[398] | 1 | /*
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| 2 | * Helper functions for the RSA module
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| 3 | *
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| 4 | * Copyright (C) 2006-2017, ARM Limited, All Rights Reserved
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| 5 | * SPDX-License-Identifier: Apache-2.0
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| 6 | *
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| 7 | * Licensed under the Apache License, Version 2.0 (the "License"); you may
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| 8 | * not use this file except in compliance with the License.
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| 9 | * You may obtain a copy of the License at
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| 10 | *
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| 11 | * http://www.apache.org/licenses/LICENSE-2.0
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| 12 | *
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| 13 | * Unless required by applicable law or agreed to in writing, software
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| 14 | * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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| 15 | * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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| 16 | * See the License for the specific language governing permissions and
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| 17 | * limitations under the License.
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| 18 | *
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| 19 | * This file is part of mbed TLS (https://tls.mbed.org)
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| 20 | *
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| 21 | */
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| 22 |
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| 23 | #if !defined(MBEDTLS_CONFIG_FILE)
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| 24 | #include "mbedtls/config.h"
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| 25 | #else
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| 26 | #include MBEDTLS_CONFIG_FILE
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| 27 | #endif
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| 28 |
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| 29 | #if defined(MBEDTLS_RSA_C)
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| 30 |
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| 31 | #include "mbedtls/rsa.h"
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| 32 | #include "mbedtls/bignum.h"
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| 33 | #include "mbedtls/rsa_internal.h"
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| 34 |
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| 35 | /*
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| 36 | * Compute RSA prime factors from public and private exponents
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| 37 | *
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| 38 | * Summary of algorithm:
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| 39 | * Setting F := lcm(P-1,Q-1), the idea is as follows:
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| 40 | *
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| 41 | * (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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| 42 | * 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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| 43 | * square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four
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| 44 | * possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1)
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| 45 | * or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime
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| 46 | * factors of N.
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| 47 | *
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| 48 | * (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same
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| 49 | * construction still applies since (-)^K is the identity on the set of
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| 50 | * roots of 1 in Z/NZ.
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| 51 | *
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| 52 | * The public and private key primitives (-)^E and (-)^D are mutually inverse
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| 53 | * bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e.
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| 54 | * if and only if DE - 1 is a multiple of F, say DE - 1 = F * L.
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| 55 | * Splitting L = 2^t * K with K odd, we have
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| 56 | *
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| 57 | * DE - 1 = FL = (F/2) * (2^(t+1)) * K,
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| 58 | *
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| 59 | * so (F / 2) * K is among the numbers
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| 60 | *
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| 61 | * (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord
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| 62 | *
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| 63 | * where ord is the order of 2 in (DE - 1).
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| 64 | * We can therefore iterate through these numbers apply the construction
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| 65 | * of (a) and (b) above to attempt to factor N.
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| 66 | *
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| 67 | */
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| 68 | int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N,
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| 69 | mbedtls_mpi const *E, mbedtls_mpi const *D,
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| 70 | mbedtls_mpi *P, mbedtls_mpi *Q )
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| 71 | {
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| 72 | int ret = 0;
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| 73 |
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| 74 | uint16_t attempt; /* Number of current attempt */
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| 75 | uint16_t iter; /* Number of squares computed in the current attempt */
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| 76 |
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| 77 | uint16_t order; /* Order of 2 in DE - 1 */
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| 78 |
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| 79 | mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */
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| 80 | mbedtls_mpi K; /* Temporary holding the current candidate */
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| 81 |
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| 82 | const unsigned char primes[] = { 2,
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| 83 | 3, 5, 7, 11, 13, 17, 19, 23,
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| 84 | 29, 31, 37, 41, 43, 47, 53, 59,
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| 85 | 61, 67, 71, 73, 79, 83, 89, 97,
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| 86 | 101, 103, 107, 109, 113, 127, 131, 137,
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| 87 | 139, 149, 151, 157, 163, 167, 173, 179,
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| 88 | 181, 191, 193, 197, 199, 211, 223, 227,
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| 89 | 229, 233, 239, 241, 251
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| 90 | };
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| 91 |
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| 92 | const size_t num_primes = sizeof( primes ) / sizeof( *primes );
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| 93 |
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| 94 | if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL )
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| 95 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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| 96 |
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| 97 | if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 ||
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| 98 | mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
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| 99 | mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
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| 100 | mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
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| 101 | mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
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| 102 | {
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| 103 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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| 104 | }
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| 105 |
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| 106 | /*
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| 107 | * Initializations and temporary changes
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| 108 | */
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| 109 |
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| 110 | mbedtls_mpi_init( &K );
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| 111 | mbedtls_mpi_init( &T );
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| 112 |
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| 113 | /* T := DE - 1 */
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| 114 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D, E ) );
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| 115 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) );
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| 116 |
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| 117 | if( ( order = (uint16_t) mbedtls_mpi_lsb( &T ) ) == 0 )
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| 118 | {
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| 119 | ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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| 120 | goto cleanup;
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| 121 | }
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| 122 |
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| 123 | /* After this operation, T holds the largest odd divisor of DE - 1. */
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| 124 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) );
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| 125 |
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| 126 | /*
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| 127 | * Actual work
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| 128 | */
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| 129 |
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| 130 | /* Skip trying 2 if N == 1 mod 8 */
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| 131 | attempt = 0;
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| 132 | if( N->p[0] % 8 == 1 )
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| 133 | attempt = 1;
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| 134 |
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| 135 | for( ; attempt < num_primes; ++attempt )
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| 136 | {
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| 137 | mbedtls_mpi_lset( &K, primes[attempt] );
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| 138 |
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| 139 | /* Check if gcd(K,N) = 1 */
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| 140 | MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
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| 141 | if( mbedtls_mpi_cmp_int( P, 1 ) != 0 )
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| 142 | continue;
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| 143 |
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| 144 | /* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ...
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| 145 | * and check whether they have nontrivial GCD with N. */
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| 146 | MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N,
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| 147 | Q /* temporarily use Q for storing Montgomery
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| 148 | * multiplication helper values */ ) );
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| 149 |
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| 150 | for( iter = 1; iter <= order; ++iter )
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| 151 | {
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| 152 | /* If we reach 1 prematurely, there's no point
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| 153 | * in continuing to square K */
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| 154 | if( mbedtls_mpi_cmp_int( &K, 1 ) == 0 )
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| 155 | break;
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| 156 |
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| 157 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) );
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| 158 | MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
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| 159 |
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| 160 | if( mbedtls_mpi_cmp_int( P, 1 ) == 1 &&
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| 161 | mbedtls_mpi_cmp_mpi( P, N ) == -1 )
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| 162 | {
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| 163 | /*
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| 164 | * Have found a nontrivial divisor P of N.
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| 165 | * Set Q := N / P.
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| 166 | */
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| 167 |
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| 168 | MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) );
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| 169 | goto cleanup;
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| 170 | }
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| 171 |
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| 172 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
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| 173 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) );
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| 174 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) );
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| 175 | }
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| 176 |
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| 177 | /*
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| 178 | * If we get here, then either we prematurely aborted the loop because
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| 179 | * we reached 1, or K holds primes[attempt]^(DE - 1) mod N, which must
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| 180 | * be 1 if D,E,N were consistent.
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| 181 | * Check if that's the case and abort if not, to avoid very long,
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| 182 | * yet eventually failing, computations if N,D,E were not sane.
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| 183 | */
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| 184 | if( mbedtls_mpi_cmp_int( &K, 1 ) != 0 )
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| 185 | {
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| 186 | break;
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| 187 | }
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| 188 | }
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| 189 |
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| 190 | ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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| 191 |
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| 192 | cleanup:
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| 193 |
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| 194 | mbedtls_mpi_free( &K );
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| 195 | mbedtls_mpi_free( &T );
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| 196 | return( ret );
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| 197 | }
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| 198 |
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| 199 | /*
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| 200 | * Given P, Q and the public exponent E, deduce D.
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| 201 | * This is essentially a modular inversion.
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| 202 | */
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| 203 | int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P,
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| 204 | mbedtls_mpi const *Q,
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| 205 | mbedtls_mpi const *E,
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| 206 | mbedtls_mpi *D )
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| 207 | {
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| 208 | int ret = 0;
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| 209 | mbedtls_mpi K, L;
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| 210 |
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| 211 | if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 )
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| 212 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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| 213 |
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| 214 | if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
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| 215 | mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ||
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| 216 | mbedtls_mpi_cmp_int( E, 0 ) == 0 )
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| 217 | {
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| 218 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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| 219 | }
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| 220 |
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| 221 | mbedtls_mpi_init( &K );
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| 222 | mbedtls_mpi_init( &L );
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| 223 |
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| 224 | /* Temporarily put K := P-1 and L := Q-1 */
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| 225 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
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| 226 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
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| 227 |
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| 228 | /* Temporarily put D := gcd(P-1, Q-1) */
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| 229 | MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) );
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| 230 |
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| 231 | /* K := LCM(P-1, Q-1) */
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| 232 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) );
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| 233 | MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) );
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| 234 |
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| 235 | /* Compute modular inverse of E in LCM(P-1, Q-1) */
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| 236 | MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) );
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| 237 |
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| 238 | cleanup:
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| 239 |
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| 240 | mbedtls_mpi_free( &K );
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| 241 | mbedtls_mpi_free( &L );
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| 242 |
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| 243 | return( ret );
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| 244 | }
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| 245 |
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| 246 | /*
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| 247 | * Check that RSA CRT parameters are in accordance with core parameters.
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| 248 | */
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| 249 | int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
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| 250 | const mbedtls_mpi *D, const mbedtls_mpi *DP,
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| 251 | const mbedtls_mpi *DQ, const mbedtls_mpi *QP )
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| 252 | {
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| 253 | int ret = 0;
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| 254 |
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| 255 | mbedtls_mpi K, L;
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| 256 | mbedtls_mpi_init( &K );
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| 257 | mbedtls_mpi_init( &L );
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| 258 |
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| 259 | /* Check that DP - D == 0 mod P - 1 */
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| 260 | if( DP != NULL )
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| 261 | {
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| 262 | if( P == NULL )
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| 263 | {
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| 264 | ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
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| 265 | goto cleanup;
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| 266 | }
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| 267 |
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| 268 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
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| 269 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) );
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| 270 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
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| 271 |
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| 272 | if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
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| 273 | {
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| 274 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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| 275 | goto cleanup;
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| 276 | }
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| 277 | }
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| 278 |
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| 279 | /* Check that DQ - D == 0 mod Q - 1 */
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| 280 | if( DQ != NULL )
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| 281 | {
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| 282 | if( Q == NULL )
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| 283 | {
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| 284 | ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
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| 285 | goto cleanup;
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| 286 | }
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| 287 |
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| 288 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
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| 289 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) );
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| 290 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
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| 291 |
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| 292 | if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
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| 293 | {
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| 294 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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| 295 | goto cleanup;
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| 296 | }
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| 297 | }
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| 298 |
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| 299 | /* Check that QP * Q - 1 == 0 mod P */
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| 300 | if( QP != NULL )
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| 301 | {
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| 302 | if( P == NULL || Q == NULL )
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| 303 | {
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| 304 | ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
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| 305 | goto cleanup;
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| 306 | }
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| 307 |
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| 308 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) );
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| 309 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
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| 310 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) );
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| 311 | if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
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| 312 | {
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| 313 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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| 314 | goto cleanup;
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| 315 | }
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| 316 | }
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| 317 |
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| 318 | cleanup:
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| 319 |
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| 320 | /* Wrap MPI error codes by RSA check failure error code */
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| 321 | if( ret != 0 &&
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| 322 | ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED &&
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| 323 | ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA )
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| 324 | {
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| 325 | ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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| 326 | }
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| 327 |
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| 328 | mbedtls_mpi_free( &K );
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| 329 | mbedtls_mpi_free( &L );
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| 330 |
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| 331 | return( ret );
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| 332 | }
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| 333 |
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| 334 | /*
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| 335 | * Check that core RSA parameters are sane.
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| 336 | */
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| 337 | int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P,
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| 338 | const mbedtls_mpi *Q, const mbedtls_mpi *D,
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| 339 | const mbedtls_mpi *E,
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| 340 | int (*f_rng)(void *, unsigned char *, size_t),
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| 341 | void *p_rng )
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| 342 | {
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| 343 | int ret = 0;
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| 344 | mbedtls_mpi K, L;
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| 345 |
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| 346 | mbedtls_mpi_init( &K );
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| 347 | mbedtls_mpi_init( &L );
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| 348 |
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| 349 | /*
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| 350 | * Step 1: If PRNG provided, check that P and Q are prime
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| 351 | */
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| 352 |
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| 353 | #if defined(MBEDTLS_GENPRIME)
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| 354 | /*
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| 355 | * When generating keys, the strongest security we support aims for an error
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| 356 | * rate of at most 2^-100 and we are aiming for the same certainty here as
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| 357 | * well.
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| 358 | */
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| 359 | if( f_rng != NULL && P != NULL &&
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| 360 | ( ret = mbedtls_mpi_is_prime_ext( P, 50, f_rng, p_rng ) ) != 0 )
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| 361 | {
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| 362 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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| 363 | goto cleanup;
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| 364 | }
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| 365 |
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| 366 | if( f_rng != NULL && Q != NULL &&
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| 367 | ( ret = mbedtls_mpi_is_prime_ext( Q, 50, f_rng, p_rng ) ) != 0 )
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| 368 | {
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| 369 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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| 370 | goto cleanup;
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| 371 | }
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| 372 | #else
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| 373 | ((void) f_rng);
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| 374 | ((void) p_rng);
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| 375 | #endif /* MBEDTLS_GENPRIME */
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| 376 |
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| 377 | /*
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| 378 | * Step 2: Check that 1 < N = P * Q
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| 379 | */
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| 380 |
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| 381 | if( P != NULL && Q != NULL && N != NULL )
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| 382 | {
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| 383 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );
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| 384 | if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 ||
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| 385 | mbedtls_mpi_cmp_mpi( &K, N ) != 0 )
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| 386 | {
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| 387 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
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| 388 | goto cleanup;
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| 389 | }
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| 390 | }
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| 391 |
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| 392 | /*
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| 393 | * Step 3: Check and 1 < D, E < N if present.
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| 394 | */
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| 395 |
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| 396 | if( N != NULL && D != NULL && E != NULL )
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| 397 | {
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| 398 | if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
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| 399 | mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
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| 400 | mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
|
---|
| 401 | mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
|
---|
| 402 | {
|
---|
| 403 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
|
---|
| 404 | goto cleanup;
|
---|
| 405 | }
|
---|
| 406 | }
|
---|
| 407 |
|
---|
| 408 | /*
|
---|
| 409 | * Step 4: Check that D, E are inverse modulo P-1 and Q-1
|
---|
| 410 | */
|
---|
| 411 |
|
---|
| 412 | if( P != NULL && Q != NULL && D != NULL && E != NULL )
|
---|
| 413 | {
|
---|
| 414 | if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
|
---|
| 415 | mbedtls_mpi_cmp_int( Q, 1 ) <= 0 )
|
---|
| 416 | {
|
---|
| 417 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
|
---|
| 418 | goto cleanup;
|
---|
| 419 | }
|
---|
| 420 |
|
---|
| 421 | /* Compute DE-1 mod P-1 */
|
---|
| 422 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
|
---|
| 423 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
|
---|
| 424 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) );
|
---|
| 425 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
|
---|
| 426 | if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
|
---|
| 427 | {
|
---|
| 428 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
|
---|
| 429 | goto cleanup;
|
---|
| 430 | }
|
---|
| 431 |
|
---|
| 432 | /* Compute DE-1 mod Q-1 */
|
---|
| 433 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
|
---|
| 434 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
|
---|
| 435 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
|
---|
| 436 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
|
---|
| 437 | if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
|
---|
| 438 | {
|
---|
| 439 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
|
---|
| 440 | goto cleanup;
|
---|
| 441 | }
|
---|
| 442 | }
|
---|
| 443 |
|
---|
| 444 | cleanup:
|
---|
| 445 |
|
---|
| 446 | mbedtls_mpi_free( &K );
|
---|
| 447 | mbedtls_mpi_free( &L );
|
---|
| 448 |
|
---|
| 449 | /* Wrap MPI error codes by RSA check failure error code */
|
---|
| 450 | if( ret != 0 && ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED )
|
---|
| 451 | {
|
---|
| 452 | ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
|
---|
| 453 | }
|
---|
| 454 |
|
---|
| 455 | return( ret );
|
---|
| 456 | }
|
---|
| 457 |
|
---|
| 458 | int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
|
---|
| 459 | const mbedtls_mpi *D, mbedtls_mpi *DP,
|
---|
| 460 | mbedtls_mpi *DQ, mbedtls_mpi *QP )
|
---|
| 461 | {
|
---|
| 462 | int ret = 0;
|
---|
| 463 | mbedtls_mpi K;
|
---|
| 464 | mbedtls_mpi_init( &K );
|
---|
| 465 |
|
---|
| 466 | /* DP = D mod P-1 */
|
---|
| 467 | if( DP != NULL )
|
---|
| 468 | {
|
---|
| 469 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
|
---|
| 470 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) );
|
---|
| 471 | }
|
---|
| 472 |
|
---|
| 473 | /* DQ = D mod Q-1 */
|
---|
| 474 | if( DQ != NULL )
|
---|
| 475 | {
|
---|
| 476 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
|
---|
| 477 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) );
|
---|
| 478 | }
|
---|
| 479 |
|
---|
| 480 | /* QP = Q^{-1} mod P */
|
---|
| 481 | if( QP != NULL )
|
---|
| 482 | {
|
---|
| 483 | MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) );
|
---|
| 484 | }
|
---|
| 485 |
|
---|
| 486 | cleanup:
|
---|
| 487 | mbedtls_mpi_free( &K );
|
---|
| 488 |
|
---|
| 489 | return( ret );
|
---|
| 490 | }
|
---|
| 491 |
|
---|
| 492 | #endif /* MBEDTLS_RSA_C */
|
---|