mirror of
https://github.com/jart/cosmopolitan.git
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3799 lines
143 KiB
C
3799 lines
143 KiB
C
/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:4;tab-width:4;coding:utf-8 -*-│
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│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│
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╞══════════════════════════════════════════════════════════════════════════════╡
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│ Copyright The Mbed TLS Contributors │
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│ │
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│ Licensed under the Apache License, Version 2.0 (the "License"); │
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│ you may not use this file except in compliance with the License. │
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│ You may obtain a copy of the License at │
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│ │
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│ http://www.apache.org/licenses/LICENSE-2.0 │
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│ │
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│ Unless required by applicable law or agreed to in writing, software │
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│ distributed under the License is distributed on an "AS IS" BASIS, │
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│ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. │
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│ See the License for the specific language governing permissions and │
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│ limitations under the License. │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/log/check.h"
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#include "libc/log/log.h"
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#include "libc/runtime/runtime.h"
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#include "libc/stdio/stdio.h"
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#include "third_party/mbedtls/bignum.h"
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#include "third_party/mbedtls/bignum_internal.h"
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#include "third_party/mbedtls/common.h"
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#include "third_party/mbedtls/config.h"
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#include "third_party/mbedtls/ctr_drbg.h"
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#include "third_party/mbedtls/ecp.h"
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#include "third_party/mbedtls/ecp_internal.h"
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#include "third_party/mbedtls/error.h"
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#include "third_party/mbedtls/hmac_drbg.h"
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#include "third_party/mbedtls/platform.h"
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#include "third_party/mbedtls/profile.h"
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asm(".ident\t\"\\n\\n\
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Mbed TLS (Apache 2.0)\\n\
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Copyright ARM Limited\\n\
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Copyright Mbed TLS Contributors\"");
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asm(".include \"libc/disclaimer.inc\"");
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/* clang-format off */
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/**
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* @fileoverview Elliptic curves over GF(p): generic functions
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*
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* References:
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*
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* SEC1 http://www.secg.org/index.php?action=secg,docs_secg
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* GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
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* FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
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* RFC 4492 for the related TLS structures and constants
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* RFC 7748 for the Curve448 and Curve25519 curve definitions
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*
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* [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
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*
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* [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
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* for elliptic curve cryptosystems. In : Cryptographic Hardware and
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* Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
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* <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
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*
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* [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
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* render ECC resistant against Side Channel Attacks. IACR Cryptology
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* ePrint Archive, 2004, vol. 2004, p. 342.
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* <http://eprint.iacr.org/2004/342.pdf>
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*/
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#define ECP_VALIDATE_RET( cond ) \
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MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
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#define ECP_VALIDATE( cond ) \
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MBEDTLS_INTERNAL_VALIDATE( cond )
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#if defined(MBEDTLS_ECP_C)
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#if !defined(MBEDTLS_ECP_ALT)
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#if defined(MBEDTLS_SELF_TEST)
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/*
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* Counts of point addition and doubling, and field multiplications.
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* Used to test resistance of point multiplication to simple timing attacks.
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*/
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static unsigned long add_count, dbl_count, mul_count;
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#endif
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#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
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/*
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* Currently ecp_mul() takes a RNG function as an argument, used for
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* side-channel protection, but it can be NULL. The initial reasoning was
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* that people will pass non-NULL RNG when they care about side-channels, but
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* unfortunately we have some APIs that call ecp_mul() with a NULL RNG, with
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* no opportunity for the user to do anything about it.
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*
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* The obvious strategies for addressing that include:
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* - change those APIs so that they take RNG arguments;
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* - require a global RNG to be available to all crypto modules.
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*
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* Unfortunately those would break compatibility. So what we do instead is
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* have our own internal DRBG instance, seeded from the secret scalar.
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*
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* The following is a light-weight abstraction layer for doing that with
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* HMAC_DRBG (first choice) or CTR_DRBG.
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*/
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#if defined(MBEDTLS_HMAC_DRBG_C)
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/* DRBG context type */
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typedef mbedtls_hmac_drbg_context ecp_drbg_context;
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/* DRBG context init */
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static inline void ecp_drbg_init( ecp_drbg_context *ctx )
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{
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mbedtls_hmac_drbg_init( ctx );
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}
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/* DRBG context free */
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static inline void ecp_drbg_free( ecp_drbg_context *ctx )
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{
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mbedtls_hmac_drbg_free( ctx );
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}
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/* DRBG function */
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static inline int ecp_drbg_random( void *p_rng,
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unsigned char *output, size_t output_len )
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{
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return( mbedtls_hmac_drbg_random( p_rng, output, output_len ) );
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}
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/* DRBG context seeding */
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static int ecp_drbg_seed( ecp_drbg_context *ctx,
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const mbedtls_mpi *secret,
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size_t secret_len )
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{
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int ret;
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unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
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/* The list starts with strong hashes */
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const mbedtls_md_type_t md_type = mbedtls_md_list()[0];
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const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type( md_type );
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if( secret_len > MBEDTLS_ECP_MAX_BYTES )
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{
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ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
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goto cleanup;
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}
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MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
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secret_bytes, secret_len ) );
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ret = mbedtls_hmac_drbg_seed_buf( ctx, md_info, secret_bytes, secret_len );
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cleanup:
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mbedtls_platform_zeroize( secret_bytes, secret_len );
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return( ret );
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}
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#elif defined(MBEDTLS_CTR_DRBG_C)
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/* DRBG context type */
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typedef mbedtls_ctr_drbg_context ecp_drbg_context;
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/* DRBG context init */
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static inline void ecp_drbg_init( ecp_drbg_context *ctx )
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{
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mbedtls_ctr_drbg_init( ctx );
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}
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/* DRBG context free */
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static inline void ecp_drbg_free( ecp_drbg_context *ctx )
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{
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mbedtls_ctr_drbg_free( ctx );
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}
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/* DRBG function */
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static inline int ecp_drbg_random( void *p_rng,
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unsigned char *output, size_t output_len )
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{
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return( mbedtls_ctr_drbg_random( p_rng, output, output_len ) );
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}
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/*
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* Since CTR_DRBG doesn't have a seed_buf() function the way HMAC_DRBG does,
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* we need to pass an entropy function when seeding. So we use a dummy
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* function for that, and pass the actual entropy as customisation string.
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* (During seeding of CTR_DRBG the entropy input and customisation string are
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* concatenated before being used to update the secret state.)
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*/
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static int ecp_ctr_drbg_null_entropy(void *ctx, unsigned char *out, size_t len)
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{
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(void) ctx;
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mbedtls_platform_zeroize( out, len );
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return( 0 );
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}
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/* DRBG context seeding */
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static int ecp_drbg_seed( ecp_drbg_context *ctx,
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const mbedtls_mpi *secret, size_t secret_len )
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{
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int ret;
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unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
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if( secret_len > MBEDTLS_ECP_MAX_BYTES )
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{
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ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
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goto cleanup;
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}
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MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
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secret_bytes, secret_len ) );
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ret = mbedtls_ctr_drbg_seed( ctx, ecp_ctr_drbg_null_entropy, NULL,
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secret_bytes, secret_len );
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cleanup:
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mbedtls_platform_zeroize( secret_bytes, secret_len );
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return( ret );
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}
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#else
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#error "Invalid configuration detected. Include check.h to ensure that the configuration is valid."
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#endif /* DRBG modules */
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#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
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#if defined(MBEDTLS_ECP_RESTARTABLE)
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/*
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* Maximum number of "basic operations" to be done in a row.
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*
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* Default value 0 means that ECC operations will not yield.
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* Note that regardless of the value of ecp_max_ops, always at
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* least one step is performed before yielding.
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*
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* Setting ecp_max_ops=1 can be suitable for testing purposes
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* as it will interrupt computation at all possible points.
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*/
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static unsigned ecp_max_ops = 0;
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/**
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* \brief Set the maximum number of basic operations done in a row.
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*
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* If more operations are needed to complete a computation,
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* #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the
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* function performing the computation. It is then the
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* caller's responsibility to either call again with the same
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* parameters until it returns 0 or an error code; or to free
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* the restart context if the operation is to be aborted.
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*
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* It is strictly required that all input parameters and the
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* restart context be the same on successive calls for the
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* same operation, but output parameters need not be the
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* same; they must not be used until the function finally
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* returns 0.
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*
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* This only applies to functions whose documentation
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* mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or
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* #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the
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* SSL module). For functions that accept a "restart context"
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* argument, passing NULL disables restart and makes the
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* function equivalent to the function with the same name
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* with \c _restartable removed. For functions in the ECDH
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* module, restart is disabled unless the function accepts
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* an "ECDH context" argument and
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* mbedtls_ecdh_enable_restart() was previously called on
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* that context. For function in the SSL module, restart is
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* only enabled for specific sides and key exchanges
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* (currently only for clients and ECDHE-ECDSA).
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*
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* \param max_ops Maximum number of basic operations done in a row.
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* Default: 0 (unlimited).
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* Lower (non-zero) values mean ECC functions will block for
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* a lesser maximum amount of time.
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*
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* \note A "basic operation" is defined as a rough equivalent of a
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* multiplication in GF(p) for the NIST P-256 curve.
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* As an indication, with default settings, a scalar
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* multiplication (full run of \c mbedtls_ecp_mul()) is:
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* - about 3300 basic operations for P-256
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* - about 9400 basic operations for P-384
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*
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* \note Very low values are not always respected: sometimes
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* functions need to block for a minimum number of
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* operations, and will do so even if max_ops is set to a
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* lower value. That minimum depends on the curve size, and
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* can be made lower by decreasing the value of
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* \c MBEDTLS_ECP_WINDOW_SIZE. As an indication, here is the
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* lowest effective value for various curves and values of
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* that parameter (w for short):
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* w=6 w=5 w=4 w=3 w=2
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* P-256 208 208 160 136 124
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* P-384 682 416 320 272 248
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* P-521 1364 832 640 544 496
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*
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* \note This setting is currently ignored by Curve25519.
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*/
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void mbedtls_ecp_set_max_ops( unsigned max_ops )
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{
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ecp_max_ops = max_ops;
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}
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/**
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* \brief Check if restart is enabled (max_ops != 0)
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*
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* \return \c 0 if \c max_ops == 0 (restart disabled)
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* \return \c 1 otherwise (restart enabled)
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*/
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int mbedtls_ecp_restart_is_enabled( void )
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{
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return( ecp_max_ops != 0 );
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}
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/*
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* Restart sub-context for ecp_mul_comb()
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*/
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struct mbedtls_ecp_restart_mul
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{
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mbedtls_ecp_point R; /* current intermediate result */
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size_t i; /* current index in various loops, 0 outside */
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mbedtls_ecp_point *T; /* table for precomputed points */
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unsigned char T_size; /* number of points in table T */
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enum { /* what were we doing last time we returned? */
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ecp_rsm_init = 0, /* nothing so far, dummy initial state */
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ecp_rsm_pre_dbl, /* precompute 2^n multiples */
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ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */
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ecp_rsm_pre_add, /* precompute remaining points by adding */
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ecp_rsm_pre_norm_add, /* normalize all precomputed points */
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ecp_rsm_comb_core, /* ecp_mul_comb_core() */
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ecp_rsm_final_norm, /* do the final normalization */
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} state;
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#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
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ecp_drbg_context drbg_ctx;
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unsigned char drbg_seeded;
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#endif
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};
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/*
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* Init restart_mul sub-context
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*/
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static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx )
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{
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mbedtls_ecp_point_init( &ctx->R );
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ctx->i = 0;
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ctx->T = NULL;
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ctx->T_size = 0;
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ctx->state = ecp_rsm_init;
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#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
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ecp_drbg_init( &ctx->drbg_ctx );
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ctx->drbg_seeded = 0;
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#endif
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}
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/*
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* Free the components of a restart_mul sub-context
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*/
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static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx )
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{
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unsigned char i;
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if( !ctx )
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return;
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mbedtls_ecp_point_free( &ctx->R );
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if( ctx->T )
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{
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for( i = 0; i < ctx->T_size; i++ )
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mbedtls_ecp_point_free( ctx->T + i );
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mbedtls_free( ctx->T );
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}
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#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
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ecp_drbg_free( &ctx->drbg_ctx );
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#endif
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ecp_restart_rsm_init( ctx );
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}
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/*
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* Restart context for ecp_muladd()
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*/
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struct mbedtls_ecp_restart_muladd
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{
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mbedtls_ecp_point mP; /* mP value */
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mbedtls_ecp_point R; /* R intermediate result */
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enum { /* what should we do next? */
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ecp_rsma_mul1 = 0, /* first multiplication */
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ecp_rsma_mul2, /* second multiplication */
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ecp_rsma_add, /* addition */
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ecp_rsma_norm, /* normalization */
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} state;
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};
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|
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/*
|
|
* Init restart_muladd sub-context
|
|
*/
|
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static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx )
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{
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mbedtls_ecp_point_init( &ctx->mP );
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mbedtls_ecp_point_init( &ctx->R );
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ctx->state = ecp_rsma_mul1;
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}
|
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|
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/*
|
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* Free the components of a restart_muladd sub-context
|
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*/
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static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx )
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{
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if( !ctx )
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return;
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mbedtls_ecp_point_free( &ctx->mP );
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mbedtls_ecp_point_free( &ctx->R );
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ecp_restart_ma_init( ctx );
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}
|
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|
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/**
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* \brief Initialize a restart context.
|
|
*
|
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* \param ctx The restart context to initialize. This must
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* not be \c NULL.
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|
*/
|
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void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx )
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|
{
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ECP_VALIDATE( ctx );
|
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ctx->ops_done = 0;
|
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ctx->depth = 0;
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|
ctx->rsm = NULL;
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ctx->ma = NULL;
|
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}
|
|
|
|
/**
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|
* \brief Free the components of a restart context.
|
|
*
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|
* \param ctx The restart context to free. This may be \c NULL, in which
|
|
* case this function returns immediately. If it is not
|
|
* \c NULL, it must point to an initialized 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 );
|
|
if( rs_ctx && 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 )
|
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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 ||
|
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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 && 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 && 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 && rs_ctx->SUB && \
|
|
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 ) \
|
|
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
|
|
*
|
|
* ELLIPTIC CURVES 101
|
|
*
|
|
* CURVE SECURITY RECOMMENDED BY
|
|
* ---------- --------- --------------------------------
|
|
* SECP256R1 128 IANA, NIST, FRANCE, GERMANY
|
|
* SECP384R1 192 IANA, NIST, FRANCE, GERMANY, NSA
|
|
* X25519 112-128 IANA
|
|
* X448 224 IANA
|
|
* BP384R1 GERMANY
|
|
* SECP521R1 FRANCE
|
|
* GC512A RUSSIA
|
|
* SM2 CHINA
|
|
*
|
|
* 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_SECP256R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
|
|
{ MBEDTLS_ECP_DP_CURVE448, 30, 448, "x448" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
|
|
{ MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
|
|
#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
|
|
{ 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];
|
|
|
|
/**
|
|
* \brief This function retrieves the information defined in
|
|
* mbedtls_ecp_curve_info() for all supported curves in order
|
|
* of preference.
|
|
*
|
|
* \note This function returns information about all curves
|
|
* supported by the library. Some curves may not be
|
|
* supported for all algorithms. Call mbedtls_ecdh_can_do()
|
|
* or mbedtls_ecdsa_can_do() to check if a curve is
|
|
* supported for ECDH or ECDSA.
|
|
*
|
|
* \return A statically allocated array. The last entry is 0.
|
|
*/
|
|
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
|
|
{
|
|
return( ecp_supported_curves );
|
|
}
|
|
|
|
/**
|
|
* \brief This function retrieves the list of internal group
|
|
* identifiers of all supported curves in the order of
|
|
* preference.
|
|
*
|
|
* \note This function returns information about all curves
|
|
* supported by the library. Some curves may not be
|
|
* supported for all algorithms. Call mbedtls_ecdh_can_do()
|
|
* or mbedtls_ecdsa_can_do() to check if a curve is
|
|
* supported for ECDH or ECDSA.
|
|
*
|
|
* \return A statically allocated array,
|
|
* terminated with MBEDTLS_ECP_DP_NONE.
|
|
*/
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function retrieves curve information from an internal
|
|
* group identifier.
|
|
*
|
|
* \param grp_id An \c MBEDTLS_ECP_DP_XXX value.
|
|
*
|
|
* \return The associated curve information on success.
|
|
* \return NULL on failure.
|
|
*/
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function retrieves curve information from a TLS
|
|
* NamedCurve value.
|
|
*
|
|
* \param tls_id An \c MBEDTLS_ECP_DP_XXX value.
|
|
*
|
|
* \return The associated curve information on success.
|
|
* \return NULL on failure.
|
|
*/
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function retrieves curve information from a
|
|
* human-readable name.
|
|
*
|
|
* \param name The human-readable name.
|
|
*
|
|
* \return The associated curve information on success.
|
|
* \return NULL on failure.
|
|
*/
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function initializes a point as zero.
|
|
*
|
|
* \param pt The point to initialize.
|
|
*/
|
|
void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
|
|
{
|
|
ECP_VALIDATE( pt );
|
|
mbedtls_mpi_init( &pt->X );
|
|
mbedtls_mpi_init( &pt->Y );
|
|
mbedtls_mpi_init( &pt->Z );
|
|
}
|
|
|
|
/**
|
|
* \brief This function initializes an ECP group context
|
|
* without loading any domain parameters.
|
|
*
|
|
* \note After this function is called, domain parameters
|
|
* for various ECP groups can be loaded through the
|
|
* mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group()
|
|
* functions.
|
|
*/
|
|
void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
|
|
{
|
|
ECP_VALIDATE( grp );
|
|
grp->id = MBEDTLS_ECP_DP_NONE;
|
|
mbedtls_mpi_init( &grp->P );
|
|
mbedtls_mpi_init( &grp->A );
|
|
mbedtls_mpi_init( &grp->B );
|
|
mbedtls_ecp_point_init( &grp->G );
|
|
mbedtls_mpi_init( &grp->N );
|
|
grp->pbits = 0;
|
|
grp->nbits = 0;
|
|
grp->h = 0;
|
|
grp->modp = NULL;
|
|
grp->t_pre = NULL;
|
|
grp->t_post = NULL;
|
|
grp->t_data = NULL;
|
|
grp->T = NULL;
|
|
grp->T_size = 0;
|
|
}
|
|
|
|
/**
|
|
* \brief This function initializes a key pair as an invalid one.
|
|
*
|
|
* \param key The key pair to initialize.
|
|
*/
|
|
void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
|
|
{
|
|
ECP_VALIDATE( key );
|
|
mbedtls_ecp_group_init( &key->grp );
|
|
mbedtls_mpi_init( &key->d );
|
|
mbedtls_ecp_point_init( &key->Q );
|
|
}
|
|
|
|
/**
|
|
* \brief This function frees the components of a point.
|
|
*
|
|
* \param pt The point to free.
|
|
*/
|
|
void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
|
|
{
|
|
if( !pt )
|
|
return;
|
|
mbedtls_mpi_free( &( pt->X ) );
|
|
mbedtls_mpi_free( &( pt->Y ) );
|
|
mbedtls_mpi_free( &( pt->Z ) );
|
|
}
|
|
|
|
/**
|
|
* \brief This function frees the components of an ECP group.
|
|
*
|
|
* \param grp The group to free. This may be \c NULL, in which
|
|
* case this function returns immediately. If it is not
|
|
* \c NULL, it must point to an initialized ECP group.
|
|
*/
|
|
void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
|
|
{
|
|
size_t i;
|
|
if( !grp )
|
|
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 )
|
|
{
|
|
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 ) );
|
|
}
|
|
|
|
/**
|
|
* \brief This function frees the components of a key pair.
|
|
*
|
|
* \param key The key pair to free. This may be \c NULL, in which
|
|
* case this function returns immediately. If it is not
|
|
* \c NULL, it must point to an initialized ECP key pair.
|
|
*/
|
|
void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
|
|
{
|
|
if( !key )
|
|
return;
|
|
mbedtls_ecp_group_free( &key->grp );
|
|
mbedtls_mpi_free( &key->d );
|
|
mbedtls_ecp_point_free( &key->Q );
|
|
}
|
|
|
|
/**
|
|
* \brief This function copies the contents of point \p Q into
|
|
* point \p P.
|
|
*
|
|
* \param P The destination point. This must be initialized.
|
|
* \param Q The source point. This must be initialized.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
|
|
* \return Another negative error code for other kinds of failure.
|
|
*/
|
|
int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
|
|
{
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
ECP_VALIDATE_RET( P );
|
|
ECP_VALIDATE_RET( Q );
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function copies the contents of group \p src into
|
|
* group \p dst.
|
|
*
|
|
* \param dst The destination group. This must be initialized.
|
|
* \param src The source group. This must be initialized.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
|
|
{
|
|
ECP_VALIDATE_RET( dst );
|
|
ECP_VALIDATE_RET( src );
|
|
return( mbedtls_ecp_group_load( dst, src->id ) );
|
|
}
|
|
|
|
/**
|
|
* \brief This function checks if a point is the point at infinity.
|
|
*
|
|
* \param pt The point to test. This must be initialized.
|
|
*
|
|
* \return \c 1 if the point is zero.
|
|
* \return \c 0 if the point is non-zero.
|
|
* \return A negative error code on failure.
|
|
*/
|
|
int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
|
|
{
|
|
ECP_VALIDATE_RET( pt );
|
|
return( mbedtls_mpi_is_zero( &pt->Z ) );
|
|
}
|
|
|
|
/**
|
|
* \brief This function compares two points.
|
|
*
|
|
* \note This assumes that the points are normalized. Otherwise,
|
|
* they may compare as "not equal" even if they are.
|
|
*
|
|
* \param P The first point to compare. This must be initialized.
|
|
* \param Q The second point to compare. This must be initialized.
|
|
*
|
|
* \return \c 0 if the points are equal.
|
|
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
|
|
*/
|
|
int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
|
|
const mbedtls_ecp_point *Q )
|
|
{
|
|
ECP_VALIDATE_RET( P );
|
|
ECP_VALIDATE_RET( Q );
|
|
if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
|
|
mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
|
|
mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
|
|
{
|
|
return( 0 );
|
|
}
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
}
|
|
|
|
/**
|
|
* \brief This function imports a non-zero point from two ASCII
|
|
* strings.
|
|
*
|
|
* \param P The destination point. This must be initialized.
|
|
* \param radix The numeric base of the input.
|
|
* \param x The first affine coordinate, as a null-terminated string.
|
|
* \param y The second affine coordinate, as a null-terminated string.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return An \c MBEDTLS_ERR_MPI_XXX error code on failure.
|
|
*/
|
|
int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
|
|
const char *x, const char *y )
|
|
{
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
ECP_VALIDATE_RET( P );
|
|
ECP_VALIDATE_RET( x );
|
|
ECP_VALIDATE_RET( y );
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function exports a point into unsigned binary data.
|
|
*
|
|
* \param grp The group to which the point should belong.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param P The point to export. This must be initialized.
|
|
* \param format The point format. This must be either
|
|
* #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
|
|
* (For groups without these formats, this parameter is
|
|
* ignored. But it still has to be either of the above
|
|
* values.)
|
|
* \param olen The address at which to store the length of
|
|
* the output in Bytes. This must not be \c NULL.
|
|
* \param buf The output buffer. This must be a writable buffer
|
|
* of length \p buflen Bytes.
|
|
* \param buflen The length of the output buffer \p buf in Bytes.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer
|
|
* is too small to hold the point.
|
|
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
|
|
* or the export for the given group is not implemented.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
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 )
|
|
{
|
|
/*
|
|
* Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748)
|
|
*/
|
|
int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
|
|
size_t plen;
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( P );
|
|
ECP_VALIDATE_RET( olen );
|
|
ECP_VALIDATE_RET( buf );
|
|
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_is_zero( &P->Z ) )
|
|
{
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function imports a point from unsigned binary data.
|
|
*
|
|
* \note This function does not check that the point actually
|
|
* belongs to the given group, see mbedtls_ecp_check_pubkey()
|
|
* for that.
|
|
*
|
|
* \param grp The group to which the point should belong.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param P The destination context to import the point to.
|
|
* This must be initialized.
|
|
* \param buf The input buffer. This must be a readable buffer
|
|
* of length \p ilen Bytes.
|
|
* \param ilen The length of the input buffer \p buf in Bytes.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
|
|
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the
|
|
* given group is not implemented.
|
|
*/
|
|
int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
|
|
mbedtls_ecp_point *pt,
|
|
const unsigned char *buf, size_t ilen )
|
|
{
|
|
/*
|
|
* Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748)
|
|
*/
|
|
int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
|
|
size_t plen;
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( pt );
|
|
ECP_VALIDATE_RET( buf );
|
|
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] )
|
|
{
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function imports a point from a TLS ECPoint record.
|
|
*
|
|
* \note On function return, \p *buf is updated to point immediately
|
|
* after the ECPoint record.
|
|
*
|
|
* \param grp The ECP group to use.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param pt The destination point.
|
|
* \param buf The address of the pointer to the start of the input buffer.
|
|
* \param len The length of the buffer.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization
|
|
* failure.
|
|
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
|
|
*/
|
|
int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
|
|
mbedtls_ecp_point *pt,
|
|
const unsigned char **buf, size_t buf_len )
|
|
{
|
|
/*
|
|
* Import a point from a TLS ECPoint record (RFC 4492)
|
|
* struct {
|
|
* opaque point <1..2^8-1>;
|
|
* } ECPoint;
|
|
*/
|
|
unsigned char data_len;
|
|
const unsigned char *buf_start;
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( pt );
|
|
ECP_VALIDATE_RET( buf );
|
|
ECP_VALIDATE_RET( *buf );
|
|
/*
|
|
* 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 ) );
|
|
}
|
|
|
|
/**
|
|
* \brief This function exports a point as a TLS ECPoint record
|
|
* defined in RFC 4492, Section 5.4.
|
|
*
|
|
* \param grp The ECP group to use.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param pt The point to be exported. This must be initialized.
|
|
* \param format The point format to use. This must be either
|
|
* #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
|
|
* \param olen The address at which to store the length in Bytes
|
|
* of the data written.
|
|
* \param buf The target buffer. This must be a writable buffer of
|
|
* length \p blen Bytes.
|
|
* \param blen The length of the target buffer \p buf in Bytes.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
|
|
* \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer
|
|
* is too small to hold the exported point.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
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 )
|
|
{
|
|
/*
|
|
* Export a point as a TLS ECPoint record (RFC 4492)
|
|
* struct {
|
|
* opaque point <1..2^8-1>;
|
|
* } ECPoint;
|
|
*/
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( pt );
|
|
ECP_VALIDATE_RET( olen );
|
|
ECP_VALIDATE_RET( buf );
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function sets up an ECP group context from a TLS
|
|
* ECParameters record as defined in RFC 4492, Section 5.4.
|
|
*
|
|
* \note The read pointer \p buf is updated to point right after
|
|
* the ECParameters record on exit.
|
|
*
|
|
* \param grp The group context to setup. This must be initialized.
|
|
* \param buf The address of the pointer to the start of the input buffer.
|
|
* \param len The length of the input buffer \c *buf in Bytes.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
|
|
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
|
|
* recognized.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
|
|
const unsigned char **buf, size_t len )
|
|
{
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
mbedtls_ecp_group_id grp_id;
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( buf );
|
|
ECP_VALIDATE_RET( *buf );
|
|
if( ( ret = mbedtls_ecp_tls_read_group_id( &grp_id, buf, len ) ) != 0 )
|
|
return( ret );
|
|
return( mbedtls_ecp_group_load( grp, grp_id ) );
|
|
}
|
|
|
|
/**
|
|
* \brief This function extracts an elliptic curve group ID from a
|
|
* TLS ECParameters record as defined in RFC 4492, Section 5.4.
|
|
*
|
|
* \note The read pointer \p buf is updated to point right after
|
|
* the ECParameters record on exit.
|
|
*
|
|
* \param grp The address at which to store the group id.
|
|
* This must not be \c NULL.
|
|
* \param buf The address of the pointer to the start of the input buffer.
|
|
* \param len The length of the input buffer \c *buf in Bytes.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
|
|
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
|
|
* recognized.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
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 );
|
|
ECP_VALIDATE_RET( buf );
|
|
ECP_VALIDATE_RET( *buf );
|
|
/*
|
|
* 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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function exports an elliptic curve as a TLS
|
|
* ECParameters record as defined in RFC 4492, Section 5.4.
|
|
*
|
|
* \param grp The ECP group to be exported.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param olen The address at which to store the number of Bytes written.
|
|
* This must not be \c NULL.
|
|
* \param buf The buffer to write to. This must be a writable buffer
|
|
* of length \p blen Bytes.
|
|
* \param blen The length of the output buffer \p buf in Bytes.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output
|
|
* buffer is too small to hold the exported group.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
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 );
|
|
ECP_VALIDATE_RET( buf );
|
|
ECP_VALIDATE_RET( olen );
|
|
if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
/*
|
|
* We are going to write 3 bytes (see below)
|
|
*/
|
|
*olen = 3;
|
|
if( blen < *olen )
|
|
return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
|
|
/*
|
|
* First byte is curve_type, always named_curve
|
|
*/
|
|
*buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
|
|
/*
|
|
* Next two bytes are the namedcurve value
|
|
*/
|
|
buf[0] = curve_info->tls_id >> 8;
|
|
buf[1] = curve_info->tls_id & 0xFF;
|
|
return( 0 );
|
|
}
|
|
|
|
/*
|
|
* Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
|
|
* See the documentation of struct mbedtls_ecp_group.
|
|
*
|
|
* This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
|
|
*/
|
|
static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
|
|
{
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
if( !grp->modp )
|
|
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_is_zero( N ) ) ||
|
|
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_is_zero( N ) )
|
|
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 )
|
|
|
|
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_THIS_CORRUPTION;
|
|
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_is_zero( &(N) ) ) \
|
|
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) ) )
|
|
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_THIS_CORRUPTION;
|
|
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_THIS_CORRUPTION;
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, A, B ) );
|
|
MOD_ADD( *X );
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
|
|
/*
|
|
* For curves in short Weierstrass form, we do all the internal operations in
|
|
* Jacobian coordinates.
|
|
*
|
|
* For multiplication, we'll use a comb method with coutermeasueres against
|
|
* SPA, hence timing attacks.
|
|
*/
|
|
|
|
/*
|
|
* Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
|
|
* Cost: 1N := 1I + 3M + 1S
|
|
*/
|
|
static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
|
|
{
|
|
if( mbedtls_ecp_is_zero( pt ) )
|
|
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
|
|
#ifdef MBEDTLS_ECP_DP_SECP384R1_ENABLED
|
|
if ( grp->modp == ecp_mod_p384 )
|
|
return mbedtls_p384_normalize_jac(grp, pt);
|
|
#endif
|
|
#ifdef MBEDTLS_ECP_DP_SECP256R1_ENABLED
|
|
if ( grp->modp == ecp_mod_p256 )
|
|
return mbedtls_p256_normalize_jac(grp, pt);
|
|
#endif
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
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
|
|
#ifdef MBEDTLS_ECP_DP_SECP384R1_ENABLED
|
|
if ( grp->modp == ecp_mod_p384 )
|
|
return mbedtls_p384_normalize_jac_many(grp, T, T_size);
|
|
#endif
|
|
#ifdef MBEDTLS_ECP_DP_SECP256R1_ENABLED
|
|
if ( grp->modp == ecp_mod_p256 )
|
|
return mbedtls_p256_normalize_jac_many(grp, T, T_size);
|
|
#endif
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
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_THIS_CORRUPTION;
|
|
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_is_zero( &Q->Y );
|
|
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
|
|
|
|
#ifdef MBEDTLS_ECP_DP_SECP256R1_ENABLED
|
|
if ( grp->modp == ecp_mod_p256 )
|
|
return mbedtls_p256_double_jac(grp, P, R);
|
|
#endif
|
|
|
|
#ifdef MBEDTLS_ECP_DP_SECP384R1_ENABLED
|
|
if ( grp->modp == ecp_mod_p384 )
|
|
return mbedtls_p384_double_jac(grp, P, R);
|
|
#endif
|
|
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
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 )
|
|
{
|
|
/* 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_is_zero( &grp->A ) )
|
|
{
|
|
/* 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 ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &T ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &S ) );
|
|
/* 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 ) );
|
|
/* 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 ) );
|
|
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_THIS_CORRUPTION;
|
|
mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
|
|
/*
|
|
* Trivial cases: P == 0 or Q == 0 (case 1)
|
|
*/
|
|
if( mbedtls_ecp_is_zero( P ) )
|
|
return( mbedtls_ecp_copy( R, Q ) );
|
|
if( Q->Z.p && mbedtls_ecp_is_zero( Q ) )
|
|
return( mbedtls_ecp_copy( R, P ) );
|
|
/*
|
|
* Make sure Q coordinates are normalized
|
|
*/
|
|
if( Q->Z.p && !mbedtls_mpi_is_one( &Q->Z ) )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
#ifdef MBEDTLS_ECP_DP_SECP384R1_ENABLED
|
|
if ( grp->modp == ecp_mod_p384 )
|
|
return mbedtls_p384_add_mixed(grp, P, Q, R);
|
|
#endif
|
|
#ifdef MBEDTLS_ECP_DP_SECP256R1_ENABLED
|
|
if ( grp->modp == ecp_mod_p256 )
|
|
return mbedtls_p256_add_mixed(grp, P, Q, R);
|
|
#endif
|
|
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_is_zero( &T1 ) )
|
|
{
|
|
if( mbedtls_mpi_is_zero( &T2 ) )
|
|
{
|
|
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 ) );
|
|
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_THIS_CORRUPTION;
|
|
mbedtls_mpi l, ll;
|
|
int count = 0;
|
|
size_t p_size = ( grp->pbits + 7 ) / 8;
|
|
mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
|
|
/* Generate l such that 1 < l < p */
|
|
do
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
|
|
while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
|
|
mbedtls_mpi_shift_r( &l, 1 );
|
|
if( count++ > 10 )
|
|
{
|
|
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
|
|
goto cleanup;
|
|
}
|
|
}
|
|
while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
|
|
/* 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 );
|
|
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;
|
|
mbedtls_platform_zeroize( x, 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_THIS_CORRUPTION;
|
|
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 && rs_ctx->rsm )
|
|
{
|
|
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 && rs_ctx->rsm )
|
|
{
|
|
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 && rs_ctx->rsm && 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 ) )
|
|
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 && rs_ctx->rsm )
|
|
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 && rs_ctx->rsm )
|
|
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 && rs_ctx->rsm )
|
|
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 && rs_ctx->rsm &&
|
|
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_THIS_CORRUPTION;
|
|
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_THIS_CORRUPTION;
|
|
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 && rs_ctx->rsm &&
|
|
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 && rs_ctx->rsm && rs_ctx->rsm->i != 0 )
|
|
{
|
|
/* restore current index (R already pointing to rs_ctx->rsm->R) */
|
|
i = rs_ctx->rsm->i;
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
/* Start with a non-zero point and randomize its coordinates */
|
|
i = d;
|
|
MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
|
|
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
|
|
if( f_rng != 0 )
|
|
#endif
|
|
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 && rs_ctx->rsm &&
|
|
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_THIS_CORRUPTION;
|
|
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_THIS_CORRUPTION;
|
|
unsigned char parity_trick;
|
|
unsigned char k[COMB_MAX_D + 1];
|
|
mbedtls_ecp_point *RR = R;
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx && rs_ctx->rsm )
|
|
{
|
|
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 && rs_ctx->rsm )
|
|
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 != 0 )
|
|
#endif
|
|
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 && rs_ctx->rsm )
|
|
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 tranfer, freeing.
|
|
*
|
|
* It delegates the actual arithmetic work to:
|
|
* ecp_precompute_comb() and ecp_mul_comb_with_precomp()
|
|
*
|
|
* See comments on ecp_comb_recode_core() regarding the computation strategy.
|
|
*/
|
|
static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng,
|
|
mbedtls_ecp_restart_ctx *rs_ctx )
|
|
{
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
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 && rs_ctx->rsm )
|
|
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 && rs_ctx->rsm )
|
|
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 )
|
|
{
|
|
/* 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 && rs_ctx->rsm && rs_ctx->rsm->T )
|
|
{
|
|
/* 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 )
|
|
{
|
|
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 && rs_ctx->rsm && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T )
|
|
{
|
|
/* 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 )
|
|
{
|
|
for( i = 0; i < T_size; i++ )
|
|
mbedtls_ecp_point_free( &T[i] );
|
|
mbedtls_free( T );
|
|
}
|
|
/* don't free R while in progress in case R == P */
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )
|
|
#endif
|
|
/* prevent caller from using invalid value */
|
|
if( ret != 0 )
|
|
mbedtls_ecp_point_free( R );
|
|
ECP_RS_LEAVE( rsm );
|
|
return( ret );
|
|
}
|
|
|
|
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
|
|
|
|
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
|
|
/*
|
|
* For Montgomery curves, we do all the internal arithmetic in projective
|
|
* coordinates. Import/export of points uses only the x coordinates, which is
|
|
* internaly represented as X / Z.
|
|
*
|
|
* For scalar multiplication, we'll use a Montgomery ladder.
|
|
*/
|
|
|
|
/*
|
|
* Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
|
|
* Cost: 1M + 1I
|
|
*/
|
|
static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
|
|
{
|
|
#if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
|
|
if( mbedtls_internal_ecp_grp_capable( grp ) )
|
|
return( mbedtls_internal_ecp_normalize_mxz( grp, P ) );
|
|
#endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
|
|
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
|
|
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
|
|
#else
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
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_THIS_CORRUPTION;
|
|
mbedtls_mpi l;
|
|
int count = 0;
|
|
size_t p_size = ( grp->pbits + 7 ) / 8;
|
|
mbedtls_mpi_init( &l );
|
|
/* Generate l such that 1 < l < p */
|
|
do
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
|
|
while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
|
|
mbedtls_mpi_shift_r( &l, 1 );
|
|
if( count++ > 10 )
|
|
{
|
|
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
|
|
goto cleanup;
|
|
}
|
|
}
|
|
while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
|
|
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 );
|
|
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_THIS_CORRUPTION;
|
|
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_THIS_CORRUPTION;
|
|
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 sligtly larger than P, so reduce it */
|
|
MOD_ADD( RP.X );
|
|
/* Randomize coordinates of the starting point */
|
|
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
|
|
if( f_rng )
|
|
#endif
|
|
MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
|
|
/* Loop invariant: R = result so far, RP = R + P */
|
|
i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
|
|
while( i-- > 0 )
|
|
{
|
|
b = mbedtls_mpi_get_bit( m, i );
|
|
/*
|
|
* if (b) R = 2R + P else R = 2R,
|
|
* which is:
|
|
* if (b) double_add( RP, R, RP, R )
|
|
* else double_add( R, RP, R, RP )
|
|
* but using safe conditional swaps to avoid leaks
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
|
|
MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
|
|
}
|
|
/*
|
|
* Knowledge of the projective coordinates may leak the last few bits of the
|
|
* scalar [1], and since our MPI implementation isn't constant-flow,
|
|
* inversion (used for coordinate normalization) may leak the full value
|
|
* of its input via side-channels [2].
|
|
*
|
|
* [1] https://eprint.iacr.org/2003/191
|
|
* [2] https://eprint.iacr.org/2020/055
|
|
*
|
|
* Avoid the leak by randomizing coordinates before we normalize them.
|
|
*/
|
|
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
|
|
if( f_rng )
|
|
#endif
|
|
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 */
|
|
|
|
/**
|
|
* \brief This function performs multiplication of a point by
|
|
* an integer: \p R = \p m * \p P in a restartable way.
|
|
*
|
|
* \see mbedtls_ecp_mul()
|
|
*
|
|
* \note This function does the same as \c mbedtls_ecp_mul(), but
|
|
* it can return early and restart according to the limit set
|
|
* with \c mbedtls_ecp_set_max_ops() to reduce blocking.
|
|
*
|
|
* \param grp The ECP group to use.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param R The point in which to store the result of the calculation.
|
|
* This must be initialized.
|
|
* \param m The integer by which to multiply. This must be initialized.
|
|
* \param P The point to multiply. This must be initialized.
|
|
* \param f_rng The RNG function. This may be \c NULL if randomization
|
|
* of intermediate results isn't desired (discouraged).
|
|
* \param p_rng The RNG context to be passed to \p p_rng.
|
|
* \param rs_ctx The restart context (NULL disables restart).
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
|
|
* key, or \p P is not a valid public key.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
|
|
* \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
|
|
* operations was reached: see \c mbedtls_ecp_set_max_ops().
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
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 );
|
|
ECP_VALIDATE_RET( R );
|
|
ECP_VALIDATE_RET( m );
|
|
ECP_VALIDATE_RET( P );
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
/* reset ops count for this call if top-level */
|
|
if( rs_ctx && rs_ctx->depth++ == 0 )
|
|
rs_ctx->ops_done = 0;
|
|
#else
|
|
(void) rs_ctx;
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
|
if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
|
|
MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
|
|
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
/* skip argument check when restarting */
|
|
if( !rs_ctx || !rs_ctx->rsm )
|
|
#endif
|
|
{
|
|
/* check_privkey is free */
|
|
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_CHK );
|
|
/* Common sanity checks */
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( grp, m ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) );
|
|
}
|
|
ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
|
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
|
|
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
|
|
MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
|
|
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
|
|
MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) );
|
|
#endif
|
|
cleanup:
|
|
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
|
if( is_grp_capable )
|
|
mbedtls_internal_ecp_free( grp );
|
|
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx )
|
|
rs_ctx->depth--;
|
|
#endif
|
|
return( ret );
|
|
}
|
|
|
|
/**
|
|
* \brief This function performs a scalar multiplication of a point
|
|
* by an integer: \p R = \p m * \p P.
|
|
*
|
|
* It is not thread-safe to use same group in multiple threads.
|
|
*
|
|
* \note To prevent timing attacks, this function
|
|
* executes the exact same sequence of base-field
|
|
* operations for any valid \p m. It avoids any if-branch or
|
|
* array index depending on the value of \p m.
|
|
*
|
|
* \note If \p f_rng is not NULL, it is used to randomize
|
|
* intermediate results to prevent potential timing attacks
|
|
* targeting these results. We recommend always providing
|
|
* a non-NULL \p f_rng. The overhead is negligible.
|
|
* Note: unless #MBEDTLS_ECP_NO_INTERNAL_RNG is defined, when
|
|
* \p f_rng is NULL, an internal RNG (seeded from the value
|
|
* of \p m) will be used instead.
|
|
*
|
|
* \param grp The ECP group to use.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param R The point in which to store the result of the calculation.
|
|
* This must be initialized.
|
|
* \param m The integer by which to multiply. This must be initialized.
|
|
* \param P The point to multiply. This must be initialized.
|
|
* \param f_rng The RNG function. This may be \c NULL if randomization
|
|
* of intermediate results isn't desired (discouraged).
|
|
* \param p_rng The RNG context to be passed to \p p_rng.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
|
|
* key, or \p P is not a valid public key.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
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 );
|
|
ECP_VALIDATE_RET( R );
|
|
ECP_VALIDATE_RET( m );
|
|
ECP_VALIDATE_RET( P );
|
|
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_THIS_CORRUPTION;
|
|
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 )
|
|
{
|
|
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 == 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_THIS_CORRUPTION;
|
|
if( mbedtls_mpi_is_one( m ) )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
|
|
}
|
|
else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
|
|
if( !mbedtls_mpi_is_zero( &R->Y ) )
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function performs multiplication and addition of two
|
|
* points by integers: \p R = \p m * \p P + \p n * \p Q in a
|
|
* restartable way.
|
|
*
|
|
* \see \c mbedtls_ecp_muladd()
|
|
*
|
|
* \note This function works the same as \c mbedtls_ecp_muladd(),
|
|
* but it can return early and restart according to the limit
|
|
* set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
|
|
*
|
|
* \note This function is only defined for short Weierstrass curves.
|
|
* It may not be included in builds without any short
|
|
* Weierstrass curve.
|
|
*
|
|
* \param grp The ECP group to use.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param R The point in which to store the result of the calculation.
|
|
* This must be initialized.
|
|
* \param m The integer by which to multiply \p P.
|
|
* This must be initialized.
|
|
* \param P The point to multiply by \p m. This must be initialized.
|
|
* \param n The integer by which to multiply \p Q.
|
|
* This must be initialized.
|
|
* \param Q The point to be multiplied by \p n.
|
|
* This must be initialized.
|
|
* \param rs_ctx The restart context (NULL disables restart).
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
|
|
* valid private keys, or \p P or \p Q are not valid public
|
|
* keys.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
|
|
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
|
|
* designate a short Weierstrass curve.
|
|
* \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
|
|
* operations was reached: see \c mbedtls_ecp_set_max_ops().
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
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_THIS_CORRUPTION;
|
|
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 );
|
|
ECP_VALIDATE_RET( R );
|
|
ECP_VALIDATE_RET( m );
|
|
ECP_VALIDATE_RET( P );
|
|
ECP_VALIDATE_RET( n );
|
|
ECP_VALIDATE_RET( Q );
|
|
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 && rs_ctx->ma )
|
|
{
|
|
/* 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 && rs_ctx->ma )
|
|
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 && rs_ctx->ma )
|
|
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 && rs_ctx->ma )
|
|
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 && rs_ctx->ma )
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function performs multiplication and addition of two
|
|
* points by integers: \p R = \p m * \p P + \p n * \p Q
|
|
*
|
|
* It is not thread-safe to use same group in multiple threads.
|
|
*
|
|
* \note In contrast to mbedtls_ecp_mul(), this function does not
|
|
* guarantee a constant execution flow and timing.
|
|
*
|
|
* \note This function is only defined for short Weierstrass curves.
|
|
* It may not be included in builds without any short
|
|
* Weierstrass curve.
|
|
*
|
|
* \param grp The ECP group to use.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param R The point in which to store the result of the calculation.
|
|
* This must be initialized.
|
|
* \param m The integer by which to multiply \p P.
|
|
* This must be initialized.
|
|
* \param P The point to multiply by \p m. This must be initialized.
|
|
* \param n The integer by which to multiply \p Q.
|
|
* This must be initialized.
|
|
* \param Q The point to be multiplied by \p n.
|
|
* This must be initialized.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
|
|
* valid private keys, or \p P or \p Q are not valid public
|
|
* keys.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
|
|
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
|
|
* designate a short Weierstrass curve.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
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 );
|
|
ECP_VALIDATE_RET( R );
|
|
ECP_VALIDATE_RET( m );
|
|
ECP_VALIDATE_RET( P );
|
|
ECP_VALIDATE_RET( n );
|
|
ECP_VALIDATE_RET( Q );
|
|
return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) );
|
|
}
|
|
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
|
|
|
|
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
|
|
/*
|
|
* 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 );
|
|
return( 0 );
|
|
}
|
|
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
|
|
|
|
/**
|
|
* \brief This function checks that a point is a valid public key
|
|
* on this curve.
|
|
*
|
|
* It only checks that the point is non-zero, has
|
|
* valid coordinates and lies on the curve. It does not verify
|
|
* that it is indeed a multiple of \p G. This additional
|
|
* check is computationally more expensive, is not required
|
|
* by standards, and should not be necessary if the group
|
|
* used has a small cofactor. In particular, it is useless for
|
|
* the NIST groups which all have a cofactor of 1.
|
|
*
|
|
* \note This function uses bare components rather than an
|
|
* ::mbedtls_ecp_keypair structure, to ease use with other
|
|
* structures, such as ::mbedtls_ecdh_context or
|
|
* ::mbedtls_ecdsa_context.
|
|
*
|
|
* \param grp The ECP group the point should belong to.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param pt The point to check. This must be initialized.
|
|
*
|
|
* \return \c 0 if the point is a valid public key.
|
|
* \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not
|
|
* a valid public key for the given curve.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
|
|
const mbedtls_ecp_point *pt )
|
|
{
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( pt );
|
|
/* Must use affine coordinates */
|
|
if( !mbedtls_mpi_is_one( &pt->Z ) )
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function checks that an \p mbedtls_mpi is a
|
|
* valid private key for this curve.
|
|
*
|
|
* \note This function uses bare components rather than an
|
|
* ::mbedtls_ecp_keypair structure to ease use with other
|
|
* structures, such as ::mbedtls_ecdh_context or
|
|
* ::mbedtls_ecdsa_context.
|
|
*
|
|
* \param grp The ECP group the private key should belong to.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param d The integer to check. This must be initialized.
|
|
*
|
|
* \return \c 0 if the point is a valid private key.
|
|
* \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid
|
|
* private key for the given curve.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
noinline int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
|
|
const mbedtls_mpi *d )
|
|
{
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( d );
|
|
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
|
|
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
|
|
{
|
|
/* see RFC 7748 sec. 5 para. 5 */
|
|
if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
|
|
mbedtls_mpi_get_bit( d, 1 ) != 0 ||
|
|
mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
|
|
return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
|
/* see [Curve25519] page 5 */
|
|
if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
|
|
return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
|
return( 0 );
|
|
}
|
|
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
|
|
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
|
|
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
|
|
{
|
|
/* see SEC1 3.2 */
|
|
if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
|
|
mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
|
|
return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
|
else
|
|
return( 0 );
|
|
}
|
|
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
}
|
|
|
|
/**
|
|
* \brief This function generates a private key.
|
|
*
|
|
* \param grp The ECP group to generate a private key for.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param d The destination MPI (secret part). This must be initialized.
|
|
* \param f_rng The RNG function. This must not be \c NULL.
|
|
* \param p_rng The RNG parameter to be passed to \p f_rng. This may be
|
|
* \c NULL if \p f_rng doesn't need a context argument.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
|
|
* on failure.
|
|
*/
|
|
int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
|
|
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_size;
|
|
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( d );
|
|
ECP_VALIDATE_RET( f_rng );
|
|
|
|
n_size = ( grp->nbits + 7 ) / 8;
|
|
|
|
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
|
|
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
|
|
{
|
|
/* [M225] page 5 */
|
|
size_t b;
|
|
|
|
do {
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
|
|
} while( mbedtls_mpi_bitlen( d ) == 0);
|
|
|
|
/* Make sure the most significant bit is nbits */
|
|
b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
|
|
if( b > grp->nbits )
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
|
|
else
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 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( grp->nbits == 254 )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
|
|
}
|
|
}
|
|
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
|
|
|
|
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
|
|
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
|
|
{
|
|
/* SEC1 3.2.1: Generate d such that 1 <= n < N */
|
|
int count = 0;
|
|
unsigned cmp = 0;
|
|
|
|
/*
|
|
* Match the procedure given in RFC 6979 (deterministic ECDSA):
|
|
* - use the same byte ordering;
|
|
* - keep the leftmost nbits bits of the generated octet string;
|
|
* - try until result is in the desired range.
|
|
* This also avoids any biais, which is especially important for ECDSA.
|
|
*/
|
|
do
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
|
|
|
|
/*
|
|
* Each try has at worst a probability 1/2 of failing (the msb has
|
|
* a probability 1/2 of being 0, and then the result will be < N),
|
|
* so after 30 tries failure probability is a most 2**(-30).
|
|
*
|
|
* For most curves, 1 try is enough with overwhelming probability,
|
|
* since N starts with a lot of 1s in binary, but some curves
|
|
* such as secp224k1 are actually very close to the worst case.
|
|
*/
|
|
if( ++count > 30 )
|
|
{
|
|
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
|
|
goto cleanup;
|
|
}
|
|
|
|
ret = mbedtls_mpi_lt_mpi_ct( d, &grp->N, &cmp );
|
|
if( ret != 0 )
|
|
{
|
|
goto cleanup;
|
|
}
|
|
}
|
|
while( mbedtls_mpi_cmp_int( d, 1 ) < 0 || cmp != 1 );
|
|
}
|
|
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/**
|
|
* \brief This function generates a keypair with a configurable base
|
|
* point.
|
|
*
|
|
* \note This function uses bare components rather than an
|
|
* ::mbedtls_ecp_keypair structure to ease use with other
|
|
* structures, such as ::mbedtls_ecdh_context or
|
|
* ::mbedtls_ecdsa_context.
|
|
*
|
|
* \param grp The ECP group to generate a key pair for.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param G The base point to use. This must be initialized
|
|
* and belong to \p grp. It replaces the default base
|
|
* point \c grp->G used by mbedtls_ecp_gen_keypair().
|
|
* \param d The destination MPI (secret part).
|
|
* This must be initialized.
|
|
* \param Q The destination point (public part).
|
|
* This must be initialized.
|
|
* \param f_rng The RNG function. This must not be \c NULL.
|
|
* \param p_rng The RNG context to be passed to \p f_rng. This may
|
|
* be \c NULL if \p f_rng doesn't need a context argument.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
|
|
* on failure.
|
|
*/
|
|
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_THIS_CORRUPTION;
|
|
ECP_VALIDATE_RET( grp );
|
|
ECP_VALIDATE_RET( d );
|
|
ECP_VALIDATE_RET( G );
|
|
ECP_VALIDATE_RET( Q );
|
|
ECP_VALIDATE_RET( f_rng );
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function generates an ECP keypair.
|
|
*
|
|
* \note This function uses bare components rather than an
|
|
* ::mbedtls_ecp_keypair structure to ease use with other
|
|
* structures, such as ::mbedtls_ecdh_context or
|
|
* ::mbedtls_ecdsa_context.
|
|
*
|
|
* \param grp The ECP group to generate a key pair for.
|
|
* This must be initialized and have group parameters
|
|
* set, for example through mbedtls_ecp_group_load().
|
|
* \param d The destination MPI (secret part).
|
|
* This must be initialized.
|
|
* \param Q The destination point (public part).
|
|
* This must be initialized.
|
|
* \param f_rng The RNG function. This must not be \c NULL.
|
|
* \param p_rng The RNG context to be passed to \p f_rng. This may
|
|
* be \c NULL if \p f_rng doesn't need a context argument.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
|
|
* on failure.
|
|
*/
|
|
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 );
|
|
ECP_VALIDATE_RET( d );
|
|
ECP_VALIDATE_RET( Q );
|
|
ECP_VALIDATE_RET( f_rng );
|
|
return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
|
|
}
|
|
|
|
/**
|
|
* \brief This function generates an ECP key.
|
|
*
|
|
* \param grp_id The ECP group identifier.
|
|
* \param key The destination key. This must be initialized.
|
|
* \param f_rng The RNG function to use. This must not be \c NULL.
|
|
* \param p_rng The RNG context to be passed to \p f_rng. This may
|
|
* be \c NULL if \p f_rng doesn't need a context argument.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
|
|
* on failure.
|
|
*/
|
|
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_THIS_CORRUPTION;
|
|
ECP_VALIDATE_RET( key );
|
|
ECP_VALIDATE_RET( f_rng );
|
|
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
|
|
|
|
/**
|
|
* \brief This function reads an elliptic curve private key.
|
|
*
|
|
* \param grp_id The ECP group identifier.
|
|
* \param key The destination key.
|
|
* \param buf The the buffer containing the binary representation of the
|
|
* key. (Big endian integer for Weierstrass curves, byte
|
|
* string for Montgomery curves.)
|
|
* \param buflen The length of the buffer in bytes.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is
|
|
* invalid.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
|
|
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
|
|
* the group is not implemented.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
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 );
|
|
ECP_VALIDATE_RET( buf );
|
|
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function exports an elliptic curve private key.
|
|
*
|
|
* \param key The private key.
|
|
* \param buf The output buffer for containing the binary representation
|
|
* of the key. (Big endian integer for Weierstrass curves, byte
|
|
* string for Montgomery curves.)
|
|
* \param buflen The total length of the buffer in bytes.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key
|
|
representation is larger than the available space in \p buf.
|
|
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
|
|
* the group is not implemented.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
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 );
|
|
ECP_VALIDATE_RET( buf );
|
|
|
|
#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 );
|
|
}
|
|
|
|
/**
|
|
* \brief This function checks that the keypair objects
|
|
* \p pub and \p prv have the same group and the
|
|
* same public point, and that the private key in
|
|
* \p prv is consistent with the public key.
|
|
*
|
|
* \param pub The keypair structure holding the public key. This
|
|
* must be initialized. If it contains a private key, that
|
|
* part is ignored.
|
|
* \param prv The keypair structure holding the full keypair.
|
|
* This must be initialized.
|
|
*
|
|
* \return \c 0 on success, meaning that the keys are valid and match.
|
|
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match.
|
|
* \return An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX
|
|
* error code on calculation failure.
|
|
*/
|
|
int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub,
|
|
const mbedtls_ecp_keypair *prv )
|
|
{
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
mbedtls_ecp_point Q;
|
|
mbedtls_ecp_group grp;
|
|
ECP_VALIDATE_RET( pub );
|
|
ECP_VALIDATE_RET( prv );
|
|
|
|
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 );
|
|
}
|
|
|
|
/**
|
|
* \brief The ECP checkup routine.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return \c 1 on failure.
|
|
*/
|
|
int mbedtls_ecp_self_test( int verbose )
|
|
{
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
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 */
|
|
|
|
/**
|
|
* \brief This function sets a point to the point at infinity.
|
|
*
|
|
* \param pt The point to set. This must be initialized.
|
|
*
|
|
* \return \c 0 on success.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
|
|
{
|
|
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
|
|
ECP_VALIDATE_RET( pt );
|
|
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 );
|
|
}
|