| /* |
| * Elliptic curves over GF(p): generic functions |
| * |
| * Copyright The Mbed TLS Contributors |
| * SPDX-License-Identifier: Apache-2.0 |
| * |
| * Licensed under the Apache License, Version 2.0 (the "License"); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| /* |
| * References: |
| * |
| * SEC1 http://www.secg.org/index.php?action=secg,docs_secg |
| * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone |
| * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf |
| * RFC 4492 for the related TLS structures and constants |
| * RFC 7748 for the Curve448 and Curve25519 curve definitions |
| * |
| * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf |
| * |
| * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis |
| * for elliptic curve cryptosystems. In : Cryptographic Hardware and |
| * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302. |
| * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25> |
| * |
| * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to |
| * render ECC resistant against Side Channel Attacks. IACR Cryptology |
| * ePrint Archive, 2004, vol. 2004, p. 342. |
| * <http://eprint.iacr.org/2004/342.pdf> |
| */ |
| |
| #include "../common.h" |
| |
| /** |
| * \brief Function level alternative implementation. |
| * |
| * The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to |
| * replace certain functions in this module. The alternative implementations are |
| * typically hardware accelerators and need to activate the hardware before the |
| * computation starts and deactivate it after it finishes. The |
| * mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve |
| * this purpose. |
| * |
| * To preserve the correct functionality the following conditions must hold: |
| * |
| * - The alternative implementation must be activated by |
| * mbedtls_internal_ecp_init() before any of the replaceable functions is |
| * called. |
| * - mbedtls_internal_ecp_free() must \b only be called when the alternative |
| * implementation is activated. |
| * - mbedtls_internal_ecp_init() must \b not be called when the alternative |
| * implementation is activated. |
| * - Public functions must not return while the alternative implementation is |
| * activated. |
| * - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and |
| * before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) ) |
| * \endcode ensures that the alternative implementation supports the current |
| * group. |
| */ |
| #if defined(MBEDTLS_ECP_INTERNAL_ALT) |
| #endif |
| |
| #if defined(MBEDTLS_ECP_C) |
| |
| #include "mbedtls/ecp.h" |
| #include "mbedtls/error.h" |
| #include "mbedtls/platform_util.h" |
| #include "mbedtls/threading.h" |
| |
| #include "bn_mul.h" |
| #include "ecp_invasive.h" |
| |
| #include <string.h> |
| |
| #if defined(MBEDTLS_ECP_ALT) |
| |
| #include "pke.h" |
| |
| /* HW accelerator functionality */ |
| extern int ecp_alt_b91_backend_check_pubkey(const mbedtls_ecp_group * grp, const mbedtls_ecp_point * pt); |
| extern int ecp_alt_b91_backend_mul(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, |
| const mbedtls_ecp_point * P); |
| extern int ecp_alt_b91_backend_muladd(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, |
| const mbedtls_ecp_point * P, const mbedtls_mpi * n, const mbedtls_ecp_point * Q); |
| /* self test functionality */ |
| #if defined(MBEDTLS_SELF_TEST) |
| extern const int __ecp_alt_b91_skip_internal_self_tests; |
| extern int ecp_alt_b91_backend_test(int verbose); |
| #endif /* MBEDTLS_SELF_TEST */ |
| |
| /* Parameter validation macros based on platform_util.h */ |
| #define ECP_VALIDATE_RET(cond) MBEDTLS_INTERNAL_VALIDATE_RET(cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA) |
| #define ECP_VALIDATE(cond) MBEDTLS_INTERNAL_VALIDATE(cond) |
| |
| #if defined(MBEDTLS_PLATFORM_C) |
| #include "mbedtls/platform.h" |
| #else |
| #include <stdio.h> |
| #include <stdlib.h> |
| #define mbedtls_printf printf |
| #define mbedtls_calloc calloc |
| #define mbedtls_free free |
| #endif |
| |
| #include "ecp_internal_alt.h" |
| |
| #if (defined(__ARMCC_VERSION) || defined(_MSC_VER)) && !defined(inline) && !defined(__cplusplus) |
| #define inline __inline |
| #endif |
| |
| #if defined(MBEDTLS_SELF_TEST) |
| /* |
| * Counts of point addition and doubling, and field multiplications. |
| * Used to test resistance of point multiplication to simple timing attacks. |
| */ |
| static unsigned long add_count, dbl_count, mul_count; |
| #endif |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| /* |
| * Maximum number of "basic operations" to be done in a row. |
| * |
| * Default value 0 means that ECC operations will not yield. |
| * Note that regardless of the value of ecp_max_ops, always at |
| * least one step is performed before yielding. |
| * |
| * Setting ecp_max_ops=1 can be suitable for testing purposes |
| * as it will interrupt computation at all possible points. |
| */ |
| static unsigned ecp_max_ops = 0; |
| |
| /* |
| * Set ecp_max_ops |
| */ |
| void mbedtls_ecp_set_max_ops(unsigned max_ops) |
| { |
| ecp_max_ops = max_ops; |
| } |
| |
| /* |
| * Check if restart is enabled |
| */ |
| int mbedtls_ecp_restart_is_enabled(void) |
| { |
| return (ecp_max_ops != 0); |
| } |
| |
| /* |
| * Restart sub-context for ecp_mul_comb() |
| */ |
| struct mbedtls_ecp_restart_mul |
| { |
| mbedtls_ecp_point R; /* current intermediate result */ |
| size_t i; /* current index in various loops, 0 outside */ |
| mbedtls_ecp_point * T; /* table for precomputed points */ |
| unsigned char T_size; /* number of points in table T */ |
| enum |
| { /* what were we doing last time we returned? */ |
| ecp_rsm_init = 0, /* nothing so far, dummy initial state */ |
| ecp_rsm_pre_dbl, /* precompute 2^n multiples */ |
| ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */ |
| ecp_rsm_pre_add, /* precompute remaining points by adding */ |
| ecp_rsm_pre_norm_add, /* normalize all precomputed points */ |
| ecp_rsm_comb_core, /* ecp_mul_comb_core() */ |
| ecp_rsm_final_norm, /* do the final normalization */ |
| } state; |
| }; |
| |
| /* |
| * Init restart_mul sub-context |
| */ |
| static void ecp_restart_rsm_init(mbedtls_ecp_restart_mul_ctx * ctx) |
| { |
| mbedtls_ecp_point_init(&ctx->R); |
| ctx->i = 0; |
| ctx->T = NULL; |
| ctx->T_size = 0; |
| ctx->state = ecp_rsm_init; |
| } |
| |
| /* |
| * Free the components of a restart_mul sub-context |
| */ |
| static void ecp_restart_rsm_free(mbedtls_ecp_restart_mul_ctx * ctx) |
| { |
| unsigned char i; |
| |
| if (ctx == NULL) |
| return; |
| |
| mbedtls_ecp_point_free(&ctx->R); |
| |
| if (ctx->T != NULL) |
| { |
| for (i = 0; i < ctx->T_size; i++) |
| mbedtls_ecp_point_free(ctx->T + i); |
| mbedtls_free(ctx->T); |
| } |
| |
| ecp_restart_rsm_init(ctx); |
| } |
| |
| /* |
| * Restart context for ecp_muladd() |
| */ |
| struct mbedtls_ecp_restart_muladd |
| { |
| mbedtls_ecp_point mP; /* mP value */ |
| mbedtls_ecp_point R; /* R intermediate result */ |
| enum |
| { /* what should we do next? */ |
| ecp_rsma_mul1 = 0, /* first multiplication */ |
| ecp_rsma_mul2, /* second multiplication */ |
| ecp_rsma_add, /* addition */ |
| ecp_rsma_norm, /* normalization */ |
| } state; |
| }; |
| |
| /* |
| * Init restart_muladd sub-context |
| */ |
| static void ecp_restart_ma_init(mbedtls_ecp_restart_muladd_ctx * ctx) |
| { |
| mbedtls_ecp_point_init(&ctx->mP); |
| mbedtls_ecp_point_init(&ctx->R); |
| ctx->state = ecp_rsma_mul1; |
| } |
| |
| /* |
| * Free the components of a restart_muladd sub-context |
| */ |
| static void ecp_restart_ma_free(mbedtls_ecp_restart_muladd_ctx * ctx) |
| { |
| if (ctx == NULL) |
| return; |
| |
| mbedtls_ecp_point_free(&ctx->mP); |
| mbedtls_ecp_point_free(&ctx->R); |
| |
| ecp_restart_ma_init(ctx); |
| } |
| |
| /* |
| * Initialize a restart context |
| */ |
| void mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx * ctx) |
| { |
| ECP_VALIDATE(ctx != NULL); |
| ctx->ops_done = 0; |
| ctx->depth = 0; |
| ctx->rsm = NULL; |
| ctx->ma = NULL; |
| } |
| |
| /* |
| * Free the components of a restart context |
| */ |
| void mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx * ctx) |
| { |
| if (ctx == NULL) |
| return; |
| |
| ecp_restart_rsm_free(ctx->rsm); |
| mbedtls_free(ctx->rsm); |
| |
| ecp_restart_ma_free(ctx->ma); |
| mbedtls_free(ctx->ma); |
| |
| mbedtls_ecp_restart_init(ctx); |
| } |
| |
| /* |
| * Check if we can do the next step |
| */ |
| int mbedtls_ecp_check_budget(const mbedtls_ecp_group * grp, mbedtls_ecp_restart_ctx * rs_ctx, unsigned ops) |
| { |
| ECP_VALIDATE_RET(grp != NULL); |
| |
| if (rs_ctx != NULL && ecp_max_ops != 0) |
| { |
| /* scale depending on curve size: the chosen reference is 256-bit, |
| * and multiplication is quadratic. Round to the closest integer. */ |
| if (grp->pbits >= 512) |
| ops *= 4; |
| else if (grp->pbits >= 384) |
| ops *= 2; |
| |
| /* Avoid infinite loops: always allow first step. |
| * Because of that, however, it's not generally true |
| * that ops_done <= ecp_max_ops, so the check |
| * ops_done > ecp_max_ops below is mandatory. */ |
| if ((rs_ctx->ops_done != 0) && (rs_ctx->ops_done > ecp_max_ops || ops > ecp_max_ops - rs_ctx->ops_done)) |
| { |
| return (MBEDTLS_ERR_ECP_IN_PROGRESS); |
| } |
| |
| /* update running count */ |
| rs_ctx->ops_done += ops; |
| } |
| |
| return (0); |
| } |
| |
| /* Call this when entering a function that needs its own sub-context */ |
| #define ECP_RS_ENTER(SUB) \ |
| do \ |
| { \ |
| /* reset ops count for this call if top-level */ \ |
| if (rs_ctx != NULL && rs_ctx->depth++ == 0) \ |
| rs_ctx->ops_done = 0; \ |
| \ |
| /* set up our own sub-context if needed */ \ |
| if (mbedtls_ecp_restart_is_enabled() && rs_ctx != NULL && rs_ctx->SUB == NULL) \ |
| { \ |
| rs_ctx->SUB = mbedtls_calloc(1, sizeof(*rs_ctx->SUB)); \ |
| if (rs_ctx->SUB == NULL) \ |
| return (MBEDTLS_ERR_ECP_ALLOC_FAILED); \ |
| \ |
| ecp_restart_##SUB##_init(rs_ctx->SUB); \ |
| } \ |
| } while (0) |
| |
| /* Call this when leaving a function that needs its own sub-context */ |
| #define ECP_RS_LEAVE(SUB) \ |
| do \ |
| { \ |
| /* clear our sub-context when not in progress (done or error) */ \ |
| if (rs_ctx != NULL && rs_ctx->SUB != NULL && ret != MBEDTLS_ERR_ECP_IN_PROGRESS) \ |
| { \ |
| ecp_restart_##SUB##_free(rs_ctx->SUB); \ |
| mbedtls_free(rs_ctx->SUB); \ |
| rs_ctx->SUB = NULL; \ |
| } \ |
| \ |
| if (rs_ctx != NULL) \ |
| rs_ctx->depth--; \ |
| } while (0) |
| |
| #else /* MBEDTLS_ECP_RESTARTABLE */ |
| |
| #define ECP_RS_ENTER(sub) (void) rs_ctx; |
| #define ECP_RS_LEAVE(sub) (void) rs_ctx; |
| |
| #endif /* MBEDTLS_ECP_RESTARTABLE */ |
| |
| /* |
| * List of supported curves: |
| * - internal ID |
| * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7) |
| * - size in bits |
| * - readable name |
| * |
| * Curves are listed in order: largest curves first, and for a given size, |
| * fastest curves first. |
| * |
| * Reminder: update profiles in x509_crt.c and ssl_tls.c when adding a new curve! |
| */ |
| static const mbedtls_ecp_curve_info ecp_supported_curves[] = { |
| #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
| { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) |
| { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
| { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) |
| { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
| { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
| { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) |
| { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
| { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
| { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
| { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
| { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| { MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" }, |
| #endif |
| #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
| { MBEDTLS_ECP_DP_CURVE448, 30, 448, "x448" }, |
| #endif |
| { MBEDTLS_ECP_DP_NONE, 0, 0, NULL }, |
| }; |
| |
| #define ECP_NB_CURVES sizeof(ecp_supported_curves) / sizeof(ecp_supported_curves[0]) |
| |
| static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES]; |
| |
| /* |
| * List of supported curves and associated info |
| */ |
| const mbedtls_ecp_curve_info * mbedtls_ecp_curve_list(void) |
| { |
| return (ecp_supported_curves); |
| } |
| |
| /* |
| * List of supported curves, group ID only |
| */ |
| const mbedtls_ecp_group_id * mbedtls_ecp_grp_id_list(void) |
| { |
| static int init_done = 0; |
| |
| if (!init_done) |
| { |
| size_t i = 0; |
| const mbedtls_ecp_curve_info * curve_info; |
| |
| for (curve_info = mbedtls_ecp_curve_list(); curve_info->grp_id != MBEDTLS_ECP_DP_NONE; curve_info++) |
| { |
| ecp_supported_grp_id[i++] = curve_info->grp_id; |
| } |
| ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE; |
| |
| init_done = 1; |
| } |
| |
| return (ecp_supported_grp_id); |
| } |
| |
| /* |
| * Get the curve info for the internal identifier |
| */ |
| const mbedtls_ecp_curve_info * mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id) |
| { |
| const mbedtls_ecp_curve_info * curve_info; |
| |
| for (curve_info = mbedtls_ecp_curve_list(); curve_info->grp_id != MBEDTLS_ECP_DP_NONE; curve_info++) |
| { |
| if (curve_info->grp_id == grp_id) |
| return (curve_info); |
| } |
| |
| return (NULL); |
| } |
| |
| /* |
| * Get the curve info from the TLS identifier |
| */ |
| const mbedtls_ecp_curve_info * mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id) |
| { |
| const mbedtls_ecp_curve_info * curve_info; |
| |
| for (curve_info = mbedtls_ecp_curve_list(); curve_info->grp_id != MBEDTLS_ECP_DP_NONE; curve_info++) |
| { |
| if (curve_info->tls_id == tls_id) |
| return (curve_info); |
| } |
| |
| return (NULL); |
| } |
| |
| /* |
| * Get the curve info from the name |
| */ |
| const mbedtls_ecp_curve_info * mbedtls_ecp_curve_info_from_name(const char * name) |
| { |
| const mbedtls_ecp_curve_info * curve_info; |
| |
| if (name == NULL) |
| return (NULL); |
| |
| for (curve_info = mbedtls_ecp_curve_list(); curve_info->grp_id != MBEDTLS_ECP_DP_NONE; curve_info++) |
| { |
| if (strcmp(curve_info->name, name) == 0) |
| return (curve_info); |
| } |
| |
| return (NULL); |
| } |
| |
| /* |
| * Get the type of a curve |
| */ |
| mbedtls_ecp_curve_type mbedtls_ecp_get_type(const mbedtls_ecp_group * grp) |
| { |
| if (grp->G.X.p == NULL) |
| return (MBEDTLS_ECP_TYPE_NONE); |
| |
| if (grp->G.Y.p == NULL) |
| return (MBEDTLS_ECP_TYPE_MONTGOMERY); |
| else |
| return (MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS); |
| } |
| |
| /* |
| * Initialize (the components of) a point |
| */ |
| void mbedtls_ecp_point_init(mbedtls_ecp_point * pt) |
| { |
| ECP_VALIDATE(pt != NULL); |
| |
| mbedtls_mpi_init(&pt->X); |
| mbedtls_mpi_init(&pt->Y); |
| mbedtls_mpi_init(&pt->Z); |
| } |
| |
| /* |
| * Initialize (the components of) a group |
| */ |
| void mbedtls_ecp_group_init(mbedtls_ecp_group * grp) |
| { |
| ECP_VALIDATE(grp != NULL); |
| |
| grp->id = MBEDTLS_ECP_DP_NONE; |
| mbedtls_mpi_init(&grp->P); |
| mbedtls_mpi_init(&grp->A); |
| mbedtls_mpi_init(&grp->B); |
| mbedtls_ecp_point_init(&grp->G); |
| mbedtls_mpi_init(&grp->N); |
| grp->pbits = 0; |
| grp->nbits = 0; |
| grp->h = 0; |
| grp->modp = NULL; |
| grp->t_pre = NULL; |
| grp->t_post = NULL; |
| grp->t_data = NULL; |
| grp->T = NULL; |
| grp->T_size = 0; |
| } |
| |
| /* |
| * Initialize (the components of) a key pair |
| */ |
| void mbedtls_ecp_keypair_init(mbedtls_ecp_keypair * key) |
| { |
| ECP_VALIDATE(key != NULL); |
| |
| mbedtls_ecp_group_init(&key->grp); |
| mbedtls_mpi_init(&key->d); |
| mbedtls_ecp_point_init(&key->Q); |
| } |
| |
| /* |
| * Unallocate (the components of) a point |
| */ |
| void mbedtls_ecp_point_free(mbedtls_ecp_point * pt) |
| { |
| if (pt == NULL) |
| return; |
| |
| mbedtls_mpi_free(&(pt->X)); |
| mbedtls_mpi_free(&(pt->Y)); |
| mbedtls_mpi_free(&(pt->Z)); |
| } |
| |
| /* |
| * Check that the comb table (grp->T) is static initialized. |
| */ |
| static int ecp_group_is_static_comb_table(const mbedtls_ecp_group * grp) |
| { |
| #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 |
| return grp->T != NULL && grp->T_size == 0; |
| #else |
| (void) grp; |
| return 0; |
| #endif |
| } |
| |
| /* |
| * Unallocate (the components of) a group |
| */ |
| void mbedtls_ecp_group_free(mbedtls_ecp_group * grp) |
| { |
| size_t i; |
| |
| if (grp == NULL) |
| return; |
| |
| if (grp->h != 1) |
| { |
| mbedtls_mpi_free(&grp->P); |
| mbedtls_mpi_free(&grp->A); |
| mbedtls_mpi_free(&grp->B); |
| mbedtls_ecp_point_free(&grp->G); |
| mbedtls_mpi_free(&grp->N); |
| } |
| |
| if (!ecp_group_is_static_comb_table(grp) && grp->T != NULL) |
| { |
| for (i = 0; i < grp->T_size; i++) |
| mbedtls_ecp_point_free(&grp->T[i]); |
| mbedtls_free(grp->T); |
| } |
| |
| mbedtls_platform_zeroize(grp, sizeof(mbedtls_ecp_group)); |
| } |
| |
| /* |
| * Unallocate (the components of) a key pair |
| */ |
| void mbedtls_ecp_keypair_free(mbedtls_ecp_keypair * key) |
| { |
| if (key == NULL) |
| return; |
| |
| mbedtls_ecp_group_free(&key->grp); |
| mbedtls_mpi_free(&key->d); |
| mbedtls_ecp_point_free(&key->Q); |
| } |
| |
| /* |
| * Copy the contents of a point |
| */ |
| int mbedtls_ecp_copy(mbedtls_ecp_point * P, const mbedtls_ecp_point * Q) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| ECP_VALIDATE_RET(P != NULL); |
| ECP_VALIDATE_RET(Q != NULL); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->X, &Q->X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Y, &Q->Y)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Z, &Q->Z)); |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Copy the contents of a group object |
| */ |
| int mbedtls_ecp_group_copy(mbedtls_ecp_group * dst, const mbedtls_ecp_group * src) |
| { |
| ECP_VALIDATE_RET(dst != NULL); |
| ECP_VALIDATE_RET(src != NULL); |
| |
| return (mbedtls_ecp_group_load(dst, src->id)); |
| } |
| |
| /* |
| * Set point to zero |
| */ |
| int mbedtls_ecp_set_zero(mbedtls_ecp_point * pt) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| ECP_VALIDATE_RET(pt != NULL); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->X, 1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Y, 1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 0)); |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Tell if a point is zero |
| */ |
| int mbedtls_ecp_is_zero(mbedtls_ecp_point * pt) |
| { |
| ECP_VALIDATE_RET(pt != NULL); |
| |
| return (mbedtls_mpi_cmp_int(&pt->Z, 0) == 0); |
| } |
| |
| /* |
| * Compare two points lazily |
| */ |
| int mbedtls_ecp_point_cmp(const mbedtls_ecp_point * P, const mbedtls_ecp_point * Q) |
| { |
| ECP_VALIDATE_RET(P != NULL); |
| ECP_VALIDATE_RET(Q != NULL); |
| |
| if (mbedtls_mpi_cmp_mpi(&P->X, &Q->X) == 0 && mbedtls_mpi_cmp_mpi(&P->Y, &Q->Y) == 0 && mbedtls_mpi_cmp_mpi(&P->Z, &Q->Z) == 0) |
| { |
| return (0); |
| } |
| |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| } |
| |
| /* |
| * Import a non-zero point from ASCII strings |
| */ |
| int mbedtls_ecp_point_read_string(mbedtls_ecp_point * P, int radix, const char * x, const char * y) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| ECP_VALIDATE_RET(P != NULL); |
| ECP_VALIDATE_RET(x != NULL); |
| ECP_VALIDATE_RET(y != NULL); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->X, radix, x)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->Y, radix, y)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&P->Z, 1)); |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748) |
| */ |
| int mbedtls_ecp_point_write_binary(const mbedtls_ecp_group * grp, const mbedtls_ecp_point * P, int format, size_t * olen, |
| unsigned char * buf, size_t buflen) |
| { |
| int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; |
| size_t plen; |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(P != NULL); |
| ECP_VALIDATE_RET(olen != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| ECP_VALIDATE_RET(format == MBEDTLS_ECP_PF_UNCOMPRESSED || format == MBEDTLS_ECP_PF_COMPRESSED); |
| |
| plen = mbedtls_mpi_size(&grp->P); |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| (void) format; /* Montgomery curves always use the same point format */ |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) |
| { |
| *olen = plen; |
| if (buflen < *olen) |
| return (MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&P->X, buf, plen)); |
| } |
| #endif |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| { |
| /* |
| * Common case: P == 0 |
| */ |
| if (mbedtls_mpi_cmp_int(&P->Z, 0) == 0) |
| { |
| if (buflen < 1) |
| return (MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL); |
| |
| buf[0] = 0x00; |
| *olen = 1; |
| |
| return (0); |
| } |
| |
| if (format == MBEDTLS_ECP_PF_UNCOMPRESSED) |
| { |
| *olen = 2 * plen + 1; |
| |
| if (buflen < *olen) |
| return (MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL); |
| |
| buf[0] = 0x04; |
| MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->Y, buf + 1 + plen, plen)); |
| } |
| else if (format == MBEDTLS_ECP_PF_COMPRESSED) |
| { |
| *olen = plen + 1; |
| |
| if (buflen < *olen) |
| return (MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL); |
| |
| buf[0] = 0x02 + mbedtls_mpi_get_bit(&P->Y, 0); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen)); |
| } |
| } |
| #endif |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748) |
| */ |
| int mbedtls_ecp_point_read_binary(const mbedtls_ecp_group * grp, mbedtls_ecp_point * pt, const unsigned char * buf, size_t ilen) |
| { |
| int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; |
| size_t plen; |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(pt != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| |
| if (ilen < 1) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| plen = mbedtls_mpi_size(&grp->P); |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) |
| { |
| if (plen != ilen) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&pt->X, buf, plen)); |
| mbedtls_mpi_free(&pt->Y); |
| |
| if (grp->id == MBEDTLS_ECP_DP_CURVE25519) |
| /* Set most significant bit to 0 as prescribed in RFC7748 §5 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&pt->X, plen * 8 - 1, 0)); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1)); |
| } |
| #endif |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| { |
| if (buf[0] == 0x00) |
| { |
| if (ilen == 1) |
| return (mbedtls_ecp_set_zero(pt)); |
| else |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| } |
| |
| if (buf[0] != 0x04) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| |
| if (ilen != 2 * plen + 1) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->X, buf + 1, plen)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->Y, buf + 1 + plen, plen)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1)); |
| } |
| #endif |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Import a point from a TLS ECPoint record (RFC 4492) |
| * struct { |
| * opaque point <1..2^8-1>; |
| * } ECPoint; |
| */ |
| int mbedtls_ecp_tls_read_point(const mbedtls_ecp_group * grp, mbedtls_ecp_point * pt, const unsigned char ** buf, size_t buf_len) |
| { |
| unsigned char data_len; |
| const unsigned char * buf_start; |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(pt != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| ECP_VALIDATE_RET(*buf != NULL); |
| |
| /* |
| * We must have at least two bytes (1 for length, at least one for data) |
| */ |
| if (buf_len < 2) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| data_len = *(*buf)++; |
| if (data_len < 1 || data_len > buf_len - 1) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| /* |
| * Save buffer start for read_binary and update buf |
| */ |
| buf_start = *buf; |
| *buf += data_len; |
| |
| return (mbedtls_ecp_point_read_binary(grp, pt, buf_start, data_len)); |
| } |
| |
| /* |
| * Export a point as a TLS ECPoint record (RFC 4492) |
| * struct { |
| * opaque point <1..2^8-1>; |
| * } ECPoint; |
| */ |
| int mbedtls_ecp_tls_write_point(const mbedtls_ecp_group * grp, const mbedtls_ecp_point * pt, int format, size_t * olen, |
| unsigned char * buf, size_t blen) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(pt != NULL); |
| ECP_VALIDATE_RET(olen != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| ECP_VALIDATE_RET(format == MBEDTLS_ECP_PF_UNCOMPRESSED || format == MBEDTLS_ECP_PF_COMPRESSED); |
| |
| /* |
| * buffer length must be at least one, for our length byte |
| */ |
| if (blen < 1) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| if ((ret = mbedtls_ecp_point_write_binary(grp, pt, format, olen, buf + 1, blen - 1)) != 0) |
| return (ret); |
| |
| /* |
| * write length to the first byte and update total length |
| */ |
| buf[0] = (unsigned char) *olen; |
| ++*olen; |
| |
| return (0); |
| } |
| |
| /* |
| * Set a group from an ECParameters record (RFC 4492) |
| */ |
| int mbedtls_ecp_tls_read_group(mbedtls_ecp_group * grp, const unsigned char ** buf, size_t len) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_ecp_group_id grp_id; |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| ECP_VALIDATE_RET(*buf != NULL); |
| |
| if ((ret = mbedtls_ecp_tls_read_group_id(&grp_id, buf, len)) != 0) |
| return (ret); |
| |
| return (mbedtls_ecp_group_load(grp, grp_id)); |
| } |
| |
| /* |
| * Read a group id from an ECParameters record (RFC 4492) and convert it to |
| * mbedtls_ecp_group_id. |
| */ |
| int mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id * grp, const unsigned char ** buf, size_t len) |
| { |
| uint16_t tls_id; |
| const mbedtls_ecp_curve_info * curve_info; |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| ECP_VALIDATE_RET(*buf != NULL); |
| |
| /* |
| * We expect at least three bytes (see below) |
| */ |
| if (len < 3) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| /* |
| * First byte is curve_type; only named_curve is handled |
| */ |
| if (*(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| /* |
| * Next two bytes are the namedcurve value |
| */ |
| tls_id = *(*buf)++; |
| tls_id <<= 8; |
| tls_id |= *(*buf)++; |
| |
| if ((curve_info = mbedtls_ecp_curve_info_from_tls_id(tls_id)) == NULL) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| |
| *grp = curve_info->grp_id; |
| |
| return (0); |
| } |
| |
| /* |
| * Write the ECParameters record corresponding to a group (RFC 4492) |
| */ |
| int mbedtls_ecp_tls_write_group(const mbedtls_ecp_group * grp, size_t * olen, unsigned char * buf, size_t blen) |
| { |
| const mbedtls_ecp_curve_info * curve_info; |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| ECP_VALIDATE_RET(olen != NULL); |
| |
| if ((curve_info = mbedtls_ecp_curve_info_from_grp_id(grp->id)) == NULL) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| /* |
| * We are going to write 3 bytes (see below) |
| */ |
| *olen = 3; |
| if (blen < *olen) |
| return (MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL); |
| |
| /* |
| * First byte is curve_type, always named_curve |
| */ |
| *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE; |
| |
| /* |
| * Next two bytes are the namedcurve value |
| */ |
| buf[0] = curve_info->tls_id >> 8; |
| buf[1] = curve_info->tls_id & 0xFF; |
| |
| return (0); |
| } |
| |
| /* |
| * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi. |
| * See the documentation of struct mbedtls_ecp_group. |
| * |
| * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf. |
| */ |
| static int ecp_modp(mbedtls_mpi * N, const mbedtls_ecp_group * grp) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| |
| if (grp->modp == NULL) |
| return (mbedtls_mpi_mod_mpi(N, N, &grp->P)); |
| |
| /* N->s < 0 is a much faster test, which fails only if N is 0 */ |
| if ((N->s < 0 && mbedtls_mpi_cmp_int(N, 0) != 0) || mbedtls_mpi_bitlen(N) > 2 * grp->pbits) |
| { |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| } |
| |
| MBEDTLS_MPI_CHK(grp->modp(N)); |
| |
| /* N->s < 0 is a much faster test, which fails only if N is 0 */ |
| while (N->s < 0 && mbedtls_mpi_cmp_int(N, 0) != 0) |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(N, N, &grp->P)); |
| |
| while (mbedtls_mpi_cmp_mpi(N, &grp->P) >= 0) |
| /* we known P, N and the result are positive */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(N, N, &grp->P)); |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Fast mod-p functions expect their argument to be in the 0..p^2 range. |
| * |
| * In order to guarantee that, we need to ensure that operands of |
| * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will |
| * bring the result back to this range. |
| * |
| * The following macros are shortcuts for doing that. |
| */ |
| |
| /* |
| * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi |
| */ |
| #if defined(MBEDTLS_SELF_TEST) |
| #define INC_MUL_COUNT mul_count++; |
| #else |
| #define INC_MUL_COUNT |
| #endif |
| |
| #define MOD_MUL(N) \ |
| do \ |
| { \ |
| MBEDTLS_MPI_CHK(ecp_modp(&(N), grp)); \ |
| INC_MUL_COUNT \ |
| } while (0) |
| |
| static inline int mbedtls_mpi_mul_mod(const mbedtls_ecp_group * grp, mbedtls_mpi * X, const mbedtls_mpi * A, const mbedtls_mpi * B) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(X, A, B)); |
| MOD_MUL(*X); |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi |
| * N->s < 0 is a very fast test, which fails only if N is 0 |
| */ |
| #define MOD_SUB(N) \ |
| while ((N).s < 0 && mbedtls_mpi_cmp_int(&(N), 0) != 0) \ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&(N), &(N), &grp->P)) |
| |
| #if (defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \ |
| !(defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && defined(MBEDTLS_ECP_ADD_MIXED_ALT))) || \ |
| (defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) && !(defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT))) |
| static inline int mbedtls_mpi_sub_mod(const mbedtls_ecp_group * grp, mbedtls_mpi * X, const mbedtls_mpi * A, const mbedtls_mpi * B) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(X, A, B)); |
| MOD_SUB(*X); |
| cleanup: |
| return (ret); |
| } |
| #endif /* All functions referencing mbedtls_mpi_sub_mod() are alt-implemented without fallback */ |
| |
| /* |
| * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int. |
| * We known P, N and the result are positive, so sub_abs is correct, and |
| * a bit faster. |
| */ |
| #define MOD_ADD(N) \ |
| while (mbedtls_mpi_cmp_mpi(&(N), &grp->P) >= 0) \ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&(N), &(N), &grp->P)) |
| |
| static inline int mbedtls_mpi_add_mod(const mbedtls_ecp_group * grp, mbedtls_mpi * X, const mbedtls_mpi * A, const mbedtls_mpi * B) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, A, B)); |
| MOD_ADD(*X); |
| cleanup: |
| return (ret); |
| } |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \ |
| !(defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && defined(MBEDTLS_ECP_ADD_MIXED_ALT)) |
| static inline int mbedtls_mpi_shift_l_mod(const mbedtls_ecp_group * grp, mbedtls_mpi * X, size_t count) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(X, count)); |
| MOD_ADD(*X); |
| cleanup: |
| return (ret); |
| } |
| #endif /* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */ |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| /* |
| * For curves in short Weierstrass form, we do all the internal operations in |
| * Jacobian coordinates. |
| * |
| * For multiplication, we'll use a comb method with coutermeasueres against |
| * SPA, hence timing attacks. |
| */ |
| |
| /* |
| * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1) |
| * Cost: 1N := 1I + 3M + 1S |
| */ |
| static int ecp_normalize_jac(const mbedtls_ecp_group * grp, mbedtls_ecp_point * pt) |
| { |
| if (mbedtls_mpi_cmp_int(&pt->Z, 0) == 0) |
| return (0); |
| |
| #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) |
| if (mbedtls_internal_ecp_grp_capable(grp)) |
| return (mbedtls_internal_ecp_normalize_jac(grp, pt)); |
| #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */ |
| |
| #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| #else |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_mpi Zi, ZZi; |
| mbedtls_mpi_init(&Zi); |
| mbedtls_mpi_init(&ZZi); |
| |
| /* |
| * X = X / Z^2 mod p |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&Zi, &pt->Z, &grp->P)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ZZi, &Zi, &Zi)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->X, &pt->X, &ZZi)); |
| |
| /* |
| * Y = Y / Z^3 mod p |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y, &pt->Y, &ZZi)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y, &pt->Y, &Zi)); |
| |
| /* |
| * Z = 1 |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1)); |
| |
| cleanup: |
| |
| mbedtls_mpi_free(&Zi); |
| mbedtls_mpi_free(&ZZi); |
| |
| return (ret); |
| #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */ |
| } |
| |
| /* |
| * Normalize jacobian coordinates of an array of (pointers to) points, |
| * using Montgomery's trick to perform only one inversion mod P. |
| * (See for example Cohen's "A Course in Computational Algebraic Number |
| * Theory", Algorithm 10.3.4.) |
| * |
| * Warning: fails (returning an error) if one of the points is zero! |
| * This should never happen, see choice of w in ecp_mul_comb(). |
| * |
| * Cost: 1N(t) := 1I + (6t - 3)M + 1S |
| */ |
| static int ecp_normalize_jac_many(const mbedtls_ecp_group * grp, mbedtls_ecp_point * T[], size_t T_size) |
| { |
| if (T_size < 2) |
| return (ecp_normalize_jac(grp, *T)); |
| |
| #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) |
| if (mbedtls_internal_ecp_grp_capable(grp)) |
| return (mbedtls_internal_ecp_normalize_jac_many(grp, T, T_size)); |
| #endif |
| |
| #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| #else |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| size_t i; |
| mbedtls_mpi *c, u, Zi, ZZi; |
| |
| if ((c = mbedtls_calloc(T_size, sizeof(mbedtls_mpi))) == NULL) |
| return (MBEDTLS_ERR_ECP_ALLOC_FAILED); |
| |
| for (i = 0; i < T_size; i++) |
| mbedtls_mpi_init(&c[i]); |
| |
| mbedtls_mpi_init(&u); |
| mbedtls_mpi_init(&Zi); |
| mbedtls_mpi_init(&ZZi); |
| |
| /* |
| * c[i] = Z_0 * ... * Z_i |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&c[0], &T[0]->Z)); |
| for (i = 1; i < T_size; i++) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &c[i], &c[i - 1], &T[i]->Z)); |
| } |
| |
| /* |
| * u = 1 / (Z_0 * ... * Z_n) mod P |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&u, &c[T_size - 1], &grp->P)); |
| |
| for (i = T_size - 1;; i--) |
| { |
| /* |
| * Zi = 1 / Z_i mod p |
| * u = 1 / (Z_0 * ... * Z_i) mod P |
| */ |
| if (i == 0) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Zi, &u)); |
| } |
| else |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &Zi, &u, &c[i - 1])); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &u, &u, &T[i]->Z)); |
| } |
| |
| /* |
| * proceed as in normalize() |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ZZi, &Zi, &Zi)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->X, &T[i]->X, &ZZi)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->Y, &T[i]->Y, &ZZi)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->Y, &T[i]->Y, &Zi)); |
| |
| /* |
| * Post-precessing: reclaim some memory by shrinking coordinates |
| * - not storing Z (always 1) |
| * - shrinking other coordinates, but still keeping the same number of |
| * limbs as P, as otherwise it will too likely be regrown too fast. |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->X, grp->P.n)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->Y, grp->P.n)); |
| mbedtls_mpi_free(&T[i]->Z); |
| |
| if (i == 0) |
| break; |
| } |
| |
| cleanup: |
| |
| mbedtls_mpi_free(&u); |
| mbedtls_mpi_free(&Zi); |
| mbedtls_mpi_free(&ZZi); |
| for (i = 0; i < T_size; i++) |
| mbedtls_mpi_free(&c[i]); |
| mbedtls_free(c); |
| |
| return (ret); |
| #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */ |
| } |
| |
| /* |
| * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak. |
| * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid |
| */ |
| static int ecp_safe_invert_jac(const mbedtls_ecp_group * grp, mbedtls_ecp_point * Q, unsigned char inv) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| unsigned char nonzero; |
| mbedtls_mpi mQY; |
| |
| mbedtls_mpi_init(&mQY); |
| |
| /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&mQY, &grp->P, &Q->Y)); |
| nonzero = mbedtls_mpi_cmp_int(&Q->Y, 0) != 0; |
| MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&Q->Y, &mQY, inv & nonzero)); |
| |
| cleanup: |
| mbedtls_mpi_free(&mQY); |
| |
| return (ret); |
| } |
| |
| /* |
| * Point doubling R = 2 P, Jacobian coordinates |
| * |
| * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 . |
| * |
| * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR |
| * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring. |
| * |
| * Standard optimizations are applied when curve parameter A is one of { 0, -3 }. |
| * |
| * Cost: 1D := 3M + 4S (A == 0) |
| * 4M + 4S (A == -3) |
| * 3M + 6S + 1a otherwise |
| */ |
| static int ecp_double_jac(const mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_ecp_point * P) |
| { |
| #if defined(MBEDTLS_SELF_TEST) |
| dbl_count++; |
| #endif |
| |
| #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) |
| if (mbedtls_internal_ecp_grp_capable(grp)) |
| return (mbedtls_internal_ecp_double_jac(grp, R, P)); |
| #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */ |
| |
| #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| #else |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_mpi M, S, T, U; |
| |
| mbedtls_mpi_init(&M); |
| mbedtls_mpi_init(&S); |
| mbedtls_mpi_init(&T); |
| mbedtls_mpi_init(&U); |
| |
| /* Special case for A = -3 */ |
| if (grp->A.p == NULL) |
| { |
| /* M = 3(X + Z^2)(X - Z^2) */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &P->Z, &P->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &T, &P->X, &S)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &U, &P->X, &S)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &T, &U)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&M, &S, 3)); |
| MOD_ADD(M); |
| } |
| else |
| { |
| /* M = 3.X^2 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &P->X, &P->X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&M, &S, 3)); |
| MOD_ADD(M); |
| |
| /* Optimize away for "koblitz" curves with A = 0 */ |
| if (mbedtls_mpi_cmp_int(&grp->A, 0) != 0) |
| { |
| /* M += A.Z^4 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &P->Z, &P->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T, &S, &S)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &T, &grp->A)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &M, &M, &S)); |
| } |
| } |
| |
| /* S = 4.X.Y^2 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T, &P->Y, &P->Y)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &T, 1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &P->X, &T)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &S, 1)); |
| |
| /* U = 8.Y^4 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &U, &T, &T)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &U, 1)); |
| |
| /* T = M^2 - 2.S */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T, &M, &M)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T, &T, &S)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T, &T, &S)); |
| |
| /* S = M(S - T) - U */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S, &S, &T)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &S, &M)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S, &S, &U)); |
| |
| /* U = 2.Y.Z */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &U, &P->Y, &P->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &U, 1)); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->X, &T)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Y, &S)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Z, &U)); |
| |
| cleanup: |
| mbedtls_mpi_free(&M); |
| mbedtls_mpi_free(&S); |
| mbedtls_mpi_free(&T); |
| mbedtls_mpi_free(&U); |
| |
| return (ret); |
| #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */ |
| } |
| |
| /* |
| * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22) |
| * |
| * The coordinates of Q must be normalized (= affine), |
| * but those of P don't need to. R is not normalized. |
| * |
| * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q. |
| * None of these cases can happen as intermediate step in ecp_mul_comb(): |
| * - at each step, P, Q and R are multiples of the base point, the factor |
| * being less than its order, so none of them is zero; |
| * - Q is an odd multiple of the base point, P an even multiple, |
| * due to the choice of precomputed points in the modified comb method. |
| * So branches for these cases do not leak secret information. |
| * |
| * We accept Q->Z being unset (saving memory in tables) as meaning 1. |
| * |
| * Cost: 1A := 8M + 3S |
| */ |
| static int ecp_add_mixed(const mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_ecp_point * P, |
| const mbedtls_ecp_point * Q) |
| { |
| #if defined(MBEDTLS_SELF_TEST) |
| add_count++; |
| #endif |
| |
| #if defined(MBEDTLS_ECP_ADD_MIXED_ALT) |
| if (mbedtls_internal_ecp_grp_capable(grp)) |
| return (mbedtls_internal_ecp_add_mixed(grp, R, P, Q)); |
| #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */ |
| |
| #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| #else |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_mpi T1, T2, T3, T4, X, Y, Z; |
| |
| /* |
| * Trivial cases: P == 0 or Q == 0 (case 1) |
| */ |
| if (mbedtls_mpi_cmp_int(&P->Z, 0) == 0) |
| return (mbedtls_ecp_copy(R, Q)); |
| |
| if (Q->Z.p != NULL && mbedtls_mpi_cmp_int(&Q->Z, 0) == 0) |
| return (mbedtls_ecp_copy(R, P)); |
| |
| /* |
| * Make sure Q coordinates are normalized |
| */ |
| if (Q->Z.p != NULL && mbedtls_mpi_cmp_int(&Q->Z, 1) != 0) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| mbedtls_mpi_init(&T1); |
| mbedtls_mpi_init(&T2); |
| mbedtls_mpi_init(&T3); |
| mbedtls_mpi_init(&T4); |
| mbedtls_mpi_init(&X); |
| mbedtls_mpi_init(&Y); |
| mbedtls_mpi_init(&Z); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T1, &P->Z, &P->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T2, &T1, &P->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T1, &T1, &Q->X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T2, &T2, &Q->Y)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T1, &T1, &P->X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T2, &T2, &P->Y)); |
| |
| /* Special cases (2) and (3) */ |
| if (mbedtls_mpi_cmp_int(&T1, 0) == 0) |
| { |
| if (mbedtls_mpi_cmp_int(&T2, 0) == 0) |
| { |
| ret = ecp_double_jac(grp, R, P); |
| goto cleanup; |
| } |
| else |
| { |
| ret = mbedtls_ecp_set_zero(R); |
| goto cleanup; |
| } |
| } |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &Z, &P->Z, &T1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3, &T1, &T1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T4, &T3, &T1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3, &T3, &P->X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T1, &T3)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &T1, 1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &X, &T2, &T2)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &X, &X, &T1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &X, &X, &T4)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T3, &T3, &X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3, &T3, &T2)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T4, &T4, &P->Y)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &Y, &T3, &T4)); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->X, &X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Y, &Y)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Z, &Z)); |
| |
| cleanup: |
| |
| mbedtls_mpi_free(&T1); |
| mbedtls_mpi_free(&T2); |
| mbedtls_mpi_free(&T3); |
| mbedtls_mpi_free(&T4); |
| mbedtls_mpi_free(&X); |
| mbedtls_mpi_free(&Y); |
| mbedtls_mpi_free(&Z); |
| |
| return (ret); |
| #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */ |
| } |
| |
| /* |
| * Randomize jacobian coordinates: |
| * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l |
| * This is sort of the reverse operation of ecp_normalize_jac(). |
| * |
| * This countermeasure was first suggested in [2]. |
| */ |
| static int ecp_randomize_jac(const mbedtls_ecp_group * grp, mbedtls_ecp_point * pt, int (*f_rng)(void *, unsigned char *, size_t), |
| void * p_rng) |
| { |
| #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) |
| if (mbedtls_internal_ecp_grp_capable(grp)) |
| return (mbedtls_internal_ecp_randomize_jac(grp, pt, f_rng, p_rng)); |
| #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */ |
| |
| #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| #else |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_mpi l, ll; |
| |
| mbedtls_mpi_init(&l); |
| mbedtls_mpi_init(&ll); |
| |
| /* Generate l such that 1 < l < p */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_random(&l, 2, &grp->P, f_rng, p_rng)); |
| |
| /* Z = l * Z */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Z, &pt->Z, &l)); |
| |
| /* X = l^2 * X */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ll, &l, &l)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->X, &pt->X, &ll)); |
| |
| /* Y = l^3 * Y */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ll, &ll, &l)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y, &pt->Y, &ll)); |
| |
| cleanup: |
| mbedtls_mpi_free(&l); |
| mbedtls_mpi_free(&ll); |
| |
| if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) |
| ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; |
| return (ret); |
| #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */ |
| } |
| |
| /* |
| * Check and define parameters used by the comb method (see below for details) |
| */ |
| #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7 |
| #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds" |
| #endif |
| |
| /* d = ceil( n / w ) */ |
| #define COMB_MAX_D (MBEDTLS_ECP_MAX_BITS + 1) / 2 |
| |
| /* number of precomputed points */ |
| #define COMB_MAX_PRE (1 << (MBEDTLS_ECP_WINDOW_SIZE - 1)) |
| |
| /* |
| * Compute the representation of m that will be used with our comb method. |
| * |
| * The basic comb method is described in GECC 3.44 for example. We use a |
| * modified version that provides resistance to SPA by avoiding zero |
| * digits in the representation as in [3]. We modify the method further by |
| * requiring that all K_i be odd, which has the small cost that our |
| * representation uses one more K_i, due to carries, but saves on the size of |
| * the precomputed table. |
| * |
| * Summary of the comb method and its modifications: |
| * |
| * - The goal is to compute m*P for some w*d-bit integer m. |
| * |
| * - The basic comb method splits m into the w-bit integers |
| * x[0] .. x[d-1] where x[i] consists of the bits in m whose |
| * index has residue i modulo d, and computes m * P as |
| * S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where |
| * S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P. |
| * |
| * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by |
| * .. + 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]] .., |
| * thereby successively converting it into a form where all summands |
| * are nonzero, at the cost of negative summands. This is the basic idea of [3]. |
| * |
| * - More generally, even if x[i+1] != 0, we can first transform the sum as |
| * .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] .., |
| * and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]]. |
| * Performing and iterating this procedure for those x[i] that are even |
| * (keeping track of carry), we can transform the original sum into one of the form |
| * S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]] |
| * with all x'[i] odd. It is therefore only necessary to know S at odd indices, |
| * which is why we are only computing half of it in the first place in |
| * ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb. |
| * |
| * - For the sake of compactness, only the seven low-order bits of x[i] |
| * are used to represent its absolute value (K_i in the paper), and the msb |
| * of x[i] encodes the sign (s_i in the paper): it is set if and only if |
| * if s_i == -1; |
| * |
| * Calling conventions: |
| * - x is an array of size d + 1 |
| * - w is the size, ie number of teeth, of the comb, and must be between |
| * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE) |
| * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d |
| * (the result will be incorrect if these assumptions are not satisfied) |
| */ |
| static void ecp_comb_recode_core(unsigned char x[], size_t d, unsigned char w, const mbedtls_mpi * m) |
| { |
| size_t i, j; |
| unsigned char c, cc, adjust; |
| |
| memset(x, 0, d + 1); |
| |
| /* First get the classical comb values (except for x_d = 0) */ |
| for (i = 0; i < d; i++) |
| for (j = 0; j < w; j++) |
| x[i] |= mbedtls_mpi_get_bit(m, i + d * j) << j; |
| |
| /* Now make sure x_1 .. x_d are odd */ |
| c = 0; |
| for (i = 1; i <= d; i++) |
| { |
| /* Add carry and update it */ |
| cc = x[i] & c; |
| x[i] = x[i] ^ c; |
| c = cc; |
| |
| /* Adjust if needed, avoiding branches */ |
| adjust = 1 - (x[i] & 0x01); |
| c |= x[i] & (x[i - 1] * adjust); |
| x[i] = x[i] ^ (x[i - 1] * adjust); |
| x[i - 1] |= adjust << 7; |
| } |
| } |
| |
| /* |
| * Precompute points for the adapted comb method |
| * |
| * Assumption: T must be able to hold 2^{w - 1} elements. |
| * |
| * Operation: If i = i_{w-1} ... i_1 is the binary representation of i, |
| * sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P. |
| * |
| * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1) |
| * |
| * Note: Even comb values (those where P would be omitted from the |
| * sum defining T[i] above) are not needed in our adaption |
| * the comb method. See ecp_comb_recode_core(). |
| * |
| * This function currently works in four steps: |
| * (1) [dbl] Computation of intermediate T[i] for 2-power values of i |
| * (2) [norm_dbl] Normalization of coordinates of these T[i] |
| * (3) [add] Computation of all T[i] |
| * (4) [norm_add] Normalization of all T[i] |
| * |
| * Step 1 can be interrupted but not the others; together with the final |
| * coordinate normalization they are the largest steps done at once, depending |
| * on the window size. Here are operation counts for P-256: |
| * |
| * step (2) (3) (4) |
| * w = 5 142 165 208 |
| * w = 4 136 77 160 |
| * w = 3 130 33 136 |
| * w = 2 124 11 124 |
| * |
| * So if ECC operations are blocking for too long even with a low max_ops |
| * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order |
| * to minimize maximum blocking time. |
| */ |
| static int ecp_precompute_comb(const mbedtls_ecp_group * grp, mbedtls_ecp_point T[], const mbedtls_ecp_point * P, unsigned char w, |
| size_t d, mbedtls_ecp_restart_ctx * rs_ctx) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| unsigned char i; |
| size_t j = 0; |
| const unsigned char T_size = 1U << (w - 1); |
| mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1]; |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL) |
| { |
| if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) |
| goto dbl; |
| if (rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl) |
| goto norm_dbl; |
| if (rs_ctx->rsm->state == ecp_rsm_pre_add) |
| goto add; |
| if (rs_ctx->rsm->state == ecp_rsm_pre_norm_add) |
| goto norm_add; |
| } |
| #else |
| (void) rs_ctx; |
| #endif |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL) |
| { |
| rs_ctx->rsm->state = ecp_rsm_pre_dbl; |
| |
| /* initial state for the loop */ |
| rs_ctx->rsm->i = 0; |
| } |
| |
| dbl: |
| #endif |
| /* |
| * Set T[0] = P and |
| * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value) |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&T[0], P)); |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) |
| j = rs_ctx->rsm->i; |
| else |
| #endif |
| j = 0; |
| |
| for (; j < d * (w - 1); j++) |
| { |
| MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL); |
| |
| i = 1U << (j / d); |
| cur = T + i; |
| |
| if (j % d == 0) |
| MBEDTLS_MPI_CHK(mbedtls_ecp_copy(cur, T + (i >> 1))); |
| |
| MBEDTLS_MPI_CHK(ecp_double_jac(grp, cur, cur)); |
| } |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL) |
| rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl; |
| |
| norm_dbl: |
| #endif |
| /* |
| * Normalize current elements in T. As T has holes, |
| * use an auxiliary array of pointers to elements in T. |
| */ |
| j = 0; |
| for (i = 1; i < T_size; i <<= 1) |
| TT[j++] = T + i; |
| |
| MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2); |
| |
| MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j)); |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL) |
| rs_ctx->rsm->state = ecp_rsm_pre_add; |
| |
| add: |
| #endif |
| /* |
| * Compute the remaining ones using the minimal number of additions |
| * Be careful to update T[2^l] only after using it! |
| */ |
| MBEDTLS_ECP_BUDGET((T_size - 1) * MBEDTLS_ECP_OPS_ADD); |
| |
| for (i = 1; i < T_size; i <<= 1) |
| { |
| j = i; |
| while (j--) |
| MBEDTLS_MPI_CHK(ecp_add_mixed(grp, &T[i + j], &T[j], &T[i])); |
| } |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL) |
| rs_ctx->rsm->state = ecp_rsm_pre_norm_add; |
| |
| norm_add: |
| #endif |
| /* |
| * Normalize final elements in T. Even though there are no holes now, we |
| * still need the auxiliary array for homogeneity with the previous |
| * call. Also, skip T[0] which is already normalised, being a copy of P. |
| */ |
| for (j = 0; j + 1 < T_size; j++) |
| TT[j] = T + j + 1; |
| |
| MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2); |
| |
| MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j)); |
| |
| cleanup: |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS) |
| { |
| if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) |
| rs_ctx->rsm->i = j; |
| } |
| #endif |
| |
| return (ret); |
| } |
| |
| /* |
| * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ] |
| * |
| * See ecp_comb_recode_core() for background |
| */ |
| static int ecp_select_comb(const mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_ecp_point T[], unsigned char T_size, |
| unsigned char i) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| unsigned char ii, j; |
| |
| /* Ignore the "sign" bit and scale down */ |
| ii = (i & 0x7Fu) >> 1; |
| |
| /* Read the whole table to thwart cache-based timing attacks */ |
| for (j = 0; j < T_size; j++) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&R->X, &T[j].X, j == ii)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&R->Y, &T[j].Y, j == ii)); |
| } |
| |
| /* Safely invert result if i is "negative" */ |
| MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, R, i >> 7)); |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Core multiplication algorithm for the (modified) comb method. |
| * This part is actually common with the basic comb method (GECC 3.44) |
| * |
| * Cost: d A + d D + 1 R |
| */ |
| static int ecp_mul_comb_core(const mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_ecp_point T[], |
| unsigned char T_size, const unsigned char x[], size_t d, int (*f_rng)(void *, unsigned char *, size_t), |
| void * p_rng, mbedtls_ecp_restart_ctx * rs_ctx) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_ecp_point Txi; |
| size_t i; |
| |
| mbedtls_ecp_point_init(&Txi); |
| |
| #if !defined(MBEDTLS_ECP_RESTARTABLE) |
| (void) rs_ctx; |
| #endif |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->state != ecp_rsm_comb_core) |
| { |
| rs_ctx->rsm->i = 0; |
| rs_ctx->rsm->state = ecp_rsm_comb_core; |
| } |
| |
| /* new 'if' instead of nested for the sake of the 'else' branch */ |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) |
| { |
| /* restore current index (R already pointing to rs_ctx->rsm->R) */ |
| i = rs_ctx->rsm->i; |
| } |
| else |
| #endif |
| { |
| /* Start with a non-zero point and randomize its coordinates */ |
| i = d; |
| MBEDTLS_MPI_CHK(ecp_select_comb(grp, R, T, T_size, x[i])); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->Z, 1)); |
| if (f_rng != 0) |
| MBEDTLS_MPI_CHK(ecp_randomize_jac(grp, R, f_rng, p_rng)); |
| } |
| |
| while (i != 0) |
| { |
| MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD); |
| --i; |
| |
| MBEDTLS_MPI_CHK(ecp_double_jac(grp, R, R)); |
| MBEDTLS_MPI_CHK(ecp_select_comb(grp, &Txi, T, T_size, x[i])); |
| MBEDTLS_MPI_CHK(ecp_add_mixed(grp, R, R, &Txi)); |
| } |
| |
| cleanup: |
| |
| mbedtls_ecp_point_free(&Txi); |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS) |
| { |
| rs_ctx->rsm->i = i; |
| /* no need to save R, already pointing to rs_ctx->rsm->R */ |
| } |
| #endif |
| |
| return (ret); |
| } |
| |
| /* |
| * Recode the scalar to get constant-time comb multiplication |
| * |
| * As the actual scalar recoding needs an odd scalar as a starting point, |
| * this wrapper ensures that by replacing m by N - m if necessary, and |
| * informs the caller that the result of multiplication will be negated. |
| * |
| * This works because we only support large prime order for Short Weierstrass |
| * curves, so N is always odd hence either m or N - m is. |
| * |
| * See ecp_comb_recode_core() for background. |
| */ |
| static int ecp_comb_recode_scalar(const mbedtls_ecp_group * grp, const mbedtls_mpi * m, unsigned char k[COMB_MAX_D + 1], size_t d, |
| unsigned char w, unsigned char * parity_trick) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_mpi M, mm; |
| |
| mbedtls_mpi_init(&M); |
| mbedtls_mpi_init(&mm); |
| |
| /* N is always odd (see above), just make extra sure */ |
| if (mbedtls_mpi_get_bit(&grp->N, 0) != 1) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| /* do we need the parity trick? */ |
| *parity_trick = (mbedtls_mpi_get_bit(m, 0) == 0); |
| |
| /* execute parity fix in constant time */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&M, m)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&mm, &grp->N, m)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&M, &mm, *parity_trick)); |
| |
| /* actual scalar recoding */ |
| ecp_comb_recode_core(k, d, w, &M); |
| |
| cleanup: |
| mbedtls_mpi_free(&mm); |
| mbedtls_mpi_free(&M); |
| |
| return (ret); |
| } |
| |
| /* |
| * Perform comb multiplication (for short Weierstrass curves) |
| * once the auxiliary table has been pre-computed. |
| * |
| * Scalar recoding may use a parity trick that makes us compute -m * P, |
| * if that is the case we'll need to recover m * P at the end. |
| */ |
| static int ecp_mul_comb_after_precomp(const mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, |
| const mbedtls_ecp_point * T, unsigned char T_size, unsigned char w, size_t d, |
| int (*f_rng)(void *, unsigned char *, size_t), void * p_rng, mbedtls_ecp_restart_ctx * rs_ctx) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| unsigned char parity_trick; |
| unsigned char k[COMB_MAX_D + 1]; |
| mbedtls_ecp_point * RR = R; |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL) |
| { |
| RR = &rs_ctx->rsm->R; |
| |
| if (rs_ctx->rsm->state == ecp_rsm_final_norm) |
| goto final_norm; |
| } |
| #endif |
| |
| MBEDTLS_MPI_CHK(ecp_comb_recode_scalar(grp, m, k, d, w, &parity_trick)); |
| MBEDTLS_MPI_CHK(ecp_mul_comb_core(grp, RR, T, T_size, k, d, f_rng, p_rng, rs_ctx)); |
| MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, RR, parity_trick)); |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL) |
| rs_ctx->rsm->state = ecp_rsm_final_norm; |
| |
| final_norm: |
| MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV); |
| #endif |
| /* |
| * Knowledge of the jacobian coordinates may leak the last few bits of the |
| * scalar [1], and since our MPI implementation isn't constant-flow, |
| * inversion (used for coordinate normalization) may leak the full value |
| * of its input via side-channels [2]. |
| * |
| * [1] https://eprint.iacr.org/2003/191 |
| * [2] https://eprint.iacr.org/2020/055 |
| * |
| * Avoid the leak by randomizing coordinates before we normalize them. |
| */ |
| if (f_rng != 0) |
| MBEDTLS_MPI_CHK(ecp_randomize_jac(grp, RR, f_rng, p_rng)); |
| |
| MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, RR)); |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL) |
| MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, RR)); |
| #endif |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Pick window size based on curve size and whether we optimize for base point |
| */ |
| static unsigned char ecp_pick_window_size(const mbedtls_ecp_group * grp, unsigned char p_eq_g) |
| { |
| unsigned char w; |
| |
| /* |
| * Minimize the number of multiplications, that is minimize |
| * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w ) |
| * (see costs of the various parts, with 1S = 1M) |
| */ |
| w = grp->nbits >= 384 ? 5 : 4; |
| |
| /* |
| * If P == G, pre-compute a bit more, since this may be re-used later. |
| * Just adding one avoids upping the cost of the first mul too much, |
| * and the memory cost too. |
| */ |
| if (p_eq_g) |
| w++; |
| |
| /* |
| * If static comb table may not be used (!p_eq_g) or static comb table does |
| * not exists, make sure w is within bounds. |
| * (The last test is useful only for very small curves in the test suite.) |
| * |
| * The user reduces MBEDTLS_ECP_WINDOW_SIZE does not changes the size of |
| * static comb table, because the size of static comb table is fixed when |
| * it is generated. |
| */ |
| #if (MBEDTLS_ECP_WINDOW_SIZE < 6) |
| if ((!p_eq_g || !ecp_group_is_static_comb_table(grp)) && w > MBEDTLS_ECP_WINDOW_SIZE) |
| w = MBEDTLS_ECP_WINDOW_SIZE; |
| #endif |
| if (w >= grp->nbits) |
| w = 2; |
| |
| return (w); |
| } |
| |
| /* |
| * Multiplication using the comb method - for curves in short Weierstrass form |
| * |
| * This function is mainly responsible for administrative work: |
| * - managing the restart context if enabled |
| * - managing the table of precomputed points (passed between the below two |
| * functions): allocation, computation, ownership tranfer, freeing. |
| * |
| * It delegates the actual arithmetic work to: |
| * ecp_precompute_comb() and ecp_mul_comb_with_precomp() |
| * |
| * See comments on ecp_comb_recode_core() regarding the computation strategy. |
| */ |
| static int ecp_mul_comb(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, const mbedtls_ecp_point * P, |
| int (*f_rng)(void *, unsigned char *, size_t), void * p_rng, mbedtls_ecp_restart_ctx * rs_ctx) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| unsigned char w, p_eq_g, i; |
| size_t d; |
| unsigned char T_size = 0, T_ok = 0; |
| mbedtls_ecp_point * T = NULL; |
| |
| ECP_RS_ENTER(rsm); |
| |
| /* Is P the base point ? */ |
| #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 |
| p_eq_g = (mbedtls_mpi_cmp_mpi(&P->Y, &grp->G.Y) == 0 && mbedtls_mpi_cmp_mpi(&P->X, &grp->G.X) == 0); |
| #else |
| p_eq_g = 0; |
| #endif |
| |
| /* Pick window size and deduce related sizes */ |
| w = ecp_pick_window_size(grp, p_eq_g); |
| T_size = 1U << (w - 1); |
| d = (grp->nbits + w - 1) / w; |
| |
| /* Pre-computed table: do we have it already for the base point? */ |
| if (p_eq_g && grp->T != NULL) |
| { |
| /* second pointer to the same table, will be deleted on exit */ |
| T = grp->T; |
| T_ok = 1; |
| } |
| else |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| /* Pre-computed table: do we have one in progress? complete? */ |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL) |
| { |
| /* transfer ownership of T from rsm to local function */ |
| T = rs_ctx->rsm->T; |
| rs_ctx->rsm->T = NULL; |
| rs_ctx->rsm->T_size = 0; |
| |
| /* This effectively jumps to the call to mul_comb_after_precomp() */ |
| T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core; |
| } |
| else |
| #endif |
| /* Allocate table if we didn't have any */ |
| { |
| T = mbedtls_calloc(T_size, sizeof(mbedtls_ecp_point)); |
| if (T == NULL) |
| { |
| ret = MBEDTLS_ERR_ECP_ALLOC_FAILED; |
| goto cleanup; |
| } |
| |
| for (i = 0; i < T_size; i++) |
| mbedtls_ecp_point_init(&T[i]); |
| |
| T_ok = 0; |
| } |
| |
| /* Compute table (or finish computing it) if not done already */ |
| if (!T_ok) |
| { |
| MBEDTLS_MPI_CHK(ecp_precompute_comb(grp, T, P, w, d, rs_ctx)); |
| |
| if (p_eq_g) |
| { |
| /* almost transfer ownership of T to the group, but keep a copy of |
| * the pointer to use for calling the next function more easily */ |
| grp->T = T; |
| grp->T_size = T_size; |
| } |
| } |
| |
| /* Actual comb multiplication using precomputed points */ |
| MBEDTLS_MPI_CHK(ecp_mul_comb_after_precomp(grp, R, m, T, T_size, w, d, f_rng, p_rng, rs_ctx)); |
| |
| cleanup: |
| |
| /* does T belong to the group? */ |
| if (T == grp->T) |
| T = NULL; |
| |
| /* does T belong to the restart context? */ |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL) |
| { |
| /* transfer ownership of T from local function to rsm */ |
| rs_ctx->rsm->T_size = T_size; |
| rs_ctx->rsm->T = T; |
| T = NULL; |
| } |
| #endif |
| |
| /* did T belong to us? then let's destroy it! */ |
| if (T != NULL) |
| { |
| for (i = 0; i < T_size; i++) |
| mbedtls_ecp_point_free(&T[i]); |
| mbedtls_free(T); |
| } |
| |
| /* don't free R while in progress in case R == P */ |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (ret != MBEDTLS_ERR_ECP_IN_PROGRESS) |
| #endif |
| /* prevent caller from using invalid value */ |
| if (ret != 0) |
| mbedtls_ecp_point_free(R); |
| |
| ECP_RS_LEAVE(rsm); |
| |
| return (ret); |
| } |
| |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| /* |
| * For Montgomery curves, we do all the internal arithmetic in projective |
| * coordinates. Import/export of points uses only the x coordinates, which is |
| * internaly represented as X / Z. |
| * |
| * For scalar multiplication, we'll use a Montgomery ladder. |
| */ |
| |
| /* |
| * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1 |
| * Cost: 1M + 1I |
| */ |
| static int ecp_normalize_mxz(const mbedtls_ecp_group * grp, mbedtls_ecp_point * P) |
| { |
| #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) |
| if (mbedtls_internal_ecp_grp_capable(grp)) |
| return (mbedtls_internal_ecp_normalize_mxz(grp, P)); |
| #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */ |
| |
| #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| #else |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&P->Z, &P->Z, &grp->P)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->X, &P->X, &P->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&P->Z, 1)); |
| |
| cleanup: |
| return (ret); |
| #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */ |
| } |
| |
| /* |
| * Randomize projective x/z coordinates: |
| * (X, Z) -> (l X, l Z) for random l |
| * This is sort of the reverse operation of ecp_normalize_mxz(). |
| * |
| * This countermeasure was first suggested in [2]. |
| * Cost: 2M |
| */ |
| static int ecp_randomize_mxz(const mbedtls_ecp_group * grp, mbedtls_ecp_point * P, int (*f_rng)(void *, unsigned char *, size_t), |
| void * p_rng) |
| { |
| #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) |
| if (mbedtls_internal_ecp_grp_capable(grp)) |
| return (mbedtls_internal_ecp_randomize_mxz(grp, P, f_rng, p_rng)); |
| #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */ |
| |
| #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| #else |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_mpi l; |
| mbedtls_mpi_init(&l); |
| |
| /* Generate l such that 1 < l < p */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_random(&l, 2, &grp->P, f_rng, p_rng)); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->X, &P->X, &l)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->Z, &P->Z, &l)); |
| |
| cleanup: |
| mbedtls_mpi_free(&l); |
| |
| if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) |
| ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; |
| return (ret); |
| #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */ |
| } |
| |
| /* |
| * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q), |
| * for Montgomery curves in x/z coordinates. |
| * |
| * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3 |
| * with |
| * d = X1 |
| * P = (X2, Z2) |
| * Q = (X3, Z3) |
| * R = (X4, Z4) |
| * S = (X5, Z5) |
| * and eliminating temporary variables tO, ..., t4. |
| * |
| * Cost: 5M + 4S |
| */ |
| static int ecp_double_add_mxz(const mbedtls_ecp_group * grp, mbedtls_ecp_point * R, mbedtls_ecp_point * S, |
| const mbedtls_ecp_point * P, const mbedtls_ecp_point * Q, const mbedtls_mpi * d) |
| { |
| #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) |
| if (mbedtls_internal_ecp_grp_capable(grp)) |
| return (mbedtls_internal_ecp_double_add_mxz(grp, R, S, P, Q, d)); |
| #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */ |
| |
| #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| #else |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB; |
| |
| mbedtls_mpi_init(&A); |
| mbedtls_mpi_init(&AA); |
| mbedtls_mpi_init(&B); |
| mbedtls_mpi_init(&BB); |
| mbedtls_mpi_init(&E); |
| mbedtls_mpi_init(&C); |
| mbedtls_mpi_init(&D); |
| mbedtls_mpi_init(&DA); |
| mbedtls_mpi_init(&CB); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &A, &P->X, &P->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &AA, &A, &A)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &B, &P->X, &P->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &BB, &B, &B)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &E, &AA, &BB)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &C, &Q->X, &Q->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &D, &Q->X, &Q->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &DA, &D, &A)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &CB, &C, &B)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &S->X, &DA, &CB)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->X, &S->X, &S->X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S->Z, &DA, &CB)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->Z, &S->Z, &S->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->Z, d, &S->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->X, &AA, &BB)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->Z, &grp->A, &E)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &R->Z, &BB, &R->Z)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->Z, &E, &R->Z)); |
| |
| cleanup: |
| mbedtls_mpi_free(&A); |
| mbedtls_mpi_free(&AA); |
| mbedtls_mpi_free(&B); |
| mbedtls_mpi_free(&BB); |
| mbedtls_mpi_free(&E); |
| mbedtls_mpi_free(&C); |
| mbedtls_mpi_free(&D); |
| mbedtls_mpi_free(&DA); |
| mbedtls_mpi_free(&CB); |
| |
| return (ret); |
| #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */ |
| } |
| |
| /* |
| * Multiplication with Montgomery ladder in x/z coordinates, |
| * for curves in Montgomery form |
| */ |
| static int ecp_mul_mxz(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, const mbedtls_ecp_point * P, |
| int (*f_rng)(void *, unsigned char *, size_t), void * p_rng) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| size_t i; |
| unsigned char b; |
| mbedtls_ecp_point RP; |
| mbedtls_mpi PX; |
| mbedtls_ecp_point_init(&RP); |
| mbedtls_mpi_init(&PX); |
| |
| if (f_rng == NULL) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| /* Save PX and read from P before writing to R, in case P == R */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&PX, &P->X)); |
| MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&RP, P)); |
| |
| /* Set R to zero in modified x/z coordinates */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->X, 1)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->Z, 0)); |
| mbedtls_mpi_free(&R->Y); |
| |
| /* RP.X might be sligtly larger than P, so reduce it */ |
| MOD_ADD(RP.X); |
| |
| /* Randomize coordinates of the starting point */ |
| MBEDTLS_MPI_CHK(ecp_randomize_mxz(grp, &RP, f_rng, p_rng)); |
| |
| /* Loop invariant: R = result so far, RP = R + P */ |
| i = mbedtls_mpi_bitlen(m); /* one past the (zero-based) most significant bit */ |
| while (i-- > 0) |
| { |
| b = mbedtls_mpi_get_bit(m, i); |
| /* |
| * if (b) R = 2R + P else R = 2R, |
| * which is: |
| * if (b) double_add( RP, R, RP, R ) |
| * else double_add( R, RP, R, RP ) |
| * but using safe conditional swaps to avoid leaks |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->X, &RP.X, b)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->Z, &RP.Z, b)); |
| MBEDTLS_MPI_CHK(ecp_double_add_mxz(grp, R, &RP, R, &RP, &PX)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->X, &RP.X, b)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->Z, &RP.Z, b)); |
| } |
| |
| /* |
| * Knowledge of the projective coordinates may leak the last few bits of the |
| * scalar [1], and since our MPI implementation isn't constant-flow, |
| * inversion (used for coordinate normalization) may leak the full value |
| * of its input via side-channels [2]. |
| * |
| * [1] https://eprint.iacr.org/2003/191 |
| * [2] https://eprint.iacr.org/2020/055 |
| * |
| * Avoid the leak by randomizing coordinates before we normalize them. |
| */ |
| MBEDTLS_MPI_CHK(ecp_randomize_mxz(grp, R, f_rng, p_rng)); |
| MBEDTLS_MPI_CHK(ecp_normalize_mxz(grp, R)); |
| |
| cleanup: |
| mbedtls_ecp_point_free(&RP); |
| mbedtls_mpi_free(&PX); |
| |
| return (ret); |
| } |
| |
| #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ |
| |
| /* |
| * Restartable multiplication R = m * P |
| * |
| * This internal function can be called without an RNG in case where we know |
| * the inputs are not sensitive. |
| */ |
| static int ecp_mul_restartable_internal(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, |
| const mbedtls_ecp_point * P, int (*f_rng)(void *, unsigned char *, size_t), void * p_rng, |
| mbedtls_ecp_restart_ctx * rs_ctx) |
| { |
| int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; |
| #if defined(MBEDTLS_ECP_INTERNAL_ALT) |
| char is_grp_capable = 0; |
| #endif |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| /* reset ops count for this call if top-level */ |
| if (rs_ctx != NULL && rs_ctx->depth++ == 0) |
| rs_ctx->ops_done = 0; |
| #else |
| (void) rs_ctx; |
| #endif |
| |
| #if defined(MBEDTLS_ECP_INTERNAL_ALT) |
| if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) |
| MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp)); |
| #endif /* MBEDTLS_ECP_INTERNAL_ALT */ |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| /* skip argument check when restarting */ |
| if (rs_ctx == NULL || rs_ctx->rsm == NULL) |
| #endif |
| { |
| /* check_privkey is free */ |
| MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_CHK); |
| |
| /* Common sanity checks */ |
| MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(grp, m)); |
| MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); |
| } |
| |
| ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) |
| MBEDTLS_MPI_CHK(ecp_mul_mxz(grp, R, m, P, f_rng, p_rng)); |
| #endif |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| MBEDTLS_MPI_CHK(ecp_mul_comb(grp, R, m, P, f_rng, p_rng, rs_ctx)); |
| #endif |
| |
| cleanup: |
| |
| #if defined(MBEDTLS_ECP_INTERNAL_ALT) |
| if (is_grp_capable) |
| mbedtls_internal_ecp_free(grp); |
| #endif /* MBEDTLS_ECP_INTERNAL_ALT */ |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL) |
| rs_ctx->depth--; |
| #endif |
| |
| return (ret); |
| } |
| |
| /* |
| * Restartable multiplication R = m * P |
| */ |
| int mbedtls_ecp_mul_restartable(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, const mbedtls_ecp_point * P, |
| int (*f_rng)(void *, unsigned char *, size_t), void * p_rng, mbedtls_ecp_restart_ctx * rs_ctx) |
| { |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(R != NULL); |
| ECP_VALIDATE_RET(m != NULL); |
| ECP_VALIDATE_RET(P != NULL); |
| |
| if (f_rng == NULL) |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| |
| if (GET_WORD_LEN(grp->pbits) <= PKE_OPERAND_MAX_WORD_LEN) |
| return (ecp_alt_b91_backend_mul(grp, R, m, P)); |
| |
| return (ecp_mul_restartable_internal(grp, R, m, P, f_rng, p_rng, rs_ctx)); |
| } |
| |
| /* |
| * Multiplication R = m * P |
| */ |
| int mbedtls_ecp_mul(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, const mbedtls_ecp_point * P, |
| int (*f_rng)(void *, unsigned char *, size_t), void * p_rng) |
| { |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(R != NULL); |
| ECP_VALIDATE_RET(m != NULL); |
| ECP_VALIDATE_RET(P != NULL); |
| return (mbedtls_ecp_mul_restartable(grp, R, m, P, f_rng, p_rng, NULL)); |
| } |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| /* |
| * Check that an affine point is valid as a public key, |
| * short weierstrass curves (SEC1 3.2.3.1) |
| */ |
| static int ecp_check_pubkey_sw(const mbedtls_ecp_group * grp, const mbedtls_ecp_point * pt) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_mpi YY, RHS; |
| |
| /* pt coordinates must be normalized for our checks */ |
| if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0 || mbedtls_mpi_cmp_int(&pt->Y, 0) < 0 || mbedtls_mpi_cmp_mpi(&pt->X, &grp->P) >= 0 || |
| mbedtls_mpi_cmp_mpi(&pt->Y, &grp->P) >= 0) |
| return (MBEDTLS_ERR_ECP_INVALID_KEY); |
| |
| mbedtls_mpi_init(&YY); |
| mbedtls_mpi_init(&RHS); |
| |
| /* |
| * YY = Y^2 |
| * RHS = X (X^2 + A) + B = X^3 + A X + B |
| */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &YY, &pt->Y, &pt->Y)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &RHS, &pt->X, &pt->X)); |
| |
| /* Special case for A = -3 */ |
| if (grp->A.p == NULL) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(&RHS, &RHS, 3)); |
| MOD_SUB(RHS); |
| } |
| else |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &RHS, &RHS, &grp->A)); |
| } |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &RHS, &RHS, &pt->X)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &RHS, &RHS, &grp->B)); |
| |
| if (mbedtls_mpi_cmp_mpi(&YY, &RHS) != 0) |
| ret = MBEDTLS_ERR_ECP_INVALID_KEY; |
| |
| cleanup: |
| |
| mbedtls_mpi_free(&YY); |
| mbedtls_mpi_free(&RHS); |
| |
| return (ret); |
| } |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| /* |
| * R = m * P with shortcuts for m == 0, m == 1 and m == -1 |
| * NOT constant-time - ONLY for short Weierstrass! |
| */ |
| static int mbedtls_ecp_mul_shortcuts(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, |
| const mbedtls_ecp_point * P, mbedtls_ecp_restart_ctx * rs_ctx) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| |
| if (mbedtls_mpi_cmp_int(m, 0) == 0) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_ecp_set_zero(R)); |
| } |
| else if (mbedtls_mpi_cmp_int(m, 1) == 0) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P)); |
| } |
| else if (mbedtls_mpi_cmp_int(m, -1) == 0) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P)); |
| if (mbedtls_mpi_cmp_int(&R->Y, 0) != 0) |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&R->Y, &grp->P, &R->Y)); |
| } |
| else |
| { |
| MBEDTLS_MPI_CHK(ecp_mul_restartable_internal(grp, R, m, P, NULL, NULL, rs_ctx)); |
| } |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Restartable linear combination |
| * NOT constant-time |
| */ |
| int mbedtls_ecp_muladd_restartable(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, |
| const mbedtls_ecp_point * P, const mbedtls_mpi * n, const mbedtls_ecp_point * Q, |
| mbedtls_ecp_restart_ctx * rs_ctx) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_ecp_point mP; |
| mbedtls_ecp_point * pmP = &mP; |
| mbedtls_ecp_point * pR = R; |
| #if defined(MBEDTLS_ECP_INTERNAL_ALT) |
| char is_grp_capable = 0; |
| #endif |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(R != NULL); |
| ECP_VALIDATE_RET(m != NULL); |
| ECP_VALIDATE_RET(P != NULL); |
| ECP_VALIDATE_RET(n != NULL); |
| ECP_VALIDATE_RET(Q != NULL); |
| |
| if (mbedtls_ecp_get_type(grp) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| return (MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE); |
| |
| if (GET_WORD_LEN(grp->pbits) <= PKE_OPERAND_MAX_WORD_LEN) |
| return (ecp_alt_b91_backend_muladd(grp, R, m, P, n, Q)); |
| |
| mbedtls_ecp_point_init(&mP); |
| |
| ECP_RS_ENTER(ma); |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->ma != NULL) |
| { |
| /* redirect intermediate results to restart context */ |
| pmP = &rs_ctx->ma->mP; |
| pR = &rs_ctx->ma->R; |
| |
| /* jump to next operation */ |
| if (rs_ctx->ma->state == ecp_rsma_mul2) |
| goto mul2; |
| if (rs_ctx->ma->state == ecp_rsma_add) |
| goto add; |
| if (rs_ctx->ma->state == ecp_rsma_norm) |
| goto norm; |
| } |
| #endif /* MBEDTLS_ECP_RESTARTABLE */ |
| |
| MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pmP, m, P, rs_ctx)); |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->ma != NULL) |
| rs_ctx->ma->state = ecp_rsma_mul2; |
| |
| mul2: |
| #endif |
| MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pR, n, Q, rs_ctx)); |
| |
| #if defined(MBEDTLS_ECP_INTERNAL_ALT) |
| if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) |
| MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp)); |
| #endif /* MBEDTLS_ECP_INTERNAL_ALT */ |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->ma != NULL) |
| rs_ctx->ma->state = ecp_rsma_add; |
| |
| add: |
| #endif |
| MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_ADD); |
| MBEDTLS_MPI_CHK(ecp_add_mixed(grp, pR, pmP, pR)); |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->ma != NULL) |
| rs_ctx->ma->state = ecp_rsma_norm; |
| |
| norm: |
| #endif |
| MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV); |
| MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, pR)); |
| |
| #if defined(MBEDTLS_ECP_RESTARTABLE) |
| if (rs_ctx != NULL && rs_ctx->ma != NULL) |
| MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, pR)); |
| #endif |
| |
| cleanup: |
| #if defined(MBEDTLS_ECP_INTERNAL_ALT) |
| if (is_grp_capable) |
| mbedtls_internal_ecp_free(grp); |
| #endif /* MBEDTLS_ECP_INTERNAL_ALT */ |
| |
| mbedtls_ecp_point_free(&mP); |
| |
| ECP_RS_LEAVE(ma); |
| |
| return (ret); |
| } |
| |
| /* |
| * Linear combination |
| * NOT constant-time |
| */ |
| int mbedtls_ecp_muladd(mbedtls_ecp_group * grp, mbedtls_ecp_point * R, const mbedtls_mpi * m, const mbedtls_ecp_point * P, |
| const mbedtls_mpi * n, const mbedtls_ecp_point * Q) |
| { |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(R != NULL); |
| ECP_VALIDATE_RET(m != NULL); |
| ECP_VALIDATE_RET(P != NULL); |
| ECP_VALIDATE_RET(n != NULL); |
| ECP_VALIDATE_RET(Q != NULL); |
| return (mbedtls_ecp_muladd_restartable(grp, R, m, P, n, Q, NULL)); |
| } |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| #define ECP_MPI_INIT(s, n, p) \ |
| { \ |
| s, (n), (mbedtls_mpi_uint *) (p) \ |
| } |
| #define ECP_MPI_INIT_ARRAY(x) ECP_MPI_INIT(1, sizeof(x) / sizeof(mbedtls_mpi_uint), x) |
| /* |
| * Constants for the two points other than 0, 1, -1 (mod p) in |
| * https://cr.yp.to/ecdh.html#validate |
| * See ecp_check_pubkey_x25519(). |
| */ |
| static const mbedtls_mpi_uint x25519_bad_point_1[] = { |
| MBEDTLS_BYTES_TO_T_UINT_8(0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae), |
| MBEDTLS_BYTES_TO_T_UINT_8(0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a), |
| MBEDTLS_BYTES_TO_T_UINT_8(0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd), |
| MBEDTLS_BYTES_TO_T_UINT_8(0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00), |
| }; |
| static const mbedtls_mpi_uint x25519_bad_point_2[] = { |
| MBEDTLS_BYTES_TO_T_UINT_8(0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24), |
| MBEDTLS_BYTES_TO_T_UINT_8(0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b), |
| MBEDTLS_BYTES_TO_T_UINT_8(0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86), |
| MBEDTLS_BYTES_TO_T_UINT_8(0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57), |
| }; |
| static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY(x25519_bad_point_1); |
| static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY(x25519_bad_point_2); |
| #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ |
| |
| /* |
| * Check that the input point is not one of the low-order points. |
| * This is recommended by the "May the Fourth" paper: |
| * https://eprint.iacr.org/2017/806.pdf |
| * Those points are never sent by an honest peer. |
| */ |
| static int ecp_check_bad_points_mx(const mbedtls_mpi * X, const mbedtls_mpi * P, const mbedtls_ecp_group_id grp_id) |
| { |
| int ret; |
| mbedtls_mpi XmP; |
| |
| mbedtls_mpi_init(&XmP); |
| |
| /* Reduce X mod P so that we only need to check values less than P. |
| * We know X < 2^256 so we can proceed by subtraction. */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&XmP, X)); |
| while (mbedtls_mpi_cmp_mpi(&XmP, P) >= 0) |
| MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&XmP, &XmP, P)); |
| |
| /* Check against the known bad values that are less than P. For Curve448 |
| * these are 0, 1 and -1. For Curve25519 we check the values less than P |
| * from the following list: https://cr.yp.to/ecdh.html#validate */ |
| if (mbedtls_mpi_cmp_int(&XmP, 1) <= 0) /* takes care of 0 and 1 */ |
| { |
| ret = MBEDTLS_ERR_ECP_INVALID_KEY; |
| goto cleanup; |
| } |
| |
| #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| if (grp_id == MBEDTLS_ECP_DP_CURVE25519) |
| { |
| if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_1) == 0) |
| { |
| ret = MBEDTLS_ERR_ECP_INVALID_KEY; |
| goto cleanup; |
| } |
| |
| if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_2) == 0) |
| { |
| ret = MBEDTLS_ERR_ECP_INVALID_KEY; |
| goto cleanup; |
| } |
| } |
| #else |
| (void) grp_id; |
| #endif |
| |
| /* Final check: check if XmP + 1 is P (final because it changes XmP!) */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&XmP, &XmP, 1)); |
| if (mbedtls_mpi_cmp_mpi(&XmP, P) == 0) |
| { |
| ret = MBEDTLS_ERR_ECP_INVALID_KEY; |
| goto cleanup; |
| } |
| |
| ret = 0; |
| |
| cleanup: |
| mbedtls_mpi_free(&XmP); |
| |
| return (ret); |
| } |
| |
| /* |
| * Check validity of a public key for Montgomery curves with x-only schemes |
| */ |
| static int ecp_check_pubkey_mx(const mbedtls_ecp_group * grp, const mbedtls_ecp_point * pt) |
| { |
| /* [Curve25519 p. 5] Just check X is the correct number of bytes */ |
| /* Allow any public value, if it's too big then we'll just reduce it mod p |
| * (RFC 7748 sec. 5 para. 3). */ |
| if (mbedtls_mpi_size(&pt->X) > (grp->nbits + 7) / 8) |
| return (MBEDTLS_ERR_ECP_INVALID_KEY); |
| |
| /* Implicit in all standards (as they don't consider negative numbers): |
| * X must be non-negative. This is normally ensured by the way it's |
| * encoded for transmission, but let's be extra sure. */ |
| if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0) |
| return (MBEDTLS_ERR_ECP_INVALID_KEY); |
| |
| return (ecp_check_bad_points_mx(&pt->X, &grp->P, grp->id)); |
| } |
| #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ |
| |
| /* |
| * Check that a point is valid as a public key |
| */ |
| int mbedtls_ecp_check_pubkey(const mbedtls_ecp_group * grp, const mbedtls_ecp_point * pt) |
| { |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(pt != NULL); |
| |
| /* Must use affine coordinates */ |
| if (mbedtls_mpi_cmp_int(&pt->Z, 1) != 0) |
| return (MBEDTLS_ERR_ECP_INVALID_KEY); |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) |
| return (ecp_check_pubkey_mx(grp, pt)); |
| #endif |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| if (GET_WORD_LEN(grp->pbits) <= PKE_OPERAND_MAX_WORD_LEN) |
| { |
| } |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| { |
| if (GET_WORD_LEN(grp->pbits) <= PKE_OPERAND_MAX_WORD_LEN) |
| return (ecp_alt_b91_backend_check_pubkey(grp, pt)); |
| else |
| return (ecp_check_pubkey_sw(grp, pt)); |
| } |
| #endif |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| } |
| |
| /* |
| * Check that an mbedtls_mpi is valid as a private key |
| */ |
| int mbedtls_ecp_check_privkey(const mbedtls_ecp_group * grp, const mbedtls_mpi * d) |
| { |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(d != NULL); |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) |
| { |
| /* see RFC 7748 sec. 5 para. 5 */ |
| if (mbedtls_mpi_get_bit(d, 0) != 0 || mbedtls_mpi_get_bit(d, 1) != 0 || |
| mbedtls_mpi_bitlen(d) - 1 != grp->nbits) /* mbedtls_mpi_bitlen is one-based! */ |
| return (MBEDTLS_ERR_ECP_INVALID_KEY); |
| |
| /* see [Curve25519] page 5 */ |
| if (grp->nbits == 254 && mbedtls_mpi_get_bit(d, 2) != 0) |
| return (MBEDTLS_ERR_ECP_INVALID_KEY); |
| |
| return (0); |
| } |
| #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| { |
| /* see SEC1 3.2 */ |
| if (mbedtls_mpi_cmp_int(d, 1) < 0 || mbedtls_mpi_cmp_mpi(d, &grp->N) >= 0) |
| return (MBEDTLS_ERR_ECP_INVALID_KEY); |
| else |
| return (0); |
| } |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| } |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| MBEDTLS_STATIC_TESTABLE |
| int mbedtls_ecp_gen_privkey_mx(size_t high_bit, mbedtls_mpi * d, int (*f_rng)(void *, unsigned char *, size_t), void * p_rng) |
| { |
| int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; |
| size_t n_random_bytes = high_bit / 8 + 1; |
| |
| /* [Curve25519] page 5 */ |
| /* Generate a (high_bit+1)-bit random number by generating just enough |
| * random bytes, then shifting out extra bits from the top (necessary |
| * when (high_bit+1) is not a multiple of 8). */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(d, n_random_bytes, f_rng, p_rng)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(d, 8 * n_random_bytes - high_bit - 1)); |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, high_bit, 1)); |
| |
| /* Make sure the last two bits are unset for Curve448, three bits for |
| Curve25519 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 0, 0)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 1, 0)); |
| if (high_bit == 254) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 2, 0)); |
| } |
| |
| cleanup: |
| return (ret); |
| } |
| #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| static int mbedtls_ecp_gen_privkey_sw(const mbedtls_mpi * N, mbedtls_mpi * d, int (*f_rng)(void *, unsigned char *, size_t), |
| void * p_rng) |
| { |
| int ret = mbedtls_mpi_random(d, 1, N, f_rng, p_rng); |
| switch (ret) |
| { |
| case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: |
| return (MBEDTLS_ERR_ECP_RANDOM_FAILED); |
| default: |
| return (ret); |
| } |
| } |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| |
| /* |
| * Generate a private key |
| */ |
| int mbedtls_ecp_gen_privkey(const mbedtls_ecp_group * grp, mbedtls_mpi * d, int (*f_rng)(void *, unsigned char *, size_t), |
| void * p_rng) |
| { |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(d != NULL); |
| ECP_VALIDATE_RET(f_rng != NULL); |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) |
| return (mbedtls_ecp_gen_privkey_mx(grp->nbits, d, f_rng, p_rng)); |
| #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| return (mbedtls_ecp_gen_privkey_sw(&grp->N, d, f_rng, p_rng)); |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| } |
| |
| /* |
| * Generate a keypair with configurable base point |
| */ |
| int mbedtls_ecp_gen_keypair_base(mbedtls_ecp_group * grp, const mbedtls_ecp_point * G, mbedtls_mpi * d, mbedtls_ecp_point * Q, |
| int (*f_rng)(void *, unsigned char *, size_t), void * p_rng) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(d != NULL); |
| ECP_VALIDATE_RET(G != NULL); |
| ECP_VALIDATE_RET(Q != NULL); |
| ECP_VALIDATE_RET(f_rng != NULL); |
| |
| MBEDTLS_MPI_CHK(mbedtls_ecp_gen_privkey(grp, d, f_rng, p_rng)); |
| MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, Q, d, G, f_rng, p_rng)); |
| |
| cleanup: |
| return (ret); |
| } |
| |
| /* |
| * Generate key pair, wrapper for conventional base point |
| */ |
| int mbedtls_ecp_gen_keypair(mbedtls_ecp_group * grp, mbedtls_mpi * d, mbedtls_ecp_point * Q, |
| int (*f_rng)(void *, unsigned char *, size_t), void * p_rng) |
| { |
| ECP_VALIDATE_RET(grp != NULL); |
| ECP_VALIDATE_RET(d != NULL); |
| ECP_VALIDATE_RET(Q != NULL); |
| ECP_VALIDATE_RET(f_rng != NULL); |
| |
| return (mbedtls_ecp_gen_keypair_base(grp, &grp->G, d, Q, f_rng, p_rng)); |
| } |
| |
| /* |
| * Generate a keypair, prettier wrapper |
| */ |
| int mbedtls_ecp_gen_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair * key, int (*f_rng)(void *, unsigned char *, size_t), |
| void * p_rng) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| ECP_VALIDATE_RET(key != NULL); |
| ECP_VALIDATE_RET(f_rng != NULL); |
| |
| if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) |
| return (ret); |
| |
| return (mbedtls_ecp_gen_keypair(&key->grp, &key->d, &key->Q, f_rng, p_rng)); |
| } |
| |
| #define ECP_CURVE25519_KEY_SIZE 32 |
| /* |
| * Read a private key. |
| */ |
| int mbedtls_ecp_read_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair * key, const unsigned char * buf, size_t buflen) |
| { |
| int ret = 0; |
| |
| ECP_VALIDATE_RET(key != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| |
| if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) |
| return (ret); |
| |
| ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) |
| { |
| /* |
| * If it is Curve25519 curve then mask the key as mandated by RFC7748 |
| */ |
| if (grp_id == MBEDTLS_ECP_DP_CURVE25519) |
| { |
| if (buflen != ECP_CURVE25519_KEY_SIZE) |
| return MBEDTLS_ERR_ECP_INVALID_KEY; |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&key->d, buf, buflen)); |
| |
| /* Set the three least significant bits to 0 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 0, 0)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 1, 0)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 2, 0)); |
| |
| /* Set the most significant bit to 0 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, ECP_CURVE25519_KEY_SIZE * 8 - 1, 0)); |
| |
| /* Set the second most significant bit to 1 */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, ECP_CURVE25519_KEY_SIZE * 8 - 2, 1)); |
| } |
| else |
| ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; |
| } |
| |
| #endif |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&key->d, buf, buflen)); |
| |
| MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(&key->grp, &key->d)); |
| } |
| |
| #endif |
| cleanup: |
| |
| if (ret != 0) |
| mbedtls_mpi_free(&key->d); |
| |
| return (ret); |
| } |
| |
| /* |
| * Write a private key. |
| */ |
| int mbedtls_ecp_write_key(mbedtls_ecp_keypair * key, unsigned char * buf, size_t buflen) |
| { |
| int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; |
| |
| ECP_VALIDATE_RET(key != NULL); |
| ECP_VALIDATE_RET(buf != NULL); |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) |
| { |
| if (key->grp.id == MBEDTLS_ECP_DP_CURVE25519) |
| { |
| if (buflen < ECP_CURVE25519_KEY_SIZE) |
| return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&key->d, buf, buflen)); |
| } |
| else |
| ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; |
| } |
| |
| #endif |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) |
| { |
| MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&key->d, buf, buflen)); |
| } |
| |
| #endif |
| cleanup: |
| |
| return (ret); |
| } |
| |
| /* |
| * Check a public-private key pair |
| */ |
| int mbedtls_ecp_check_pub_priv(const mbedtls_ecp_keypair * pub, const mbedtls_ecp_keypair * prv, |
| int (*f_rng)(void *, unsigned char *, size_t), void * p_rng) |
| { |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_ecp_point Q; |
| mbedtls_ecp_group grp; |
| ECP_VALIDATE_RET(pub != NULL); |
| ECP_VALIDATE_RET(prv != NULL); |
| |
| if (pub->grp.id == MBEDTLS_ECP_DP_NONE || pub->grp.id != prv->grp.id || mbedtls_mpi_cmp_mpi(&pub->Q.X, &prv->Q.X) || |
| mbedtls_mpi_cmp_mpi(&pub->Q.Y, &prv->Q.Y) || mbedtls_mpi_cmp_mpi(&pub->Q.Z, &prv->Q.Z)) |
| { |
| return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA); |
| } |
| |
| mbedtls_ecp_point_init(&Q); |
| mbedtls_ecp_group_init(&grp); |
| |
| /* mbedtls_ecp_mul() needs a non-const group... */ |
| mbedtls_ecp_group_copy(&grp, &prv->grp); |
| |
| /* Also checks d is valid */ |
| MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &Q, &prv->d, &prv->grp.G, f_rng, p_rng)); |
| |
| if (mbedtls_mpi_cmp_mpi(&Q.X, &prv->Q.X) || mbedtls_mpi_cmp_mpi(&Q.Y, &prv->Q.Y) || mbedtls_mpi_cmp_mpi(&Q.Z, &prv->Q.Z)) |
| { |
| ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; |
| goto cleanup; |
| } |
| |
| cleanup: |
| mbedtls_ecp_point_free(&Q); |
| mbedtls_ecp_group_free(&grp); |
| |
| return (ret); |
| } |
| |
| #if defined(MBEDTLS_SELF_TEST) |
| |
| /* |
| * PRNG for test - !!!INSECURE NEVER USE IN PRODUCTION!!! |
| * |
| * This is the linear congruential generator from numerical recipes, |
| * except we only use the low byte as the output. See |
| * https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use |
| */ |
| static int self_test_rng(void * ctx, unsigned char * out, size_t len) |
| { |
| static uint32_t state = 42; |
| |
| (void) ctx; |
| |
| for (size_t i = 0; i < len; i++) |
| { |
| state = state * 1664525u + 1013904223u; |
| out[i] = (unsigned char) state; |
| } |
| |
| return (0); |
| } |
| |
| /* Adjust the exponent to be a valid private point for the specified curve. |
| * This is sometimes necessary because we use a single set of exponents |
| * for all curves but the validity of values depends on the curve. */ |
| static int self_test_adjust_exponent(const mbedtls_ecp_group * grp, mbedtls_mpi * m) |
| { |
| int ret = 0; |
| switch (grp->id) |
| { |
| /* If Curve25519 is available, then that's what we use for the |
| * Montgomery test, so we don't need the adjustment code. */ |
| #if !defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
| case MBEDTLS_ECP_DP_CURVE448: |
| /* Move highest bit from 254 to N-1. Setting bit N-1 is |
| * necessary to enforce the highest-bit-set constraint. */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, 254, 0)); |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, grp->nbits, 1)); |
| /* Copy second-highest bit from 253 to N-2. This is not |
| * necessary but improves the test variety a bit. */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, grp->nbits - 1, mbedtls_mpi_get_bit(m, 253))); |
| break; |
| #endif |
| #endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */ |
| default: |
| /* Non-Montgomery curves and Curve25519 need no adjustment. */ |
| (void) grp; |
| (void) m; |
| goto cleanup; |
| } |
| cleanup: |
| return (ret); |
| } |
| |
| /* Calculate R = m.P for each m in exponents. Check that the number of |
| * basic operations doesn't depend on the value of m. */ |
| static int self_test_point(int verbose, mbedtls_ecp_group * grp, mbedtls_ecp_point * R, mbedtls_mpi * m, |
| const mbedtls_ecp_point * P, const char * const * exponents, size_t n_exponents) |
| { |
| int ret = 0; |
| size_t i = 0; |
| unsigned long add_c_prev, dbl_c_prev, mul_c_prev; |
| add_count = 0; |
| dbl_count = 0; |
| mul_count = 0; |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(m, 16, exponents[0])); |
| MBEDTLS_MPI_CHK(self_test_adjust_exponent(grp, m)); |
| MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, R, m, P, self_test_rng, NULL)); |
| |
| for (i = 1; i < n_exponents; i++) |
| { |
| add_c_prev = add_count; |
| dbl_c_prev = dbl_count; |
| mul_c_prev = mul_count; |
| add_count = 0; |
| dbl_count = 0; |
| mul_count = 0; |
| |
| MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(m, 16, exponents[i])); |
| MBEDTLS_MPI_CHK(self_test_adjust_exponent(grp, m)); |
| MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, R, m, P, self_test_rng, NULL)); |
| |
| if (add_count != add_c_prev || dbl_count != dbl_c_prev || mul_count != mul_c_prev) |
| { |
| ret = 1; |
| break; |
| } |
| } |
| |
| cleanup: |
| if (verbose != 0) |
| { |
| if (ret != 0) |
| mbedtls_printf("failed (%u)\n", (unsigned int) i); |
| else |
| mbedtls_printf("passed\n"); |
| } |
| return (ret); |
| } |
| |
| /* |
| * Checkup routine |
| */ |
| int mbedtls_ecp_self_test(int verbose) |
| { |
| if (__ecp_alt_b91_skip_internal_self_tests) |
| return ecp_alt_b91_backend_test(verbose); |
| |
| int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; |
| mbedtls_ecp_group grp; |
| mbedtls_ecp_point R, P; |
| mbedtls_mpi m; |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| /* Exponents especially adapted for secp192k1, which has the lowest |
| * order n of all supported curves (secp192r1 is in a slightly larger |
| * field but the order of its base point is slightly smaller). */ |
| const char * sw_exponents[] = { |
| "000000000000000000000000000000000000000000000001", /* one */ |
| "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */ |
| "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */ |
| "400000000000000000000000000000000000000000000000", /* one and zeros */ |
| "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */ |
| "555555555555555555555555555555555555555555555555", /* 101010... */ |
| }; |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| const char * m_exponents[] = { |
| /* Valid private values for Curve25519. In a build with Curve448 |
| * but not Curve25519, they will be adjusted in |
| * self_test_adjust_exponent(). */ |
| "4000000000000000000000000000000000000000000000000000000000000000", |
| "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30", |
| "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8", |
| "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460", |
| "5555555555555555555555555555555555555555555555555555555555555550", |
| "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8", |
| }; |
| #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ |
| |
| mbedtls_ecp_group_init(&grp); |
| mbedtls_ecp_point_init(&R); |
| mbedtls_ecp_point_init(&P); |
| mbedtls_mpi_init(&m); |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| /* Use secp192r1 if available, or any available curve */ |
| #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
| MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_SECP192R1)); |
| #else |
| MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, mbedtls_ecp_curve_list()->grp_id)); |
| #endif |
| |
| if (verbose != 0) |
| mbedtls_printf(" ECP SW test #1 (constant op_count, base point G): "); |
| /* Do a dummy multiplication first to trigger precomputation */ |
| MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&m, 2)); |
| MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &P, &m, &grp.G, self_test_rng, NULL)); |
| ret = self_test_point(verbose, &grp, &R, &m, &grp.G, sw_exponents, sizeof(sw_exponents) / sizeof(sw_exponents[0])); |
| if (ret != 0) |
| goto cleanup; |
| |
| if (verbose != 0) |
| mbedtls_printf(" ECP SW test #2 (constant op_count, other point): "); |
| /* We computed P = 2G last time, use it */ |
| ret = self_test_point(verbose, &grp, &R, &m, &P, sw_exponents, sizeof(sw_exponents) / sizeof(sw_exponents[0])); |
| if (ret != 0) |
| goto cleanup; |
| |
| mbedtls_ecp_group_free(&grp); |
| mbedtls_ecp_point_free(&R); |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if (verbose != 0) |
| mbedtls_printf(" ECP Montgomery test (constant op_count): "); |
| #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE25519)); |
| #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
| MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE448)); |
| #else |
| #error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test" |
| #endif |
| ret = self_test_point(verbose, &grp, &R, &m, &grp.G, m_exponents, sizeof(m_exponents) / sizeof(m_exponents[0])); |
| if (ret != 0) |
| goto cleanup; |
| #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ |
| |
| cleanup: |
| |
| if (ret < 0 && verbose != 0) |
| mbedtls_printf("Unexpected error, return code = %08X\n", (unsigned int) ret); |
| |
| mbedtls_ecp_group_free(&grp); |
| mbedtls_ecp_point_free(&R); |
| mbedtls_ecp_point_free(&P); |
| mbedtls_mpi_free(&m); |
| |
| if (verbose != 0) |
| mbedtls_printf("\n"); |
| |
| return (ret); |
| } |
| |
| #endif /* MBEDTLS_SELF_TEST */ |
| |
| #endif /* !MBEDTLS_ECP_ALT */ |
| |
| #endif /* MBEDTLS_ECP_C */ |