diff --git a/library/CMakeLists.txt b/library/CMakeLists.txt index 3901927306..259cad9673 100644 --- a/library/CMakeLists.txt +++ b/library/CMakeLists.txt @@ -37,7 +37,6 @@ set(src_crypto ecdsa.c ecjpake.c ecp.c - ecp_new.c ecp_curves.c ecp_curves_new.c entropy.c diff --git a/library/Makefile b/library/Makefile index fdab4f4ba0..194a847396 100644 --- a/library/Makefile +++ b/library/Makefile @@ -102,7 +102,6 @@ OBJS_CRYPTO= \ ecdsa.o \ ecjpake.o \ ecp.o \ - ecp_new.o \ ecp_curves.o \ ecp_curves_new.o \ entropy.o \ diff --git a/library/ecp.c b/library/ecp.c index d027564d54..870773c136 100644 --- a/library/ecp.c +++ b/library/ecp.c @@ -43,8 +43,6 @@ #include "common.h" -#if !defined(MBEDTLS_ECP_WITH_MPI_UINT) - /** * \brief Function level alternative implementation. * @@ -591,11 +589,14 @@ void mbedtls_ecp_group_free(mbedtls_ecp_group *grp) } 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); + +#if !defined(MBEDTLS_ECP_WITH_MPI_UINT) mbedtls_mpi_free(&grp->N); + mbedtls_mpi_free(&grp->P); +#endif } if (!ecp_group_is_static_comb_table(grp) && grp->T != NULL) { @@ -3641,5 +3642,3 @@ cleanup: #endif /* !MBEDTLS_ECP_ALT */ #endif /* MBEDTLS_ECP_LIGHT */ - -#endif /* !MBEDTLS_ECP_WITH_MPI_UINT */ diff --git a/library/ecp_new.c b/library/ecp_new.c deleted file mode 100644 index f86f0e9e2a..0000000000 --- a/library/ecp_new.c +++ /dev/null @@ -1,3643 +0,0 @@ -/* - * 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 https://www.secg.org/sec1-v2.pdf - * 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 - * - https://www.rfc-editor.org/rfc/rfc4492 - * RFC 7748 for the Curve448 and Curve25519 curve definitions - * - https://www.rfc-editor.org/rfc/rfc7748 - * - * [Curve25519] https://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. - * - * - * [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. - * - */ - -#include "common.h" - -#if defined(MBEDTLS_ECP_WITH_MPI_UINT) - -/** - * \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_LIGHT) - -#include "mbedtls/ecp.h" -#include "mbedtls/threading.h" -#include "mbedtls/platform_util.h" -#include "mbedtls/error.h" - -#include "bn_mul.h" -#include "ecp_invasive.h" - -#include - -#if !defined(MBEDTLS_ECP_ALT) - -#include "mbedtls/platform.h" - -#include "ecp_internal_alt.h" - -#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. - */ -#if defined(MBEDTLS_ECP_C) -static unsigned long add_count, dbl_count; -#endif /* MBEDTLS_ECP_C */ -static unsigned long 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) -{ - 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) -{ - 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 */ - -#if defined(MBEDTLS_ECP_C) -static void mpi_init_many(mbedtls_mpi *arr, size_t size) -{ - while (size--) { - mbedtls_mpi_init(arr++); - } -} - -static void mpi_free_many(mbedtls_mpi *arr, size_t size) -{ - while (size--) { - mbedtls_mpi_free(arr++); - } -} -#endif /* MBEDTLS_ECP_C */ - -/* - * 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) -{ - 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) -{ - 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) -{ - 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->A); - mbedtls_mpi_free(&grp->B); - mbedtls_ecp_point_free(&grp->G); - } - - 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; - 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) -{ - 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; - 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) -{ - 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) -{ - 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; - 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; - if (format != MBEDTLS_ECP_PF_UNCOMPRESSED && - format != MBEDTLS_ECP_PF_COMPRESSED) { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - - 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; -} - -#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) -static int mbedtls_ecp_sw_derive_y(const mbedtls_ecp_group *grp, - const mbedtls_mpi *X, - mbedtls_mpi *Y, - int parity_bit); -#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ - -/* - * 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; - 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 ยง5 */ - 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 (ilen < 1 + plen) { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - - MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->X, buf + 1, plen)); - MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1)); - - if (buf[0] == 0x04) { - /* format == MBEDTLS_ECP_PF_UNCOMPRESSED */ - if (ilen != 1 + plen * 2) { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - return mbedtls_mpi_read_binary(&pt->Y, buf + 1 + plen, plen); - } else if (buf[0] == 0x02 || buf[0] == 0x03) { - /* format == MBEDTLS_ECP_PF_COMPRESSED */ - if (ilen != 1 + plen) { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - return mbedtls_ecp_sw_derive_y(grp, &pt->X, &pt->Y, - (buf[0] & 1)); - } else { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - } -#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; - /* - * 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; - if (format != MBEDTLS_ECP_PF_UNCOMPRESSED && - format != MBEDTLS_ECP_PF_COMPRESSED) { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - - /* - * 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; - 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; - /* - * 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; - 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 - */ - MBEDTLS_PUT_UINT16_BE(curve_info->tls_id, buf, 0); - - 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) \ - do { \ - while ((N)->s < 0 && mbedtls_mpi_cmp_int((N), 0) != 0) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi((N), (N), &grp->P)); \ - } while (0) - -#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; -} - -static inline int mbedtls_mpi_mul_int_mod(const mbedtls_ecp_group *grp, - mbedtls_mpi *X, - const mbedtls_mpi *A, - mbedtls_mpi_uint c) -{ - int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; - - MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(X, A, c)); - MOD_ADD(X); -cleanup: - return ret; -} - -static inline int mbedtls_mpi_sub_int_mod(const mbedtls_ecp_group *grp, - mbedtls_mpi *X, - const mbedtls_mpi *A, - mbedtls_mpi_uint c) -{ - int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; - - MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(X, A, c)); - MOD_SUB(X); -cleanup: - return ret; -} - -#define MPI_ECP_SUB_INT(X, A, c) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int_mod(grp, X, A, c)) - -#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 */ - -/* - * Macro wrappers around ECP modular arithmetic - * - * Currently, these wrappers are defined via the bignum module. - */ - -#define MPI_ECP_ADD(X, A, B) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, X, A, B)) - -#define MPI_ECP_SUB(X, A, B) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, X, A, B)) - -#define MPI_ECP_MUL(X, A, B) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, X, A, B)) - -#define MPI_ECP_SQR(X, A) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, X, A, A)) - -#define MPI_ECP_MUL_INT(X, A, c) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int_mod(grp, X, A, c)) - -#define MPI_ECP_INV(dst, src) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod((dst), (src), &grp->P)) - -#define MPI_ECP_MOV(X, A) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A)) - -#define MPI_ECP_SHIFT_L(X, count) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, X, count)) - -#define MPI_ECP_LSET(X, c) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, c)) - -#define MPI_ECP_CMP_INT(X, c) \ - mbedtls_mpi_cmp_int(X, c) - -#define MPI_ECP_CMP(X, Y) \ - mbedtls_mpi_cmp_mpi(X, Y) - -/* Needs f_rng, p_rng to be defined. */ -#define MPI_ECP_RAND(X) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_random((X), 2, &grp->P, f_rng, p_rng)) - -/* Conditional negation - * Needs grp and a temporary MPI tmp to be defined. */ -#define MPI_ECP_COND_NEG(X, cond) \ - do \ - { \ - unsigned char nonzero = mbedtls_mpi_cmp_int((X), 0) != 0; \ - MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&tmp, &grp->P, (X))); \ - MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign((X), &tmp, \ - nonzero & cond)); \ - } while (0) - -#define MPI_ECP_NEG(X) MPI_ECP_COND_NEG((X), 1) - -#define MPI_ECP_VALID(X) \ - ((X)->p != NULL) - -#define MPI_ECP_COND_ASSIGN(X, Y, cond) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign((X), (Y), (cond))) - -#define MPI_ECP_COND_SWAP(X, Y, cond) \ - MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap((X), (Y), (cond))) - -#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) - -/* - * Computes the right-hand side of the Short Weierstrass equation - * RHS = X^3 + A X + B - */ -static int ecp_sw_rhs(const mbedtls_ecp_group *grp, - mbedtls_mpi *rhs, - const mbedtls_mpi *X) -{ - int ret; - - /* Compute X^3 + A X + B as X (X^2 + A) + B */ - MPI_ECP_SQR(rhs, X); - - /* Special case for A = -3 */ - if (grp->A.p == NULL) { - MPI_ECP_SUB_INT(rhs, rhs, 3); - } else { - MPI_ECP_ADD(rhs, rhs, &grp->A); - } - - MPI_ECP_MUL(rhs, rhs, X); - MPI_ECP_ADD(rhs, rhs, &grp->B); - -cleanup: - return ret; -} - -/* - * Derive Y from X and a parity bit - */ -static int mbedtls_ecp_sw_derive_y(const mbedtls_ecp_group *grp, - const mbedtls_mpi *X, - mbedtls_mpi *Y, - int parity_bit) -{ - /* w = y^2 = x^3 + ax + b - * y = sqrt(w) = w^((p+1)/4) mod p (for prime p where p = 3 mod 4) - * - * Note: this method for extracting square root does not validate that w - * was indeed a square so this function will return garbage in Y if X - * does not correspond to a point on the curve. - */ - - /* Check prerequisite p = 3 mod 4 */ - if (mbedtls_mpi_get_bit(&grp->P, 0) != 1 || - mbedtls_mpi_get_bit(&grp->P, 1) != 1) { - return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; - } - - int ret; - mbedtls_mpi exp; - mbedtls_mpi_init(&exp); - - /* use Y to store intermediate result, actually w above */ - MBEDTLS_MPI_CHK(ecp_sw_rhs(grp, Y, X)); - - /* w = y^2 */ /* Y contains y^2 intermediate result */ - /* exp = ((p+1)/4) */ - MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&exp, &grp->P, 1)); - MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&exp, 2)); - /* sqrt(w) = w^((p+1)/4) mod p (for prime p where p = 3 mod 4) */ - MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(Y, Y /*y^2*/, &exp, &grp->P, NULL)); - - /* check parity bit match or else invert Y */ - /* This quick inversion implementation is valid because Y != 0 for all - * Short Weierstrass curves supported by mbedtls, as each supported curve - * has an order that is a large prime, so each supported curve does not - * have any point of order 2, and a point with Y == 0 would be of order 2 */ - if (mbedtls_mpi_get_bit(Y, 0) != parity_bit) { - MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(Y, &grp->P, Y)); - } - -cleanup: - - mbedtls_mpi_free(&exp); - return ret; -} -#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ - -#if defined(MBEDTLS_ECP_C) -#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 countermeasures 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 (MPI_ECP_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 T; - mbedtls_mpi_init(&T); - - MPI_ECP_INV(&T, &pt->Z); /* T <- 1 / Z */ - MPI_ECP_MUL(&pt->Y, &pt->Y, &T); /* Y' <- Y*T = Y / Z */ - MPI_ECP_SQR(&T, &T); /* T <- T^2 = 1 / Z^2 */ - MPI_ECP_MUL(&pt->X, &pt->X, &T); /* X <- X * T = X / Z^2 */ - MPI_ECP_MUL(&pt->Y, &pt->Y, &T); /* Y'' <- Y' * T = Y / Z^3 */ - - MPI_ECP_LSET(&pt->Z, 1); - -cleanup: - - mbedtls_mpi_free(&T); - - 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, t; - - if ((c = mbedtls_calloc(T_size, sizeof(mbedtls_mpi))) == NULL) { - return MBEDTLS_ERR_ECP_ALLOC_FAILED; - } - - mbedtls_mpi_init(&t); - - mpi_init_many(c, T_size); - /* - * c[i] = Z_0 * ... * Z_i, i = 0,..,n := T_size-1 - */ - MPI_ECP_MOV(&c[0], &T[0]->Z); - for (i = 1; i < T_size; i++) { - MPI_ECP_MUL(&c[i], &c[i-1], &T[i]->Z); - } - - /* - * c[n] = 1 / (Z_0 * ... * Z_n) mod P - */ - MPI_ECP_INV(&c[T_size-1], &c[T_size-1]); - - for (i = T_size - 1;; i--) { - /* At the start of iteration i (note that i decrements), we have - * - c[j] = Z_0 * .... * Z_j for j < i, - * - c[j] = 1 / (Z_0 * .... * Z_j) for j == i, - * - * This is maintained via - * - c[i-1] <- c[i] * Z_i - * - * We also derive 1/Z_i = c[i] * c[i-1] for i>0 and use that - * to do the actual normalization. For i==0, we already have - * c[0] = 1 / Z_0. - */ - - if (i > 0) { - /* Compute 1/Z_i and establish invariant for the next iteration. */ - MPI_ECP_MUL(&t, &c[i], &c[i-1]); - MPI_ECP_MUL(&c[i-1], &c[i], &T[i]->Z); - } else { - MPI_ECP_MOV(&t, &c[0]); - } - - /* Now t holds 1 / Z_i; normalize as in ecp_normalize_jac() */ - MPI_ECP_MUL(&T[i]->Y, &T[i]->Y, &t); - MPI_ECP_SQR(&t, &t); - MPI_ECP_MUL(&T[i]->X, &T[i]->X, &t); - MPI_ECP_MUL(&T[i]->Y, &T[i]->Y, &t); - - /* - * 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)); - - MPI_ECP_LSET(&T[i]->Z, 1); - - if (i == 0) { - break; - } - } - -cleanup: - - mbedtls_mpi_free(&t); - mpi_free_many(c, T_size); - 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; - mbedtls_mpi tmp; - mbedtls_mpi_init(&tmp); - - MPI_ECP_COND_NEG(&Q->Y, inv); - -cleanup: - mbedtls_mpi_free(&tmp); - 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, - mbedtls_mpi tmp[4]) -{ -#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; - - /* Special case for A = -3 */ - if (grp->A.p == NULL) { - /* tmp[0] <- M = 3(X + Z^2)(X - Z^2) */ - MPI_ECP_SQR(&tmp[1], &P->Z); - MPI_ECP_ADD(&tmp[2], &P->X, &tmp[1]); - MPI_ECP_SUB(&tmp[3], &P->X, &tmp[1]); - MPI_ECP_MUL(&tmp[1], &tmp[2], &tmp[3]); - MPI_ECP_MUL_INT(&tmp[0], &tmp[1], 3); - } else { - /* tmp[0] <- M = 3.X^2 + A.Z^4 */ - MPI_ECP_SQR(&tmp[1], &P->X); - MPI_ECP_MUL_INT(&tmp[0], &tmp[1], 3); - - /* Optimize away for "koblitz" curves with A = 0 */ - if (MPI_ECP_CMP_INT(&grp->A, 0) != 0) { - /* M += A.Z^4 */ - MPI_ECP_SQR(&tmp[1], &P->Z); - MPI_ECP_SQR(&tmp[2], &tmp[1]); - MPI_ECP_MUL(&tmp[1], &tmp[2], &grp->A); - MPI_ECP_ADD(&tmp[0], &tmp[0], &tmp[1]); - } - } - - /* tmp[1] <- S = 4.X.Y^2 */ - MPI_ECP_SQR(&tmp[2], &P->Y); - MPI_ECP_SHIFT_L(&tmp[2], 1); - MPI_ECP_MUL(&tmp[1], &P->X, &tmp[2]); - MPI_ECP_SHIFT_L(&tmp[1], 1); - - /* tmp[3] <- U = 8.Y^4 */ - MPI_ECP_SQR(&tmp[3], &tmp[2]); - MPI_ECP_SHIFT_L(&tmp[3], 1); - - /* tmp[2] <- T = M^2 - 2.S */ - MPI_ECP_SQR(&tmp[2], &tmp[0]); - MPI_ECP_SUB(&tmp[2], &tmp[2], &tmp[1]); - MPI_ECP_SUB(&tmp[2], &tmp[2], &tmp[1]); - - /* tmp[1] <- S = M(S - T) - U */ - MPI_ECP_SUB(&tmp[1], &tmp[1], &tmp[2]); - MPI_ECP_MUL(&tmp[1], &tmp[1], &tmp[0]); - MPI_ECP_SUB(&tmp[1], &tmp[1], &tmp[3]); - - /* tmp[3] <- U = 2.Y.Z */ - MPI_ECP_MUL(&tmp[3], &P->Y, &P->Z); - MPI_ECP_SHIFT_L(&tmp[3], 1); - - /* Store results */ - MPI_ECP_MOV(&R->X, &tmp[2]); - MPI_ECP_MOV(&R->Y, &tmp[1]); - MPI_ECP_MOV(&R->Z, &tmp[3]); - -cleanup: - - 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. - * - * P,Q,R may alias, but only at the level of EC points: they must be either - * equal as pointers, or disjoint (including the coordinate data buffers). - * Fine-grained aliasing at the level of coordinates is not supported. - * - * 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. - * - * 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, - mbedtls_mpi tmp[4]) -{ -#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; - - /* NOTE: Aliasing between input and output is allowed, so one has to make - * sure that at the point X,Y,Z are written, {P,Q}->{X,Y,Z} are no - * longer read from. */ - mbedtls_mpi * const X = &R->X; - mbedtls_mpi * const Y = &R->Y; - mbedtls_mpi * const Z = &R->Z; - - if (!MPI_ECP_VALID(&Q->Z)) { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - - /* - * Trivial cases: P == 0 or Q == 0 (case 1) - */ - if (MPI_ECP_CMP_INT(&P->Z, 0) == 0) { - return mbedtls_ecp_copy(R, Q); - } - - if (MPI_ECP_CMP_INT(&Q->Z, 0) == 0) { - return mbedtls_ecp_copy(R, P); - } - - /* - * Make sure Q coordinates are normalized - */ - if (MPI_ECP_CMP_INT(&Q->Z, 1) != 0) { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - - MPI_ECP_SQR(&tmp[0], &P->Z); - MPI_ECP_MUL(&tmp[1], &tmp[0], &P->Z); - MPI_ECP_MUL(&tmp[0], &tmp[0], &Q->X); - MPI_ECP_MUL(&tmp[1], &tmp[1], &Q->Y); - MPI_ECP_SUB(&tmp[0], &tmp[0], &P->X); - MPI_ECP_SUB(&tmp[1], &tmp[1], &P->Y); - - /* Special cases (2) and (3) */ - if (MPI_ECP_CMP_INT(&tmp[0], 0) == 0) { - if (MPI_ECP_CMP_INT(&tmp[1], 0) == 0) { - ret = ecp_double_jac(grp, R, P, tmp); - goto cleanup; - } else { - ret = mbedtls_ecp_set_zero(R); - goto cleanup; - } - } - - /* {P,Q}->Z no longer used, so OK to write to Z even if there's aliasing. */ - MPI_ECP_MUL(Z, &P->Z, &tmp[0]); - MPI_ECP_SQR(&tmp[2], &tmp[0]); - MPI_ECP_MUL(&tmp[3], &tmp[2], &tmp[0]); - MPI_ECP_MUL(&tmp[2], &tmp[2], &P->X); - - MPI_ECP_MOV(&tmp[0], &tmp[2]); - MPI_ECP_SHIFT_L(&tmp[0], 1); - - /* {P,Q}->X no longer used, so OK to write to X even if there's aliasing. */ - MPI_ECP_SQR(X, &tmp[1]); - MPI_ECP_SUB(X, X, &tmp[0]); - MPI_ECP_SUB(X, X, &tmp[3]); - MPI_ECP_SUB(&tmp[2], &tmp[2], X); - MPI_ECP_MUL(&tmp[2], &tmp[2], &tmp[1]); - MPI_ECP_MUL(&tmp[3], &tmp[3], &P->Y); - /* {P,Q}->Y no longer used, so OK to write to Y even if there's aliasing. */ - MPI_ECP_SUB(Y, &tmp[2], &tmp[3]); - -cleanup: - - 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; - - mbedtls_mpi_init(&l); - - /* Generate l such that 1 < l < p */ - MPI_ECP_RAND(&l); - - /* Z' = l * Z */ - MPI_ECP_MUL(&pt->Z, &pt->Z, &l); - - /* Y' = l * Y */ - MPI_ECP_MUL(&pt->Y, &pt->Y, &l); - - /* X' = l^2 * X */ - MPI_ECP_SQR(&l, &l); - MPI_ECP_MUL(&pt->X, &pt->X, &l); - - /* Y'' = l^2 * Y' = l^3 * Y */ - MPI_ECP_MUL(&pt->Y, &pt->Y, &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_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] = { NULL }; - - mbedtls_mpi tmp[4]; - - mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); - -#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, tmp)); - } - -#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 to allow them to be used in - * ecp_add_mixed() below, which requires one normalized input. - * - * 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], tmp)); - } - } - -#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)); - - /* Free Z coordinate (=1 after normalization) to save RAM. - * This makes T[i] invalid as mbedtls_ecp_points, but this is OK - * since from this point onwards, they are only accessed indirectly - * via the getter function ecp_select_comb() which does set the - * target's Z coordinate to 1. */ - for (i = 0; i < T_size; i++) { - mbedtls_mpi_free(&T[i].Z); - } - -cleanup: - - mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); - -#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++) { - MPI_ECP_COND_ASSIGN(&R->X, &T[j].X, j == ii); - MPI_ECP_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)); - - MPI_ECP_LSET(&R->Z, 1); - -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; - mbedtls_mpi tmp[4]; - size_t i; - - mbedtls_ecp_point_init(&Txi); - mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); - -#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])); - 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, tmp)); - MBEDTLS_MPI_CHK(ecp_select_comb(grp, &Txi, T, T_size, x[i])); - MBEDTLS_MPI_CHK(ecp_add_mixed(grp, R, R, &Txi, tmp)); - } - -cleanup: - - mbedtls_ecp_point_free(&Txi); - mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); - -#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 transfer, 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 = (MPI_ECP_CMP(&P->Y, &grp->G.Y) == 0 && - MPI_ECP_CMP(&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); - } - - /* prevent caller from using invalid value */ - int should_free_R = (ret != 0); -#if defined(MBEDTLS_ECP_RESTARTABLE) - /* don't free R while in progress in case R == P */ - if (ret == MBEDTLS_ERR_ECP_IN_PROGRESS) { - should_free_R = 0; - } -#endif - if (should_free_R) { - 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 - * internally 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; - MPI_ECP_INV(&P->Z, &P->Z); - MPI_ECP_MUL(&P->X, &P->X, &P->Z); - MPI_ECP_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 */ - MPI_ECP_RAND(&l); - - MPI_ECP_MUL(&P->X, &P->X, &l); - MPI_ECP_MUL(&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, - mbedtls_mpi T[4]) -{ -#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; - - MPI_ECP_ADD(&T[0], &P->X, &P->Z); /* Pp := PX + PZ */ - MPI_ECP_SUB(&T[1], &P->X, &P->Z); /* Pm := PX - PZ */ - MPI_ECP_ADD(&T[2], &Q->X, &Q->Z); /* Qp := QX + XZ */ - MPI_ECP_SUB(&T[3], &Q->X, &Q->Z); /* Qm := QX - QZ */ - MPI_ECP_MUL(&T[3], &T[3], &T[0]); /* Qm * Pp */ - MPI_ECP_MUL(&T[2], &T[2], &T[1]); /* Qp * Pm */ - MPI_ECP_SQR(&T[0], &T[0]); /* Pp^2 */ - MPI_ECP_SQR(&T[1], &T[1]); /* Pm^2 */ - MPI_ECP_MUL(&R->X, &T[0], &T[1]); /* Pp^2 * Pm^2 */ - MPI_ECP_SUB(&T[0], &T[0], &T[1]); /* Pp^2 - Pm^2 */ - MPI_ECP_MUL(&R->Z, &grp->A, &T[0]); /* A * (Pp^2 - Pm^2) */ - MPI_ECP_ADD(&R->Z, &T[1], &R->Z); /* [ A * (Pp^2-Pm^2) ] + Pm^2 */ - MPI_ECP_ADD(&S->X, &T[3], &T[2]); /* Qm*Pp + Qp*Pm */ - MPI_ECP_SQR(&S->X, &S->X); /* (Qm*Pp + Qp*Pm)^2 */ - MPI_ECP_SUB(&S->Z, &T[3], &T[2]); /* Qm*Pp - Qp*Pm */ - MPI_ECP_SQR(&S->Z, &S->Z); /* (Qm*Pp - Qp*Pm)^2 */ - MPI_ECP_MUL(&S->Z, d, &S->Z); /* d * ( Qm*Pp - Qp*Pm )^2 */ - MPI_ECP_MUL(&R->Z, &T[0], &R->Z); /* [A*(Pp^2-Pm^2)+Pm^2]*(Pp^2-Pm^2) */ - -cleanup: - - 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_mpi tmp[4]; - mbedtls_ecp_point_init(&RP); mbedtls_mpi_init(&PX); - - mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); - - 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 */ - MPI_ECP_MOV(&PX, &P->X); - MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&RP, P)); - - /* Set R to zero in modified x/z coordinates */ - MPI_ECP_LSET(&R->X, 1); - MPI_ECP_LSET(&R->Z, 0); - mbedtls_mpi_free(&R->Y); - - /* RP.X might be slightly 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 = grp->nbits + 1; /* one past the (zero-based) required msb for private keys */ - 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 - */ - MPI_ECP_COND_SWAP(&R->X, &RP.X, b); - MPI_ECP_COND_SWAP(&R->Z, &RP.Z, b); - MBEDTLS_MPI_CHK(ecp_double_add_mxz(grp, R, &RP, R, &RP, &PX, tmp)); - MPI_ECP_COND_SWAP(&R->X, &RP.X, b); - MPI_ECP_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); - - mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); - 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 */ - - int restarting = 0; -#if defined(MBEDTLS_ECP_RESTARTABLE) - restarting = (rs_ctx != NULL && rs_ctx->rsm != NULL); -#endif - /* skip argument check when restarting */ - if (!restarting) { - /* 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) -{ - if (f_rng == NULL) { - return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; - } - - 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) -{ - return mbedtls_ecp_mul_restartable(grp, R, m, P, f_rng, p_rng, NULL); -} -#endif /* MBEDTLS_ECP_C */ - -#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^3 + A X + B - */ - MPI_ECP_SQR(&YY, &pt->Y); - MBEDTLS_MPI_CHK(ecp_sw_rhs(grp, &RHS, &pt->X)); - - if (MPI_ECP_CMP(&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_C) -#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; - mbedtls_mpi tmp; - mbedtls_mpi_init(&tmp); - - if (mbedtls_mpi_cmp_int(m, 0) == 0) { - MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); - MBEDTLS_MPI_CHK(mbedtls_ecp_set_zero(R)); - } else if (mbedtls_mpi_cmp_int(m, 1) == 0) { - MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); - MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P)); - } else if (mbedtls_mpi_cmp_int(m, -1) == 0) { - MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P)); - MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P)); - MPI_ECP_NEG(&R->Y); - } else { - MBEDTLS_MPI_CHK(ecp_mul_restartable_internal(grp, R, m, P, - NULL, NULL, rs_ctx)); - } - -cleanup: - mbedtls_mpi_free(&tmp); - - 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; - mbedtls_mpi tmp[4]; -#if defined(MBEDTLS_ECP_INTERNAL_ALT) - char is_grp_capable = 0; -#endif - if (mbedtls_ecp_get_type(grp) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { - return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; - } - - mbedtls_ecp_point_init(&mP); - mpi_init_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); - - 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, tmp)); -#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: - - mpi_free_many(tmp, sizeof(tmp) / sizeof(mbedtls_mpi)); - -#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) -{ - return mbedtls_ecp_muladd_restartable(grp, R, m, P, n, Q, NULL); -} -#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ -#endif /* MBEDTLS_ECP_C */ - -#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) -#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) -#define ECP_MPI_INIT(_p, _n) { .p = (mbedtls_mpi_uint *) (_p), .s = 1, .n = (_n) } -#define ECP_MPI_INIT_ARRAY(x) \ - ECP_MPI_INIT(x, sizeof(x) / sizeof(mbedtls_mpi_uint)) -/* - * 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) -{ - /* 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 (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) { - 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) -{ -#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) -{ -#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; -} - -#if defined(MBEDTLS_ECP_C) -/* - * 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; - 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) -{ - 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; - 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); -} -#endif /* MBEDTLS_ECP_C */ - -#define ECP_CURVE25519_KEY_SIZE 32 -#define ECP_CURVE448_KEY_SIZE 56 -/* - * 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; - - 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) { - /* - * Mask the key as mandated by RFC7748 for Curve25519 and Curve448. - */ - 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 if (grp_id == MBEDTLS_ECP_DP_CURVE448) { - if (buflen != ECP_CURVE448_KEY_SIZE) { - return MBEDTLS_ERR_ECP_INVALID_KEY; - } - - MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&key->d, buf, buflen)); - - /* Set the two 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)); - - /* Set the most significant bit to 1 */ - MBEDTLS_MPI_CHK( - mbedtls_mpi_set_bit(&key->d, - ECP_CURVE448_KEY_SIZE * 8 - 1, 1) - ); - } - } -#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)); - } -#endif - MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(&key->grp, &key->d)); - -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; - -#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; - } - - } else if (key->grp.id == MBEDTLS_ECP_DP_CURVE448) { - if (buflen < ECP_CURVE448_KEY_SIZE) { - return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; - } - } - MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&key->d, buf, buflen)); - } -#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; -} - -#if defined(MBEDTLS_ECP_C) -/* - * 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; - 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; -} -#endif /* MBEDTLS_ECP_C */ - -/* - * Export generic key-pair parameters. - */ -int mbedtls_ecp_export(const mbedtls_ecp_keypair *key, mbedtls_ecp_group *grp, - mbedtls_mpi *d, mbedtls_ecp_point *Q) -{ - int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; - - if ((ret = mbedtls_ecp_group_copy(grp, &key->grp)) != 0) { - return ret; - } - - if ((ret = mbedtls_mpi_copy(d, &key->d)) != 0) { - return ret; - } - - if ((ret = mbedtls_ecp_copy(Q, &key->Q)) != 0) { - return ret; - } - - return 0; -} - -#if defined(MBEDTLS_SELF_TEST) - -#if defined(MBEDTLS_ECP_C) -/* - * 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; -} -#endif /* MBEDTLS_ECP_C */ - -/* - * Checkup routine - */ -int mbedtls_ecp_self_test(int verbose) -{ -#if defined(MBEDTLS_ECP_C) - 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; -#else /* MBEDTLS_ECP_C */ - (void) verbose; - return 0; -#endif /* MBEDTLS_ECP_C */ -} - -#endif /* MBEDTLS_SELF_TEST */ - -#endif /* !MBEDTLS_ECP_ALT */ - -#endif /* MBEDTLS_ECP_LIGHT */ - -#endif /* MBEDTLS_ECP_WITH_MPI_UINT */