From a565f54c4c0edf84ef598648e0fdb9a6d5f8f037 Mon Sep 17 00:00:00 2001 From: Hanno Becker Date: Wed, 11 Oct 2017 11:00:19 +0100 Subject: [PATCH] Introduce new files rsa_internal.[ch] for RSA helper functions This commit splits off the RSA helper functions into separate headers and compilation units to have a clearer separation of the public RSA interface, intended to be used by end-users, and the helper functions which are publicly provided only for the benefit of designers of alternative RSA implementations. --- include/mbedtls/config.h | 2 + include/mbedtls/rsa.h | 156 --------- include/mbedtls/rsa_internal.h | 219 ++++++++++++ library/CMakeLists.txt | 1 + library/Makefile | 6 +- library/rsa.c | 475 +-------------------------- library/rsa_internal.c | 471 ++++++++++++++++++++++++++ tests/suites/test_suite_rsa.function | 1 + 8 files changed, 700 insertions(+), 631 deletions(-) create mode 100644 include/mbedtls/rsa_internal.h create mode 100644 library/rsa_internal.c diff --git a/include/mbedtls/config.h b/include/mbedtls/config.h index ec004f5b3..a93b0aae2 100644 --- a/include/mbedtls/config.h +++ b/include/mbedtls/config.h @@ -1650,6 +1650,7 @@ * library/ecp.c * library/ecdsa.c * library/rsa.c + * library/rsa_internal.c * library/ssl_tls.c * * This module is required for RSA, DHM and ECC (ECDH, ECDSA) support. @@ -2263,6 +2264,7 @@ * Enable the RSA public-key cryptosystem. * * Module: library/rsa.c + * library/rsa_internal.c * Caller: library/ssl_cli.c * library/ssl_srv.c * library/ssl_tls.c diff --git a/include/mbedtls/rsa.h b/include/mbedtls/rsa.h index c85e6c81d..eab8e0dfe 100644 --- a/include/mbedtls/rsa.h +++ b/include/mbedtls/rsa.h @@ -74,162 +74,6 @@ extern "C" { #endif -/** - * Helper functions for RSA-related operations on MPI's. - */ - -/** - * \brief Compute RSA prime moduli P, Q from public modulus N=PQ - * and a pair of private and public key. - * - * \note This is a 'static' helper function not operating on - * an RSA context. Alternative implementations need not - * overwrite it. - * - * \param N RSA modulus N = PQ, with P, Q to be found - * \param D RSA private exponent - * \param E RSA public exponent - * \param P Pointer to MPI holding first prime factor of N on success - * \param Q Pointer to MPI holding second prime factor of N on success - * - * \return - * - 0 if successful. In this case, P and Q constitute a - * factorization of N. - * - A non-zero error code otherwise. - * - * \note It is neither checked that P, Q are prime nor that - * D, E are modular inverses wrt. P-1 and Q-1. For that, - * use the helper function \c mbedtls_rsa_validate_params. - * - */ -int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N, mbedtls_mpi const *D, - mbedtls_mpi const *E, - mbedtls_mpi *P, mbedtls_mpi *Q ); - -/** - * \brief Compute RSA private exponent from - * prime moduli and public key. - * - * \note This is a 'static' helper function not operating on - * an RSA context. Alternative implementations need not - * overwrite it. - * - * \param P First prime factor of RSA modulus - * \param Q Second prime factor of RSA modulus - * \param E RSA public exponent - * \param D Pointer to MPI holding the private exponent on success. - * - * \return - * - 0 if successful. In this case, D is set to a simultaneous - * modular inverse of E modulo both P-1 and Q-1. - * - A non-zero error code otherwise. - * - * \note This function does not check whether P and Q are primes. - * - */ -int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P, - mbedtls_mpi const *Q, - mbedtls_mpi const *E, - mbedtls_mpi *D ); - - -/** - * \brief Generate RSA-CRT parameters - * - * \note This is a 'static' helper function not operating on - * an RSA context. Alternative implementations need not - * overwrite it. - * - * \param P First prime factor of N - * \param Q Second prime factor of N - * \param D RSA private exponent - * \param DP Output variable for D modulo P-1 - * \param DQ Output variable for D modulo Q-1 - * \param QP Output variable for the modular inverse of Q modulo P. - * - * \return 0 on success, non-zero error code otherwise. - * - * \note This function does not check whether P, Q are - * prime and whether D is a valid private exponent. - * - */ -int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, - const mbedtls_mpi *D, mbedtls_mpi *DP, - mbedtls_mpi *DQ, mbedtls_mpi *QP ); - - -/** - * \brief Check validity of core RSA parameters - * - * \note This is a 'static' helper function not operating on - * an RSA context. Alternative implementations need not - * overwrite it. - * - * \param N RSA modulus N = PQ - * \param P First prime factor of N - * \param Q Second prime factor of N - * \param D RSA private exponent - * \param E RSA public exponent - * \param f_rng PRNG to be used for primality check, or NULL - * \param p_rng PRNG context for f_rng, or NULL - * - * \return - * - 0 if the following conditions are satisfied - * if all relevant parameters are provided: - * - P prime if f_rng != NULL - * - Q prime if f_rng != NULL - * - 1 < N = PQ - * - 1 < D, E < N - * - D and E are modular inverses modulo P-1 and Q-1 - * - A non-zero error code otherwise. - * - * \note The function can be used with a restricted set of arguments - * to perform specific checks only. E.g., calling it with - * (-,P,-,-,-) and a PRNG amounts to a primality check for P. - */ -int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P, - const mbedtls_mpi *Q, const mbedtls_mpi *D, - const mbedtls_mpi *E, - int (*f_rng)(void *, unsigned char *, size_t), - void *p_rng ); - -/** - * \brief Check validity of RSA CRT parameters - * - * \note This is a 'static' helper function not operating on - * an RSA context. Alternative implementations need not - * overwrite it. - * - * \param P First prime factor of RSA modulus - * \param Q Second prime factor of RSA modulus - * \param D RSA private exponent - * \param DP MPI to check for D modulo P-1 - * \param DQ MPI to check for D modulo P-1 - * \param QP MPI to check for the modular inverse of Q modulo P. - * - * \return - * - 0 if the following conditions are satisfied: - * - D = DP mod P-1 if P, D, DP != NULL - * - Q = DQ mod P-1 if P, D, DQ != NULL - * - QP = Q^-1 mod P if P, Q, QP != NULL - * - \c MBEDTLS_ERR_RSA_KEY_CHECK_FAILED if check failed, - * potentially including \c MBEDTLS_ERR_MPI_XXX if some - * MPI calculations failed. - * - \c MBEDTLS_ERR_RSA_BAD_INPUT_DATA if insufficient - * data was provided to check DP, DQ or QP. - * - * \note The function can be used with a restricted set of arguments - * to perform specific checks only. E.g., calling it with the - * parameters (P, -, D, DP, -, -) will check DP = D mod P-1. - */ -int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, - const mbedtls_mpi *D, const mbedtls_mpi *DP, - const mbedtls_mpi *DQ, const mbedtls_mpi *QP ); - -/** - * Implementation of RSA interface - */ - #if !defined(MBEDTLS_RSA_ALT) /** diff --git a/include/mbedtls/rsa_internal.h b/include/mbedtls/rsa_internal.h new file mode 100644 index 000000000..235347046 --- /dev/null +++ b/include/mbedtls/rsa_internal.h @@ -0,0 +1,219 @@ +/** + * \file rsa_internal.h + * + * \brief Context-independent RSA helper functions + * + * Copyright (C) 2006-2017, ARM Limited, All Rights Reserved + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the "License"); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + * + * This file is part of mbed TLS (https://tls.mbed.org) + * + * + * This file declares some RSA-related helper functions useful when + * implementing the RSA interface. They are public and provided in a + * separate compilation unit in order to make it easy for designers of + * alternative RSA implementations to use them in their code, as it is + * conceived that the functionality they provide will be necessary + * for most complete implementations. + * + * End-users of Mbed TLS not intending to re-implement the RSA functionality + * are not expected to get into the need of making use of these functions directly, + * but instead should be able to make do with the implementation of the RSA module. + * + * There are two classes of helper functions: + * (1) Parameter-generating helpers. These are: + * - mbedtls_rsa_deduce_primes + * - mbedtls_rsa_deduce_private_exponent + * - mbedtls_rsa_deduce_crt + * Each of these functions takes a set of core RSA parameters + * and generates some other, or CRT related parameters. + * (2) Parameter-checking helpers. These are: + * - mbedtls_rsa_validate_params + * - mbedtls_rsa_validate_crt + * They take a set of core or CRT related RSA parameters + * and check their validity. + * + */ + +#ifndef MBEDTLS_RSA_INTERNAL_H +#define MBEDTLS_RSA_INTERNAL_H + +#if !defined(MBEDTLS_CONFIG_FILE) +#include "config.h" +#else +#include MBEDTLS_CONFIG_FILE +#endif + +#include "bignum.h" + +#if defined(MBEDTLS_RSA_C) + +#ifdef __cplusplus +extern "C" { +#endif + + +/** + * \brief Compute RSA prime moduli P, Q from public modulus N=PQ + * and a pair of private and public key. + * + * \note This is a 'static' helper function not operating on + * an RSA context. Alternative implementations need not + * overwrite it. + * + * \param N RSA modulus N = PQ, with P, Q to be found + * \param D RSA private exponent + * \param E RSA public exponent + * \param P Pointer to MPI holding first prime factor of N on success + * \param Q Pointer to MPI holding second prime factor of N on success + * + * \return + * - 0 if successful. In this case, P and Q constitute a + * factorization of N. + * - A non-zero error code otherwise. + * + * \note It is neither checked that P, Q are prime nor that + * D, E are modular inverses wrt. P-1 and Q-1. For that, + * use the helper function \c mbedtls_rsa_validate_params. + * + */ +int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N, mbedtls_mpi const *D, + mbedtls_mpi const *E, + mbedtls_mpi *P, mbedtls_mpi *Q ); + +/** + * \brief Compute RSA private exponent from + * prime moduli and public key. + * + * \note This is a 'static' helper function not operating on + * an RSA context. Alternative implementations need not + * overwrite it. + * + * \param P First prime factor of RSA modulus + * \param Q Second prime factor of RSA modulus + * \param E RSA public exponent + * \param D Pointer to MPI holding the private exponent on success. + * + * \return + * - 0 if successful. In this case, D is set to a simultaneous + * modular inverse of E modulo both P-1 and Q-1. + * - A non-zero error code otherwise. + * + * \note This function does not check whether P and Q are primes. + * + */ +int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P, + mbedtls_mpi const *Q, + mbedtls_mpi const *E, + mbedtls_mpi *D ); + + +/** + * \brief Generate RSA-CRT parameters + * + * \note This is a 'static' helper function not operating on + * an RSA context. Alternative implementations need not + * overwrite it. + * + * \param P First prime factor of N + * \param Q Second prime factor of N + * \param D RSA private exponent + * \param DP Output variable for D modulo P-1 + * \param DQ Output variable for D modulo Q-1 + * \param QP Output variable for the modular inverse of Q modulo P. + * + * \return 0 on success, non-zero error code otherwise. + * + * \note This function does not check whether P, Q are + * prime and whether D is a valid private exponent. + * + */ +int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, + const mbedtls_mpi *D, mbedtls_mpi *DP, + mbedtls_mpi *DQ, mbedtls_mpi *QP ); + + +/** + * \brief Check validity of core RSA parameters + * + * \note This is a 'static' helper function not operating on + * an RSA context. Alternative implementations need not + * overwrite it. + * + * \param N RSA modulus N = PQ + * \param P First prime factor of N + * \param Q Second prime factor of N + * \param D RSA private exponent + * \param E RSA public exponent + * \param f_rng PRNG to be used for primality check, or NULL + * \param p_rng PRNG context for f_rng, or NULL + * + * \return + * - 0 if the following conditions are satisfied + * if all relevant parameters are provided: + * - P prime if f_rng != NULL + * - Q prime if f_rng != NULL + * - 1 < N = PQ + * - 1 < D, E < N + * - D and E are modular inverses modulo P-1 and Q-1 + * - A non-zero error code otherwise. + * + * \note The function can be used with a restricted set of arguments + * to perform specific checks only. E.g., calling it with + * (-,P,-,-,-) and a PRNG amounts to a primality check for P. + */ +int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P, + const mbedtls_mpi *Q, const mbedtls_mpi *D, + const mbedtls_mpi *E, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ); + +/** + * \brief Check validity of RSA CRT parameters + * + * \note This is a 'static' helper function not operating on + * an RSA context. Alternative implementations need not + * overwrite it. + * + * \param P First prime factor of RSA modulus + * \param Q Second prime factor of RSA modulus + * \param D RSA private exponent + * \param DP MPI to check for D modulo P-1 + * \param DQ MPI to check for D modulo P-1 + * \param QP MPI to check for the modular inverse of Q modulo P. + * + * \return + * - 0 if the following conditions are satisfied: + * - D = DP mod P-1 if P, D, DP != NULL + * - Q = DQ mod P-1 if P, D, DQ != NULL + * - QP = Q^-1 mod P if P, Q, QP != NULL + * - \c MBEDTLS_ERR_RSA_KEY_CHECK_FAILED if check failed, + * potentially including \c MBEDTLS_ERR_MPI_XXX if some + * MPI calculations failed. + * - \c MBEDTLS_ERR_RSA_BAD_INPUT_DATA if insufficient + * data was provided to check DP, DQ or QP. + * + * \note The function can be used with a restricted set of arguments + * to perform specific checks only. E.g., calling it with the + * parameters (P, -, D, DP, -, -) will check DP = D mod P-1. + */ +int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, + const mbedtls_mpi *D, const mbedtls_mpi *DP, + const mbedtls_mpi *DQ, const mbedtls_mpi *QP ); + + +#endif /* MBEDTLS_RSA_C */ + +#endif /* rsa_internal.h */ diff --git a/library/CMakeLists.txt b/library/CMakeLists.txt index 7a9f185e2..49f037c8c 100644 --- a/library/CMakeLists.txt +++ b/library/CMakeLists.txt @@ -48,6 +48,7 @@ set(src_crypto platform.c ripemd160.c rsa.c + rsa_internal.c sha1.c sha256.c sha512.c diff --git a/library/Makefile b/library/Makefile index 28f92315a..541d47fe9 100644 --- a/library/Makefile +++ b/library/Makefile @@ -59,9 +59,9 @@ OBJS_CRYPTO= aes.o aesni.o arc4.o \ padlock.o pem.o pk.o \ pk_wrap.o pkcs12.o pkcs5.o \ pkparse.o pkwrite.o platform.o \ - ripemd160.o rsa.o sha1.o \ - sha256.o sha512.o threading.o \ - timing.o version.o \ + ripemd160.o rsa_internal.o rsa.o \ + sha1.o sha256.o sha512.o \ + threading.o timing.o version.o \ version_features.o xtea.o OBJS_X509= certs.o pkcs11.o x509.o \ diff --git a/library/rsa.c b/library/rsa.c index 493cd1c12..83e2b2be3 100644 --- a/library/rsa.c +++ b/library/rsa.c @@ -46,6 +46,7 @@ #if defined(MBEDTLS_RSA_C) #include "mbedtls/rsa.h" +#include "mbedtls/rsa_internal.h" #include "mbedtls/oid.h" #include @@ -67,483 +68,13 @@ #define mbedtls_free free #endif +#if !defined(MBEDTLS_RSA_ALT) + /* Implementation that should never be optimized out by the compiler */ static void mbedtls_zeroize( void *v, size_t n ) { volatile unsigned char *p = (unsigned char*)v; while( n-- ) *p++ = 0; } -/* - * Context-independent RSA helper functions. - * - * There are two classes of helper functions: - * (1) Parameter-generating helpers. These are: - * - mbedtls_rsa_deduce_primes - * - mbedtls_rsa_deduce_private_exponent - * - mbedtls_rsa_deduce_crt - * Each of these functions takes a set of core RSA parameters - * and generates some other, or CRT related parameters. - * (2) Parameter-checking helpers. These are: - * - mbedtls_rsa_validate_params - * - mbedtls_rsa_validate_crt - * They take a set of core or CRT related RSA parameters - * and check their validity. - * - * The helper functions do not use the RSA context structure - * and therefore do not need to be replaced when providing - * an alternative RSA implementation. - * - * Their main purpose is to provide common MPI operations in the context - * of RSA that can be easily shared across multiple implementations. - */ - -/* - * - * Given the modulus N=PQ and a pair of public and private - * exponents E and D, respectively, factor N. - * - * Setting F := lcm(P-1,Q-1), the idea is as follows: - * - * (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2) - * is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the - * square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four - * possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1) - * or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime - * factors of N. - * - * (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same - * construction still applies since (-)^K is the identity on the set of - * roots of 1 in Z/NZ. - * - * The public and private key primitives (-)^E and (-)^D are mutually inverse - * bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e. - * if and only if DE - 1 is a multiple of F, say DE - 1 = F * L. - * Splitting L = 2^t * K with K odd, we have - * - * DE - 1 = FL = (F/2) * (2^(t+1)) * K, - * - * so (F / 2) * K is among the numbers - * - * (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord - * - * where ord is the order of 2 in (DE - 1). - * We can therefore iterate through these numbers apply the construction - * of (a) and (b) above to attempt to factor N. - * - */ -int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N, - mbedtls_mpi const *D, mbedtls_mpi const *E, - mbedtls_mpi *P, mbedtls_mpi *Q ) -{ - int ret = 0; - - uint16_t attempt; /* Number of current attempt */ - uint16_t iter; /* Number of squares computed in the current attempt */ - - uint16_t order; /* Order of 2 in DE - 1 */ - - mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */ - mbedtls_mpi K; /* During factorization attempts, stores a random integer - * in the range of [0,..,N] */ - - const unsigned int primes[] = { 2, - 3, 5, 7, 11, 13, 17, 19, 23, - 29, 31, 37, 41, 43, 47, 53, 59, - 61, 67, 71, 73, 79, 83, 89, 97, - 101, 103, 107, 109, 113, 127, 131, 137, - 139, 149, 151, 157, 163, 167, 173, 179, - 181, 191, 193, 197, 199, 211, 223, 227, - 229, 233, 239, 241, 251, 257, 263, 269, - 271, 277, 281, 283, 293, 307, 311, 313 - }; - - const size_t num_primes = sizeof( primes ) / sizeof( *primes ); - - if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL ) - return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); - - if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 || - mbedtls_mpi_cmp_int( D, 1 ) <= 0 || - mbedtls_mpi_cmp_mpi( D, N ) >= 0 || - mbedtls_mpi_cmp_int( E, 1 ) <= 0 || - mbedtls_mpi_cmp_mpi( E, N ) >= 0 ) - { - return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); - } - - /* - * Initializations and temporary changes - */ - - mbedtls_mpi_init( &K ); - mbedtls_mpi_init( &T ); - - /* T := DE - 1 */ - MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D, E ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) ); - - if( ( order = mbedtls_mpi_lsb( &T ) ) == 0 ) - { - ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; - goto cleanup; - } - - /* After this operation, T holds the largest odd divisor of DE - 1. */ - MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) ); - - /* - * Actual work - */ - - /* Skip trying 2 if N == 1 mod 8 */ - attempt = 0; - if( N->p[0] % 8 == 1 ) - attempt = 1; - - for( ; attempt < num_primes; ++attempt ) - { - mbedtls_mpi_lset( &K, primes[attempt] ); - - /* Check if gcd(K,N) = 1 */ - MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) ); - if( mbedtls_mpi_cmp_int( P, 1 ) != 0 ) - continue; - - /* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ... - * and check whether they have nontrivial GCD with N. */ - MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N, - Q /* temporarily use Q for storing Montgomery - * multiplication helper values */ ) ); - - for( iter = 1; iter < order; ++iter ) - { - MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) ); - - if( mbedtls_mpi_cmp_int( P, 1 ) == 1 && - mbedtls_mpi_cmp_mpi( P, N ) == -1 ) - { - /* - * Have found a nontrivial divisor P of N. - * Set Q := N / P. - */ - - MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) ); - goto cleanup; - } - - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) ); - } - } - - ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; - -cleanup: - - mbedtls_mpi_free( &K ); - mbedtls_mpi_free( &T ); - return( ret ); -} - -/* - * Given P, Q and the public exponent E, deduce D. - * This is essentially a modular inversion. - */ - -int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P, - mbedtls_mpi const *Q, - mbedtls_mpi const *E, - mbedtls_mpi *D ) -{ - int ret = 0; - mbedtls_mpi K, L; - - if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 ) - return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); - - if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 || - mbedtls_mpi_cmp_int( Q, 1 ) <= 0 || - mbedtls_mpi_cmp_int( E, 0 ) == 0 ) - { - return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); - } - - mbedtls_mpi_init( &K ); - mbedtls_mpi_init( &L ); - - /* Temporarily put K := P-1 and L := Q-1 */ - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) ); - - /* Temporarily put D := gcd(P-1, Q-1) */ - MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) ); - - /* K := LCM(P-1, Q-1) */ - MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) ); - - /* Compute modular inverse of E in LCM(P-1, Q-1) */ - MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) ); - -cleanup: - - mbedtls_mpi_free( &K ); - mbedtls_mpi_free( &L ); - - return( ret ); -} - -/* - * Check that RSA CRT parameters are in accordance with core parameters. - */ - -int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, - const mbedtls_mpi *D, const mbedtls_mpi *DP, - const mbedtls_mpi *DQ, const mbedtls_mpi *QP ) -{ - int ret = 0; - - mbedtls_mpi K, L; - mbedtls_mpi_init( &K ); - mbedtls_mpi_init( &L ); - - /* Check that DP - D == 0 mod P - 1 */ - if( DP != NULL ) - { - if( P == NULL ) - { - ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; - goto cleanup; - } - - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) ); - - if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - } - - /* Check that DQ - D == 0 mod Q - 1 */ - if( DQ != NULL ) - { - if( Q == NULL ) - { - ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; - goto cleanup; - } - - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) ); - - if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - } - - /* Check that QP * Q - 1 == 0 mod P */ - if( QP != NULL ) - { - if( P == NULL || Q == NULL ) - { - ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; - goto cleanup; - } - - MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) ); - if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - } - -cleanup: - - /* Wrap MPI error codes by RSA check failure error code */ - if( ret != 0 && - ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED && - ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA ) - { - ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - } - - mbedtls_mpi_free( &K ); - mbedtls_mpi_free( &L ); - - return( ret ); -} - -/* - * Check that core RSA parameters are sane. - */ - -int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P, - const mbedtls_mpi *Q, const mbedtls_mpi *D, - const mbedtls_mpi *E, - int (*f_rng)(void *, unsigned char *, size_t), - void *p_rng ) -{ - int ret = 0; - mbedtls_mpi K, L; - - mbedtls_mpi_init( &K ); - mbedtls_mpi_init( &L ); - - /* - * Step 1: If PRNG provided, check that P and Q are prime - */ - -#if defined(MBEDTLS_GENPRIME) - if( f_rng != NULL && P != NULL && - ( ret = mbedtls_mpi_is_prime( P, f_rng, p_rng ) ) != 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - - if( f_rng != NULL && Q != NULL && - ( ret = mbedtls_mpi_is_prime( Q, f_rng, p_rng ) ) != 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } -#else - ((void) f_rng); - ((void) p_rng); -#endif /* MBEDTLS_GENPRIME */ - - /* - * Step 2: Check that 1 < N = PQ - */ - - if( P != NULL && Q != NULL && N != NULL ) - { - MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) ); - if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 || - mbedtls_mpi_cmp_mpi( &K, N ) != 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - } - - /* - * Step 3: Check and 1 < D, E < N if present. - */ - - if( N != NULL && D != NULL && E != NULL ) - { - if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 || - mbedtls_mpi_cmp_int( E, 1 ) <= 0 || - mbedtls_mpi_cmp_mpi( D, N ) >= 0 || - mbedtls_mpi_cmp_mpi( E, N ) >= 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - } - - /* - * Step 4: Check that D, E are inverse modulo P-1 and Q-1 - */ - - if( P != NULL && Q != NULL && D != NULL && E != NULL ) - { - if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 || - mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - - /* Compute DE-1 mod P-1 */ - MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) ); - if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - - /* Compute DE-1 mod Q-1 */ - MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) ); - if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) - { - ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - goto cleanup; - } - } - -cleanup: - - mbedtls_mpi_free( &K ); - mbedtls_mpi_free( &L ); - - /* Wrap MPI error codes by RSA check failure error code */ - if( ret != 0 && ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ) - { - ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; - } - - return( ret ); -} - -int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, - const mbedtls_mpi *D, mbedtls_mpi *DP, - mbedtls_mpi *DQ, mbedtls_mpi *QP ) -{ - int ret = 0; - mbedtls_mpi K; - mbedtls_mpi_init( &K ); - - /* DP = D mod P-1 */ - if( DP != NULL ) - { - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) ); - } - - /* DQ = D mod Q-1 */ - if( DQ != NULL ) - { - MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) ); - } - - /* QP = Q^{-1} mod P */ - if( QP != NULL ) - { - MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) ); - } - -cleanup: - mbedtls_mpi_free( &K ); - - return( ret ); -} - - -/* - * Default RSA interface implementation - */ - -#if !defined(MBEDTLS_RSA_ALT) - int mbedtls_rsa_import( mbedtls_rsa_context *ctx, const mbedtls_mpi *N, const mbedtls_mpi *P, const mbedtls_mpi *Q, diff --git a/library/rsa_internal.c b/library/rsa_internal.c new file mode 100644 index 000000000..879e2d5d7 --- /dev/null +++ b/library/rsa_internal.c @@ -0,0 +1,471 @@ +/* + * Helper functions for the RSA module + * + * Copyright (C) 2006-2017, ARM Limited, All Rights Reserved + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the "License"); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + * + * This file is part of mbed TLS (https://tls.mbed.org) + * + */ + +#if !defined(MBEDTLS_CONFIG_FILE) +#include "mbedtls/config.h" +#else +#include MBEDTLS_CONFIG_FILE +#endif + +#if defined(MBEDTLS_RSA_C) + +#include "mbedtls/rsa.h" +#include "mbedtls/bignum.h" +#include "mbedtls/rsa_internal.h" + +/* + * Compute RSA prime factors from public and private exponents + * + * Summary of algorithm: + * Setting F := lcm(P-1,Q-1), the idea is as follows: + * + * (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2) + * is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the + * square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four + * possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1) + * or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime + * factors of N. + * + * (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same + * construction still applies since (-)^K is the identity on the set of + * roots of 1 in Z/NZ. + * + * The public and private key primitives (-)^E and (-)^D are mutually inverse + * bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e. + * if and only if DE - 1 is a multiple of F, say DE - 1 = F * L. + * Splitting L = 2^t * K with K odd, we have + * + * DE - 1 = FL = (F/2) * (2^(t+1)) * K, + * + * so (F / 2) * K is among the numbers + * + * (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord + * + * where ord is the order of 2 in (DE - 1). + * We can therefore iterate through these numbers apply the construction + * of (a) and (b) above to attempt to factor N. + * + */ +int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N, + mbedtls_mpi const *D, mbedtls_mpi const *E, + mbedtls_mpi *P, mbedtls_mpi *Q ) +{ + int ret = 0; + + uint16_t attempt; /* Number of current attempt */ + uint16_t iter; /* Number of squares computed in the current attempt */ + + uint16_t order; /* Order of 2 in DE - 1 */ + + mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */ + mbedtls_mpi K; /* Temporary holding the current candidate */ + + const unsigned int primes[] = { 2, + 3, 5, 7, 11, 13, 17, 19, 23, + 29, 31, 37, 41, 43, 47, 53, 59, + 61, 67, 71, 73, 79, 83, 89, 97, + 101, 103, 107, 109, 113, 127, 131, 137, + 139, 149, 151, 157, 163, 167, 173, 179, + 181, 191, 193, 197, 199, 211, 223, 227, + 229, 233, 239, 241, 251, 257, 263, 269, + 271, 277, 281, 283, 293, 307, 311, 313 + }; + + const size_t num_primes = sizeof( primes ) / sizeof( *primes ); + + if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 || + mbedtls_mpi_cmp_int( D, 1 ) <= 0 || + mbedtls_mpi_cmp_mpi( D, N ) >= 0 || + mbedtls_mpi_cmp_int( E, 1 ) <= 0 || + mbedtls_mpi_cmp_mpi( E, N ) >= 0 ) + { + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + } + + /* + * Initializations and temporary changes + */ + + mbedtls_mpi_init( &K ); + mbedtls_mpi_init( &T ); + + /* T := DE - 1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D, E ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) ); + + if( ( order = mbedtls_mpi_lsb( &T ) ) == 0 ) + { + ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + goto cleanup; + } + + /* After this operation, T holds the largest odd divisor of DE - 1. */ + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) ); + + /* + * Actual work + */ + + /* Skip trying 2 if N == 1 mod 8 */ + attempt = 0; + if( N->p[0] % 8 == 1 ) + attempt = 1; + + for( ; attempt < num_primes; ++attempt ) + { + mbedtls_mpi_lset( &K, primes[attempt] ); + + /* Check if gcd(K,N) = 1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) ); + if( mbedtls_mpi_cmp_int( P, 1 ) != 0 ) + continue; + + /* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ... + * and check whether they have nontrivial GCD with N. */ + MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N, + Q /* temporarily use Q for storing Montgomery + * multiplication helper values */ ) ); + + for( iter = 1; iter < order; ++iter ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) ); + + if( mbedtls_mpi_cmp_int( P, 1 ) == 1 && + mbedtls_mpi_cmp_mpi( P, N ) == -1 ) + { + /* + * Have found a nontrivial divisor P of N. + * Set Q := N / P. + */ + + MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) ); + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) ); + } + } + + ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + +cleanup: + + mbedtls_mpi_free( &K ); + mbedtls_mpi_free( &T ); + return( ret ); +} + +/* + * Given P, Q and the public exponent E, deduce D. + * This is essentially a modular inversion. + */ +int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P, + mbedtls_mpi const *Q, + mbedtls_mpi const *E, + mbedtls_mpi *D ) +{ + int ret = 0; + mbedtls_mpi K, L; + + if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 || + mbedtls_mpi_cmp_int( Q, 1 ) <= 0 || + mbedtls_mpi_cmp_int( E, 0 ) == 0 ) + { + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + } + + mbedtls_mpi_init( &K ); + mbedtls_mpi_init( &L ); + + /* Temporarily put K := P-1 and L := Q-1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) ); + + /* Temporarily put D := gcd(P-1, Q-1) */ + MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) ); + + /* K := LCM(P-1, Q-1) */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) ); + + /* Compute modular inverse of E in LCM(P-1, Q-1) */ + MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) ); + +cleanup: + + mbedtls_mpi_free( &K ); + mbedtls_mpi_free( &L ); + + return( ret ); +} + +/* + * Check that RSA CRT parameters are in accordance with core parameters. + */ +int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, + const mbedtls_mpi *D, const mbedtls_mpi *DP, + const mbedtls_mpi *DQ, const mbedtls_mpi *QP ) +{ + int ret = 0; + + mbedtls_mpi K, L; + mbedtls_mpi_init( &K ); + mbedtls_mpi_init( &L ); + + /* Check that DP - D == 0 mod P - 1 */ + if( DP != NULL ) + { + if( P == NULL ) + { + ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) ); + + if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + } + + /* Check that DQ - D == 0 mod Q - 1 */ + if( DQ != NULL ) + { + if( Q == NULL ) + { + ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) ); + + if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + } + + /* Check that QP * Q - 1 == 0 mod P */ + if( QP != NULL ) + { + if( P == NULL || Q == NULL ) + { + ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) ); + if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + } + +cleanup: + + /* Wrap MPI error codes by RSA check failure error code */ + if( ret != 0 && + ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED && + ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA ) + { + ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + } + + mbedtls_mpi_free( &K ); + mbedtls_mpi_free( &L ); + + return( ret ); +} + +/* + * Check that core RSA parameters are sane. + */ +int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P, + const mbedtls_mpi *Q, const mbedtls_mpi *D, + const mbedtls_mpi *E, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + int ret = 0; + mbedtls_mpi K, L; + + mbedtls_mpi_init( &K ); + mbedtls_mpi_init( &L ); + + /* + * Step 1: If PRNG provided, check that P and Q are prime + */ + +#if defined(MBEDTLS_GENPRIME) + if( f_rng != NULL && P != NULL && + ( ret = mbedtls_mpi_is_prime( P, f_rng, p_rng ) ) != 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + + if( f_rng != NULL && Q != NULL && + ( ret = mbedtls_mpi_is_prime( Q, f_rng, p_rng ) ) != 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } +#else + ((void) f_rng); + ((void) p_rng); +#endif /* MBEDTLS_GENPRIME */ + + /* + * Step 2: Check that 1 < N = PQ + */ + + if( P != NULL && Q != NULL && N != NULL ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) ); + if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 || + mbedtls_mpi_cmp_mpi( &K, N ) != 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + } + + /* + * Step 3: Check and 1 < D, E < N if present. + */ + + if( N != NULL && D != NULL && E != NULL ) + { + if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 || + mbedtls_mpi_cmp_int( E, 1 ) <= 0 || + mbedtls_mpi_cmp_mpi( D, N ) >= 0 || + mbedtls_mpi_cmp_mpi( E, N ) >= 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + } + + /* + * Step 4: Check that D, E are inverse modulo P-1 and Q-1 + */ + + if( P != NULL && Q != NULL && D != NULL && E != NULL ) + { + if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 || + mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + + /* Compute DE-1 mod P-1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) ); + if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + + /* Compute DE-1 mod Q-1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) ); + if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) + { + ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + goto cleanup; + } + } + +cleanup: + + mbedtls_mpi_free( &K ); + mbedtls_mpi_free( &L ); + + /* Wrap MPI error codes by RSA check failure error code */ + if( ret != 0 && ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ) + { + ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; + } + + return( ret ); +} + +int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, + const mbedtls_mpi *D, mbedtls_mpi *DP, + mbedtls_mpi *DQ, mbedtls_mpi *QP ) +{ + int ret = 0; + mbedtls_mpi K; + mbedtls_mpi_init( &K ); + + /* DP = D mod P-1 */ + if( DP != NULL ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) ); + } + + /* DQ = D mod Q-1 */ + if( DQ != NULL ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) ); + } + + /* QP = Q^{-1} mod P */ + if( QP != NULL ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) ); + } + +cleanup: + mbedtls_mpi_free( &K ); + + return( ret ); +} + +#endif /* MBEDTLS_RSA_C */ diff --git a/tests/suites/test_suite_rsa.function b/tests/suites/test_suite_rsa.function index 9ee8ea1fe..3f892f71c 100644 --- a/tests/suites/test_suite_rsa.function +++ b/tests/suites/test_suite_rsa.function @@ -1,5 +1,6 @@ /* BEGIN_HEADER */ #include "mbedtls/rsa.h" +#include "mbedtls/rsa_internal.h" #include "mbedtls/md2.h" #include "mbedtls/md4.h" #include "mbedtls/md5.h"