diff options
Diffstat (limited to 'lib/mbedtls-2.27.0/library/rsa_internal.c')
| -rw-r--r-- | lib/mbedtls-2.27.0/library/rsa_internal.c | 486 |
1 files changed, 0 insertions, 486 deletions
diff --git a/lib/mbedtls-2.27.0/library/rsa_internal.c b/lib/mbedtls-2.27.0/library/rsa_internal.c deleted file mode 100644 index d6ba97a..0000000 --- a/lib/mbedtls-2.27.0/library/rsa_internal.c +++ /dev/null @@ -1,486 +0,0 @@ -/* - * Helper functions for the RSA module - * - * Copyright The Mbed TLS Contributors - * 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. - * - */ - -#include "common.h" - -#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) - /* - * When generating keys, the strongest security we support aims for an error - * rate of at most 2^-100 and we are aiming for the same certainty here as - * well. - */ - if( f_rng != NULL && P != NULL && - ( ret = mbedtls_mpi_is_prime_ext( P, 50, 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_ext( Q, 50, 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 */ |