_t buf_len) 851 { 852 unsigned char data_len; 853 const unsigned char *buf_start; 854 /* 855 * We must have at least two bytes (1 for length, at least one for data) 856 */ 857 if (buf_len < 2) { 858 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 859 } 860 861 data_len = *(*buf)++; 862 if (data_len < 1 || data_len > buf_len - 1) { 863 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 864 } 865 866 /* 867 * Save buffer start for read_binary and update buf 868 */ 869 buf_start = *buf; 870 *buf += data_len; 871 872 return mbedtls_ecp_point_read_binary(grp, pt, buf_start, data_len); 873 } 874 875 /* 876 * Export a point as a TLS ECPoint record (RFC 4492) 877 * struct { 878 * opaque point <1..2^8-1>; 879 * } ECPoint; 880 */ 881 int mbedtls_ecp_tls_write_point(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt, 882 int format, size_t *olen, 883 unsigned char *buf, size_t blen) 884 { 885 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 886 if (format != MBEDTLS_ECP_PF_UNCOMPRESSED && 887 format != MBEDTLS_ECP_PF_COMPRESSED) { 888 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 889 } 890 891 /* 892 * buffer length must be at least one, for our length byte 893 */ 894 if (blen < 1) { 895 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 896 } 897 898 if ((ret = mbedtls_ecp_point_write_binary(grp, pt, format, 899 olen, buf + 1, blen - 1)) != 0) { 900 return ret; 901 } 902 903 /* 904 * write length to the first byte and update total length 905 */ 906 buf[0] = (unsigned char) *olen; 907 ++*olen; 908 909 return 0; 910 } 911 912 /* 913 * Set a group from an ECParameters record (RFC 4492) 914 */ 915 int mbedtls_ecp_tls_read_group(mbedtls_ecp_group *grp, 916 const unsigned char **buf, size_t len) 917 { 918 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 919 mbedtls_ecp_group_id grp_id; 920 if ((ret = mbedtls_ecp_tls_read_group_id(&grp_id, buf, len)) != 0) { 921 return ret; 922 } 923 924 return mbedtls_ecp_group_load(grp, grp_id); 925 } 926 927 /* 928 * Read a group id from an ECParameters record (RFC 4492) and convert it to 929 * mbedtls_ecp_group_id. 930 */ 931 int mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id *grp, 932 const unsigned char **buf, size_t len) 933 { 934 uint16_t tls_id; 935 const mbedtls_ecp_curve_info *curve_info; 936 /* 937 * We expect at least three bytes (see below) 938 */ 939 if (len < 3) { 940 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 941 } 942 943 /* 944 * First byte is curve_type; only named_curve is handled 945 */ 946 if (*(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE) { 947 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 948 } 949 950 /* 951 * Next two bytes are the namedcurve value 952 */ 953 tls_id = MBEDTLS_GET_UINT16_BE(*buf, 0); 954 *buf += 2; 955 956 if ((curve_info = mbedtls_ecp_curve_info_from_tls_id(tls_id)) == NULL) { 957 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 958 } 959 960 *grp = curve_info->grp_id; 961 962 return 0; 963 } 964 965 /* 966 * Write the ECParameters record corresponding to a group (RFC 4492) 967 */ 968 int mbedtls_ecp_tls_write_group(const mbedtls_ecp_group *grp, size_t *olen, 969 unsigned char *buf, size_t blen) 970 { 971 const mbedtls_ecp_curve_info *curve_info; 972 if ((curve_info = mbedtls_ecp_curve_info_from_grp_id(grp->id)) == NULL) { 973 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 974 } 975 976 /* 977 * We are going to write 3 bytes (see below) 978 */ 979 *olen = 3; 980 if (blen < *olen) { 981 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 982 } 983 984 /* 985 * First byte is curve_type, always named_curve 986 */ 987 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE; 988 989 /* 990 * Next two bytes are the namedcurve value 991 */ 992 MBEDTLS_PUT_UINT16_BE(curve_info->tls_id, buf, 0); 993 994 return 0; 995 } 996 997 /* 998 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi. 999 * See the documentation of struct mbedtls_ecp_group. 1000 * 1001 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf. 1002 */ 1003 static int ecp_modp(mbedtls_mpi *N, const mbedtls_ecp_group *grp) 1004 { 1005 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1006 1007 if (grp->modp == NULL) { 1008 return mbedtls_mpi_mod_mpi(N, N, &grp->P); 1009 } 1010 1011 /* N->s < 0 is a much faster test, which fails only if N is 0 */ 1012 if ((N->s < 0 && mbedtls_mpi_cmp_int(N, 0) != 0) || 1013 mbedtls_mpi_bitlen(N) > 2 * grp->pbits) { 1014 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 1015 } 1016 1017 MBEDTLS_MPI_CHK(grp->modp(N)); 1018 1019 /* N->s < 0 is a much faster test, which fails only if N is 0 */ 1020 while (N->s < 0 && mbedtls_mpi_cmp_int(N, 0) != 0) { 1021 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(N, N, &grp->P)); 1022 } 1023 1024 while (mbedtls_mpi_cmp_mpi(N, &grp->P) >= 0) { 1025 /* we known P, N and the result are positive */ 1026 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(N, N, &grp->P)); 1027 } 1028 1029 cleanup: 1030 return ret; 1031 } 1032 1033 /* 1034 * Fast mod-p functions expect their argument to be in the 0..p^2 range. 1035 * 1036 * In order to guarantee that, we need to ensure that operands of 1037 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will 1038 * bring the result back to this range. 1039 * 1040 * The following macros are shortcuts for doing that. 1041 */ 1042 1043 /* 1044 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi 1045 */ 1046 #if defined(MBEDTLS_SELF_TEST) 1047 #define INC_MUL_COUNT mul_count++; 1048 #else 1049 #define INC_MUL_COUNT 1050 #endif 1051 1052 #define MOD_MUL(N) \ 1053 do \ 1054 { \ 1055 MBEDTLS_MPI_CHK(ecp_modp(&(N), grp)); \ 1056 INC_MUL_COUNT \ 1057 } while (0) 1058 1059 static inline int mbedtls_mpi_mul_mod(const mbedtls_ecp_group *grp, 1060 mbedtls_mpi *X, 1061 const mbedtls_mpi *A, 1062 const mbedtls_mpi *B) 1063 { 1064 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1065 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(X, A, B)); 1066 MOD_MUL(*X); 1067 cleanup: 1068 return ret; 1069 } 1070 1071 /* 1072 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi 1073 * N->s < 0 is a very fast test, which fails only if N is 0 1074 */ 1075 #define MOD_SUB(N) \ 1076 do { \ 1077 while ((N)->s < 0 && mbedtls_mpi_cmp_int((N), 0) != 0) \ 1078 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi((N), (N), &grp->P)); \ 1079 } while (0) 1080 1081 MBEDTLS_MAYBE_UNUSED 1082 static inline int mbedtls_mpi_sub_mod(const mbedtls_ecp_group *grp, 1083 mbedtls_mpi *X, 1084 const mbedtls_mpi *A, 1085 const mbedtls_mpi *B) 1086 { 1087 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1088 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(X, A, B)); 1089 MOD_SUB(X); 1090 cleanup: 1091 return ret; 1092 } 1093 1094 /* 1095 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int. 1096 * We known P, N and the result are positive, so sub_abs is correct, and 1097 * a bit faster. 1098 */ 1099 #define MOD_ADD(N) \ 1100 while (mbedtls_mpi_cmp_mpi((N), &grp->P) >= 0) \ 1101 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs((N), (N), &grp->P)) 1102 1103 static inline int mbedtls_mpi_add_mod(const mbedtls_ecp_group *grp, 1104 mbedtls_mpi *X, 1105 const mbedtls_mpi *A, 1106 const mbedtls_mpi *B) 1107 { 1108 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1109 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, A, B)); 1110 MOD_ADD(X); 1111 cleanup: 1112 return ret; 1113 } 1114 1115 MBEDTLS_MAYBE_UNUSED 1116 static inline int mbedtls_mpi_mul_int_mod(const mbedtls_ecp_group *grp, 1117 mbedtls_mpi *X, 1118 const mbedtls_mpi *A, 1119 mbedtls_mpi_uint c) 1120 { 1121 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1122 1123 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(X, A, c)); 1124 MOD_ADD(X); 1125 cleanup: 1126 return ret; 1127 } 1128 1129 MBEDTLS_MAYBE_UNUSED 1130 static inline int mbedtls_mpi_sub_int_mod(const mbedtls_ecp_group *grp, 1131 mbedtls_mpi *X, 1132 const mbedtls_mpi *A, 1133 mbedtls_mpi_uint c) 1134 { 1135 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1136 1137 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(X, A, c)); 1138 MOD_SUB(X); 1139 cleanup: 1140 return ret; 1141 } 1142 1143 #define MPI_ECP_SUB_INT(X, A, c) \ 1144 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int_mod(grp, X, A, c)) 1145 1146 MBEDTLS_MAYBE_UNUSED 1147 static inline int mbedtls_mpi_shift_l_mod(const mbedtls_ecp_group *grp, 1148 mbedtls_mpi *X, 1149 size_t count) 1150 { 1151 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1152 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(X, count)); 1153 MOD_ADD(X); 1154 cleanup: 1155 return ret; 1156 } 1157 1158 /* 1159 * Macro wrappers around ECP modular arithmetic 1160 * 1161 * Currently, these wrappers are defined via the bignum module. 1162 */ 1163 1164 #define MPI_ECP_ADD(X, A, B) \ 1165 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, X, A, B)) 1166 1167 #define MPI_ECP_SUB(X, A, B) \ 1168 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, X, A, B)) 1169 1170 #define MPI_ECP_MUL(X, A, B) \ 1171 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, X, A, B)) 1172 1173 #define MPI_ECP_SQR(X, A) \ 1174 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, X, A, A)) 1175 1176 #define MPI_ECP_MUL_INT(X, A, c) \ 1177 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int_mod(grp, X, A, c)) 1178 1179 #define MPI_ECP_INV(dst, src) \ 1180 MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod((dst), (src), &grp->P)) 1181 1182 #define MPI_ECP_MOV(X, A) \ 1183 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A)) 1184 1185 #define MPI_ECP_SHIFT_L(X, count) \ 1186 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, X, count)) 1187 1188 #define MPI_ECP_LSET(X, c) \ 1189 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, c)) 1190 1191 #define MPI_ECP_CMP_INT(X, c) \ 1192 mbedtls_mpi_cmp_int(X, c) 1193 1194 #define MPI_ECP_CMP(X, Y) \ 1195 mbedtls_mpi_cmp_mpi(X, Y) 1196 1197 /* Needs f_rng, p_rng to be defined. */ 1198 #define MPI_ECP_RAND(X) \ 1199 MBEDTLS_MPI_CHK(mbedtls_mpi_random((X), 2, &grp->P, f_rng, p_rng)) 1200 1201 /* Conditional negation 1202 * Needs grp and a temporary MPI tmp to be defined. */ 1203 #define MPI_ECP_COND_NEG(X, cond) \ 1204 do \ 1205 { \ 1206 unsigned char nonzero = mbedtls_mpi_cmp_int((X), 0) != 0; \ 1207 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&tmp, &grp->P, (X))); \ 1208 MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign((X), &tmp, \ 1209 nonzero & cond)); \ 1210 } while (0) 1211 1212 #define MPI_ECP_NEG(X) MPI_ECP_COND_NEG((X), 1) 1213 1214 #define MPI_ECP_VALID(X) \ 1215 ((X)->p != NULL) 1216 1217 #define MPI_ECP_COND_ASSIGN(X, Y, cond) \ 1218 MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign((X), (Y), (cond))) 1219 1220 #define MPI_ECP_COND_SWAP(X, Y, cond) \ 1221 MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap((X), (Y), (cond))) 1222 1223 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 1224 1225 /* 1226 * Computes the right-hand side of the Short Weierstrass equation 1227 * RHS = X^3 + A X + B 1228 */ 1229 static int ecp_sw_rhs(const mbedtls_ecp_group *grp, 1230 mbedtls_mpi *rhs, 1231 const mbedtls_mpi *X) 1232 { 1233 int ret; 1234 1235 /* Compute X^3 + A X + B as X (X^2 + A) + B */ 1236 MPI_ECP_SQR(rhs, X); 1237 1238 /* Special case for A = -3 */ 1239 if (mbedtls_ecp_group_a_is_minus_3(grp)) { 1240 MPI_ECP_SUB_INT(rhs, rhs, 3); 1241 } else { 1242 MPI_ECP_ADD(rhs, rhs, &grp->A); 1243 } 1244 1245 MPI_ECP_MUL(rhs, rhs, X); 1246 MPI_ECP_ADD(rhs, rhs, &grp->B); 1247 1248 cleanup: 1249 return ret; 1250 } 1251 1252 /* 1253 * Derive Y from X and a parity bit 1254 */ 1255 static int mbedtls_ecp_sw_derive_y(const mbedtls_ecp_group *grp, 1256 const mbedtls_mpi *X, 1257 mbedtls_mpi *Y, 1258 int parity_bit) 1259 { 1260 /* w = y^2 = x^3 + ax + b 1261 * y = sqrt(w) = w^((p+1)/4) mod p (for prime p where p = 3 mod 4) 1262 * 1263 * Note: this method for extracting square root does not validate that w 1264 * was indeed a square so this function will return garbage in Y if X 1265 * does not correspond to a point on the curve. 1266 */ 1267 1268 /* Check prerequisite p = 3 mod 4 */ 1269 if (mbedtls_mpi_get_bit(&grp->P, 0) != 1 || 1270 mbedtls_mpi_get_bit(&grp->P, 1) != 1) { 1271 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1272 } 1273 1274 int ret; 1275 mbedtls_mpi exp; 1276 mbedtls_mpi_init(&exp); 1277 1278 /* use Y to store intermediate result, actually w above */ 1279 MBEDTLS_MPI_CHK(ecp_sw_rhs(grp, Y, X)); 1280 1281 /* w = y^2 */ /* Y contains y^2 intermediate result */ 1282 /* exp = ((p+1)/4) */ 1283 MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&exp, &grp->P, 1)); 1284 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&exp, 2)); 1285 /* sqrt(w) = w^((p+1)/4) mod p (for prime p where p = 3 mod 4) */ 1286 MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(Y, Y /*y^2*/, &exp, &grp->P, NULL)); 1287 1288 /* check parity bit match or else invert Y */ 1289 /* This quick inversion implementation is valid because Y != 0 for all 1290 * Short Weierstrass curves supported by mbedtls, as each supported curve 1291 * has an order that is a large prime, so each supported curve does not 1292 * have any point of order 2, and a point with Y == 0 would be of order 2 */ 1293 if (mbedtls_mpi_get_bit(Y, 0) != parity_bit) { 1294 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(Y, &grp->P, Y)); 1295 } 1296 1297 cleanup: 1298 1299 mbedtls_mpi_free(&exp); 1300 return ret; 1301 } 1302 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 1303 1304 #if defined(MBEDTLS_ECP_C) 1305 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 1306 /* 1307 * For curves in short Weierstrass form, we do all the internal operations in 1308 * Jacobian coordinates. 1309 * 1310 * For multiplication, we'll use a comb method with countermeasures against 1311 * SPA, hence timing attacks. 1312 */ 1313 1314 /* 1315 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1) 1316 * Cost: 1N := 1I + 3M + 1S 1317 */ 1318 static int ecp_normalize_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt) 1319 { 1320 if (MPI_ECP_CMP_INT(&pt->Z, 0) == 0) { 1321 return 0; 1322 } 1323 1324 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) 1325 if (mbedtls_internal_ecp_grp_capable(grp)) { 1326 return mbedtls_internal_ecp_normalize_jac(grp, pt); 1327 } 1328 #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */ 1329 1330 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) 1331 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1332 #else 1333 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1334 mbedtls_mpi T; 1335 mbedtls_mpi_init(&T); 1336 1337 MPI_ECP_INV(&T, &pt->Z); /* T <- 1 / Z */ 1338 MPI_ECP_MUL(&pt->Y, &pt->Y, &T); /* Y' <- Y*T = Y / Z */ 1339 MPI_ECP_SQR(&T, &T); /* T <- T^2 = 1 / Z^2 */ 1340 MPI_ECP_MUL(&pt->X, &pt->X, &T); /* X <- X * T = X / Z^2 */ 1341 MPI_ECP_MUL(&pt->Y, &pt->Y, &T); /* Y'' <- Y' * T = Y / Z^3 */ 1342 1343 MPI_ECP_LSET(&pt->Z, 1); 1344 1345 cleanup: 1346 1347 mbedtls_mpi_free(&T); 1348 1349 return ret; 1350 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */ 1351 } 1352 1353 /* 1354 * Normalize jacobian coordinates of an array of (pointers to) points, 1355 * using Montgomery's trick to perform only one inversion mod P. 1356 * (See for example Cohen's "A Course in Computational Algebraic Number 1357 * Theory", Algorithm 10.3.4.) 1358 * 1359 * Warning: fails (returning an error) if one of the points is zero! 1360 * This should never happen, see choice of w in ecp_mul_comb(). 1361 * 1362 * Cost: 1N(t) := 1I + (6t - 3)M + 1S 1363 */ 1364 static int ecp_normalize_jac_many(const mbedtls_ecp_group *grp, 1365 mbedtls_ecp_point *T[], size_t T_size) 1366 { 1367 if (T_size < 2) { 1368 return ecp_normalize_jac(grp, *T); 1369 } 1370 1371 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) 1372 if (mbedtls_internal_ecp_grp_capable(grp)) { 1373 return mbedtls_internal_ecp_normalize_jac_many(grp, T, T_size); 1374 } 1375 #endif 1376 1377 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) 1378 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1379 #else 1380 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1381 size_t i; 1382 mbedtls_mpi *c, t; 1383 1384 if ((c = mbedtls_calloc(T_size, sizeof(mbedtls_mpi))) == NULL) { 1385 return MBEDTLS_ERR_ECP_ALLOC_FAILED; 1386 } 1387 1388 mbedtls_mpi_init(&t); 1389 1390 mpi_init_many(c, T_size); 1391 /* 1392 * c[i] = Z_0 * ... * Z_i, i = 0,..,n := T_size-1 1393 */ 1394 MPI_ECP_MOV(&c[0], &T[0]->Z); 1395 for (i = 1; i < T_size; i++) { 1396 MPI_ECP_MUL(&c[i], &c[i-1], &T[i]->Z); 1397 } 1398 1399 /* 1400 * c[n] = 1 / (Z_0 * ... * Z_n) mod P 1401 */ 1402 MPI_ECP_INV(&c[T_size-1], &c[T_size-1]); 1403 1404 for (i = T_size - 1;; i--) { 1405 /* At the start of iteration i (note that i decrements), we have 1406 * - c[j] = Z_0 * .... * Z_j for j < i, 1407 * - c[j] = 1 / (Z_0 * .... * Z_j) for j == i, 1408 * 1409 * This is maintained via 1410 * - c[i-1] <- c[i] * Z_i 1411 * 1412 * We also derive 1/Z_i = c[i] * c[i-1] for i>0 and use that 1413 * to do the actual normalization. For i==0, we already have 1414 * c[0] = 1 / Z_0. 1415 */ 1416 1417 if (i > 0) { 1418 /* Compute 1/Z_i and establish invariant for the next iteration. */ 1419 MPI_ECP_MUL(&t, &c[i], &c[i-1]); 1420 MPI_ECP_MUL(&c[i-1], &c[i], &T[i]->Z); 1421 } else { 1422 MPI_ECP_MOV(&t, &c[0]); 1423 } 1424 1425 /* Now t holds 1 / Z_i; normalize as in ecp_normalize_jac() */ 1426 MPI_ECP_MUL(&T[i]->Y, &T[i]->Y, &t); 1427 MPI_ECP_SQR(&t, &t); 1428 MPI_ECP_MUL(&T[i]->X, &T[i]->X, &t); 1429 MPI_ECP_MUL(&T[i]->Y, &T[i]->Y, &t); 1430 1431 /* 1432 * Post-precessing: reclaim some memory by shrinking coordinates 1433 * - not storing Z (always 1) 1434 * - shrinking other coordinates, but still keeping the same number of 1435 * limbs as P, as otherwise it will too likely be regrown too fast. 1436 */ 1437 MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->X, grp->P.n)); 1438 MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->Y, grp->P.n)); 1439 1440 MPI_ECP_LSET(&T[i]->Z, 1); 1441 1442 if (i == 0) { 1443 break; 1444 } 1445 } 1446 1447 cleanup: 1448 1449 mbedtls_mpi_free(&t); 1450 mpi_free_many(c, T_size); 1451 mbedtls_free(c); 1452 1453 return ret; 1454 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */ 1455 } 1456 1457 /* 1458 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak. 1459 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid 1460 */ 1461 static int ecp_safe_invert_jac(const mbedtls_ecp_group *grp, 1462 mbedtls_ecp_point *Q, 1463 unsigned char inv) 1464 { 1465 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1466 mbedtls_mpi tmp; 1467 mbedtls_mpi_init(&tmp); 1468 1469 MPI_ECP_COND_NEG(&Q->Y, inv); 1470 1471 cleanup: 1472 mbedtls_mpi_free(&tmp); 1473 return ret; 1474 } 1475 1476 /* 1477 * Point doubling R = 2 P, Jacobian coordinates 1478 * 1479 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 . 1480 * 1481 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR 1482 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring. 1483 * 1484 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }. 1485 * 1486 * Cost: 1D := 3M + 4S (A == 0) 1487 * 4M + 4S (A == -3) 1488 * 3M + 6S + 1a otherwise 1489 */ 1490 static int ecp_double_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1491 const mbedtls_ecp_point *P, 1492 mbedtls_mpi tmp[4]) 1493 { 1494 #if defined(MBEDTLS_SELF_TEST) 1495 dbl_count++; 1496 #endif 1497 1498 #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) 1499 if (mbedtls_internal_ecp_grp_capable(grp)) { 1500 return mbedtls_internal_ecp_double_jac(grp, R, P); 1501 } 1502 #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */ 1503 1504 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) 1505 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1506 #else 1507 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1508 1509 /* Special case for A = -3 */ 1510 if (mbedtls_ecp_group_a_is_minus_3(grp)) { 1511 /* tmp[0] <- M = 3(X + Z^2)(X - Z^2) */ 1512 MPI_ECP_SQR(&tmp[1], &P->Z); 1513 MPI_ECP_ADD(&tmp[2], &P->X, &tmp[1]); 1514 MPI_ECP_SUB(&tmp[3], &P->X, &tmp[1]); 1515 MPI_ECP_MUL(&tmp[1], &tmp[2], &tmp[3]); 1516 MPI_ECP_MUL_INT(&tmp[0], &tmp[1], 3); 1517 } else { 1518 /* tmp[0] <- M = 3.X^2 + A.Z^4 */ 1519 MPI_ECP_SQR(&tmp[1], &P->X); 1520 MPI_ECP_MUL_INT(&tmp[0], &tmp[1], 3); 1521 1522 /* Optimize away for "koblitz" curves with A = 0 */ 1523 if (MPI_ECP_CMP_INT(&grp->A, 0) != 0) { 1524 /* M += A.Z^4 */ 1525 MPI_ECP_SQR(&tmp[1], &P->Z); 1526 MPI_ECP_SQR(&tmp[2], &tmp[1]); 1527 MPI_ECP_MUL(&tmp[1], &tmp[2], &grp->A); 1528 MPI_ECP_ADD(&tmp[0], &tmp[0], &tmp[1]); 1529 } 1530 } 1531 1532 /* tmp[1] <- S = 4.X.Y^2 */ 1533 MPI_ECP_SQR(&tmp[2], &P->Y); 1534 MPI_ECP_SHIFT_L(&tmp[2], 1); 1535 MPI_ECP_MUL(&tmp[1], &P->X, &tmp[2]); 1536 MPI_ECP_SHIFT_L(&tmp[1], 1); 1537 1538 /* tmp[3] <- U = 8.Y^4 */ 1539 MPI_ECP_SQR(&tmp[3], &tmp[2]); 1540 MPI_ECP_SHIFT_L(&tmp[3], 1); 1541 1542 /* tmp[2] <- T = M^2 - 2.S */ 1543 MPI_ECP_SQR(&tmp[2], &tmp[0]); 1544 MPI_ECP_SUB(&tmp[2], &tmp[2], &tmp[1]); 1545 MPI_ECP_SUB(&tmp[2], &tmp[2], &tmp[1]); 1546 1547 /* tmp[1] <- S = M(S - T) - U */ 1548 MPI_ECP_SUB(&tmp[1], &tmp[1], &tmp[2]); 1549 MPI_ECP_MUL(&tmp[1], &tmp[1], &tmp[0]); 1550 MPI_ECP_SUB(&tmp[1], &tmp[1], &tmp[3]); 1551 1552 /* tmp[3] <- U = 2.Y.Z */ 1553 MPI_ECP_MUL(&tmp[3], &P->Y, &P->Z); 1554 MPI_ECP_SHIFT_L(&tmp[3], 1); 1555 1556 /* Store results */ 1557 MPI_ECP_MOV(&R->X, &tmp[2]); 1558 MPI_ECP_MOV(&R->Y, &tmp[1]); 1559 MPI_ECP_MOV(&R->Z, &tmp[3]); 1560 1561 cleanup: 1562 1563 return ret; 1564 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */ 1565 } 1566 1567 /* 1568 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22) 1569 * 1570 * The coordinates of Q must be normalized (= affine), 1571 * but those of P don't need to. R is not normalized. 1572 * 1573 * P,Q,R may alias, but only at the level of EC points: they must be either 1574 * equal as pointers, or disjoint (including the coordinate data buffers). 1575 * Fine-grained aliasing at the level of coordinates is not supported. 1576 * 1577 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q. 1578 * None of these cases can happen as intermediate step in ecp_mul_comb(): 1579 * - at each step, P, Q and R are multiples of the base point, the factor 1580 * being less than its order, so none of them is zero; 1581 * - Q is an odd multiple of the base point, P an even multiple, 1582 * due to the choice of precomputed points in the modified comb method. 1583 * So branches for these cases do not leak secret information. 1584 * 1585 * Cost: 1A := 8M + 3S 1586 */ 1587 static int ecp_add_mixed(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1588 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q, 1589 mbedtls_mpi tmp[4]) 1590 { 1591 #if defined(MBEDTLS_SELF_TEST) 1592 add_count++; 1593 #endif 1594 1595 #if defined(MBEDTLS_ECP_ADD_MIXED_ALT) 1596 if (mbedtls_internal_ecp_grp_capable(grp)) { 1597 return mbedtls_internal_ecp_add_mixed(grp, R, P, Q); 1598 } 1599 #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */ 1600 1601 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT) 1602 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1603 #else 1604 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1605 1606 /* NOTE: Aliasing between input and output is allowed, so one has to make 1607 * sure that at the point X,Y,Z are written, {P,Q}->{X,Y,Z} are no 1608 * longer read from. */ 1609 mbedtls_mpi * const X = &R->X; 1610 mbedtls_mpi * const Y = &R->Y; 1611 mbedtls_mpi * const Z = &R->Z; 1612 1613 if (!MPI_ECP_VALID(&Q->Z)) { 1614 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 1615 } 1616 1617 /* 1618 * Trivial cases: P == 0 or Q == 0 (case 1) 1619 */ 1620 if (MPI_ECP_CMP_INT(&P->Z, 0) == 0) { 1621 return mbedtls_ecp_copy(R, Q); 1622 } 1623 1624 if (MPI_ECP_CMP_INT(&Q->Z, 0) == 0) { 1625 return mbedtls_ecp_copy(R, P); 1626 } 1627 1628 /* 1629 * Make sure Q coordinates are normalized 1630 */ 1631 if (MPI_ECP_CMP_INT(&Q->Z, 1) != 0) { 1632 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 1633 } 1634 1635 MPI_ECP_SQR(&tmp[0], &P->Z); 1636 MPI_ECP_MUL(&tmp[1], &tmp[0], &P->Z); 1637 MPI_ECP_MUL(&tmp[0], &tmp[0], &Q->X); 1638 MPI_ECP_MUL(&tmp[1], &tmp[1], &Q->Y); 1639 MPI_ECP_SUB(&tmp[0], &tmp[0], &P->X); 1640 MPI_ECP_SUB(&tmp[1], &tmp[1], &P->Y); 1641 1642 /* Special cases (2) and (3) */ 1643 if (MPI_ECP_CMP_INT(&tmp[0], 0) == 0) { 1644 if (MPI_ECP_CMP_INT(&tmp[1], 0) == 0) { 1645 ret = ecp_double_jac(grp, R, P, tmp); 1646 goto cleanup; 1647 } else { 1648 ret = mbedtls_ecp_set_zero(R); 1649 goto cleanup; 1650 } 1651 } 1652 1653 /* {P,Q}->Z no longer used, so OK to write to Z even if there's aliasing. */ 1654 MPI_ECP_MUL(Z, &P->Z, &tmp[0]); 1655 MPI_ECP_SQR(&tmp[2], &tmp[0]); 1656 MPI_ECP_MUL(&tmp[3], &tmp[2], &tmp[0]); 1657 MPI_ECP_MUL(&tmp[2], &tmp[2], &P->X); 1658 1659 MPI_ECP_MOV(&tmp[0], &tmp[2]); 1660 MPI_ECP_SHIFT_L(&tmp[0], 1); 1661 1662 /* {P,Q}->X no longer used, so OK to write to X even if there's aliasing. */ 1663 MPI_ECP_SQR(X, &tmp[1]); 1664 MPI_ECP_SUB(X, X, &tmp[0]); 1665 MPI_ECP_SUB(X, X, &tmp[3]); 1666 MPI_ECP_SUB(&tmp[2], &tmp[2], X); 1667 MPI_ECP_MUL(&tmp[2], &tmp[2], &tmp[1]); 1668 MPI_ECP_MUL(&tmp[3], &tmp[3], &P->Y); 1669 /* {P,Q}->Y no longer used, so OK to write to Y even if there's aliasing. */ 1670 MPI_ECP_SUB(Y, &tmp[2], &tmp[3]); 1671 1672 cleanup: 1673 1674 return ret; 1675 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */ 1676 } 1677 1678 /* 1679 * Randomize jacobian coordinates: 1680 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l 1681 * This is sort of the reverse operation of ecp_normalize_jac(). 1682 * 1683 * This countermeasure was first suggested in [2]. 1684 */ 1685 static int ecp_randomize_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, 1686 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 1687 { 1688 #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) 1689 if (mbedtls_internal_ecp_grp_capable(grp)) { 1690 return mbedtls_internal_ecp_randomize_jac(grp, pt, f_rng, p_rng); 1691 } 1692 #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */ 1693 1694 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) 1695 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 1696 #else 1697 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1698 mbedtls_mpi l; 1699 1700 mbedtls_mpi_init(&l); 1701 1702 /* Generate l such that 1 < l < p */ 1703 MPI_ECP_RAND(&l); 1704 1705 /* Z' = l * Z */ 1706 MPI_ECP_MUL(&pt->Z, &pt->Z, &l); 1707 1708 /* Y' = l * Y */ 1709 MPI_ECP_MUL(&pt->Y, &pt->Y, &l); 1710 1711 /* X' = l^2 * X */ 1712 MPI_ECP_SQR(&l, &l); 1713 MPI_ECP_MUL(&pt->X, &pt->X, &l); 1714 1715 /* Y'' = l^2 * Y' = l^3 * Y */ 1716 MPI_ECP_MUL(&pt->Y, &pt->Y, &l); 1717 1718 cleanup: 1719 mbedtls_mpi_free(&l); 1720 1721 if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) { 1722 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; 1723 } 1724 return ret; 1725 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */ 1726 } 1727 1728 /* 1729 * Check and define parameters used by the comb method (see below for details) 1730 */ 1731 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7 1732 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds" 1733 #endif 1734 1735 /* d = ceil( n / w ) */ 1736 #define COMB_MAX_D (MBEDTLS_ECP_MAX_BITS + 1) / 2 1737 1738 /* number of precomputed points */ 1739 #define COMB_MAX_PRE (1 << (MBEDTLS_ECP_WINDOW_SIZE - 1)) 1740 1741 /* 1742 * Compute the representation of m that will be used with our comb method. 1743 * 1744 * The basic comb method is described in GECC 3.44 for example. We use a 1745 * modified version that provides resistance to SPA by avoiding zero 1746 * digits in the representation as in [3]. We modify the method further by 1747 * requiring that all K_i be odd, which has the small cost that our 1748 * representation uses one more K_i, due to carries, but saves on the size of 1749 * the precomputed table. 1750 * 1751 * Summary of the comb method and its modifications: 1752 * 1753 * - The goal is to compute m*P for some w*d-bit integer m. 1754 * 1755 * - The basic comb method splits m into the w-bit integers 1756 * x[0] .. x[d-1] where x[i] consists of the bits in m whose 1757 * index has residue i modulo d, and computes m * P as 1758 * S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where 1759 * S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P. 1760 * 1761 * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by 1762 * .. + 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]] .., 1763 * thereby successively converting it into a form where all summands 1764 * are nonzero, at the cost of negative summands. This is the basic idea of [3]. 1765 * 1766 * - More generally, even if x[i+1] != 0, we can first transform the sum as 1767 * .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] .., 1768 * and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]]. 1769 * Performing and iterating this procedure for those x[i] that are even 1770 * (keeping track of carry), we can transform the original sum into one of the form 1771 * S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]] 1772 * with all x'[i] odd. It is therefore only necessary to know S at odd indices, 1773 * which is why we are only computing half of it in the first place in 1774 * ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb. 1775 * 1776 * - For the sake of compactness, only the seven low-order bits of x[i] 1777 * are used to represent its absolute value (K_i in the paper), and the msb 1778 * of x[i] encodes the sign (s_i in the paper): it is set if and only if 1779 * if s_i == -1; 1780 * 1781 * Calling conventions: 1782 * - x is an array of size d + 1 1783 * - w is the size, ie number of teeth, of the comb, and must be between 1784 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE) 1785 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d 1786 * (the result will be incorrect if these assumptions are not satisfied) 1787 */ 1788 static void ecp_comb_recode_core(unsigned char x[], size_t d, 1789 unsigned char w, const mbedtls_mpi *m) 1790 { 1791 size_t i, j; 1792 unsigned char c, cc, adjust; 1793 1794 memset(x, 0, d+1); 1795 1796 /* First get the classical comb values (except for x_d = 0) */ 1797 for (i = 0; i < d; i++) { 1798 for (j = 0; j < w; j++) { 1799 x[i] |= mbedtls_mpi_get_bit(m, i + d * j) << j; 1800 } 1801 } 1802 1803 /* Now make sure x_1 .. x_d are odd */ 1804 c = 0; 1805 for (i = 1; i <= d; i++) { 1806 /* Add carry and update it */ 1807 cc = x[i] & c; 1808 x[i] = x[i] ^ c; 1809 c = cc; 1810 1811 /* Adjust if needed, avoiding branches */ 1812 adjust = 1 - (x[i] & 0x01); 1813 c |= x[i] & (x[i-1] * adjust); 1814 x[i] = x[i] ^ (x[i-1] * adjust); 1815 x[i-1] |= adjust << 7; 1816 } 1817 } 1818 1819 /* 1820 * Precompute points for the adapted comb method 1821 * 1822 * Assumption: T must be able to hold 2^{w - 1} elements. 1823 * 1824 * Operation: If i = i_{w-1} ... i_1 is the binary representation of i, 1825 * sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P. 1826 * 1827 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1) 1828 * 1829 * Note: Even comb values (those where P would be omitted from the 1830 * sum defining T[i] above) are not needed in our adaption 1831 * the comb method. See ecp_comb_recode_core(). 1832 * 1833 * This function currently works in four steps: 1834 * (1) [dbl] Computation of intermediate T[i] for 2-power values of i 1835 * (2) [norm_dbl] Normalization of coordinates of these T[i] 1836 * (3) [add] Computation of all T[i] 1837 * (4) [norm_add] Normalization of all T[i] 1838 * 1839 * Step 1 can be interrupted but not the others; together with the final 1840 * coordinate normalization they are the largest steps done at once, depending 1841 * on the window size. Here are operation counts for P-256: 1842 * 1843 * step (2) (3) (4) 1844 * w = 5 142 165 208 1845 * w = 4 136 77 160 1846 * w = 3 130 33 136 1847 * w = 2 124 11 124 1848 * 1849 * So if ECC operations are blocking for too long even with a low max_ops 1850 * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order 1851 * to minimize maximum blocking time. 1852 */ 1853 static int ecp_precompute_comb(const mbedtls_ecp_group *grp, 1854 mbedtls_ecp_point T[], const mbedtls_ecp_point *P, 1855 unsigned char w, size_t d, 1856 mbedtls_ecp_restart_ctx *rs_ctx) 1857 { 1858 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1859 unsigned char i; 1860 size_t j = 0; 1861 const unsigned char T_size = 1U << (w - 1); 1862 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1] = { NULL }; 1863 1864 mbedtls_mpi tmp[4]; 1865 1866 mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 1867 1868 #if defined(MBEDTLS_ECP_RESTARTABLE) 1869 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1870 if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) { 1871 goto dbl; 1872 } 1873 if (rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl) { 1874 goto norm_dbl; 1875 } 1876 if (rs_ctx->rsm->state == ecp_rsm_pre_add) { 1877 goto add; 1878 } 1879 if (rs_ctx->rsm->state == ecp_rsm_pre_norm_add) { 1880 goto norm_add; 1881 } 1882 } 1883 #else 1884 (void) rs_ctx; 1885 #endif 1886 1887 #if defined(MBEDTLS_ECP_RESTARTABLE) 1888 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1889 rs_ctx->rsm->state = ecp_rsm_pre_dbl; 1890 1891 /* initial state for the loop */ 1892 rs_ctx->rsm->i = 0; 1893 } 1894 1895 dbl: 1896 #endif 1897 /* 1898 * Set T[0] = P and 1899 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value) 1900 */ 1901 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&T[0], P)); 1902 1903 #if defined(MBEDTLS_ECP_RESTARTABLE) 1904 if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) { 1905 j = rs_ctx->rsm->i; 1906 } else 1907 #endif 1908 j = 0; 1909 1910 for (; j < d * (w - 1); j++) { 1911 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL); 1912 1913 i = 1U << (j / d); 1914 cur = T + i; 1915 1916 if (j % d == 0) { 1917 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(cur, T + (i >> 1))); 1918 } 1919 1920 MBEDTLS_MPI_CHK(ecp_double_jac(grp, cur, cur, tmp)); 1921 } 1922 1923 #if defined(MBEDTLS_ECP_RESTARTABLE) 1924 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1925 rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl; 1926 } 1927 1928 norm_dbl: 1929 #endif 1930 /* 1931 * Normalize current elements in T to allow them to be used in 1932 * ecp_add_mixed() below, which requires one normalized input. 1933 * 1934 * As T has holes, use an auxiliary array of pointers to elements in T. 1935 * 1936 */ 1937 j = 0; 1938 for (i = 1; i < T_size; i <<= 1) { 1939 TT[j++] = T + i; 1940 } 1941 1942 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2); 1943 1944 MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j)); 1945 1946 #if defined(MBEDTLS_ECP_RESTARTABLE) 1947 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1948 rs_ctx->rsm->state = ecp_rsm_pre_add; 1949 } 1950 1951 add: 1952 #endif 1953 /* 1954 * Compute the remaining ones using the minimal number of additions 1955 * Be careful to update T[2^l] only after using it! 1956 */ 1957 MBEDTLS_ECP_BUDGET((T_size - 1) * MBEDTLS_ECP_OPS_ADD); 1958 1959 for (i = 1; i < T_size; i <<= 1) { 1960 j = i; 1961 while (j--) { 1962 MBEDTLS_MPI_CHK(ecp_add_mixed(grp, &T[i + j], &T[j], &T[i], tmp)); 1963 } 1964 } 1965 1966 #if defined(MBEDTLS_ECP_RESTARTABLE) 1967 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 1968 rs_ctx->rsm->state = ecp_rsm_pre_norm_add; 1969 } 1970 1971 norm_add: 1972 #endif 1973 /* 1974 * Normalize final elements in T. Even though there are no holes now, we 1975 * still need the auxiliary array for homogeneity with the previous 1976 * call. Also, skip T[0] which is already normalised, being a copy of P. 1977 */ 1978 for (j = 0; j + 1 < T_size; j++) { 1979 TT[j] = T + j + 1; 1980 } 1981 1982 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2); 1983 1984 MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j)); 1985 1986 /* Free Z coordinate (=1 after normalization) to save RAM. 1987 * This makes T[i] invalid as mbedtls_ecp_points, but this is OK 1988 * since from this point onwards, they are only accessed indirectly 1989 * via the getter function ecp_select_comb() which does set the 1990 * target's Z coordinate to 1. */ 1991 for (i = 0; i < T_size; i++) { 1992 mbedtls_mpi_free(&T[i].Z); 1993 } 1994 1995 cleanup: 1996 1997 mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 1998 1999 #if defined(MBEDTLS_ECP_RESTARTABLE) 2000 if (rs_ctx != NULL && rs_ctx->rsm != NULL && 2001 ret == MBEDTLS_ERR_ECP_IN_PROGRESS) { 2002 if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) { 2003 rs_ctx->rsm->i = j; 2004 } 2005 } 2006 #endif 2007 2008 return ret; 2009 } 2010 2011 /* 2012 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ] 2013 * 2014 * See ecp_comb_recode_core() for background 2015 */ 2016 static int ecp_select_comb(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2017 const mbedtls_ecp_point T[], unsigned char T_size, 2018 unsigned char i) 2019 { 2020 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2021 unsigned char ii, j; 2022 2023 /* Ignore the "sign" bit and scale down */ 2024 ii = (i & 0x7Fu) >> 1; 2025 2026 /* Read the whole table to thwart cache-based timing attacks */ 2027 for (j = 0; j < T_size; j++) { 2028 MPI_ECP_COND_ASSIGN(&R->X, &T[j].X, j == ii); 2029 MPI_ECP_COND_ASSIGN(&R->Y, &T[j].Y, j == ii); 2030 } 2031 2032 /* Safely invert result if i is "negative" */ 2033 MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, R, i >> 7)); 2034 2035 MPI_ECP_LSET(&R->Z, 1); 2036 2037 cleanup: 2038 return ret; 2039 } 2040 2041 /* 2042 * Core multiplication algorithm for the (modified) comb method. 2043 * This part is actually common with the basic comb method (GECC 3.44) 2044 * 2045 * Cost: d A + d D + 1 R 2046 */ 2047 static int ecp_mul_comb_core(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2048 const mbedtls_ecp_point T[], unsigned char T_size, 2049 const unsigned char x[], size_t d, 2050 int (*f_rng)(void *, unsigned char *, size_t), 2051 void *p_rng, 2052 mbedtls_ecp_restart_ctx *rs_ctx) 2053 { 2054 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2055 mbedtls_ecp_point Txi; 2056 mbedtls_mpi tmp[4]; 2057 size_t i; 2058 2059 mbedtls_ecp_point_init(&Txi); 2060 mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2061 2062 #if !defined(MBEDTLS_ECP_RESTARTABLE) 2063 (void) rs_ctx; 2064 #endif 2065 2066 #if defined(MBEDTLS_ECP_RESTARTABLE) 2067 if (rs_ctx != NULL && rs_ctx->rsm != NULL && 2068 rs_ctx->rsm->state != ecp_rsm_comb_core) { 2069 rs_ctx->rsm->i = 0; 2070 rs_ctx->rsm->state = ecp_rsm_comb_core; 2071 } 2072 2073 /* new 'if' instead of nested for the sake of the 'else' branch */ 2074 if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) { 2075 /* restore current index (R already pointing to rs_ctx->rsm->R) */ 2076 i = rs_ctx->rsm->i; 2077 } else 2078 #endif 2079 { 2080 /* Start with a non-zero point and randomize its coordinates */ 2081 i = d; 2082 MBEDTLS_MPI_CHK(ecp_select_comb(grp, R, T, T_size, x[i])); 2083 if (f_rng != 0) { 2084 MBEDTLS_MPI_CHK(ecp_randomize_jac(grp, R, f_rng, p_rng)); 2085 } 2086 } 2087 2088 while (i != 0) { 2089 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD); 2090 --i; 2091 2092 MBEDTLS_MPI_CHK(ecp_double_jac(grp, R, R, tmp)); 2093 MBEDTLS_MPI_CHK(ecp_select_comb(grp, &Txi, T, T_size, x[i])); 2094 MBEDTLS_MPI_CHK(ecp_add_mixed(grp, R, R, &Txi, tmp)); 2095 } 2096 2097 cleanup: 2098 2099 mbedtls_ecp_point_free(&Txi); 2100 mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2101 2102 #if defined(MBEDTLS_ECP_RESTARTABLE) 2103 if (rs_ctx != NULL && rs_ctx->rsm != NULL && 2104 ret == MBEDTLS_ERR_ECP_IN_PROGRESS) { 2105 rs_ctx->rsm->i = i; 2106 /* no need to save R, already pointing to rs_ctx->rsm->R */ 2107 } 2108 #endif 2109 2110 return ret; 2111 } 2112 2113 /* 2114 * Recode the scalar to get constant-time comb multiplication 2115 * 2116 * As the actual scalar recoding needs an odd scalar as a starting point, 2117 * this wrapper ensures that by replacing m by N - m if necessary, and 2118 * informs the caller that the result of multiplication will be negated. 2119 * 2120 * This works because we only support large prime order for Short Weierstrass 2121 * curves, so N is always odd hence either m or N - m is. 2122 * 2123 * See ecp_comb_recode_core() for background. 2124 */ 2125 static int ecp_comb_recode_scalar(const mbedtls_ecp_group *grp, 2126 const mbedtls_mpi *m, 2127 unsigned char k[COMB_MAX_D + 1], 2128 size_t d, 2129 unsigned char w, 2130 unsigned char *parity_trick) 2131 { 2132 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2133 mbedtls_mpi M, mm; 2134 2135 mbedtls_mpi_init(&M); 2136 mbedtls_mpi_init(&mm); 2137 2138 /* N is always odd (see above), just make extra sure */ 2139 if (mbedtls_mpi_get_bit(&grp->N, 0) != 1) { 2140 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2141 } 2142 2143 /* do we need the parity trick? */ 2144 *parity_trick = (mbedtls_mpi_get_bit(m, 0) == 0); 2145 2146 /* execute parity fix in constant time */ 2147 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&M, m)); 2148 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&mm, &grp->N, m)); 2149 MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&M, &mm, *parity_trick)); 2150 2151 /* actual scalar recoding */ 2152 ecp_comb_recode_core(k, d, w, &M); 2153 2154 cleanup: 2155 mbedtls_mpi_free(&mm); 2156 mbedtls_mpi_free(&M); 2157 2158 return ret; 2159 } 2160 2161 /* 2162 * Perform comb multiplication (for short Weierstrass curves) 2163 * once the auxiliary table has been pre-computed. 2164 * 2165 * Scalar recoding may use a parity trick that makes us compute -m * P, 2166 * if that is the case we'll need to recover m * P at the end. 2167 */ 2168 static int ecp_mul_comb_after_precomp(const mbedtls_ecp_group *grp, 2169 mbedtls_ecp_point *R, 2170 const mbedtls_mpi *m, 2171 const mbedtls_ecp_point *T, 2172 unsigned char T_size, 2173 unsigned char w, 2174 size_t d, 2175 int (*f_rng)(void *, unsigned char *, size_t), 2176 void *p_rng, 2177 mbedtls_ecp_restart_ctx *rs_ctx) 2178 { 2179 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2180 unsigned char parity_trick; 2181 unsigned char k[COMB_MAX_D + 1]; 2182 mbedtls_ecp_point *RR = R; 2183 2184 #if defined(MBEDTLS_ECP_RESTARTABLE) 2185 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 2186 RR = &rs_ctx->rsm->R; 2187 2188 if (rs_ctx->rsm->state == ecp_rsm_final_norm) { 2189 goto final_norm; 2190 } 2191 } 2192 #endif 2193 2194 MBEDTLS_MPI_CHK(ecp_comb_recode_scalar(grp, m, k, d, w, 2195 &parity_trick)); 2196 MBEDTLS_MPI_CHK(ecp_mul_comb_core(grp, RR, T, T_size, k, d, 2197 f_rng, p_rng, rs_ctx)); 2198 MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, RR, parity_trick)); 2199 2200 #if defined(MBEDTLS_ECP_RESTARTABLE) 2201 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 2202 rs_ctx->rsm->state = ecp_rsm_final_norm; 2203 } 2204 2205 final_norm: 2206 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV); 2207 #endif 2208 /* 2209 * Knowledge of the jacobian coordinates may leak the last few bits of the 2210 * scalar [1], and since our MPI implementation isn't constant-flow, 2211 * inversion (used for coordinate normalization) may leak the full value 2212 * of its input via side-channels [2]. 2213 * 2214 * [1] https://eprint.iacr.org/2003/191 2215 * [2] https://eprint.iacr.org/2020/055 2216 * 2217 * Avoid the leak by randomizing coordinates before we normalize them. 2218 */ 2219 if (f_rng != 0) { 2220 MBEDTLS_MPI_CHK(ecp_randomize_jac(grp, RR, f_rng, p_rng)); 2221 } 2222 2223 MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, RR)); 2224 2225 #if defined(MBEDTLS_ECP_RESTARTABLE) 2226 if (rs_ctx != NULL && rs_ctx->rsm != NULL) { 2227 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, RR)); 2228 } 2229 #endif 2230 2231 cleanup: 2232 return ret; 2233 } 2234 2235 /* 2236 * Pick window size based on curve size and whether we optimize for base point 2237 */ 2238 static unsigned char ecp_pick_window_size(const mbedtls_ecp_group *grp, 2239 unsigned char p_eq_g) 2240 { 2241 unsigned char w; 2242 2243 /* 2244 * Minimize the number of multiplications, that is minimize 2245 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w ) 2246 * (see costs of the various parts, with 1S = 1M) 2247 */ 2248 w = grp->nbits >= 384 ? 5 : 4; 2249 2250 /* 2251 * If P == G, pre-compute a bit more, since this may be re-used later. 2252 * Just adding one avoids upping the cost of the first mul too much, 2253 * and the memory cost too. 2254 */ 2255 if (p_eq_g) { 2256 w++; 2257 } 2258 2259 /* 2260 * If static comb table may not be used (!p_eq_g) or static comb table does 2261 * not exists, make sure w is within bounds. 2262 * (The last test is useful only for very small curves in the test suite.) 2263 * 2264 * The user reduces MBEDTLS_ECP_WINDOW_SIZE does not changes the size of 2265 * static comb table, because the size of static comb table is fixed when 2266 * it is generated. 2267 */ 2268 #if (MBEDTLS_ECP_WINDOW_SIZE < 6) 2269 if ((!p_eq_g || !ecp_group_is_static_comb_table(grp)) && w > MBEDTLS_ECP_WINDOW_SIZE) { 2270 w = MBEDTLS_ECP_WINDOW_SIZE; 2271 } 2272 #endif 2273 if (w >= grp->nbits) { 2274 w = 2; 2275 } 2276 2277 return w; 2278 } 2279 2280 /* 2281 * Multiplication using the comb method - for curves in short Weierstrass form 2282 * 2283 * This function is mainly responsible for administrative work: 2284 * - managing the restart context if enabled 2285 * - managing the table of precomputed points (passed between the below two 2286 * functions): allocation, computation, ownership transfer, freeing. 2287 * 2288 * It delegates the actual arithmetic work to: 2289 * ecp_precompute_comb() and ecp_mul_comb_with_precomp() 2290 * 2291 * See comments on ecp_comb_recode_core() regarding the computation strategy. 2292 */ 2293 static int ecp_mul_comb(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2294 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2295 int (*f_rng)(void *, unsigned char *, size_t), 2296 void *p_rng, 2297 mbedtls_ecp_restart_ctx *rs_ctx) 2298 { 2299 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2300 unsigned char w, p_eq_g, i; 2301 size_t d; 2302 unsigned char T_size = 0, T_ok = 0; 2303 mbedtls_ecp_point *T = NULL; 2304 2305 ECP_RS_ENTER(rsm); 2306 2307 /* Is P the base point ? */ 2308 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 2309 p_eq_g = (MPI_ECP_CMP(&P->Y, &grp->G.Y) == 0 && 2310 MPI_ECP_CMP(&P->X, &grp->G.X) == 0); 2311 #else 2312 p_eq_g = 0; 2313 #endif 2314 2315 /* Pick window size and deduce related sizes */ 2316 w = ecp_pick_window_size(grp, p_eq_g); 2317 T_size = 1U << (w - 1); 2318 d = (grp->nbits + w - 1) / w; 2319 2320 /* Pre-computed table: do we have it already for the base point? */ 2321 if (p_eq_g && grp->T != NULL) { 2322 /* second pointer to the same table, will be deleted on exit */ 2323 T = grp->T; 2324 T_ok = 1; 2325 } else 2326 #if defined(MBEDTLS_ECP_RESTARTABLE) 2327 /* Pre-computed table: do we have one in progress? complete? */ 2328 if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL) { 2329 /* transfer ownership of T from rsm to local function */ 2330 T = rs_ctx->rsm->T; 2331 rs_ctx->rsm->T = NULL; 2332 rs_ctx->rsm->T_size = 0; 2333 2334 /* This effectively jumps to the call to mul_comb_after_precomp() */ 2335 T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core; 2336 } else 2337 #endif 2338 /* Allocate table if we didn't have any */ 2339 { 2340 T = mbedtls_calloc(T_size, sizeof(mbedtls_ecp_point)); 2341 if (T == NULL) { 2342 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED; 2343 goto cleanup; 2344 } 2345 2346 for (i = 0; i < T_size; i++) { 2347 mbedtls_ecp_point_init(&T[i]); 2348 } 2349 2350 T_ok = 0; 2351 } 2352 2353 /* Compute table (or finish computing it) if not done already */ 2354 if (!T_ok) { 2355 MBEDTLS_MPI_CHK(ecp_precompute_comb(grp, T, P, w, d, rs_ctx)); 2356 2357 if (p_eq_g) { 2358 /* almost transfer ownership of T to the group, but keep a copy of 2359 * the pointer to use for calling the next function more easily */ 2360 grp->T = T; 2361 grp->T_size = T_size; 2362 } 2363 } 2364 2365 /* Actual comb multiplication using precomputed points */ 2366 MBEDTLS_MPI_CHK(ecp_mul_comb_after_precomp(grp, R, m, 2367 T, T_size, w, d, 2368 f_rng, p_rng, rs_ctx)); 2369 2370 cleanup: 2371 2372 /* does T belong to the group? */ 2373 if (T == grp->T) { 2374 T = NULL; 2375 } 2376 2377 /* does T belong to the restart context? */ 2378 #if defined(MBEDTLS_ECP_RESTARTABLE) 2379 if (rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL) { 2380 /* transfer ownership of T from local function to rsm */ 2381 rs_ctx->rsm->T_size = T_size; 2382 rs_ctx->rsm->T = T; 2383 T = NULL; 2384 } 2385 #endif 2386 2387 /* did T belong to us? then let's destroy it! */ 2388 if (T != NULL) { 2389 for (i = 0; i < T_size; i++) { 2390 mbedtls_ecp_point_free(&T[i]); 2391 } 2392 mbedtls_free(T); 2393 } 2394 2395 /* prevent caller from using invalid value */ 2396 int should_free_R = (ret != 0); 2397 #if defined(MBEDTLS_ECP_RESTARTABLE) 2398 /* don't free R while in progress in case R == P */ 2399 if (ret == MBEDTLS_ERR_ECP_IN_PROGRESS) { 2400 should_free_R = 0; 2401 } 2402 #endif 2403 if (should_free_R) { 2404 mbedtls_ecp_point_free(R); 2405 } 2406 2407 ECP_RS_LEAVE(rsm); 2408 2409 return ret; 2410 } 2411 2412 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 2413 2414 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 2415 /* 2416 * For Montgomery curves, we do all the internal arithmetic in projective 2417 * coordinates. Import/export of points uses only the x coordinates, which is 2418 * internally represented as X / Z. 2419 * 2420 * For scalar multiplication, we'll use a Montgomery ladder. 2421 */ 2422 2423 /* 2424 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1 2425 * Cost: 1M + 1I 2426 */ 2427 static int ecp_normalize_mxz(const mbedtls_ecp_group *grp, mbedtls_ecp_point *P) 2428 { 2429 #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) 2430 if (mbedtls_internal_ecp_grp_capable(grp)) { 2431 return mbedtls_internal_ecp_normalize_mxz(grp, P); 2432 } 2433 #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */ 2434 2435 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) 2436 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 2437 #else 2438 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2439 MPI_ECP_INV(&P->Z, &P->Z); 2440 MPI_ECP_MUL(&P->X, &P->X, &P->Z); 2441 MPI_ECP_LSET(&P->Z, 1); 2442 2443 cleanup: 2444 return ret; 2445 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */ 2446 } 2447 2448 /* 2449 * Randomize projective x/z coordinates: 2450 * (X, Z) -> (l X, l Z) for random l 2451 * This is sort of the reverse operation of ecp_normalize_mxz(). 2452 * 2453 * This countermeasure was first suggested in [2]. 2454 * Cost: 2M 2455 */ 2456 static int ecp_randomize_mxz(const mbedtls_ecp_group *grp, mbedtls_ecp_point *P, 2457 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 2458 { 2459 #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) 2460 if (mbedtls_internal_ecp_grp_capable(grp)) { 2461 return mbedtls_internal_ecp_randomize_mxz(grp, P, f_rng, p_rng); 2462 } 2463 #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */ 2464 2465 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) 2466 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 2467 #else 2468 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2469 mbedtls_mpi l; 2470 mbedtls_mpi_init(&l); 2471 2472 /* Generate l such that 1 < l < p */ 2473 MPI_ECP_RAND(&l); 2474 2475 MPI_ECP_MUL(&P->X, &P->X, &l); 2476 MPI_ECP_MUL(&P->Z, &P->Z, &l); 2477 2478 cleanup: 2479 mbedtls_mpi_free(&l); 2480 2481 if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) { 2482 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; 2483 } 2484 return ret; 2485 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */ 2486 } 2487 2488 /* 2489 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q), 2490 * for Montgomery curves in x/z coordinates. 2491 * 2492 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3 2493 * with 2494 * d = X1 2495 * P = (X2, Z2) 2496 * Q = (X3, Z3) 2497 * R = (X4, Z4) 2498 * S = (X5, Z5) 2499 * and eliminating temporary variables tO, ..., t4. 2500 * 2501 * Cost: 5M + 4S 2502 */ 2503 static int ecp_double_add_mxz(const mbedtls_ecp_group *grp, 2504 mbedtls_ecp_point *R, mbedtls_ecp_point *S, 2505 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q, 2506 const mbedtls_mpi *d, 2507 mbedtls_mpi T[4]) 2508 { 2509 #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) 2510 if (mbedtls_internal_ecp_grp_capable(grp)) { 2511 return mbedtls_internal_ecp_double_add_mxz(grp, R, S, P, Q, d); 2512 } 2513 #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */ 2514 2515 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) 2516 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 2517 #else 2518 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2519 2520 MPI_ECP_ADD(&T[0], &P->X, &P->Z); /* Pp := PX + PZ */ 2521 MPI_ECP_SUB(&T[1], &P->X, &P->Z); /* Pm := PX - PZ */ 2522 MPI_ECP_ADD(&T[2], &Q->X, &Q->Z); /* Qp := QX + XZ */ 2523 MPI_ECP_SUB(&T[3], &Q->X, &Q->Z); /* Qm := QX - QZ */ 2524 MPI_ECP_MUL(&T[3], &T[3], &T[0]); /* Qm * Pp */ 2525 MPI_ECP_MUL(&T[2], &T[2], &T[1]); /* Qp * Pm */ 2526 MPI_ECP_SQR(&T[0], &T[0]); /* Pp^2 */ 2527 MPI_ECP_SQR(&T[1], &T[1]); /* Pm^2 */ 2528 MPI_ECP_MUL(&R->X, &T[0], &T[1]); /* Pp^2 * Pm^2 */ 2529 MPI_ECP_SUB(&T[0], &T[0], &T[1]); /* Pp^2 - Pm^2 */ 2530 MPI_ECP_MUL(&R->Z, &grp->A, &T[0]); /* A * (Pp^2 - Pm^2) */ 2531 MPI_ECP_ADD(&R->Z, &T[1], &R->Z); /* [ A * (Pp^2-Pm^2) ] + Pm^2 */ 2532 MPI_ECP_ADD(&S->X, &T[3], &T[2]); /* Qm*Pp + Qp*Pm */ 2533 MPI_ECP_SQR(&S->X, &S->X); /* (Qm*Pp + Qp*Pm)^2 */ 2534 MPI_ECP_SUB(&S->Z, &T[3], &T[2]); /* Qm*Pp - Qp*Pm */ 2535 MPI_ECP_SQR(&S->Z, &S->Z); /* (Qm*Pp - Qp*Pm)^2 */ 2536 MPI_ECP_MUL(&S->Z, d, &S->Z); /* d * ( Qm*Pp - Qp*Pm )^2 */ 2537 MPI_ECP_MUL(&R->Z, &T[0], &R->Z); /* [A*(Pp^2-Pm^2)+Pm^2]*(Pp^2-Pm^2) */ 2538 2539 cleanup: 2540 2541 return ret; 2542 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */ 2543 } 2544 2545 /* 2546 * Multiplication with Montgomery ladder in x/z coordinates, 2547 * for curves in Montgomery form 2548 */ 2549 static int ecp_mul_mxz(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2550 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2551 int (*f_rng)(void *, unsigned char *, size_t), 2552 void *p_rng) 2553 { 2554 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2555 size_t i; 2556 unsigned char b; 2557 mbedtls_ecp_point RP; 2558 mbedtls_mpi PX; 2559 mbedtls_mpi tmp[4]; 2560 mbedtls_ecp_point_init(&RP); mbedtls_mpi_init(&PX); 2561 2562 mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2563 2564 if (f_rng == NULL) { 2565 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2566 } 2567 2568 /* Save PX and read from P before writing to R, in case P == R */ 2569 MPI_ECP_MOV(&PX, &P->X); 2570 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&RP, P)); 2571 2572 /* Set R to zero in modified x/z coordinates */ 2573 MPI_ECP_LSET(&R->X, 1); 2574 MPI_ECP_LSET(&R->Z, 0); 2575 mbedtls_mpi_free(&R->Y); 2576 2577 /* RP.X might be slightly larger than P, so reduce it */ 2578 MOD_ADD(&RP.X); 2579 2580 /* Randomize coordinates of the starting point */ 2581 MBEDTLS_MPI_CHK(ecp_randomize_mxz(grp, &RP, f_rng, p_rng)); 2582 2583 /* Loop invariant: R = result so far, RP = R + P */ 2584 i = grp->nbits + 1; /* one past the (zero-based) required msb for private keys */ 2585 while (i-- > 0) { 2586 b = mbedtls_mpi_get_bit(m, i); 2587 /* 2588 * if (b) R = 2R + P else R = 2R, 2589 * which is: 2590 * if (b) double_add( RP, R, RP, R ) 2591 * else double_add( R, RP, R, RP ) 2592 * but using safe conditional swaps to avoid leaks 2593 */ 2594 MPI_ECP_COND_SWAP(&R->X, &RP.X, b); 2595 MPI_ECP_COND_SWAP(&R->Z, &RP.Z, b); 2596 MBEDTLS_MPI_CHK(ecp_double_add_mxz(grp, R, &RP, R, &RP, &PX, tmp)); 2597 MPI_ECP_COND_SWAP(&R->X, &RP.X, b); 2598 MPI_ECP_COND_SWAP(&R->Z, &RP.Z, b); 2599 } 2600 2601 /* 2602 * Knowledge of the projective coordinates may leak the last few bits of the 2603 * scalar [1], and since our MPI implementation isn't constant-flow, 2604 * inversion (used for coordinate normalization) may leak the full value 2605 * of its input via side-channels [2]. 2606 * 2607 * [1] https://eprint.iacr.org/2003/191 2608 * [2] https://eprint.iacr.org/2020/055 2609 * 2610 * Avoid the leak by randomizing coordinates before we normalize them. 2611 */ 2612 MBEDTLS_MPI_CHK(ecp_randomize_mxz(grp, R, f_rng, p_rng)); 2613 MBEDTLS_MPI_CHK(ecp_normalize_mxz(grp, R)); 2614 2615 cleanup: 2616 mbedtls_ecp_point_free(&RP); mbedtls_mpi_free(&PX); 2617 2618 mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2619 return ret; 2620 } 2621 2622 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 2623 2624 /* 2625 * Restartable multiplication R = m * P 2626 * 2627 * This internal function can be called without an RNG in case where we know 2628 * the inputs are not sensitive. 2629 */ 2630 static int ecp_mul_restartable_internal(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2631 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2632 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 2633 mbedtls_ecp_restart_ctx *rs_ctx) 2634 { 2635 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2636 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2637 char is_grp_capable = 0; 2638 #endif 2639 2640 #if defined(MBEDTLS_ECP_RESTARTABLE) 2641 /* reset ops count for this call if top-level */ 2642 if (rs_ctx != NULL && rs_ctx->depth++ == 0) { 2643 rs_ctx->ops_done = 0; 2644 } 2645 #else 2646 (void) rs_ctx; 2647 #endif 2648 2649 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2650 if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) { 2651 MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp)); 2652 } 2653 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 2654 2655 int restarting = 0; 2656 #if defined(MBEDTLS_ECP_RESTARTABLE) 2657 restarting = (rs_ctx != NULL && rs_ctx->rsm != NULL); 2658 #endif 2659 /* skip argument check when restarting */ 2660 if (!restarting) { 2661 /* check_privkey is free */ 2662 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_CHK); 2663 2664 /* Common sanity checks */ 2665 MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(grp, m)); 2666 MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); 2667 } 2668 2669 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2670 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 2671 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 2672 MBEDTLS_MPI_CHK(ecp_mul_mxz(grp, R, m, P, f_rng, p_rng)); 2673 } 2674 #endif 2675 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 2676 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 2677 MBEDTLS_MPI_CHK(ecp_mul_comb(grp, R, m, P, f_rng, p_rng, rs_ctx)); 2678 } 2679 #endif 2680 2681 cleanup: 2682 2683 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2684 if (is_grp_capable) { 2685 mbedtls_internal_ecp_free(grp); 2686 } 2687 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 2688 2689 #if defined(MBEDTLS_ECP_RESTARTABLE) 2690 if (rs_ctx != NULL) { 2691 rs_ctx->depth--; 2692 } 2693 #endif 2694 2695 return ret; 2696 } 2697 2698 /* 2699 * Restartable multiplication R = m * P 2700 */ 2701 int mbedtls_ecp_mul_restartable(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2702 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2703 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 2704 mbedtls_ecp_restart_ctx *rs_ctx) 2705 { 2706 if (f_rng == NULL) { 2707 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 2708 } 2709 2710 return ecp_mul_restartable_internal(grp, R, m, P, f_rng, p_rng, rs_ctx); 2711 } 2712 2713 /* 2714 * Multiplication R = m * P 2715 */ 2716 int mbedtls_ecp_mul(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2717 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2718 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 2719 { 2720 return mbedtls_ecp_mul_restartable(grp, R, m, P, f_rng, p_rng, NULL); 2721 } 2722 #endif /* MBEDTLS_ECP_C */ 2723 2724 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 2725 /* 2726 * Check that an affine point is valid as a public key, 2727 * short weierstrass curves (SEC1 3.2.3.1) 2728 */ 2729 static int ecp_check_pubkey_sw(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt) 2730 { 2731 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2732 mbedtls_mpi YY, RHS; 2733 2734 /* pt coordinates must be normalized for our checks */ 2735 if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0 || 2736 mbedtls_mpi_cmp_int(&pt->Y, 0) < 0 || 2737 mbedtls_mpi_cmp_mpi(&pt->X, &grp->P) >= 0 || 2738 mbedtls_mpi_cmp_mpi(&pt->Y, &grp->P) >= 0) { 2739 return MBEDTLS_ERR_ECP_INVALID_KEY; 2740 } 2741 2742 mbedtls_mpi_init(&YY); mbedtls_mpi_init(&RHS); 2743 2744 /* 2745 * YY = Y^2 2746 * RHS = X^3 + A X + B 2747 */ 2748 MPI_ECP_SQR(&YY, &pt->Y); 2749 MBEDTLS_MPI_CHK(ecp_sw_rhs(grp, &RHS, &pt->X)); 2750 2751 if (MPI_ECP_CMP(&YY, &RHS) != 0) { 2752 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2753 } 2754 2755 cleanup: 2756 2757 mbedtls_mpi_free(&YY); mbedtls_mpi_free(&RHS); 2758 2759 return ret; 2760 } 2761 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 2762 2763 #if defined(MBEDTLS_ECP_C) 2764 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 2765 /* 2766 * R = m * P with shortcuts for m == 0, m == 1 and m == -1 2767 * NOT constant-time - ONLY for short Weierstrass! 2768 */ 2769 static int mbedtls_ecp_mul_shortcuts(mbedtls_ecp_group *grp, 2770 mbedtls_ecp_point *R, 2771 const mbedtls_mpi *m, 2772 const mbedtls_ecp_point *P, 2773 mbedtls_ecp_restart_ctx *rs_ctx) 2774 { 2775 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2776 mbedtls_mpi tmp; 2777 mbedtls_mpi_init(&tmp); 2778 2779 if (mbedtls_mpi_cmp_int(m, 0) == 0) { 2780 MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); 2781 MBEDTLS_MPI_CHK(mbedtls_ecp_set_zero(R)); 2782 } else if (mbedtls_mpi_cmp_int(m, 1) == 0) { 2783 MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); 2784 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P)); 2785 } else if (mbedtls_mpi_cmp_int(m, -1) == 0) { 2786 MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); 2787 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P)); 2788 MPI_ECP_NEG(&R->Y); 2789 } else { 2790 MBEDTLS_MPI_CHK(ecp_mul_restartable_internal(grp, R, m, P, 2791 NULL, NULL, rs_ctx)); 2792 } 2793 2794 cleanup: 2795 mbedtls_mpi_free(&tmp); 2796 2797 return ret; 2798 } 2799 2800 /* 2801 * Restartable linear combination 2802 * NOT constant-time 2803 */ 2804 int mbedtls_ecp_muladd_restartable( 2805 mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2806 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2807 const mbedtls_mpi *n, const mbedtls_ecp_point *Q, 2808 mbedtls_ecp_restart_ctx *rs_ctx) 2809 { 2810 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 2811 mbedtls_ecp_point mP; 2812 mbedtls_ecp_point *pmP = &mP; 2813 mbedtls_ecp_point *pR = R; 2814 mbedtls_mpi tmp[4]; 2815 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2816 char is_grp_capable = 0; 2817 #endif 2818 if (mbedtls_ecp_get_type(grp) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 2819 return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 2820 } 2821 2822 mbedtls_ecp_point_init(&mP); 2823 mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2824 2825 ECP_RS_ENTER(ma); 2826 2827 #if defined(MBEDTLS_ECP_RESTARTABLE) 2828 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2829 /* redirect intermediate results to restart context */ 2830 pmP = &rs_ctx->ma->mP; 2831 pR = &rs_ctx->ma->R; 2832 2833 /* jump to next operation */ 2834 if (rs_ctx->ma->state == ecp_rsma_mul2) { 2835 goto mul2; 2836 } 2837 if (rs_ctx->ma->state == ecp_rsma_add) { 2838 goto add; 2839 } 2840 if (rs_ctx->ma->state == ecp_rsma_norm) { 2841 goto norm; 2842 } 2843 } 2844 #endif /* MBEDTLS_ECP_RESTARTABLE */ 2845 2846 MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pmP, m, P, rs_ctx)); 2847 #if defined(MBEDTLS_ECP_RESTARTABLE) 2848 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2849 rs_ctx->ma->state = ecp_rsma_mul2; 2850 } 2851 2852 mul2: 2853 #endif 2854 MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pR, n, Q, rs_ctx)); 2855 2856 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2857 if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) { 2858 MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp)); 2859 } 2860 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 2861 2862 #if defined(MBEDTLS_ECP_RESTARTABLE) 2863 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2864 rs_ctx->ma->state = ecp_rsma_add; 2865 } 2866 2867 add: 2868 #endif 2869 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_ADD); 2870 MBEDTLS_MPI_CHK(ecp_add_mixed(grp, pR, pmP, pR, tmp)); 2871 #if defined(MBEDTLS_ECP_RESTARTABLE) 2872 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2873 rs_ctx->ma->state = ecp_rsma_norm; 2874 } 2875 2876 norm: 2877 #endif 2878 MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV); 2879 MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, pR)); 2880 2881 #if defined(MBEDTLS_ECP_RESTARTABLE) 2882 if (rs_ctx != NULL && rs_ctx->ma != NULL) { 2883 MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, pR)); 2884 } 2885 #endif 2886 2887 cleanup: 2888 2889 mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); 2890 2891 #if defined(MBEDTLS_ECP_INTERNAL_ALT) 2892 if (is_grp_capable) { 2893 mbedtls_internal_ecp_free(grp); 2894 } 2895 #endif /* MBEDTLS_ECP_INTERNAL_ALT */ 2896 2897 mbedtls_ecp_point_free(&mP); 2898 2899 ECP_RS_LEAVE(ma); 2900 2901 return ret; 2902 } 2903 2904 /* 2905 * Linear combination 2906 * NOT constant-time 2907 */ 2908 int mbedtls_ecp_muladd(mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 2909 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 2910 const mbedtls_mpi *n, const mbedtls_ecp_point *Q) 2911 { 2912 return mbedtls_ecp_muladd_restartable(grp, R, m, P, n, Q, NULL); 2913 } 2914 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 2915 #endif /* MBEDTLS_ECP_C */ 2916 2917 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 2918 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 2919 #define ECP_MPI_INIT(_p, _n) { .p = (mbedtls_mpi_uint *) (_p), .s = 1, .n = (_n), .use_mempool = 0 } 2920 #define ECP_MPI_INIT_ARRAY(x) \ 2921 ECP_MPI_INIT(x, sizeof(x) / sizeof(mbedtls_mpi_uint)) 2922 /* 2923 * Constants for the two points other than 0, 1, -1 (mod p) in 2924 * https://cr.yp.to/ecdh.html#validate 2925 * See ecp_check_pubkey_x25519(). 2926 */ 2927 static const mbedtls_mpi_uint x25519_bad_point_1[] = { 2928 MBEDTLS_BYTES_TO_T_UINT_8(0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae), 2929 MBEDTLS_BYTES_TO_T_UINT_8(0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a), 2930 MBEDTLS_BYTES_TO_T_UINT_8(0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd), 2931 MBEDTLS_BYTES_TO_T_UINT_8(0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00), 2932 }; 2933 static const mbedtls_mpi_uint x25519_bad_point_2[] = { 2934 MBEDTLS_BYTES_TO_T_UINT_8(0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24), 2935 MBEDTLS_BYTES_TO_T_UINT_8(0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b), 2936 MBEDTLS_BYTES_TO_T_UINT_8(0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86), 2937 MBEDTLS_BYTES_TO_T_UINT_8(0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57), 2938 }; 2939 static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY( 2940 x25519_bad_point_1); 2941 static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY( 2942 x25519_bad_point_2); 2943 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 2944 2945 /* 2946 * Check that the input point is not one of the low-order points. 2947 * This is recommended by the "May the Fourth" paper: 2948 * https://eprint.iacr.org/2017/806.pdf 2949 * Those points are never sent by an honest peer. 2950 */ 2951 static int ecp_check_bad_points_mx(const mbedtls_mpi *X, const mbedtls_mpi *P, 2952 const mbedtls_ecp_group_id grp_id) 2953 { 2954 int ret; 2955 mbedtls_mpi XmP; 2956 2957 mbedtls_mpi_init(&XmP); 2958 2959 /* Reduce X mod P so that we only need to check values less than P. 2960 * We know X < 2^256 so we can proceed by subtraction. */ 2961 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&XmP, X)); 2962 while (mbedtls_mpi_cmp_mpi(&XmP, P) >= 0) { 2963 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&XmP, &XmP, P)); 2964 } 2965 2966 /* Check against the known bad values that are less than P. For Curve448 2967 * these are 0, 1 and -1. For Curve25519 we check the values less than P 2968 * from the following list: https://cr.yp.to/ecdh.html#validate */ 2969 if (mbedtls_mpi_cmp_int(&XmP, 1) <= 0) { /* takes care of 0 and 1 */ 2970 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2971 goto cleanup; 2972 } 2973 2974 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 2975 if (grp_id == MBEDTLS_ECP_DP_CURVE25519) { 2976 if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_1) == 0) { 2977 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2978 goto cleanup; 2979 } 2980 2981 if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_2) == 0) { 2982 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2983 goto cleanup; 2984 } 2985 } 2986 #else 2987 (void) grp_id; 2988 #endif 2989 2990 /* Final check: check if XmP + 1 is P (final because it changes XmP!) */ 2991 MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&XmP, &XmP, 1)); 2992 if (mbedtls_mpi_cmp_mpi(&XmP, P) == 0) { 2993 ret = MBEDTLS_ERR_ECP_INVALID_KEY; 2994 goto cleanup; 2995 } 2996 2997 ret = 0; 2998 2999 cleanup: 3000 mbedtls_mpi_free(&XmP); 3001 3002 return ret; 3003 } 3004 3005 /* 3006 * Check validity of a public key for Montgomery curves with x-only schemes 3007 */ 3008 static int ecp_check_pubkey_mx(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt) 3009 { 3010 /* [Curve25519 p. 5] Just check X is the correct number of bytes */ 3011 /* Allow any public value, if it's too big then we'll just reduce it mod p 3012 * (RFC 7748 sec. 5 para. 3). */ 3013 if (mbedtls_mpi_size(&pt->X) > (grp->nbits + 7) / 8) { 3014 return MBEDTLS_ERR_ECP_INVALID_KEY; 3015 } 3016 3017 /* Implicit in all standards (as they don't consider negative numbers): 3018 * X must be non-negative. This is normally ensured by the way it's 3019 * encoded for transmission, but let's be extra sure. */ 3020 if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0) { 3021 return MBEDTLS_ERR_ECP_INVALID_KEY; 3022 } 3023 3024 return ecp_check_bad_points_mx(&pt->X, &grp->P, grp->id); 3025 } 3026 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3027 3028 /* 3029 * Check that a point is valid as a public key 3030 */ 3031 int mbedtls_ecp_check_pubkey(const mbedtls_ecp_group *grp, 3032 const mbedtls_ecp_point *pt) 3033 { 3034 /* Must use affine coordinates */ 3035 if (mbedtls_mpi_cmp_int(&pt->Z, 1) != 0) { 3036 return MBEDTLS_ERR_ECP_INVALID_KEY; 3037 } 3038 3039 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3040 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3041 return ecp_check_pubkey_mx(grp, pt); 3042 } 3043 #endif 3044 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3045 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3046 return ecp_check_pubkey_sw(grp, pt); 3047 } 3048 #endif 3049 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3050 } 3051 3052 /* 3053 * Check that an mbedtls_mpi is valid as a private key 3054 */ 3055 int mbedtls_ecp_check_privkey(const mbedtls_ecp_group *grp, 3056 const mbedtls_mpi *d) 3057 { 3058 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3059 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3060 /* see RFC 7748 sec. 5 para. 5 */ 3061 if (mbedtls_mpi_get_bit(d, 0) != 0 || 3062 mbedtls_mpi_get_bit(d, 1) != 0 || 3063 mbedtls_mpi_bitlen(d) - 1 != grp->nbits) { /* mbedtls_mpi_bitlen is one-based! */ 3064 return MBEDTLS_ERR_ECP_INVALID_KEY; 3065 } 3066 3067 /* see [Curve25519] page 5 */ 3068 if (grp->nbits == 254 && mbedtls_mpi_get_bit(d, 2) != 0) { 3069 return MBEDTLS_ERR_ECP_INVALID_KEY; 3070 } 3071 3072 return 0; 3073 } 3074 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3075 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3076 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3077 /* see SEC1 3.2 */ 3078 if (mbedtls_mpi_cmp_int(d, 1) < 0 || 3079 mbedtls_mpi_cmp_mpi(d, &grp->N) >= 0) { 3080 return MBEDTLS_ERR_ECP_INVALID_KEY; 3081 } else { 3082 return 0; 3083 } 3084 } 3085 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3086 3087 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3088 } 3089 3090 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3091 MBEDTLS_STATIC_TESTABLE 3092 int mbedtls_ecp_gen_privkey_mx(size_t high_bit, 3093 mbedtls_mpi *d, 3094 int (*f_rng)(void *, unsigned char *, size_t), 3095 void *p_rng) 3096 { 3097 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3098 size_t n_random_bytes = high_bit / 8 + 1; 3099 3100 /* [Curve25519] page 5 */ 3101 /* Generate a (high_bit+1)-bit random number by generating just enough 3102 * random bytes, then shifting out extra bits from the top (necessary 3103 * when (high_bit+1) is not a multiple of 8). */ 3104 MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(d, n_random_bytes, 3105 f_rng, p_rng)); 3106 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(d, 8 * n_random_bytes - high_bit - 1)); 3107 3108 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, high_bit, 1)); 3109 3110 /* Make sure the last two bits are unset for Curve448, three bits for 3111 Curve25519 */ 3112 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 0, 0)); 3113 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 1, 0)); 3114 if (high_bit == 254) { 3115 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 2, 0)); 3116 } 3117 3118 cleanup: 3119 return ret; 3120 } 3121 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3122 3123 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3124 static int mbedtls_ecp_gen_privkey_sw( 3125 const mbedtls_mpi *N, mbedtls_mpi *d, 3126 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 3127 { 3128 int ret = mbedtls_mpi_random(d, 1, N, f_rng, p_rng); 3129 switch (ret) { 3130 case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: 3131 return MBEDTLS_ERR_ECP_RANDOM_FAILED; 3132 default: 3133 return ret; 3134 } 3135 } 3136 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3137 3138 /* 3139 * Generate a private key 3140 */ 3141 int mbedtls_ecp_gen_privkey(const mbedtls_ecp_group *grp, 3142 mbedtls_mpi *d, 3143 int (*f_rng)(void *, unsigned char *, size_t), 3144 void *p_rng) 3145 { 3146 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3147 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3148 return mbedtls_ecp_gen_privkey_mx(grp->nbits, d, f_rng, p_rng); 3149 } 3150 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3151 3152 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3153 if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3154 return mbedtls_ecp_gen_privkey_sw(&grp->N, d, f_rng, p_rng); 3155 } 3156 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3157 3158 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3159 } 3160 3161 #if defined(MBEDTLS_ECP_C) 3162 /* 3163 * Generate a keypair with configurable base point 3164 */ 3165 int mbedtls_ecp_gen_keypair_base(mbedtls_ecp_group *grp, 3166 const mbedtls_ecp_point *G, 3167 mbedtls_mpi *d, mbedtls_ecp_point *Q, 3168 int (*f_rng)(void *, unsigned char *, size_t), 3169 void *p_rng) 3170 { 3171 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3172 MBEDTLS_MPI_CHK(mbedtls_ecp_gen_privkey(grp, d, f_rng, p_rng)); 3173 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, Q, d, G, f_rng, p_rng)); 3174 3175 cleanup: 3176 return ret; 3177 } 3178 3179 /* 3180 * Generate key pair, wrapper for conventional base point 3181 */ 3182 int mbedtls_ecp_gen_keypair(mbedtls_ecp_group *grp, 3183 mbedtls_mpi *d, mbedtls_ecp_point *Q, 3184 int (*f_rng)(void *, unsigned char *, size_t), 3185 void *p_rng) 3186 { 3187 return mbedtls_ecp_gen_keypair_base(grp, &grp->G, d, Q, f_rng, p_rng); 3188 } 3189 3190 /* 3191 * Generate a keypair, prettier wrapper 3192 */ 3193 int mbedtls_ecp_gen_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 3194 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 3195 { 3196 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3197 if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) { 3198 return ret; 3199 } 3200 3201 return mbedtls_ecp_gen_keypair(&key->grp, &key->d, &key->Q, f_rng, p_rng); 3202 } 3203 #endif /* MBEDTLS_ECP_C */ 3204 3205 int mbedtls_ecp_set_public_key(mbedtls_ecp_group_id grp_id, 3206 mbedtls_ecp_keypair *key, 3207 const mbedtls_ecp_point *Q) 3208 { 3209 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3210 3211 if (key->grp.id == MBEDTLS_ECP_DP_NONE) { 3212 /* Group not set yet */ 3213 if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) { 3214 return ret; 3215 } 3216 } else if (key->grp.id != grp_id) { 3217 /* Group mismatch */ 3218 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3219 } 3220 return mbedtls_ecp_copy(&key->Q, Q); 3221 } 3222 3223 3224 #define ECP_CURVE25519_KEY_SIZE 32 3225 #define ECP_CURVE448_KEY_SIZE 56 3226 /* 3227 * Read a private key. 3228 */ 3229 int mbedtls_ecp_read_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 3230 const unsigned char *buf, size_t buflen) 3231 { 3232 int ret = 0; 3233 3234 if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) { 3235 return ret; 3236 } 3237 3238 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; 3239 3240 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3241 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3242 /* 3243 * Mask the key as mandated by RFC7748 for Curve25519 and Curve448. 3244 */ 3245 if (grp_id == MBEDTLS_ECP_DP_CURVE25519) { 3246 if (buflen != ECP_CURVE25519_KEY_SIZE) { 3247 return MBEDTLS_ERR_ECP_INVALID_KEY; 3248 } 3249 3250 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&key->d, buf, buflen)); 3251 3252 /* Set the three least significant bits to 0 */ 3253 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 0, 0)); 3254 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 1, 0)); 3255 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 2, 0)); 3256 3257 /* Set the most significant bit to 0 */ 3258 MBEDTLS_MPI_CHK( 3259 mbedtls_mpi_set_bit(&key->d, 3260 ECP_CURVE25519_KEY_SIZE * 8 - 1, 0) 3261 ); 3262 3263 /* Set the second most significant bit to 1 */ 3264 MBEDTLS_MPI_CHK( 3265 mbedtls_mpi_set_bit(&key->d, 3266 ECP_CURVE25519_KEY_SIZE * 8 - 2, 1) 3267 ); 3268 } else if (grp_id == MBEDTLS_ECP_DP_CURVE448) { 3269 if (buflen != ECP_CURVE448_KEY_SIZE) { 3270 return MBEDTLS_ERR_ECP_INVALID_KEY; 3271 } 3272 3273 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&key->d, buf, buflen)); 3274 3275 /* Set the two least significant bits to 0 */ 3276 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 0, 0)); 3277 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 1, 0)); 3278 3279 /* Set the most significant bit to 1 */ 3280 MBEDTLS_MPI_CHK( 3281 mbedtls_mpi_set_bit(&key->d, 3282 ECP_CURVE448_KEY_SIZE * 8 - 1, 1) 3283 ); 3284 } 3285 } 3286 #endif 3287 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3288 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3289 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&key->d, buf, buflen)); 3290 } 3291 #endif 3292 3293 if (ret == 0) { 3294 MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(&key->grp, &key->d)); 3295 } 3296 3297 cleanup: 3298 3299 if (ret != 0) { 3300 mbedtls_mpi_free(&key->d); 3301 } 3302 3303 return ret; 3304 } 3305 3306 /* 3307 * Write a private key. 3308 */ 3309 #if !defined MBEDTLS_DEPRECATED_REMOVED 3310 int mbedtls_ecp_write_key(mbedtls_ecp_keypair *key, 3311 unsigned char *buf, size_t buflen) 3312 { 3313 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3314 3315 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3316 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3317 if (key->grp.id == MBEDTLS_ECP_DP_CURVE25519) { 3318 if (buflen < ECP_CURVE25519_KEY_SIZE) { 3319 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 3320 } 3321 3322 } else if (key->grp.id == MBEDTLS_ECP_DP_CURVE448) { 3323 if (buflen < ECP_CURVE448_KEY_SIZE) { 3324 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 3325 } 3326 } 3327 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&key->d, buf, buflen)); 3328 } 3329 #endif 3330 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3331 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3332 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&key->d, buf, buflen)); 3333 } 3334 3335 #endif 3336 cleanup: 3337 3338 return ret; 3339 } 3340 #endif /* MBEDTLS_DEPRECATED_REMOVED */ 3341 3342 int mbedtls_ecp_write_key_ext(const mbedtls_ecp_keypair *key, 3343 size_t *olen, unsigned char *buf, size_t buflen) 3344 { 3345 size_t len = (key->grp.nbits + 7) / 8; 3346 if (len > buflen) { 3347 /* For robustness, ensure *olen <= buflen even on error. */ 3348 *olen = 0; 3349 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; 3350 } 3351 *olen = len; 3352 3353 /* Private key not set */ 3354 if (key->d.n == 0) { 3355 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3356 } 3357 3358 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3359 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) { 3360 return mbedtls_mpi_write_binary_le(&key->d, buf, len); 3361 } 3362 #endif 3363 3364 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3365 if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { 3366 return mbedtls_mpi_write_binary(&key->d, buf, len); 3367 } 3368 #endif 3369 3370 /* Private key set but no recognized curve type? This shouldn't happen. */ 3371 return MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3372 } 3373 3374 /* 3375 * Write a public key. 3376 */ 3377 int mbedtls_ecp_write_public_key(const mbedtls_ecp_keypair *key, 3378 int format, size_t *olen, 3379 unsigned char *buf, size_t buflen) 3380 { 3381 return mbedtls_ecp_point_write_binary(&key->grp, &key->Q, 3382 format, olen, buf, buflen); 3383 } 3384 3385 3386 #if defined(MBEDTLS_ECP_C) 3387 /* 3388 * Check a public-private key pair 3389 */ 3390 int mbedtls_ecp_check_pub_priv( 3391 const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv, 3392 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) 3393 { 3394 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3395 mbedtls_ecp_point Q; 3396 mbedtls_ecp_group grp; 3397 if (pub->grp.id == MBEDTLS_ECP_DP_NONE || 3398 pub->grp.id != prv->grp.id || 3399 mbedtls_mpi_cmp_mpi(&pub->Q.X, &prv->Q.X) || 3400 mbedtls_mpi_cmp_mpi(&pub->Q.Y, &prv->Q.Y) || 3401 mbedtls_mpi_cmp_mpi(&pub->Q.Z, &prv->Q.Z)) { 3402 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3403 } 3404 3405 mbedtls_ecp_point_init(&Q); 3406 mbedtls_ecp_group_init(&grp); 3407 3408 /* mbedtls_ecp_mul() needs a non-const group... */ 3409 mbedtls_ecp_group_copy(&grp, &prv->grp); 3410 3411 /* Also checks d is valid */ 3412 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &Q, &prv->d, &prv->grp.G, f_rng, p_rng)); 3413 3414 if (mbedtls_mpi_cmp_mpi(&Q.X, &prv->Q.X) || 3415 mbedtls_mpi_cmp_mpi(&Q.Y, &prv->Q.Y) || 3416 mbedtls_mpi_cmp_mpi(&Q.Z, &prv->Q.Z)) { 3417 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; 3418 goto cleanup; 3419 } 3420 3421 cleanup: 3422 mbedtls_ecp_point_free(&Q); 3423 mbedtls_ecp_group_free(&grp); 3424 3425 return ret; 3426 } 3427 3428 int mbedtls_ecp_keypair_calc_public(mbedtls_ecp_keypair *key, 3429 int (*f_rng)(void *, unsigned char *, size_t), 3430 void *p_rng) 3431 { 3432 return mbedtls_ecp_mul(&key->grp, &key->Q, &key->d, &key->grp.G, 3433 f_rng, p_rng); 3434 } 3435 #endif /* MBEDTLS_ECP_C */ 3436 3437 mbedtls_ecp_group_id mbedtls_ecp_keypair_get_group_id( 3438 const mbedtls_ecp_keypair *key) 3439 { 3440 return key->grp.id; 3441 } 3442 3443 /* 3444 * Export generic key-pair parameters. 3445 */ 3446 int mbedtls_ecp_export(const mbedtls_ecp_keypair *key, mbedtls_ecp_group *grp, 3447 mbedtls_mpi *d, mbedtls_ecp_point *Q) 3448 { 3449 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3450 3451 if (grp != NULL && (ret = mbedtls_ecp_group_copy(grp, &key->grp)) != 0) { 3452 return ret; 3453 } 3454 3455 if (d != NULL && (ret = mbedtls_mpi_copy(d, &key->d)) != 0) { 3456 return ret; 3457 } 3458 3459 if (Q != NULL && (ret = mbedtls_ecp_copy(Q, &key->Q)) != 0) { 3460 return ret; 3461 } 3462 3463 return 0; 3464 } 3465 3466 #if defined(MBEDTLS_SELF_TEST) 3467 3468 #if defined(MBEDTLS_ECP_C) 3469 /* 3470 * PRNG for test - !!!INSECURE NEVER USE IN PRODUCTION!!! 3471 * 3472 * This is the linear congruential generator from numerical recipes, 3473 * except we only use the low byte as the output. See 3474 * https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use 3475 */ 3476 static int self_test_rng(void *ctx, unsigned char *out, size_t len) 3477 { 3478 static uint32_t state = 42; 3479 3480 (void) ctx; 3481 3482 for (size_t i = 0; i < len; i++) { 3483 state = state * 1664525u + 1013904223u; 3484 out[i] = (unsigned char) state; 3485 } 3486 3487 return 0; 3488 } 3489 3490 /* Adjust the exponent to be a valid private point for the specified curve. 3491 * This is sometimes necessary because we use a single set of exponents 3492 * for all curves but the validity of values depends on the curve. */ 3493 static int self_test_adjust_exponent(const mbedtls_ecp_group *grp, 3494 mbedtls_mpi *m) 3495 { 3496 int ret = 0; 3497 switch (grp->id) { 3498 /* If Curve25519 is available, then that's what we use for the 3499 * Montgomery test, so we don't need the adjustment code. */ 3500 #if !defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 3501 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 3502 case MBEDTLS_ECP_DP_CURVE448: 3503 /* Move highest bit from 254 to N-1. Setting bit N-1 is 3504 * necessary to enforce the highest-bit-set constraint. */ 3505 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, 254, 0)); 3506 MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, grp->nbits, 1)); 3507 /* Copy second-highest bit from 253 to N-2. This is not 3508 * necessary but improves the test variety a bit. */ 3509 MBEDTLS_MPI_CHK( 3510 mbedtls_mpi_set_bit(m, grp->nbits - 1, 3511 mbedtls_mpi_get_bit(m, 253))); 3512 break; 3513 #endif 3514 #endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */ 3515 default: 3516 /* Non-Montgomery curves and Curve25519 need no adjustment. */ 3517 (void) grp; 3518 (void) m; 3519 goto cleanup; 3520 } 3521 cleanup: 3522 return ret; 3523 } 3524 3525 /* Calculate R = m.P for each m in exponents. Check that the number of 3526 * basic operations doesn't depend on the value of m. */ 3527 static int self_test_point(int verbose, 3528 mbedtls_ecp_group *grp, 3529 mbedtls_ecp_point *R, 3530 mbedtls_mpi *m, 3531 const mbedtls_ecp_point *P, 3532 const char *const *exponents, 3533 size_t n_exponents) 3534 { 3535 int ret = 0; 3536 size_t i = 0; 3537 unsigned long add_c_prev, dbl_c_prev, mul_c_prev; 3538 add_count = 0; 3539 dbl_count = 0; 3540 mul_count = 0; 3541 3542 MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(m, 16, exponents[0])); 3543 MBEDTLS_MPI_CHK(self_test_adjust_exponent(grp, m)); 3544 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, R, m, P, self_test_rng, NULL)); 3545 3546 for (i = 1; i < n_exponents; i++) { 3547 add_c_prev = add_count; 3548 dbl_c_prev = dbl_count; 3549 mul_c_prev = mul_count; 3550 add_count = 0; 3551 dbl_count = 0; 3552 mul_count = 0; 3553 3554 MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(m, 16, exponents[i])); 3555 MBEDTLS_MPI_CHK(self_test_adjust_exponent(grp, m)); 3556 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, R, m, P, self_test_rng, NULL)); 3557 3558 if (add_count != add_c_prev || 3559 dbl_count != dbl_c_prev || 3560 mul_count != mul_c_prev) { 3561 ret = 1; 3562 break; 3563 } 3564 } 3565 3566 cleanup: 3567 if (verbose != 0) { 3568 if (ret != 0) { 3569 mbedtls_printf("failed (%u)\n", (unsigned int) i); 3570 } else { 3571 mbedtls_printf("passed\n"); 3572 } 3573 } 3574 return ret; 3575 } 3576 #endif /* MBEDTLS_ECP_C */ 3577 3578 /* 3579 * Checkup routine 3580 */ 3581 int mbedtls_ecp_self_test(int verbose) 3582 { 3583 #if defined(MBEDTLS_ECP_C) 3584 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 3585 mbedtls_ecp_group grp; 3586 mbedtls_ecp_point R, P; 3587 mbedtls_mpi m; 3588 3589 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3590 /* Exponents especially adapted for secp192k1, which has the lowest 3591 * order n of all supported curves (secp192r1 is in a slightly larger 3592 * field but the order of its base point is slightly smaller). */ 3593 const char *sw_exponents[] = 3594 { 3595 "000000000000000000000000000000000000000000000001", /* one */ 3596 "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */ 3597 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */ 3598 "400000000000000000000000000000000000000000000000", /* one and zeros */ 3599 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */ 3600 "555555555555555555555555555555555555555555555555", /* 101010... */ 3601 }; 3602 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3603 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3604 const char *m_exponents[] = 3605 { 3606 /* Valid private values for Curve25519. In a build with Curve448 3607 * but not Curve25519, they will be adjusted in 3608 * self_test_adjust_exponent(). */ 3609 "4000000000000000000000000000000000000000000000000000000000000000", 3610 "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30", 3611 "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8", 3612 "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460", 3613 "5555555555555555555555555555555555555555555555555555555555555550", 3614 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8", 3615 }; 3616 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3617 3618 mbedtls_ecp_group_init(&grp); 3619 mbedtls_ecp_point_init(&R); 3620 mbedtls_ecp_point_init(&P); 3621 mbedtls_mpi_init(&m); 3622 3623 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 3624 /* Use secp192r1 if available, or any available curve */ 3625 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 3626 MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_SECP192R1)); 3627 #else 3628 MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, mbedtls_ecp_curve_list()->grp_id)); 3629 #endif 3630 3631 if (verbose != 0) { 3632 mbedtls_printf(" ECP SW test #1 (constant op_count, base point G): "); 3633 } 3634 /* Do a dummy multiplication first to trigger precomputation */ 3635 MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&m, 2)); 3636 MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &P, &m, &grp.G, self_test_rng, NULL)); 3637 ret = self_test_point(verbose, 3638 &grp, &R, &m, &grp.G, 3639 sw_exponents, 3640 sizeof(sw_exponents) / sizeof(sw_exponents[0])); 3641 if (ret != 0) { 3642 goto cleanup; 3643 } 3644 3645 if (verbose != 0) { 3646 mbedtls_printf(" ECP SW test #2 (constant op_count, other point): "); 3647 } 3648 /* We computed P = 2G last time, use it */ 3649 ret = self_test_point(verbose, 3650 &grp, &R, &m, &P, 3651 sw_exponents, 3652 sizeof(sw_exponents) / sizeof(sw_exponents[0])); 3653 if (ret != 0) { 3654 goto cleanup; 3655 } 3656 3657 mbedtls_ecp_group_free(&grp); 3658 mbedtls_ecp_point_free(&R); 3659 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 3660 3661 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) 3662 if (verbose != 0) { 3663 mbedtls_printf(" ECP Montgomery test (constant op_count): "); 3664 } 3665 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 3666 MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE25519)); 3667 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 3668 MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE448)); 3669 #else 3670 #error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test" 3671 #endif 3672 ret = self_test_point(verbose, 3673 &grp, &R, &m, &grp.G, 3674 m_exponents, 3675 sizeof(m_exponents) / sizeof(m_exponents[0])); 3676 if (ret != 0) { 3677 goto cleanup; 3678 } 3679 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ 3680 3681 cleanup: 3682 3683 if (ret < 0 && verbose != 0) { 3684 mbedtls_printf("Unexpected error, return code = %08X\n", (unsigned int) ret); 3685 } 3686 3687 mbedtls_ecp_group_free(&grp); 3688 mbedtls_ecp_point_free(&R); 3689 mbedtls_ecp_point_free(&P); 3690 mbedtls_mpi_free(&m); 3691 3692 if (verbose != 0) { 3693 mbedtls_printf("\n"); 3694 } 3695 3696 return ret; 3697 #else /* MBEDTLS_ECP_C */ 3698 (void) verbose; 3699 return 0; 3700 #endif /* MBEDTLS_ECP_C */ 3701 } 3702 3703 #endif /* MBEDTLS_SELF_TEST */ 3704 3705 #endif /* !MBEDTLS_ECP_ALT */ 3706 3707 #endif /* MBEDTLS_ECP_LIGHT */ 3708