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