diff options
Diffstat (limited to 'library/rsa_alt_helpers.c')
| -rw-r--r-- | library/rsa_alt_helpers.c | 486 |
1 files changed, 486 insertions, 0 deletions
diff --git a/library/rsa_alt_helpers.c b/library/rsa_alt_helpers.c new file mode 100644 index 000000000..dff2d9345 --- /dev/null +++ b/library/rsa_alt_helpers.c @@ -0,0 +1,486 @@ +/* + * 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 "rsa_alt_helpers.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 ); +} + +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 ); +} + +/* + * 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 ); +} + +/* + * 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 ); +} + +#endif /* MBEDTLS_RSA_C */ |