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mbedtls/library/ecp.c
Xiaokang Qian 0e5a27b640 Update links of references in bignum code 
Signed-off-by: Xiaokang Qian <xiaokang.qian@arm.com>
2023-04-21 09:58:07 +00:00

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/*
* 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.
* <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
*
* [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
* render ECC resistant against Side Channel Attacks. IACR Cryptology
* ePrint Archive, 2004, vol. 2004, p. 342.
* <http://eprint.iacr.org/2004/342.pdf>
*/
#include "common.h"
/**
* \brief Function level alternative implementation.
*
* The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to
* replace certain functions in this module. The alternative implementations are
* typically hardware accelerators and need to activate the hardware before the
* computation starts and deactivate it after it finishes. The
* mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve
* this purpose.
*
* To preserve the correct functionality the following conditions must hold:
*
* - The alternative implementation must be activated by
* mbedtls_internal_ecp_init() before any of the replaceable functions is
* called.
* - mbedtls_internal_ecp_free() must \b only be called when the alternative
* implementation is activated.
* - mbedtls_internal_ecp_init() must \b not be called when the alternative
* implementation is activated.
* - Public functions must not return while the alternative implementation is
* activated.
* - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and
* before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) )
* \endcode ensures that the alternative implementation supports the current
* group.
*/
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
#endif
#if defined(MBEDTLS_ECP_C)
#include "mbedtls/ecp.h"
#include "mbedtls/threading.h"
#include "mbedtls/platform_util.h"
#include "mbedtls/error.h"
#include "mbedtls/bn_mul.h"
#include "ecp_invasive.h"
#include <string.h>
#if !defined(MBEDTLS_ECP_ALT)
/* Parameter validation macros based on platform_util.h */
#define ECP_VALIDATE_RET(cond) \
MBEDTLS_INTERNAL_VALIDATE_RET(cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA)
#define ECP_VALIDATE(cond) \
MBEDTLS_INTERNAL_VALIDATE(cond)
#include "mbedtls/platform.h"
#include "mbedtls/ecp_internal.h"
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
#if defined(MBEDTLS_HMAC_DRBG_C)
#include "mbedtls/hmac_drbg.h"
#elif defined(MBEDTLS_CTR_DRBG_C)
#include "mbedtls/ctr_drbg.h"
#else
#error \
"Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
#endif
#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
#if defined(MBEDTLS_SELF_TEST)
/*
* Counts of point addition and doubling, and field multiplications.
* Used to test resistance of point multiplication to simple timing attacks.
*/
static unsigned long add_count, dbl_count, mul_count;
#endif
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
/*
* Currently ecp_mul() takes a RNG function as an argument, used for
* side-channel protection, but it can be NULL. The initial reasoning was
* that people will pass non-NULL RNG when they care about side-channels, but
* unfortunately we have some APIs that call ecp_mul() with a NULL RNG, with
* no opportunity for the user to do anything about it.
*
* The obvious strategies for addressing that include:
* - change those APIs so that they take RNG arguments;
* - require a global RNG to be available to all crypto modules.
*
* Unfortunately those would break compatibility. So what we do instead is
* have our own internal DRBG instance, seeded from the secret scalar.
*
* The following is a light-weight abstraction layer for doing that with
* HMAC_DRBG (first choice) or CTR_DRBG.
*/
#if defined(MBEDTLS_HMAC_DRBG_C)
/* DRBG context type */
typedef mbedtls_hmac_drbg_context ecp_drbg_context;
/* DRBG context init */
static inline void ecp_drbg_init(ecp_drbg_context *ctx)
{
mbedtls_hmac_drbg_init(ctx);
}
/* DRBG context free */
static inline void ecp_drbg_free(ecp_drbg_context *ctx)
{
mbedtls_hmac_drbg_free(ctx);
}
/* DRBG function */
static inline int ecp_drbg_random(void *p_rng,
unsigned char *output, size_t output_len)
{
return mbedtls_hmac_drbg_random(p_rng, output, output_len);
}
/* DRBG context seeding */
static int ecp_drbg_seed(ecp_drbg_context *ctx,
const mbedtls_mpi *secret, size_t secret_len)
{
int ret;
unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
/* The list starts with strong hashes */
const mbedtls_md_type_t md_type =
(const mbedtls_md_type_t) (mbedtls_md_list()[0]);
const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type(md_type);
if (secret_len > MBEDTLS_ECP_MAX_BYTES) {
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(secret,
secret_bytes, secret_len));
ret = mbedtls_hmac_drbg_seed_buf(ctx, md_info, secret_bytes, secret_len);
cleanup:
mbedtls_platform_zeroize(secret_bytes, secret_len);
return ret;
}
#elif defined(MBEDTLS_CTR_DRBG_C)
/* DRBG context type */
typedef mbedtls_ctr_drbg_context ecp_drbg_context;
/* DRBG context init */
static inline void ecp_drbg_init(ecp_drbg_context *ctx)
{
mbedtls_ctr_drbg_init(ctx);
}
/* DRBG context free */
static inline void ecp_drbg_free(ecp_drbg_context *ctx)
{
mbedtls_ctr_drbg_free(ctx);
}
/* DRBG function */
static inline int ecp_drbg_random(void *p_rng,
unsigned char *output, size_t output_len)
{
return mbedtls_ctr_drbg_random(p_rng, output, output_len);
}
/*
* Since CTR_DRBG doesn't have a seed_buf() function the way HMAC_DRBG does,
* we need to pass an entropy function when seeding. So we use a dummy
* function for that, and pass the actual entropy as customisation string.
* (During seeding of CTR_DRBG the entropy input and customisation string are
* concatenated before being used to update the secret state.)
*/
static int ecp_ctr_drbg_null_entropy(void *ctx, unsigned char *out, size_t len)
{
(void) ctx;
memset(out, 0, len);
return 0;
}
/* DRBG context seeding */
static int ecp_drbg_seed(ecp_drbg_context *ctx,
const mbedtls_mpi *secret, size_t secret_len)
{
int ret;
unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
if (secret_len > MBEDTLS_ECP_MAX_BYTES) {
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(secret,
secret_bytes, secret_len));
ret = mbedtls_ctr_drbg_seed(ctx, ecp_ctr_drbg_null_entropy, NULL,
secret_bytes, secret_len);
cleanup:
mbedtls_platform_zeroize(secret_bytes, secret_len);
return ret;
}
#else
#error \
"Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
#endif /* DRBG modules */
#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
#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;
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
ecp_drbg_context drbg_ctx;
unsigned char drbg_seeded;
#endif
};
/*
* 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;
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
ecp_drbg_init(&ctx->drbg_ctx);
ctx->drbg_seeded = 0;
#endif
}
/*
* 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);
}
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
ecp_drbg_free(&ctx->drbg_ctx);
#endif
ecp_restart_rsm_init(ctx);
}
/*
* Restart context for ecp_muladd()
*/
struct mbedtls_ecp_restart_muladd {
mbedtls_ecp_point mP; /* mP value */
mbedtls_ecp_point R; /* R intermediate result */
enum { /* what should we do next? */
ecp_rsma_mul1 = 0, /* first multiplication */
ecp_rsma_mul2, /* second multiplication */
ecp_rsma_add, /* addition */
ecp_rsma_norm, /* normalization */
} state;
};
/*
* Init restart_muladd sub-context
*/
static void ecp_restart_ma_init(mbedtls_ecp_restart_muladd_ctx *ctx)
{
mbedtls_ecp_point_init(&ctx->mP);
mbedtls_ecp_point_init(&ctx->R);
ctx->state = ecp_rsma_mul1;
}
/*
* Free the components of a restart_muladd sub-context
*/
static void ecp_restart_ma_free(mbedtls_ecp_restart_muladd_ctx *ctx)
{
if (ctx == NULL) {
return;
}
mbedtls_ecp_point_free(&ctx->mP);
mbedtls_ecp_point_free(&ctx->R);
ecp_restart_ma_init(ctx);
}
/*
* Initialize a restart context
*/
void mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx *ctx)
{
ECP_VALIDATE(ctx != NULL);
ctx->ops_done = 0;
ctx->depth = 0;
ctx->rsm = NULL;
ctx->ma = NULL;
}
/*
* Free the components of a restart context
*/
void mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx *ctx)
{
if (ctx == NULL) {
return;
}
ecp_restart_rsm_free(ctx->rsm);
mbedtls_free(ctx->rsm);
ecp_restart_ma_free(ctx->ma);
mbedtls_free(ctx->ma);
mbedtls_ecp_restart_init(ctx);
}
/*
* Check if we can do the next step
*/
int mbedtls_ecp_check_budget(const mbedtls_ecp_group *grp,
mbedtls_ecp_restart_ctx *rs_ctx,
unsigned ops)
{
ECP_VALIDATE_RET(grp != NULL);
if (rs_ctx != NULL && ecp_max_ops != 0) {
/* scale depending on curve size: the chosen reference is 256-bit,
* and multiplication is quadratic. Round to the closest integer. */
if (grp->pbits >= 512) {
ops *= 4;
} else if (grp->pbits >= 384) {
ops *= 2;
}
/* Avoid infinite loops: always allow first step.
* Because of that, however, it's not generally true
* that ops_done <= ecp_max_ops, so the check
* ops_done > ecp_max_ops below is mandatory. */
if ((rs_ctx->ops_done != 0) &&
(rs_ctx->ops_done > ecp_max_ops ||
ops > ecp_max_ops - rs_ctx->ops_done)) {
return MBEDTLS_ERR_ECP_IN_PROGRESS;
}
/* update running count */
rs_ctx->ops_done += ops;
}
return 0;
}
/* Call this when entering a function that needs its own sub-context */
#define ECP_RS_ENTER(SUB) do { \
/* reset ops count for this call if top-level */ \
if (rs_ctx != NULL && rs_ctx->depth++ == 0) \
rs_ctx->ops_done = 0; \
\
/* set up our own sub-context if needed */ \
if (mbedtls_ecp_restart_is_enabled() && \
rs_ctx != NULL && rs_ctx->SUB == NULL) \
{ \
rs_ctx->SUB = mbedtls_calloc(1, sizeof(*rs_ctx->SUB)); \
if (rs_ctx->SUB == NULL) \
return MBEDTLS_ERR_ECP_ALLOC_FAILED; \
\
ecp_restart_## SUB ##_init(rs_ctx->SUB); \
} \
} while (0)
/* Call this when leaving a function that needs its own sub-context */
#define ECP_RS_LEAVE(SUB) do { \
/* clear our sub-context when not in progress (done or error) */ \
if (rs_ctx != NULL && rs_ctx->SUB != NULL && \
ret != MBEDTLS_ERR_ECP_IN_PROGRESS) \
{ \
ecp_restart_## SUB ##_free(rs_ctx->SUB); \
mbedtls_free(rs_ctx->SUB); \
rs_ctx->SUB = NULL; \
} \
\
if (rs_ctx != NULL) \
rs_ctx->depth--; \
} while (0)
#else /* MBEDTLS_ECP_RESTARTABLE */
#define ECP_RS_ENTER(sub) (void) rs_ctx;
#define ECP_RS_LEAVE(sub) (void) rs_ctx;
#endif /* MBEDTLS_ECP_RESTARTABLE */
/*
* List of supported curves:
* - internal ID
* - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7)
* - size in bits
* - readable name
*
* Curves are listed in order: largest curves first, and for a given size,
* fastest curves first. This provides the default order for the SSL module.
*
* Reminder: update profiles in x509_crt.c when adding a new curves!
*/
static const mbedtls_ecp_curve_info ecp_supported_curves[] =
{
#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
{ MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
#endif
#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
{ MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
#endif
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
{ MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
#endif
#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
{ MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
#endif
#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
{ MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
#endif
#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
{ MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
#endif
#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
{ MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
#endif
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
{ MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
#endif
#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
{ MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
#endif
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
{ MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
#endif
#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
{ MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
#endif
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
{ MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" },
#endif
#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
{ MBEDTLS_ECP_DP_CURVE448, 30, 448, "x448" },
#endif
{ MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
};
#define ECP_NB_CURVES sizeof(ecp_supported_curves) / \
sizeof(ecp_supported_curves[0])
static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
/*
* List of supported curves and associated info
*/
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list(void)
{
return ecp_supported_curves;
}
/*
* List of supported curves, group ID only
*/
const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list(void)
{
static int init_done = 0;
if (!init_done) {
size_t i = 0;
const mbedtls_ecp_curve_info *curve_info;
for (curve_info = mbedtls_ecp_curve_list();
curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
curve_info++) {
ecp_supported_grp_id[i++] = curve_info->grp_id;
}
ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
init_done = 1;
}
return ecp_supported_grp_id;
}
/*
* Get the curve info for the internal identifier
*/
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id)
{
const mbedtls_ecp_curve_info *curve_info;
for (curve_info = mbedtls_ecp_curve_list();
curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
curve_info++) {
if (curve_info->grp_id == grp_id) {
return curve_info;
}
}
return NULL;
}
/*
* Get the curve info from the TLS identifier
*/
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id)
{
const mbedtls_ecp_curve_info *curve_info;
for (curve_info = mbedtls_ecp_curve_list();
curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
curve_info++) {
if (curve_info->tls_id == tls_id) {
return curve_info;
}
}
return NULL;
}
/*
* Get the curve info from the name
*/
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name(const char *name)
{
const mbedtls_ecp_curve_info *curve_info;
if (name == NULL) {
return NULL;
}
for (curve_info = mbedtls_ecp_curve_list();
curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
curve_info++) {
if (strcmp(curve_info->name, name) == 0) {
return curve_info;
}
}
return NULL;
}
/*
* Get the type of a curve
*/
mbedtls_ecp_curve_type mbedtls_ecp_get_type(const mbedtls_ecp_group *grp)
{
if (grp->G.X.p == NULL) {
return MBEDTLS_ECP_TYPE_NONE;
}
if (grp->G.Y.p == NULL) {
return MBEDTLS_ECP_TYPE_MONTGOMERY;
} else {
return MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS;
}
}
/*
* Initialize (the components of) a point
*/
void mbedtls_ecp_point_init(mbedtls_ecp_point *pt)
{
ECP_VALIDATE(pt != NULL);
mbedtls_mpi_init(&pt->X);
mbedtls_mpi_init(&pt->Y);
mbedtls_mpi_init(&pt->Z);
}
/*
* Initialize (the components of) a group
*/
void mbedtls_ecp_group_init(mbedtls_ecp_group *grp)
{
ECP_VALIDATE(grp != NULL);
grp->id = MBEDTLS_ECP_DP_NONE;
mbedtls_mpi_init(&grp->P);
mbedtls_mpi_init(&grp->A);
mbedtls_mpi_init(&grp->B);
mbedtls_ecp_point_init(&grp->G);
mbedtls_mpi_init(&grp->N);
grp->pbits = 0;
grp->nbits = 0;
grp->h = 0;
grp->modp = NULL;
grp->t_pre = NULL;
grp->t_post = NULL;
grp->t_data = NULL;
grp->T = NULL;
grp->T_size = 0;
}
/*
* Initialize (the components of) a key pair
*/
void mbedtls_ecp_keypair_init(mbedtls_ecp_keypair *key)
{
ECP_VALIDATE(key != NULL);
mbedtls_ecp_group_init(&key->grp);
mbedtls_mpi_init(&key->d);
mbedtls_ecp_point_init(&key->Q);
}
/*
* Unallocate (the components of) a point
*/
void mbedtls_ecp_point_free(mbedtls_ecp_point *pt)
{
if (pt == NULL) {
return;
}
mbedtls_mpi_free(&(pt->X));
mbedtls_mpi_free(&(pt->Y));
mbedtls_mpi_free(&(pt->Z));
}
/*
* Unallocate (the components of) a group
*/
void mbedtls_ecp_group_free(mbedtls_ecp_group *grp)
{
size_t i;
if (grp == NULL) {
return;
}
if (grp->h != 1) {
mbedtls_mpi_free(&grp->P);
mbedtls_mpi_free(&grp->A);
mbedtls_mpi_free(&grp->B);
mbedtls_ecp_point_free(&grp->G);
mbedtls_mpi_free(&grp->N);
}
if (grp->T != NULL) {
for (i = 0; i < grp->T_size; i++) {
mbedtls_ecp_point_free(&grp->T[i]);
}
mbedtls_free(grp->T);
}
mbedtls_platform_zeroize(grp, sizeof(mbedtls_ecp_group));
}
/*
* Unallocate (the components of) a key pair
*/
void mbedtls_ecp_keypair_free(mbedtls_ecp_keypair *key)
{
if (key == NULL) {
return;
}
mbedtls_ecp_group_free(&key->grp);
mbedtls_mpi_free(&key->d);
mbedtls_ecp_point_free(&key->Q);
}
/*
* Copy the contents of a point
*/
int mbedtls_ecp_copy(mbedtls_ecp_point *P, const mbedtls_ecp_point *Q)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
ECP_VALIDATE_RET(P != NULL);
ECP_VALIDATE_RET(Q != NULL);
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->X, &Q->X));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Y, &Q->Y));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Z, &Q->Z));
cleanup:
return ret;
}
/*
* Copy the contents of a group object
*/
int mbedtls_ecp_group_copy(mbedtls_ecp_group *dst, const mbedtls_ecp_group *src)
{
ECP_VALIDATE_RET(dst != NULL);
ECP_VALIDATE_RET(src != NULL);
return mbedtls_ecp_group_load(dst, src->id);
}
/*
* Set point to zero
*/
int mbedtls_ecp_set_zero(mbedtls_ecp_point *pt)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
ECP_VALIDATE_RET(pt != NULL);
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->X, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Y, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 0));
cleanup:
return ret;
}
/*
* Tell if a point is zero
*/
int mbedtls_ecp_is_zero(mbedtls_ecp_point *pt)
{
ECP_VALIDATE_RET(pt != NULL);
return mbedtls_mpi_cmp_int(&pt->Z, 0) == 0;
}
/*
* Compare two points lazily
*/
int mbedtls_ecp_point_cmp(const mbedtls_ecp_point *P,
const mbedtls_ecp_point *Q)
{
ECP_VALIDATE_RET(P != NULL);
ECP_VALIDATE_RET(Q != NULL);
if (mbedtls_mpi_cmp_mpi(&P->X, &Q->X) == 0 &&
mbedtls_mpi_cmp_mpi(&P->Y, &Q->Y) == 0 &&
mbedtls_mpi_cmp_mpi(&P->Z, &Q->Z) == 0) {
return 0;
}
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
/*
* Import a non-zero point from ASCII strings
*/
int mbedtls_ecp_point_read_string(mbedtls_ecp_point *P, int radix,
const char *x, const char *y)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
ECP_VALIDATE_RET(P != NULL);
ECP_VALIDATE_RET(x != NULL);
ECP_VALIDATE_RET(y != NULL);
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->X, radix, x));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->Y, radix, y));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&P->Z, 1));
cleanup:
return ret;
}
/*
* Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748)
*/
int mbedtls_ecp_point_write_binary(const mbedtls_ecp_group *grp,
const mbedtls_ecp_point *P,
int format, size_t *olen,
unsigned char *buf, size_t buflen)
{
int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
size_t plen;
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(P != NULL);
ECP_VALIDATE_RET(olen != NULL);
ECP_VALIDATE_RET(buf != NULL);
ECP_VALIDATE_RET(format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
format == MBEDTLS_ECP_PF_COMPRESSED);
plen = mbedtls_mpi_size(&grp->P);
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
(void) format; /* Montgomery curves always use the same point format */
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
*olen = plen;
if (buflen < *olen) {
return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&P->X, buf, plen));
}
#endif
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
/*
* Common case: P == 0
*/
if (mbedtls_mpi_cmp_int(&P->Z, 0) == 0) {
if (buflen < 1) {
return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
}
buf[0] = 0x00;
*olen = 1;
return 0;
}
if (format == MBEDTLS_ECP_PF_UNCOMPRESSED) {
*olen = 2 * plen + 1;
if (buflen < *olen) {
return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
}
buf[0] = 0x04;
MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen));
MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->Y, buf + 1 + plen, plen));
} else if (format == MBEDTLS_ECP_PF_COMPRESSED) {
*olen = plen + 1;
if (buflen < *olen) {
return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
}
buf[0] = 0x02 + mbedtls_mpi_get_bit(&P->Y, 0);
MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen));
}
}
#endif
cleanup:
return ret;
}
/*
* Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748)
*/
int mbedtls_ecp_point_read_binary(const mbedtls_ecp_group *grp,
mbedtls_ecp_point *pt,
const unsigned char *buf, size_t ilen)
{
int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
size_t plen;
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(pt != NULL);
ECP_VALIDATE_RET(buf != NULL);
if (ilen < 1) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
plen = mbedtls_mpi_size(&grp->P);
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
if (plen != ilen) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&pt->X, buf, plen));
mbedtls_mpi_free(&pt->Y);
if (grp->id == MBEDTLS_ECP_DP_CURVE25519) {
/* Set most significant bit to 0 as prescribed in RFC7748 §5 */
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&pt->X, plen * 8 - 1, 0));
}
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1));
}
#endif
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
if (buf[0] == 0x00) {
if (ilen == 1) {
return mbedtls_ecp_set_zero(pt);
} else {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
}
if (buf[0] != 0x04) {
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
}
if (ilen != 2 * plen + 1) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->X, buf + 1, plen));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->Y,
buf + 1 + plen, plen));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1));
}
#endif
cleanup:
return ret;
}
/*
* Import a point from a TLS ECPoint record (RFC 4492)
* struct {
* opaque point <1..2^8-1>;
* } ECPoint;
*/
int mbedtls_ecp_tls_read_point(const mbedtls_ecp_group *grp,
mbedtls_ecp_point *pt,
const unsigned char **buf, size_t buf_len)
{
unsigned char data_len;
const unsigned char *buf_start;
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(pt != NULL);
ECP_VALIDATE_RET(buf != NULL);
ECP_VALIDATE_RET(*buf != NULL);
/*
* We must have at least two bytes (1 for length, at least one for data)
*/
if (buf_len < 2) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
data_len = *(*buf)++;
if (data_len < 1 || data_len > buf_len - 1) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
/*
* Save buffer start for read_binary and update buf
*/
buf_start = *buf;
*buf += data_len;
return mbedtls_ecp_point_read_binary(grp, pt, buf_start, data_len);
}
/*
* Export a point as a TLS ECPoint record (RFC 4492)
* struct {
* opaque point <1..2^8-1>;
* } ECPoint;
*/
int mbedtls_ecp_tls_write_point(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
int format, size_t *olen,
unsigned char *buf, size_t blen)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(pt != NULL);
ECP_VALIDATE_RET(olen != NULL);
ECP_VALIDATE_RET(buf != NULL);
ECP_VALIDATE_RET(format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
format == MBEDTLS_ECP_PF_COMPRESSED);
/*
* buffer length must be at least one, for our length byte
*/
if (blen < 1) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
if ((ret = mbedtls_ecp_point_write_binary(grp, pt, format,
olen, buf + 1, blen - 1)) != 0) {
return ret;
}
/*
* write length to the first byte and update total length
*/
buf[0] = (unsigned char) *olen;
++*olen;
return 0;
}
/*
* Set a group from an ECParameters record (RFC 4492)
*/
int mbedtls_ecp_tls_read_group(mbedtls_ecp_group *grp,
const unsigned char **buf, size_t len)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_ecp_group_id grp_id;
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(buf != NULL);
ECP_VALIDATE_RET(*buf != NULL);
if ((ret = mbedtls_ecp_tls_read_group_id(&grp_id, buf, len)) != 0) {
return ret;
}
return mbedtls_ecp_group_load(grp, grp_id);
}
/*
* Read a group id from an ECParameters record (RFC 4492) and convert it to
* mbedtls_ecp_group_id.
*/
int mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id *grp,
const unsigned char **buf, size_t len)
{
uint16_t tls_id;
const mbedtls_ecp_curve_info *curve_info;
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(buf != NULL);
ECP_VALIDATE_RET(*buf != NULL);
/*
* We expect at least three bytes (see below)
*/
if (len < 3) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
/*
* First byte is curve_type; only named_curve is handled
*/
if (*(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
/*
* Next two bytes are the namedcurve value
*/
tls_id = *(*buf)++;
tls_id <<= 8;
tls_id |= *(*buf)++;
if ((curve_info = mbedtls_ecp_curve_info_from_tls_id(tls_id)) == NULL) {
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
}
*grp = curve_info->grp_id;
return 0;
}
/*
* Write the ECParameters record corresponding to a group (RFC 4492)
*/
int mbedtls_ecp_tls_write_group(const mbedtls_ecp_group *grp, size_t *olen,
unsigned char *buf, size_t blen)
{
const mbedtls_ecp_curve_info *curve_info;
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(buf != NULL);
ECP_VALIDATE_RET(olen != NULL);
if ((curve_info = mbedtls_ecp_curve_info_from_grp_id(grp->id)) == NULL) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
/*
* We are going to write 3 bytes (see below)
*/
*olen = 3;
if (blen < *olen) {
return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
}
/*
* First byte is curve_type, always named_curve
*/
*buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
/*
* Next two bytes are the namedcurve value
*/
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) \
while ((N).s < 0 && mbedtls_mpi_cmp_int(&(N), 0) != 0) \
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&(N), &(N), &grp->P))
#if (defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
!(defined(MBEDTLS_ECP_NO_FALLBACK) && \
defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
defined(MBEDTLS_ECP_ADD_MIXED_ALT))) || \
(defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) && \
!(defined(MBEDTLS_ECP_NO_FALLBACK) && \
defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)))
static inline int mbedtls_mpi_sub_mod(const mbedtls_ecp_group *grp,
mbedtls_mpi *X,
const mbedtls_mpi *A,
const mbedtls_mpi *B)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(X, A, B));
MOD_SUB(*X);
cleanup:
return ret;
}
#endif /* All functions referencing mbedtls_mpi_sub_mod() are alt-implemented without fallback */
/*
* Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
* We known P, N and the result are positive, so sub_abs is correct, and
* a bit faster.
*/
#define MOD_ADD(N) \
while (mbedtls_mpi_cmp_mpi(&(N), &grp->P) >= 0) \
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&(N), &(N), &grp->P))
static inline int mbedtls_mpi_add_mod(const mbedtls_ecp_group *grp,
mbedtls_mpi *X,
const mbedtls_mpi *A,
const mbedtls_mpi *B)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, A, B));
MOD_ADD(*X);
cleanup:
return ret;
}
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
!(defined(MBEDTLS_ECP_NO_FALLBACK) && \
defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
defined(MBEDTLS_ECP_ADD_MIXED_ALT))
static inline int mbedtls_mpi_shift_l_mod(const mbedtls_ecp_group *grp,
mbedtls_mpi *X,
size_t count)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(X, count));
MOD_ADD(*X);
cleanup:
return ret;
}
#endif \
/* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
/*
* For curves in short Weierstrass form, we do all the internal operations in
* Jacobian coordinates.
*
* For multiplication, we'll use a comb method with 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 (mbedtls_mpi_cmp_int(&pt->Z, 0) == 0) {
return 0;
}
#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
if (mbedtls_internal_ecp_grp_capable(grp)) {
return mbedtls_internal_ecp_normalize_jac(grp, pt);
}
#endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi Zi, ZZi;
mbedtls_mpi_init(&Zi); mbedtls_mpi_init(&ZZi);
/*
* X = X / Z^2 mod p
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&Zi, &pt->Z, &grp->P));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ZZi, &Zi, &Zi));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->X, &pt->X, &ZZi));
/*
* Y = Y / Z^3 mod p
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y, &pt->Y, &ZZi));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y, &pt->Y, &Zi));
/*
* Z = 1
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1));
cleanup:
mbedtls_mpi_free(&Zi); mbedtls_mpi_free(&ZZi);
return ret;
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */
}
/*
* Normalize jacobian coordinates of an array of (pointers to) points,
* using Montgomery's trick to perform only one inversion mod P.
* (See for example Cohen's "A Course in Computational Algebraic Number
* Theory", Algorithm 10.3.4.)
*
* Warning: fails (returning an error) if one of the points is zero!
* This should never happen, see choice of w in ecp_mul_comb().
*
* Cost: 1N(t) := 1I + (6t - 3)M + 1S
*/
static int ecp_normalize_jac_many(const mbedtls_ecp_group *grp,
mbedtls_ecp_point *T[], size_t T_size)
{
if (T_size < 2) {
return ecp_normalize_jac(grp, *T);
}
#if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
if (mbedtls_internal_ecp_grp_capable(grp)) {
return mbedtls_internal_ecp_normalize_jac_many(grp, T, T_size);
}
#endif
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i;
mbedtls_mpi *c, u, Zi, ZZi;
if ((c = mbedtls_calloc(T_size, sizeof(mbedtls_mpi))) == NULL) {
return MBEDTLS_ERR_ECP_ALLOC_FAILED;
}
for (i = 0; i < T_size; i++) {
mbedtls_mpi_init(&c[i]);
}
mbedtls_mpi_init(&u); mbedtls_mpi_init(&Zi); mbedtls_mpi_init(&ZZi);
/*
* c[i] = Z_0 * ... * Z_i
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&c[0], &T[0]->Z));
for (i = 1; i < T_size; i++) {
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &c[i], &c[i-1], &T[i]->Z));
}
/*
* u = 1 / (Z_0 * ... * Z_n) mod P
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&u, &c[T_size-1], &grp->P));
for (i = T_size - 1;; i--) {
/*
* Zi = 1 / Z_i mod p
* u = 1 / (Z_0 * ... * Z_i) mod P
*/
if (i == 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Zi, &u));
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &Zi, &u, &c[i-1]));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &u, &u, &T[i]->Z));
}
/*
* proceed as in normalize()
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ZZi, &Zi, &Zi));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->X, &T[i]->X, &ZZi));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->Y, &T[i]->Y, &ZZi));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->Y, &T[i]->Y, &Zi));
/*
* Post-precessing: reclaim some memory by shrinking coordinates
* - not storing Z (always 1)
* - shrinking other coordinates, but still keeping the same number of
* limbs as P, as otherwise it will too likely be regrown too fast.
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->X, grp->P.n));
MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->Y, grp->P.n));
mbedtls_mpi_free(&T[i]->Z);
if (i == 0) {
break;
}
}
cleanup:
mbedtls_mpi_free(&u); mbedtls_mpi_free(&Zi); mbedtls_mpi_free(&ZZi);
for (i = 0; i < T_size; i++) {
mbedtls_mpi_free(&c[i]);
}
mbedtls_free(c);
return ret;
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */
}
/*
* Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
* "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
*/
static int ecp_safe_invert_jac(const mbedtls_ecp_group *grp,
mbedtls_ecp_point *Q,
unsigned char inv)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
unsigned char nonzero;
mbedtls_mpi mQY;
mbedtls_mpi_init(&mQY);
/* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&mQY, &grp->P, &Q->Y));
nonzero = mbedtls_mpi_cmp_int(&Q->Y, 0) != 0;
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&Q->Y, &mQY, inv & nonzero));
cleanup:
mbedtls_mpi_free(&mQY);
return ret;
}
/*
* Point doubling R = 2 P, Jacobian coordinates
*
* Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
*
* We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
* (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
*
* Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
*
* Cost: 1D := 3M + 4S (A == 0)
* 4M + 4S (A == -3)
* 3M + 6S + 1a otherwise
*/
static int ecp_double_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_ecp_point *P)
{
#if defined(MBEDTLS_SELF_TEST)
dbl_count++;
#endif
#if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
if (mbedtls_internal_ecp_grp_capable(grp)) {
return mbedtls_internal_ecp_double_jac(grp, R, P);
}
#endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi M, S, T, U;
mbedtls_mpi_init(&M); mbedtls_mpi_init(&S); mbedtls_mpi_init(&T); mbedtls_mpi_init(&U);
/* Special case for A = -3 */
if (grp->A.p == NULL) {
/* M = 3(X + Z^2)(X - Z^2) */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &P->Z, &P->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &T, &P->X, &S));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &U, &P->X, &S));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &T, &U));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&M, &S, 3)); MOD_ADD(M);
} else {
/* M = 3.X^2 */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &P->X, &P->X));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&M, &S, 3)); MOD_ADD(M);
/* Optimize away for "koblitz" curves with A = 0 */
if (mbedtls_mpi_cmp_int(&grp->A, 0) != 0) {
/* M += A.Z^4 */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &P->Z, &P->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T, &S, &S));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &T, &grp->A));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &M, &M, &S));
}
}
/* S = 4.X.Y^2 */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T, &P->Y, &P->Y));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &T, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &P->X, &T));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &S, 1));
/* U = 8.Y^4 */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &U, &T, &T));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &U, 1));
/* T = M^2 - 2.S */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T, &M, &M));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T, &T, &S));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T, &T, &S));
/* S = M(S - T) - U */
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S, &S, &T));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S, &S, &M));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S, &S, &U));
/* U = 2.Y.Z */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &U, &P->Y, &P->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &U, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->X, &T));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Y, &S));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Z, &U));
cleanup:
mbedtls_mpi_free(&M); mbedtls_mpi_free(&S); mbedtls_mpi_free(&T); mbedtls_mpi_free(&U);
return ret;
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */
}
/*
* Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
*
* The coordinates of Q must be normalized (= affine),
* but those of P don't need to. R is not normalized.
*
* Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
* None of these cases can happen as intermediate step in ecp_mul_comb():
* - at each step, P, Q and R are multiples of the base point, the factor
* being less than its order, so none of them is zero;
* - Q is an odd multiple of the base point, P an even multiple,
* due to the choice of precomputed points in the modified comb method.
* So branches for these cases do not leak secret information.
*
* We accept Q->Z being unset (saving memory in tables) as meaning 1.
*
* Cost: 1A := 8M + 3S
*/
static int ecp_add_mixed(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q)
{
#if defined(MBEDTLS_SELF_TEST)
add_count++;
#endif
#if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
if (mbedtls_internal_ecp_grp_capable(grp)) {
return mbedtls_internal_ecp_add_mixed(grp, R, P, Q);
}
#endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT)
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
/*
* Trivial cases: P == 0 or Q == 0 (case 1)
*/
if (mbedtls_mpi_cmp_int(&P->Z, 0) == 0) {
return mbedtls_ecp_copy(R, Q);
}
if (Q->Z.p != NULL && mbedtls_mpi_cmp_int(&Q->Z, 0) == 0) {
return mbedtls_ecp_copy(R, P);
}
/*
* Make sure Q coordinates are normalized
*/
if (Q->Z.p != NULL && mbedtls_mpi_cmp_int(&Q->Z, 1) != 0) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
mbedtls_mpi_init(&T1); mbedtls_mpi_init(&T2); mbedtls_mpi_init(&T3); mbedtls_mpi_init(&T4);
mbedtls_mpi_init(&X); mbedtls_mpi_init(&Y); mbedtls_mpi_init(&Z);
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T1, &P->Z, &P->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T2, &T1, &P->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T1, &T1, &Q->X));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T2, &T2, &Q->Y));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T1, &T1, &P->X));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T2, &T2, &P->Y));
/* Special cases (2) and (3) */
if (mbedtls_mpi_cmp_int(&T1, 0) == 0) {
if (mbedtls_mpi_cmp_int(&T2, 0) == 0) {
ret = ecp_double_jac(grp, R, P);
goto cleanup;
} else {
ret = mbedtls_ecp_set_zero(R);
goto cleanup;
}
}
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &Z, &P->Z, &T1));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3, &T1, &T1));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T4, &T3, &T1));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3, &T3, &P->X));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T1, &T3));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &T1, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &X, &T2, &T2));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &X, &X, &T1));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &X, &X, &T4));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T3, &T3, &X));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3, &T3, &T2));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T4, &T4, &P->Y));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &Y, &T3, &T4));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->X, &X));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Y, &Y));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Z, &Z));
cleanup:
mbedtls_mpi_free(&T1); mbedtls_mpi_free(&T2); mbedtls_mpi_free(&T3); mbedtls_mpi_free(&T4);
mbedtls_mpi_free(&X); mbedtls_mpi_free(&Y); mbedtls_mpi_free(&Z);
return ret;
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */
}
/*
* Randomize jacobian coordinates:
* (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
* This is sort of the reverse operation of ecp_normalize_jac().
*
* This countermeasure was first suggested in [2].
*/
static int ecp_randomize_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
#if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
if (mbedtls_internal_ecp_grp_capable(grp)) {
return mbedtls_internal_ecp_randomize_jac(grp, pt, f_rng, p_rng);
}
#endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi l, ll;
mbedtls_mpi_init(&l); mbedtls_mpi_init(&ll);
/* Generate l such that 1 < l < p */
MBEDTLS_MPI_CHK(mbedtls_mpi_random(&l, 2, &grp->P, f_rng, p_rng));
/* Z = l * Z */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Z, &pt->Z, &l));
/* X = l^2 * X */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ll, &l, &l));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->X, &pt->X, &ll));
/* Y = l^3 * Y */
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ll, &ll, &l));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y, &pt->Y, &ll));
cleanup:
mbedtls_mpi_free(&l); mbedtls_mpi_free(&ll);
if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) {
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
}
return ret;
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */
}
/*
* Check and define parameters used by the comb method (see below for details)
*/
#if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
#error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
#endif
/* d = ceil( n / w ) */
#define COMB_MAX_D (MBEDTLS_ECP_MAX_BITS + 1) / 2
/* number of precomputed points */
#define COMB_MAX_PRE (1 << (MBEDTLS_ECP_WINDOW_SIZE - 1))
/*
* Compute the representation of m that will be used with our comb method.
*
* The basic comb method is described in GECC 3.44 for example. We use a
* modified version that provides resistance to SPA by avoiding zero
* digits in the representation as in [3]. We modify the method further by
* requiring that all K_i be odd, which has the small cost that our
* representation uses one more K_i, due to carries, but saves on the size of
* the precomputed table.
*
* Summary of the comb method and its modifications:
*
* - The goal is to compute m*P for some w*d-bit integer m.
*
* - The basic comb method splits m into the w-bit integers
* x[0] .. x[d-1] where x[i] consists of the bits in m whose
* index has residue i modulo d, and computes m * P as
* S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where
* S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P.
*
* - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by
* .. + 2^{i-1} S[x[i-1]] - 2^i S[x[i]] + 2^{i+1} S[x[i]] + 2^{i+2} S[x[i+2]] ..,
* thereby successively converting it into a form where all summands
* are nonzero, at the cost of negative summands. This is the basic idea of [3].
*
* - More generally, even if x[i+1] != 0, we can first transform the sum as
* .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] ..,
* and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]].
* Performing and iterating this procedure for those x[i] that are even
* (keeping track of carry), we can transform the original sum into one of the form
* S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]]
* with all x'[i] odd. It is therefore only necessary to know S at odd indices,
* which is why we are only computing half of it in the first place in
* ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb.
*
* - For the sake of compactness, only the seven low-order bits of x[i]
* are used to represent its absolute value (K_i in the paper), and the msb
* of x[i] encodes the sign (s_i in the paper): it is set if and only if
* if s_i == -1;
*
* Calling conventions:
* - x is an array of size d + 1
* - w is the size, ie number of teeth, of the comb, and must be between
* 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
* - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
* (the result will be incorrect if these assumptions are not satisfied)
*/
static void ecp_comb_recode_core(unsigned char x[], size_t d,
unsigned char w, const mbedtls_mpi *m)
{
size_t i, j;
unsigned char c, cc, adjust;
memset(x, 0, d+1);
/* First get the classical comb values (except for x_d = 0) */
for (i = 0; i < d; i++) {
for (j = 0; j < w; j++) {
x[i] |= mbedtls_mpi_get_bit(m, i + d * j) << j;
}
}
/* Now make sure x_1 .. x_d are odd */
c = 0;
for (i = 1; i <= d; i++) {
/* Add carry and update it */
cc = x[i] & c;
x[i] = x[i] ^ c;
c = cc;
/* Adjust if needed, avoiding branches */
adjust = 1 - (x[i] & 0x01);
c |= x[i] & (x[i-1] * adjust);
x[i] = x[i] ^ (x[i-1] * adjust);
x[i-1] |= adjust << 7;
}
}
/*
* Precompute points for the adapted comb method
*
* Assumption: T must be able to hold 2^{w - 1} elements.
*
* Operation: If i = i_{w-1} ... i_1 is the binary representation of i,
* sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P.
*
* Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
*
* Note: Even comb values (those where P would be omitted from the
* sum defining T[i] above) are not needed in our adaption
* the comb method. See ecp_comb_recode_core().
*
* This function currently works in four steps:
* (1) [dbl] Computation of intermediate T[i] for 2-power values of i
* (2) [norm_dbl] Normalization of coordinates of these T[i]
* (3) [add] Computation of all T[i]
* (4) [norm_add] Normalization of all T[i]
*
* Step 1 can be interrupted but not the others; together with the final
* coordinate normalization they are the largest steps done at once, depending
* on the window size. Here are operation counts for P-256:
*
* step (2) (3) (4)
* w = 5 142 165 208
* w = 4 136 77 160
* w = 3 130 33 136
* w = 2 124 11 124
*
* So if ECC operations are blocking for too long even with a low max_ops
* value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order
* to minimize maximum blocking time.
*/
static int ecp_precompute_comb(const mbedtls_ecp_group *grp,
mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
unsigned char w, size_t d,
mbedtls_ecp_restart_ctx *rs_ctx)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
unsigned char i;
size_t j = 0;
const unsigned char T_size = 1U << (w - 1);
mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) {
goto dbl;
}
if (rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl) {
goto norm_dbl;
}
if (rs_ctx->rsm->state == ecp_rsm_pre_add) {
goto add;
}
if (rs_ctx->rsm->state == ecp_rsm_pre_norm_add) {
goto norm_add;
}
}
#else
(void) rs_ctx;
#endif
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
rs_ctx->rsm->state = ecp_rsm_pre_dbl;
/* initial state for the loop */
rs_ctx->rsm->i = 0;
}
dbl:
#endif
/*
* Set T[0] = P and
* T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
*/
MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&T[0], P));
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) {
j = rs_ctx->rsm->i;
} else
#endif
j = 0;
for (; j < d * (w - 1); j++) {
MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL);
i = 1U << (j / d);
cur = T + i;
if (j % d == 0) {
MBEDTLS_MPI_CHK(mbedtls_ecp_copy(cur, T + (i >> 1)));
}
MBEDTLS_MPI_CHK(ecp_double_jac(grp, cur, cur));
}
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl;
}
norm_dbl:
#endif
/*
* Normalize current elements in T. As T has holes,
* use an auxiliary array of pointers to elements in T.
*/
j = 0;
for (i = 1; i < T_size; i <<= 1) {
TT[j++] = T + i;
}
MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2);
MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j));
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
rs_ctx->rsm->state = ecp_rsm_pre_add;
}
add:
#endif
/*
* Compute the remaining ones using the minimal number of additions
* Be careful to update T[2^l] only after using it!
*/
MBEDTLS_ECP_BUDGET((T_size - 1) * MBEDTLS_ECP_OPS_ADD);
for (i = 1; i < T_size; i <<= 1) {
j = i;
while (j--) {
MBEDTLS_MPI_CHK(ecp_add_mixed(grp, &T[i + j], &T[j], &T[i]));
}
}
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
rs_ctx->rsm->state = ecp_rsm_pre_norm_add;
}
norm_add:
#endif
/*
* Normalize final elements in T. Even though there are no holes now, we
* still need the auxiliary array for homogeneity with the previous
* call. Also, skip T[0] which is already normalised, being a copy of P.
*/
for (j = 0; j + 1 < T_size; j++) {
TT[j] = T + j + 1;
}
MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2);
MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j));
cleanup:
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL &&
ret == MBEDTLS_ERR_ECP_IN_PROGRESS) {
if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) {
rs_ctx->rsm->i = j;
}
}
#endif
return ret;
}
/*
* Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
*
* See ecp_comb_recode_core() for background
*/
static int ecp_select_comb(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_ecp_point T[], unsigned char T_size,
unsigned char i)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
unsigned char ii, j;
/* Ignore the "sign" bit and scale down */
ii = (i & 0x7Fu) >> 1;
/* Read the whole table to thwart cache-based timing attacks */
for (j = 0; j < T_size; j++) {
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&R->X, &T[j].X, j == ii));
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&R->Y, &T[j].Y, j == ii));
}
/* Safely invert result if i is "negative" */
MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, R, i >> 7));
cleanup:
return ret;
}
/*
* Core multiplication algorithm for the (modified) comb method.
* This part is actually common with the basic comb method (GECC 3.44)
*
* Cost: d A + d D + 1 R
*/
static int ecp_mul_comb_core(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_ecp_point T[], unsigned char T_size,
const unsigned char x[], size_t d,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng,
mbedtls_ecp_restart_ctx *rs_ctx)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_ecp_point Txi;
size_t i;
mbedtls_ecp_point_init(&Txi);
#if !defined(MBEDTLS_ECP_RESTARTABLE)
(void) rs_ctx;
#endif
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL &&
rs_ctx->rsm->state != ecp_rsm_comb_core) {
rs_ctx->rsm->i = 0;
rs_ctx->rsm->state = ecp_rsm_comb_core;
}
/* new 'if' instead of nested for the sake of the 'else' branch */
if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) {
/* restore current index (R already pointing to rs_ctx->rsm->R) */
i = rs_ctx->rsm->i;
} else
#endif
{
int have_rng = 1;
/* Start with a non-zero point and randomize its coordinates */
i = d;
MBEDTLS_MPI_CHK(ecp_select_comb(grp, R, T, T_size, x[i]));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->Z, 1));
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
if (f_rng == NULL) {
have_rng = 0;
}
#endif
if (have_rng) {
MBEDTLS_MPI_CHK(ecp_randomize_jac(grp, R, f_rng, p_rng));
}
}
while (i != 0) {
MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD);
--i;
MBEDTLS_MPI_CHK(ecp_double_jac(grp, R, R));
MBEDTLS_MPI_CHK(ecp_select_comb(grp, &Txi, T, T_size, x[i]));
MBEDTLS_MPI_CHK(ecp_add_mixed(grp, R, R, &Txi));
}
cleanup:
mbedtls_ecp_point_free(&Txi);
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL &&
ret == MBEDTLS_ERR_ECP_IN_PROGRESS) {
rs_ctx->rsm->i = i;
/* no need to save R, already pointing to rs_ctx->rsm->R */
}
#endif
return ret;
}
/*
* Recode the scalar to get constant-time comb multiplication
*
* As the actual scalar recoding needs an odd scalar as a starting point,
* this wrapper ensures that by replacing m by N - m if necessary, and
* informs the caller that the result of multiplication will be negated.
*
* This works because we only support large prime order for Short Weierstrass
* curves, so N is always odd hence either m or N - m is.
*
* See ecp_comb_recode_core() for background.
*/
static int ecp_comb_recode_scalar(const mbedtls_ecp_group *grp,
const mbedtls_mpi *m,
unsigned char k[COMB_MAX_D + 1],
size_t d,
unsigned char w,
unsigned char *parity_trick)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi M, mm;
mbedtls_mpi_init(&M);
mbedtls_mpi_init(&mm);
/* N is always odd (see above), just make extra sure */
if (mbedtls_mpi_get_bit(&grp->N, 0) != 1) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
/* do we need the parity trick? */
*parity_trick = (mbedtls_mpi_get_bit(m, 0) == 0);
/* execute parity fix in constant time */
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&M, m));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&mm, &grp->N, m));
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&M, &mm, *parity_trick));
/* actual scalar recoding */
ecp_comb_recode_core(k, d, w, &M);
cleanup:
mbedtls_mpi_free(&mm);
mbedtls_mpi_free(&M);
return ret;
}
/*
* Perform comb multiplication (for short Weierstrass curves)
* once the auxiliary table has been pre-computed.
*
* Scalar recoding may use a parity trick that makes us compute -m * P,
* if that is the case we'll need to recover m * P at the end.
*/
static int ecp_mul_comb_after_precomp(const mbedtls_ecp_group *grp,
mbedtls_ecp_point *R,
const mbedtls_mpi *m,
const mbedtls_ecp_point *T,
unsigned char T_size,
unsigned char w,
size_t d,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng,
mbedtls_ecp_restart_ctx *rs_ctx)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
unsigned char parity_trick;
unsigned char k[COMB_MAX_D + 1];
mbedtls_ecp_point *RR = R;
int have_rng = 1;
#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 defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
if (f_rng == NULL) {
have_rng = 0;
}
#endif
if (have_rng) {
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++;
}
/*
* Make sure w is within bounds.
* (The last test is useful only for very small curves in the test suite.)
*/
#if (MBEDTLS_ECP_WINDOW_SIZE < 6)
if (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;
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
ecp_drbg_context drbg_ctx;
ecp_drbg_init(&drbg_ctx);
#endif
ECP_RS_ENTER(rsm);
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
if (f_rng == NULL) {
/* Adjust pointers */
f_rng = &ecp_drbg_random;
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
p_rng = &rs_ctx->rsm->drbg_ctx;
} else
#endif
p_rng = &drbg_ctx;
/* Initialize internal DRBG if necessary */
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx == NULL || rs_ctx->rsm == NULL ||
rs_ctx->rsm->drbg_seeded == 0)
#endif
{
const size_t m_len = (grp->nbits + 7) / 8;
MBEDTLS_MPI_CHK(ecp_drbg_seed(p_rng, m, m_len));
}
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
rs_ctx->rsm->drbg_seeded = 1;
}
#endif
}
#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
/* Is P the base point ? */
#if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
p_eq_g = (mbedtls_mpi_cmp_mpi(&P->Y, &grp->G.Y) == 0 &&
mbedtls_mpi_cmp_mpi(&P->X, &grp->G.X) == 0);
#else
p_eq_g = 0;
#endif
/* Pick window size and deduce related sizes */
w = ecp_pick_window_size(grp, p_eq_g);
T_size = 1U << (w - 1);
d = (grp->nbits + w - 1) / w;
/* Pre-computed table: do we have it already for the base point? */
if (p_eq_g && grp->T != NULL) {
/* second pointer to the same table, will be deleted on exit */
T = grp->T;
T_ok = 1;
} else
#if defined(MBEDTLS_ECP_RESTARTABLE)
/* Pre-computed table: do we have one in progress? complete? */
if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL) {
/* transfer ownership of T from rsm to local function */
T = rs_ctx->rsm->T;
rs_ctx->rsm->T = NULL;
rs_ctx->rsm->T_size = 0;
/* This effectively jumps to the call to mul_comb_after_precomp() */
T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core;
} else
#endif
/* Allocate table if we didn't have any */
{
T = mbedtls_calloc(T_size, sizeof(mbedtls_ecp_point));
if (T == NULL) {
ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
goto cleanup;
}
for (i = 0; i < T_size; i++) {
mbedtls_ecp_point_init(&T[i]);
}
T_ok = 0;
}
/* Compute table (or finish computing it) if not done already */
if (!T_ok) {
MBEDTLS_MPI_CHK(ecp_precompute_comb(grp, T, P, w, d, rs_ctx));
if (p_eq_g) {
/* almost transfer ownership of T to the group, but keep a copy of
* the pointer to use for calling the next function more easily */
grp->T = T;
grp->T_size = T_size;
}
}
/* Actual comb multiplication using precomputed points */
MBEDTLS_MPI_CHK(ecp_mul_comb_after_precomp(grp, R, m,
T, T_size, w, d,
f_rng, p_rng, rs_ctx));
cleanup:
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
ecp_drbg_free(&drbg_ctx);
#endif
/* 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;
MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&P->Z, &P->Z, &grp->P));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->X, &P->X, &P->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&P->Z, 1));
cleanup:
return ret;
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */
}
/*
* Randomize projective x/z coordinates:
* (X, Z) -> (l X, l Z) for random l
* This is sort of the reverse operation of ecp_normalize_mxz().
*
* This countermeasure was first suggested in [2].
* Cost: 2M
*/
static int ecp_randomize_mxz(const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
#if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
if (mbedtls_internal_ecp_grp_capable(grp)) {
return mbedtls_internal_ecp_randomize_mxz(grp, P, f_rng, p_rng);
}
#endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi l;
mbedtls_mpi_init(&l);
/* Generate l such that 1 < l < p */
MBEDTLS_MPI_CHK(mbedtls_mpi_random(&l, 2, &grp->P, f_rng, p_rng));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->X, &P->X, &l));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->Z, &P->Z, &l));
cleanup:
mbedtls_mpi_free(&l);
if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) {
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
}
return ret;
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */
}
/*
* Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
* for Montgomery curves in x/z coordinates.
*
* http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
* with
* d = X1
* P = (X2, Z2)
* Q = (X3, Z3)
* R = (X4, Z4)
* S = (X5, Z5)
* and eliminating temporary variables tO, ..., t4.
*
* Cost: 5M + 4S
*/
static int ecp_double_add_mxz(const mbedtls_ecp_group *grp,
mbedtls_ecp_point *R, mbedtls_ecp_point *S,
const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
const mbedtls_mpi *d)
{
#if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
if (mbedtls_internal_ecp_grp_capable(grp)) {
return mbedtls_internal_ecp_double_add_mxz(grp, R, S, P, Q, d);
}
#endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
mbedtls_mpi_init(&A); mbedtls_mpi_init(&AA); mbedtls_mpi_init(&B);
mbedtls_mpi_init(&BB); mbedtls_mpi_init(&E); mbedtls_mpi_init(&C);
mbedtls_mpi_init(&D); mbedtls_mpi_init(&DA); mbedtls_mpi_init(&CB);
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &A, &P->X, &P->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &AA, &A, &A));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &B, &P->X, &P->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &BB, &B, &B));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &E, &AA, &BB));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &C, &Q->X, &Q->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &D, &Q->X, &Q->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &DA, &D, &A));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &CB, &C, &B));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &S->X, &DA, &CB));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->X, &S->X, &S->X));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S->Z, &DA, &CB));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->Z, &S->Z, &S->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->Z, d, &S->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->X, &AA, &BB));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->Z, &grp->A, &E));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &R->Z, &BB, &R->Z));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->Z, &E, &R->Z));
cleanup:
mbedtls_mpi_free(&A); mbedtls_mpi_free(&AA); mbedtls_mpi_free(&B);
mbedtls_mpi_free(&BB); mbedtls_mpi_free(&E); mbedtls_mpi_free(&C);
mbedtls_mpi_free(&D); mbedtls_mpi_free(&DA); mbedtls_mpi_free(&CB);
return ret;
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */
}
/*
* Multiplication with Montgomery ladder in x/z coordinates,
* for curves in Montgomery form
*/
static int ecp_mul_mxz(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i;
unsigned char b;
mbedtls_ecp_point RP;
mbedtls_mpi PX;
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
ecp_drbg_context drbg_ctx;
ecp_drbg_init(&drbg_ctx);
#endif
mbedtls_ecp_point_init(&RP); mbedtls_mpi_init(&PX);
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
if (f_rng == NULL) {
const size_t m_len = (grp->nbits + 7) / 8;
MBEDTLS_MPI_CHK(ecp_drbg_seed(&drbg_ctx, m, m_len));
f_rng = &ecp_drbg_random;
p_rng = &drbg_ctx;
}
#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
/* Save PX and read from P before writing to R, in case P == R */
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&PX, &P->X));
MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&RP, P));
/* Set R to zero in modified x/z coordinates */
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->X, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->Z, 0));
mbedtls_mpi_free(&R->Y);
/* RP.X might be slightly larger than P, so reduce it */
MOD_ADD(RP.X);
/* Randomize coordinates of the starting point */
int have_rng = 1;
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
if (f_rng == NULL) {
have_rng = 0;
}
#endif
if (have_rng) {
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
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->X, &RP.X, b));
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->Z, &RP.Z, b));
MBEDTLS_MPI_CHK(ecp_double_add_mxz(grp, R, &RP, R, &RP, &PX));
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->X, &RP.X, b));
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->Z, &RP.Z, b));
}
/*
* Knowledge of the projective coordinates may leak the last few bits of the
* scalar [1], and since our MPI implementation isn't constant-flow,
* inversion (used for coordinate normalization) may leak the full value
* of its input via side-channels [2].
*
* [1] https://eprint.iacr.org/2003/191
* [2] https://eprint.iacr.org/2020/055
*
* Avoid the leak by randomizing coordinates before we normalize them.
*/
have_rng = 1;
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
if (f_rng == NULL) {
have_rng = 0;
}
#endif
if (have_rng) {
MBEDTLS_MPI_CHK(ecp_randomize_mxz(grp, R, f_rng, p_rng));
}
MBEDTLS_MPI_CHK(ecp_normalize_mxz(grp, R));
cleanup:
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
ecp_drbg_free(&drbg_ctx);
#endif
mbedtls_ecp_point_free(&RP); mbedtls_mpi_free(&PX);
return ret;
}
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
/*
* 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)
{
int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
char is_grp_capable = 0;
#endif
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(R != NULL);
ECP_VALIDATE_RET(m != NULL);
ECP_VALIDATE_RET(P != NULL);
#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;
}
/*
* Multiplication R = m * P
*/
int mbedtls_ecp_mul(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(R != NULL);
ECP_VALIDATE_RET(m != NULL);
ECP_VALIDATE_RET(P != NULL);
return mbedtls_ecp_mul_restartable(grp, R, m, P, f_rng, p_rng, NULL);
}
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
/*
* Check that an affine point is valid as a public key,
* short weierstrass curves (SEC1 3.2.3.1)
*/
static int ecp_check_pubkey_sw(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi YY, RHS;
/* pt coordinates must be normalized for our checks */
if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0 ||
mbedtls_mpi_cmp_int(&pt->Y, 0) < 0 ||
mbedtls_mpi_cmp_mpi(&pt->X, &grp->P) >= 0 ||
mbedtls_mpi_cmp_mpi(&pt->Y, &grp->P) >= 0) {
return MBEDTLS_ERR_ECP_INVALID_KEY;
}
mbedtls_mpi_init(&YY); mbedtls_mpi_init(&RHS);
/*
* YY = Y^2
* RHS = X (X^2 + A) + B = X^3 + A X + B
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &YY, &pt->Y, &pt->Y));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &RHS, &pt->X, &pt->X));
/* Special case for A = -3 */
if (grp->A.p == NULL) {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(&RHS, &RHS, 3)); MOD_SUB(RHS);
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &RHS, &RHS, &grp->A));
}
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &RHS, &RHS, &pt->X));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &RHS, &RHS, &grp->B));
if (mbedtls_mpi_cmp_mpi(&YY, &RHS) != 0) {
ret = MBEDTLS_ERR_ECP_INVALID_KEY;
}
cleanup:
mbedtls_mpi_free(&YY); mbedtls_mpi_free(&RHS);
return ret;
}
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
/*
* R = m * P with shortcuts for m == 0, m == 1 and m == -1
* NOT constant-time - ONLY for short Weierstrass!
*/
static int mbedtls_ecp_mul_shortcuts(mbedtls_ecp_group *grp,
mbedtls_ecp_point *R,
const mbedtls_mpi *m,
const mbedtls_ecp_point *P,
mbedtls_ecp_restart_ctx *rs_ctx)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
if (mbedtls_mpi_cmp_int(m, 0) == 0) {
MBEDTLS_MPI_CHK(mbedtls_ecp_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));
if (mbedtls_mpi_cmp_int(&R->Y, 0) != 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&R->Y, &grp->P, &R->Y));
}
} else {
MBEDTLS_MPI_CHK(mbedtls_ecp_mul_restartable(grp, R, m, P,
NULL, NULL, rs_ctx));
}
cleanup:
return ret;
}
/*
* Restartable linear combination
* NOT constant-time
*/
int mbedtls_ecp_muladd_restartable(
mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
mbedtls_ecp_restart_ctx *rs_ctx)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_ecp_point mP;
mbedtls_ecp_point *pmP = &mP;
mbedtls_ecp_point *pR = R;
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
char is_grp_capable = 0;
#endif
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(R != NULL);
ECP_VALIDATE_RET(m != NULL);
ECP_VALIDATE_RET(P != NULL);
ECP_VALIDATE_RET(n != NULL);
ECP_VALIDATE_RET(Q != NULL);
if (mbedtls_ecp_get_type(grp) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
}
mbedtls_ecp_point_init(&mP);
ECP_RS_ENTER(ma);
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->ma != NULL) {
/* redirect intermediate results to restart context */
pmP = &rs_ctx->ma->mP;
pR = &rs_ctx->ma->R;
/* jump to next operation */
if (rs_ctx->ma->state == ecp_rsma_mul2) {
goto mul2;
}
if (rs_ctx->ma->state == ecp_rsma_add) {
goto add;
}
if (rs_ctx->ma->state == ecp_rsma_norm) {
goto norm;
}
}
#endif /* MBEDTLS_ECP_RESTARTABLE */
MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pmP, m, P, rs_ctx));
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->ma != NULL) {
rs_ctx->ma->state = ecp_rsma_mul2;
}
mul2:
#endif
MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pR, n, Q, rs_ctx));
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) {
MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp));
}
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->ma != NULL) {
rs_ctx->ma->state = ecp_rsma_add;
}
add:
#endif
MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_ADD);
MBEDTLS_MPI_CHK(ecp_add_mixed(grp, pR, pmP, pR));
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->ma != NULL) {
rs_ctx->ma->state = ecp_rsma_norm;
}
norm:
#endif
MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV);
MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, pR));
#if defined(MBEDTLS_ECP_RESTARTABLE)
if (rs_ctx != NULL && rs_ctx->ma != NULL) {
MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, pR));
}
#endif
cleanup:
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
if (is_grp_capable) {
mbedtls_internal_ecp_free(grp);
}
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
mbedtls_ecp_point_free(&mP);
ECP_RS_LEAVE(ma);
return ret;
}
/*
* Linear combination
* NOT constant-time
*/
int mbedtls_ecp_muladd(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
const mbedtls_mpi *n, const mbedtls_ecp_point *Q)
{
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(R != NULL);
ECP_VALIDATE_RET(m != NULL);
ECP_VALIDATE_RET(P != NULL);
ECP_VALIDATE_RET(n != NULL);
ECP_VALIDATE_RET(Q != NULL);
return mbedtls_ecp_muladd_restartable(grp, R, m, P, n, Q, NULL);
}
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
#define ECP_MPI_INIT(s, n, p) { s, (n), (mbedtls_mpi_uint *) (p) }
#define ECP_MPI_INIT_ARRAY(x) \
ECP_MPI_INIT(1, sizeof(x) / sizeof(mbedtls_mpi_uint), x)
/*
* Constants for the two points other than 0, 1, -1 (mod p) in
* https://cr.yp.to/ecdh.html#validate
* See ecp_check_pubkey_x25519().
*/
static const mbedtls_mpi_uint x25519_bad_point_1[] = {
MBEDTLS_BYTES_TO_T_UINT_8(0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae),
MBEDTLS_BYTES_TO_T_UINT_8(0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a),
MBEDTLS_BYTES_TO_T_UINT_8(0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd),
MBEDTLS_BYTES_TO_T_UINT_8(0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00),
};
static const mbedtls_mpi_uint x25519_bad_point_2[] = {
MBEDTLS_BYTES_TO_T_UINT_8(0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24),
MBEDTLS_BYTES_TO_T_UINT_8(0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b),
MBEDTLS_BYTES_TO_T_UINT_8(0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86),
MBEDTLS_BYTES_TO_T_UINT_8(0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57),
};
static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY(
x25519_bad_point_1);
static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY(
x25519_bad_point_2);
#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
/*
* Check that the input point is not one of the low-order points.
* This is recommended by the "May the Fourth" paper:
* https://eprint.iacr.org/2017/806.pdf
* Those points are never sent by an honest peer.
*/
static int ecp_check_bad_points_mx(const mbedtls_mpi *X, const mbedtls_mpi *P,
const mbedtls_ecp_group_id grp_id)
{
int ret;
mbedtls_mpi XmP;
mbedtls_mpi_init(&XmP);
/* Reduce X mod P so that we only need to check values less than P.
* We know X < 2^256 so we can proceed by subtraction. */
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&XmP, X));
while (mbedtls_mpi_cmp_mpi(&XmP, P) >= 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&XmP, &XmP, P));
}
/* Check against the known bad values that are less than P. For Curve448
* these are 0, 1 and -1. For Curve25519 we check the values less than P
* from the following list: https://cr.yp.to/ecdh.html#validate */
if (mbedtls_mpi_cmp_int(&XmP, 1) <= 0) { /* takes care of 0 and 1 */
ret = MBEDTLS_ERR_ECP_INVALID_KEY;
goto cleanup;
}
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
if (grp_id == MBEDTLS_ECP_DP_CURVE25519) {
if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_1) == 0) {
ret = MBEDTLS_ERR_ECP_INVALID_KEY;
goto cleanup;
}
if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_2) == 0) {
ret = MBEDTLS_ERR_ECP_INVALID_KEY;
goto cleanup;
}
}
#else
(void) grp_id;
#endif
/* Final check: check if XmP + 1 is P (final because it changes XmP!) */
MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&XmP, &XmP, 1));
if (mbedtls_mpi_cmp_mpi(&XmP, P) == 0) {
ret = MBEDTLS_ERR_ECP_INVALID_KEY;
goto cleanup;
}
ret = 0;
cleanup:
mbedtls_mpi_free(&XmP);
return ret;
}
/*
* Check validity of a public key for Montgomery curves with x-only schemes
*/
static int ecp_check_pubkey_mx(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt)
{
/* [Curve25519 p. 5] Just check X is the correct number of bytes */
/* Allow any public value, if it's too big then we'll just reduce it mod p
* (RFC 7748 sec. 5 para. 3). */
if (mbedtls_mpi_size(&pt->X) > (grp->nbits + 7) / 8) {
return MBEDTLS_ERR_ECP_INVALID_KEY;
}
/* Implicit in all standards (as they don't consider negative numbers):
* X must be non-negative. This is normally ensured by the way it's
* encoded for transmission, but let's be extra sure. */
if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0) {
return MBEDTLS_ERR_ECP_INVALID_KEY;
}
return ecp_check_bad_points_mx(&pt->X, &grp->P, grp->id);
}
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
/*
* Check that a point is valid as a public key
*/
int mbedtls_ecp_check_pubkey(const mbedtls_ecp_group *grp,
const mbedtls_ecp_point *pt)
{
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(pt != NULL);
/* Must use affine coordinates */
if (mbedtls_mpi_cmp_int(&pt->Z, 1) != 0) {
return MBEDTLS_ERR_ECP_INVALID_KEY;
}
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
return ecp_check_pubkey_mx(grp, pt);
}
#endif
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
if (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)
{
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(d != NULL);
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
/* see RFC 7748 sec. 5 para. 5 */
if (mbedtls_mpi_get_bit(d, 0) != 0 ||
mbedtls_mpi_get_bit(d, 1) != 0 ||
mbedtls_mpi_bitlen(d) - 1 != grp->nbits) { /* mbedtls_mpi_bitlen is one-based! */
return MBEDTLS_ERR_ECP_INVALID_KEY;
}
/* see [Curve25519] page 5 */
if (grp->nbits == 254 && mbedtls_mpi_get_bit(d, 2) != 0) {
return MBEDTLS_ERR_ECP_INVALID_KEY;
}
return 0;
}
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
/* see SEC1 3.2 */
if (mbedtls_mpi_cmp_int(d, 1) < 0 ||
mbedtls_mpi_cmp_mpi(d, &grp->N) >= 0) {
return MBEDTLS_ERR_ECP_INVALID_KEY;
} else {
return 0;
}
}
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
MBEDTLS_STATIC_TESTABLE
int mbedtls_ecp_gen_privkey_mx(size_t high_bit,
mbedtls_mpi *d,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng)
{
int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
size_t n_random_bytes = high_bit / 8 + 1;
/* [Curve25519] page 5 */
/* Generate a (high_bit+1)-bit random number by generating just enough
* random bytes, then shifting out extra bits from the top (necessary
* when (high_bit+1) is not a multiple of 8). */
MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(d, n_random_bytes,
f_rng, p_rng));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(d, 8 * n_random_bytes - high_bit - 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, high_bit, 1));
/* Make sure the last two bits are unset for Curve448, three bits for
Curve25519 */
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 0, 0));
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 1, 0));
if (high_bit == 254) {
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 2, 0));
}
cleanup:
return ret;
}
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
static int mbedtls_ecp_gen_privkey_sw(
const mbedtls_mpi *N, mbedtls_mpi *d,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
int ret = mbedtls_mpi_random(d, 1, N, f_rng, p_rng);
switch (ret) {
case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE:
return MBEDTLS_ERR_ECP_RANDOM_FAILED;
default:
return ret;
}
}
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
/*
* Generate a private key
*/
int mbedtls_ecp_gen_privkey(const mbedtls_ecp_group *grp,
mbedtls_mpi *d,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng)
{
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(d != NULL);
ECP_VALIDATE_RET(f_rng != NULL);
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
return mbedtls_ecp_gen_privkey_mx(grp->nbits, d, f_rng, p_rng);
}
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
return mbedtls_ecp_gen_privkey_sw(&grp->N, d, f_rng, p_rng);
}
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
/*
* Generate a keypair with configurable base point
*/
int mbedtls_ecp_gen_keypair_base(mbedtls_ecp_group *grp,
const mbedtls_ecp_point *G,
mbedtls_mpi *d, mbedtls_ecp_point *Q,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(d != NULL);
ECP_VALIDATE_RET(G != NULL);
ECP_VALIDATE_RET(Q != NULL);
ECP_VALIDATE_RET(f_rng != NULL);
MBEDTLS_MPI_CHK(mbedtls_ecp_gen_privkey(grp, d, f_rng, p_rng));
MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, Q, d, G, f_rng, p_rng));
cleanup:
return ret;
}
/*
* Generate key pair, wrapper for conventional base point
*/
int mbedtls_ecp_gen_keypair(mbedtls_ecp_group *grp,
mbedtls_mpi *d, mbedtls_ecp_point *Q,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng)
{
ECP_VALIDATE_RET(grp != NULL);
ECP_VALIDATE_RET(d != NULL);
ECP_VALIDATE_RET(Q != NULL);
ECP_VALIDATE_RET(f_rng != NULL);
return mbedtls_ecp_gen_keypair_base(grp, &grp->G, d, Q, f_rng, p_rng);
}
/*
* Generate a keypair, prettier wrapper
*/
int mbedtls_ecp_gen_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
ECP_VALIDATE_RET(key != NULL);
ECP_VALIDATE_RET(f_rng != NULL);
if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) {
return ret;
}
return mbedtls_ecp_gen_keypair(&key->grp, &key->d, &key->Q, f_rng, p_rng);
}
#define ECP_CURVE25519_KEY_SIZE 32
/*
* Read a private key.
*/
int mbedtls_ecp_read_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
const unsigned char *buf, size_t buflen)
{
int ret = 0;
ECP_VALIDATE_RET(key != NULL);
ECP_VALIDATE_RET(buf != NULL);
if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) {
return ret;
}
ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
/*
* If it is Curve25519 curve then mask the key as mandated by RFC7748
*/
if (grp_id == MBEDTLS_ECP_DP_CURVE25519) {
if (buflen != ECP_CURVE25519_KEY_SIZE) {
return MBEDTLS_ERR_ECP_INVALID_KEY;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&key->d, buf, buflen));
/* Set the three least significant bits to 0 */
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 0, 0));
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 1, 0));
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 2, 0));
/* Set the most significant bit to 0 */
MBEDTLS_MPI_CHK(
mbedtls_mpi_set_bit(&key->d,
ECP_CURVE25519_KEY_SIZE * 8 - 1, 0)
);
/* Set the second most significant bit to 1 */
MBEDTLS_MPI_CHK(
mbedtls_mpi_set_bit(&key->d,
ECP_CURVE25519_KEY_SIZE * 8 - 2, 1)
);
} else {
ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
}
}
#endif
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&key->d, buf, buflen));
MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(&key->grp, &key->d));
}
#endif
cleanup:
if (ret != 0) {
mbedtls_mpi_free(&key->d);
}
return ret;
}
/*
* Write a private key.
*/
int mbedtls_ecp_write_key(mbedtls_ecp_keypair *key,
unsigned char *buf, size_t buflen)
{
int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
ECP_VALIDATE_RET(key != NULL);
ECP_VALIDATE_RET(buf != NULL);
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
if (key->grp.id == MBEDTLS_ECP_DP_CURVE25519) {
if (buflen < ECP_CURVE25519_KEY_SIZE) {
return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&key->d, buf, buflen));
} else {
ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
}
}
#endif
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&key->d, buf, buflen));
}
#endif
cleanup:
return ret;
}
/*
* Check a public-private key pair
*/
int mbedtls_ecp_check_pub_priv(const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_ecp_point Q;
mbedtls_ecp_group grp;
ECP_VALIDATE_RET(pub != NULL);
ECP_VALIDATE_RET(prv != NULL);
if (pub->grp.id == MBEDTLS_ECP_DP_NONE ||
pub->grp.id != prv->grp.id ||
mbedtls_mpi_cmp_mpi(&pub->Q.X, &prv->Q.X) ||
mbedtls_mpi_cmp_mpi(&pub->Q.Y, &prv->Q.Y) ||
mbedtls_mpi_cmp_mpi(&pub->Q.Z, &prv->Q.Z)) {
return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
}
mbedtls_ecp_point_init(&Q);
mbedtls_ecp_group_init(&grp);
/* mbedtls_ecp_mul() needs a non-const group... */
mbedtls_ecp_group_copy(&grp, &prv->grp);
/* Also checks d is valid */
MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &Q, &prv->d, &prv->grp.G, NULL, NULL));
if (mbedtls_mpi_cmp_mpi(&Q.X, &prv->Q.X) ||
mbedtls_mpi_cmp_mpi(&Q.Y, &prv->Q.Y) ||
mbedtls_mpi_cmp_mpi(&Q.Z, &prv->Q.Z)) {
ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
goto cleanup;
}
cleanup:
mbedtls_ecp_point_free(&Q);
mbedtls_ecp_group_free(&grp);
return ret;
}
#if defined(MBEDTLS_SELF_TEST)
/* 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, NULL, 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, NULL, NULL));
if (add_count != add_c_prev ||
dbl_count != dbl_c_prev ||
mul_count != mul_c_prev) {
ret = 1;
break;
}
}
cleanup:
if (verbose != 0) {
if (ret != 0) {
mbedtls_printf("failed (%u)\n", (unsigned int) i);
} else {
mbedtls_printf("passed\n");
}
}
return ret;
}
/*
* Checkup routine
*/
int mbedtls_ecp_self_test(int verbose)
{
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, NULL, NULL));
ret = self_test_point(verbose,
&grp, &R, &m, &grp.G,
sw_exponents,
sizeof(sw_exponents) / sizeof(sw_exponents[0]));
if (ret != 0) {
goto cleanup;
}
if (verbose != 0) {
mbedtls_printf(" ECP SW test #2 (constant op_count, other point): ");
}
/* We computed P = 2G last time, use it */
ret = self_test_point(verbose,
&grp, &R, &m, &P,
sw_exponents,
sizeof(sw_exponents) / sizeof(sw_exponents[0]));
if (ret != 0) {
goto cleanup;
}
mbedtls_ecp_group_free(&grp);
mbedtls_ecp_point_free(&R);
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
if (verbose != 0) {
mbedtls_printf(" ECP Montgomery test (constant op_count): ");
}
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE25519));
#elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE448));
#else
#error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test"
#endif
ret = self_test_point(verbose,
&grp, &R, &m, &grp.G,
m_exponents,
sizeof(m_exponents) / sizeof(m_exponents[0]));
if (ret != 0) {
goto cleanup;
}
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
cleanup:
if (ret < 0 && verbose != 0) {
mbedtls_printf("Unexpected error, return code = %08X\n", (unsigned int) ret);
}
mbedtls_ecp_group_free(&grp);
mbedtls_ecp_point_free(&R);
mbedtls_ecp_point_free(&P);
mbedtls_mpi_free(&m);
if (verbose != 0) {
mbedtls_printf("\n");
}
return ret;
}
#endif /* MBEDTLS_SELF_TEST */
#endif /* !MBEDTLS_ECP_ALT */
#endif /* MBEDTLS_ECP_C */
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