517 lines
15 KiB
C
Executable file
517 lines
15 KiB
C
Executable file
/*
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* Helper functions for the RSA module
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*
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* Copyright The Mbed TLS Contributors
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* SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
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*
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* This file is provided under the Apache License 2.0, or the
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* GNU General Public License v2.0 or later.
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*
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* **********
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* Apache License 2.0:
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*
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* Licensed under the Apache License, Version 2.0 (the "License"); you may
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* 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, WITHOUT
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* 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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* **********
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*
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* **********
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* GNU General Public License v2.0 or later:
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* **********
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*
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*/
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#if !defined(MBEDTLS_CONFIG_FILE)
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#include "mbedtls/config.h"
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#else
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#include MBEDTLS_CONFIG_FILE
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#endif
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#if defined(MBEDTLS_RSA_C)
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#include "mbedtls/rsa.h"
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#include "mbedtls/bignum.h"
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#include "mbedtls/rsa_internal.h"
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/*
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* Compute RSA prime factors from public and private exponents
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*
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* Summary of algorithm:
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* Setting F := lcm(P-1,Q-1), the idea is as follows:
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*
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* (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2)
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* is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the
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* square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four
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* possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1)
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* or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime
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* factors of N.
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*
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* (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same
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* construction still applies since (-)^K is the identity on the set of
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* roots of 1 in Z/NZ.
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*
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* The public and private key primitives (-)^E and (-)^D are mutually inverse
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* bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e.
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* if and only if DE - 1 is a multiple of F, say DE - 1 = F * L.
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* Splitting L = 2^t * K with K odd, we have
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*
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* DE - 1 = FL = (F/2) * (2^(t+1)) * K,
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*
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* so (F / 2) * K is among the numbers
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*
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* (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord
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*
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* where ord is the order of 2 in (DE - 1).
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* We can therefore iterate through these numbers apply the construction
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* of (a) and (b) above to attempt to factor N.
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*
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*/
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int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N,
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mbedtls_mpi const *E, mbedtls_mpi const *D,
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mbedtls_mpi *P, mbedtls_mpi *Q )
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{
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int ret = 0;
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uint16_t attempt; /* Number of current attempt */
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uint16_t iter; /* Number of squares computed in the current attempt */
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uint16_t order; /* Order of 2 in DE - 1 */
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mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */
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mbedtls_mpi K; /* Temporary holding the current candidate */
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const unsigned char primes[] = { 2,
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3, 5, 7, 11, 13, 17, 19, 23,
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29, 31, 37, 41, 43, 47, 53, 59,
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61, 67, 71, 73, 79, 83, 89, 97,
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101, 103, 107, 109, 113, 127, 131, 137,
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139, 149, 151, 157, 163, 167, 173, 179,
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181, 191, 193, 197, 199, 211, 223, 227,
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229, 233, 239, 241, 251
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};
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const size_t num_primes = sizeof( primes ) / sizeof( *primes );
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if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL )
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return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 ||
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mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
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mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
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mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
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mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
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{
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return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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}
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/*
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* Initializations and temporary changes
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*/
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mbedtls_mpi_init( &K );
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mbedtls_mpi_init( &T );
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/* T := DE - 1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D, E ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) );
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if( ( order = (uint16_t) mbedtls_mpi_lsb( &T ) ) == 0 )
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{
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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goto cleanup;
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}
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/* After this operation, T holds the largest odd divisor of DE - 1. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) );
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/*
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* Actual work
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*/
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/* Skip trying 2 if N == 1 mod 8 */
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attempt = 0;
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if( N->p[0] % 8 == 1 )
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attempt = 1;
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for( ; attempt < num_primes; ++attempt )
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{
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mbedtls_mpi_lset( &K, primes[attempt] );
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/* Check if gcd(K,N) = 1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
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if( mbedtls_mpi_cmp_int( P, 1 ) != 0 )
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continue;
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/* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ...
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* and check whether they have nontrivial GCD with N. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N,
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Q /* temporarily use Q for storing Montgomery
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* multiplication helper values */ ) );
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for( iter = 1; iter <= order; ++iter )
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{
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/* If we reach 1 prematurely, there's no point
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* in continuing to square K */
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if( mbedtls_mpi_cmp_int( &K, 1 ) == 0 )
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break;
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
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if( mbedtls_mpi_cmp_int( P, 1 ) == 1 &&
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mbedtls_mpi_cmp_mpi( P, N ) == -1 )
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{
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/*
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* Have found a nontrivial divisor P of N.
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* Set Q := N / P.
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*/
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MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) );
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goto cleanup;
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}
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) );
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}
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/*
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* If we get here, then either we prematurely aborted the loop because
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* we reached 1, or K holds primes[attempt]^(DE - 1) mod N, which must
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* be 1 if D,E,N were consistent.
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* Check if that's the case and abort if not, to avoid very long,
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* yet eventually failing, computations if N,D,E were not sane.
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*/
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if( mbedtls_mpi_cmp_int( &K, 1 ) != 0 )
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{
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break;
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}
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}
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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cleanup:
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mbedtls_mpi_free( &K );
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mbedtls_mpi_free( &T );
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return( ret );
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}
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/*
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* Given P, Q and the public exponent E, deduce D.
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* This is essentially a modular inversion.
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*/
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int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P,
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mbedtls_mpi const *Q,
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mbedtls_mpi const *E,
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mbedtls_mpi *D )
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{
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int ret = 0;
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mbedtls_mpi K, L;
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if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 )
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return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
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mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ||
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mbedtls_mpi_cmp_int( E, 0 ) == 0 )
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{
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return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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}
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mbedtls_mpi_init( &K );
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mbedtls_mpi_init( &L );
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/* Temporarily put K := P-1 and L := Q-1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
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/* Temporarily put D := gcd(P-1, Q-1) */
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MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) );
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/* K := LCM(P-1, Q-1) */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) );
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/* Compute modular inverse of E in LCM(P-1, Q-1) */
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MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) );
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cleanup:
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mbedtls_mpi_free( &K );
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mbedtls_mpi_free( &L );
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return( ret );
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}
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/*
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* Check that RSA CRT parameters are in accordance with core parameters.
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*/
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int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
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const mbedtls_mpi *D, const mbedtls_mpi *DP,
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const mbedtls_mpi *DQ, const mbedtls_mpi *QP )
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{
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int ret = 0;
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mbedtls_mpi K, L;
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mbedtls_mpi_init( &K );
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mbedtls_mpi_init( &L );
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/* Check that DP - D == 0 mod P - 1 */
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if( DP != NULL )
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{
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if( P == NULL )
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{
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ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
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goto cleanup;
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}
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
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if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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}
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/* Check that DQ - D == 0 mod Q - 1 */
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if( DQ != NULL )
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{
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if( Q == NULL )
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{
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ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
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goto cleanup;
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}
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
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if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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}
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/* Check that QP * Q - 1 == 0 mod P */
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if( QP != NULL )
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{
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if( P == NULL || Q == NULL )
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{
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ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
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goto cleanup;
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}
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) );
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if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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}
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cleanup:
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/* Wrap MPI error codes by RSA check failure error code */
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if( ret != 0 &&
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ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED &&
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ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA )
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{
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ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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}
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mbedtls_mpi_free( &K );
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mbedtls_mpi_free( &L );
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return( ret );
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}
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/*
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* Check that core RSA parameters are sane.
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*/
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int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P,
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const mbedtls_mpi *Q, const mbedtls_mpi *D,
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const mbedtls_mpi *E,
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int (*f_rng)(void *, unsigned char *, size_t),
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void *p_rng )
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{
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int ret = 0;
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mbedtls_mpi K, L;
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mbedtls_mpi_init( &K );
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mbedtls_mpi_init( &L );
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/*
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* Step 1: If PRNG provided, check that P and Q are prime
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*/
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#if defined(MBEDTLS_GENPRIME)
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/*
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* When generating keys, the strongest security we support aims for an error
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* rate of at most 2^-100 and we are aiming for the same certainty here as
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* well.
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*/
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if( f_rng != NULL && P != NULL &&
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( ret = mbedtls_mpi_is_prime_ext( P, 50, f_rng, p_rng ) ) != 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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if( f_rng != NULL && Q != NULL &&
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( ret = mbedtls_mpi_is_prime_ext( Q, 50, f_rng, p_rng ) ) != 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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#else
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((void) f_rng);
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((void) p_rng);
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#endif /* MBEDTLS_GENPRIME */
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/*
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* Step 2: Check that 1 < N = P * Q
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*/
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if( P != NULL && Q != NULL && N != NULL )
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{
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );
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if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 ||
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mbedtls_mpi_cmp_mpi( &K, N ) != 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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}
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/*
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* Step 3: Check and 1 < D, E < N if present.
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*/
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if( N != NULL && D != NULL && E != NULL )
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{
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if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
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mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
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mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
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mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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}
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/*
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* Step 4: Check that D, E are inverse modulo P-1 and Q-1
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*/
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if( P != NULL && Q != NULL && D != NULL && E != NULL )
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{
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if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
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mbedtls_mpi_cmp_int( Q, 1 ) <= 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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/* Compute DE-1 mod P-1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
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if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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/* Compute DE-1 mod Q-1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
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if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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goto cleanup;
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}
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}
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cleanup:
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mbedtls_mpi_free( &K );
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mbedtls_mpi_free( &L );
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/* 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 */
|