--- /dev/null
+/*
+ * Helper functions for the RSA module
+ *
+ * Copyright (C) 2006-2017, ARM Limited, All Rights Reserved
+ * SPDX-License-Identifier: GPL-2.0
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License along
+ * with this program; if not, write to the Free Software Foundation, Inc.,
+ * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ *
+ * 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 *E, mbedtls_mpi const *D,
+ 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 char 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
+ };
+
+ 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 = (uint16_t) 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 )
+ {
+ /* If we reach 1 prematurely, there's no point
+ * in continuing to square K */
+ if( mbedtls_mpi_cmp_int( &K, 1 ) == 0 )
+ break;
+
+ 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 ) );
+ }
+
+ /*
+ * If we get here, then either we prematurely aborted the loop because
+ * we reached 1, or K holds primes[attempt]^(DE - 1) mod N, which must
+ * be 1 if D,E,N were consistent.
+ * Check if that's the case and abort if not, to avoid very long,
+ * yet eventually failing, computations if N,D,E were not sane.
+ */
+ if( mbedtls_mpi_cmp_int( &K, 1 ) != 0 )
+ {
+ break;
+ }
+ }
+
+ 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 = P * Q
+ */
+
+ 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 */
projects / reactos.git / blobdiff