--- /dev/null
+/*\r
+ * Helper functions for the RSA module\r
+ *\r
+ * Copyright (C) 2006-2017, ARM Limited, All Rights Reserved\r
+ * SPDX-License-Identifier: Apache-2.0\r
+ *\r
+ * Licensed under the Apache License, Version 2.0 (the "License"); you may\r
+ * not use this file except in compliance with the License.\r
+ * You may obtain a copy of the License at\r
+ *\r
+ * http://www.apache.org/licenses/LICENSE-2.0\r
+ *\r
+ * Unless required by applicable law or agreed to in writing, software\r
+ * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT\r
+ * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\r
+ * See the License for the specific language governing permissions and\r
+ * limitations under the License.\r
+ *\r
+ * This file is part of mbed TLS (https://tls.mbed.org)\r
+ *\r
+ */\r
+\r
+#if !defined(MBEDTLS_CONFIG_FILE)\r
+#include "mbedtls/config.h"\r
+#else\r
+#include MBEDTLS_CONFIG_FILE\r
+#endif\r
+\r
+#if defined(MBEDTLS_RSA_C)\r
+\r
+#include "mbedtls/rsa.h"\r
+#include "mbedtls/bignum.h"\r
+#include "mbedtls/rsa_internal.h"\r
+\r
+/*\r
+ * Compute RSA prime factors from public and private exponents\r
+ *\r
+ * Summary of algorithm:\r
+ * Setting F := lcm(P-1,Q-1), the idea is as follows:\r
+ *\r
+ * (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2)\r
+ * is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the\r
+ * square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four\r
+ * possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1)\r
+ * or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime\r
+ * factors of N.\r
+ *\r
+ * (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same\r
+ * construction still applies since (-)^K is the identity on the set of\r
+ * roots of 1 in Z/NZ.\r
+ *\r
+ * The public and private key primitives (-)^E and (-)^D are mutually inverse\r
+ * bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e.\r
+ * if and only if DE - 1 is a multiple of F, say DE - 1 = F * L.\r
+ * Splitting L = 2^t * K with K odd, we have\r
+ *\r
+ * DE - 1 = FL = (F/2) * (2^(t+1)) * K,\r
+ *\r
+ * so (F / 2) * K is among the numbers\r
+ *\r
+ * (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord\r
+ *\r
+ * where ord is the order of 2 in (DE - 1).\r
+ * We can therefore iterate through these numbers apply the construction\r
+ * of (a) and (b) above to attempt to factor N.\r
+ *\r
+ */\r
+int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N,\r
+ mbedtls_mpi const *E, mbedtls_mpi const *D,\r
+ mbedtls_mpi *P, mbedtls_mpi *Q )\r
+{\r
+ int ret = 0;\r
+\r
+ uint16_t attempt; /* Number of current attempt */\r
+ uint16_t iter; /* Number of squares computed in the current attempt */\r
+\r
+ uint16_t order; /* Order of 2 in DE - 1 */\r
+\r
+ mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */\r
+ mbedtls_mpi K; /* Temporary holding the current candidate */\r
+\r
+ const unsigned char primes[] = { 2,\r
+ 3, 5, 7, 11, 13, 17, 19, 23,\r
+ 29, 31, 37, 41, 43, 47, 53, 59,\r
+ 61, 67, 71, 73, 79, 83, 89, 97,\r
+ 101, 103, 107, 109, 113, 127, 131, 137,\r
+ 139, 149, 151, 157, 163, 167, 173, 179,\r
+ 181, 191, 193, 197, 199, 211, 223, 227,\r
+ 229, 233, 239, 241, 251\r
+ };\r
+\r
+ const size_t num_primes = sizeof( primes ) / sizeof( *primes );\r
+\r
+ if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL )\r
+ return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );\r
+\r
+ if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 ||\r
+ mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||\r
+ mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||\r
+ mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||\r
+ mbedtls_mpi_cmp_mpi( E, N ) >= 0 )\r
+ {\r
+ return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );\r
+ }\r
+\r
+ /*\r
+ * Initializations and temporary changes\r
+ */\r
+\r
+ mbedtls_mpi_init( &K );\r
+ mbedtls_mpi_init( &T );\r
+\r
+ /* T := DE - 1 */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D, E ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) );\r
+\r
+ if( ( order = (uint16_t) mbedtls_mpi_lsb( &T ) ) == 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;\r
+ goto cleanup;\r
+ }\r
+\r
+ /* After this operation, T holds the largest odd divisor of DE - 1. */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) );\r
+\r
+ /*\r
+ * Actual work\r
+ */\r
+\r
+ /* Skip trying 2 if N == 1 mod 8 */\r
+ attempt = 0;\r
+ if( N->p[0] % 8 == 1 )\r
+ attempt = 1;\r
+\r
+ for( ; attempt < num_primes; ++attempt )\r
+ {\r
+ mbedtls_mpi_lset( &K, primes[attempt] );\r
+\r
+ /* Check if gcd(K,N) = 1 */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );\r
+ if( mbedtls_mpi_cmp_int( P, 1 ) != 0 )\r
+ continue;\r
+\r
+ /* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ...\r
+ * and check whether they have nontrivial GCD with N. */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N,\r
+ Q /* temporarily use Q for storing Montgomery\r
+ * multiplication helper values */ ) );\r
+\r
+ for( iter = 1; iter <= order; ++iter )\r
+ {\r
+ /* If we reach 1 prematurely, there's no point\r
+ * in continuing to square K */\r
+ if( mbedtls_mpi_cmp_int( &K, 1 ) == 0 )\r
+ break;\r
+\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );\r
+\r
+ if( mbedtls_mpi_cmp_int( P, 1 ) == 1 &&\r
+ mbedtls_mpi_cmp_mpi( P, N ) == -1 )\r
+ {\r
+ /*\r
+ * Have found a nontrivial divisor P of N.\r
+ * Set Q := N / P.\r
+ */\r
+\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) );\r
+ goto cleanup;\r
+ }\r
+\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) );\r
+ }\r
+\r
+ /*\r
+ * If we get here, then either we prematurely aborted the loop because\r
+ * we reached 1, or K holds primes[attempt]^(DE - 1) mod N, which must\r
+ * be 1 if D,E,N were consistent.\r
+ * Check if that's the case and abort if not, to avoid very long,\r
+ * yet eventually failing, computations if N,D,E were not sane.\r
+ */\r
+ if( mbedtls_mpi_cmp_int( &K, 1 ) != 0 )\r
+ {\r
+ break;\r
+ }\r
+ }\r
+\r
+ ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;\r
+\r
+cleanup:\r
+\r
+ mbedtls_mpi_free( &K );\r
+ mbedtls_mpi_free( &T );\r
+ return( ret );\r
+}\r
+\r
+/*\r
+ * Given P, Q and the public exponent E, deduce D.\r
+ * This is essentially a modular inversion.\r
+ */\r
+int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P,\r
+ mbedtls_mpi const *Q,\r
+ mbedtls_mpi const *E,\r
+ mbedtls_mpi *D )\r
+{\r
+ int ret = 0;\r
+ mbedtls_mpi K, L;\r
+\r
+ if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 )\r
+ return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );\r
+\r
+ if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||\r
+ mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ||\r
+ mbedtls_mpi_cmp_int( E, 0 ) == 0 )\r
+ {\r
+ return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );\r
+ }\r
+\r
+ mbedtls_mpi_init( &K );\r
+ mbedtls_mpi_init( &L );\r
+\r
+ /* Temporarily put K := P-1 and L := Q-1 */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );\r
+\r
+ /* Temporarily put D := gcd(P-1, Q-1) */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) );\r
+\r
+ /* K := LCM(P-1, Q-1) */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) );\r
+\r
+ /* Compute modular inverse of E in LCM(P-1, Q-1) */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) );\r
+\r
+cleanup:\r
+\r
+ mbedtls_mpi_free( &K );\r
+ mbedtls_mpi_free( &L );\r
+\r
+ return( ret );\r
+}\r
+\r
+/*\r
+ * Check that RSA CRT parameters are in accordance with core parameters.\r
+ */\r
+int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,\r
+ const mbedtls_mpi *D, const mbedtls_mpi *DP,\r
+ const mbedtls_mpi *DQ, const mbedtls_mpi *QP )\r
+{\r
+ int ret = 0;\r
+\r
+ mbedtls_mpi K, L;\r
+ mbedtls_mpi_init( &K );\r
+ mbedtls_mpi_init( &L );\r
+\r
+ /* Check that DP - D == 0 mod P - 1 */\r
+ if( DP != NULL )\r
+ {\r
+ if( P == NULL )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;\r
+ goto cleanup;\r
+ }\r
+\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );\r
+\r
+ if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+ }\r
+\r
+ /* Check that DQ - D == 0 mod Q - 1 */\r
+ if( DQ != NULL )\r
+ {\r
+ if( Q == NULL )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;\r
+ goto cleanup;\r
+ }\r
+\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );\r
+\r
+ if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+ }\r
+\r
+ /* Check that QP * Q - 1 == 0 mod P */\r
+ if( QP != NULL )\r
+ {\r
+ if( P == NULL || Q == NULL )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;\r
+ goto cleanup;\r
+ }\r
+\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) );\r
+ if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+ }\r
+\r
+cleanup:\r
+\r
+ /* Wrap MPI error codes by RSA check failure error code */\r
+ if( ret != 0 &&\r
+ ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED &&\r
+ ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA )\r
+ {\r
+ ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ }\r
+\r
+ mbedtls_mpi_free( &K );\r
+ mbedtls_mpi_free( &L );\r
+\r
+ return( ret );\r
+}\r
+\r
+/*\r
+ * Check that core RSA parameters are sane.\r
+ */\r
+int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P,\r
+ const mbedtls_mpi *Q, const mbedtls_mpi *D,\r
+ const mbedtls_mpi *E,\r
+ int (*f_rng)(void *, unsigned char *, size_t),\r
+ void *p_rng )\r
+{\r
+ int ret = 0;\r
+ mbedtls_mpi K, L;\r
+\r
+ mbedtls_mpi_init( &K );\r
+ mbedtls_mpi_init( &L );\r
+\r
+ /*\r
+ * Step 1: If PRNG provided, check that P and Q are prime\r
+ */\r
+\r
+#if defined(MBEDTLS_GENPRIME)\r
+ /*\r
+ * When generating keys, the strongest security we support aims for an error\r
+ * rate of at most 2^-100 and we are aiming for the same certainty here as\r
+ * well.\r
+ */\r
+ if( f_rng != NULL && P != NULL &&\r
+ ( ret = mbedtls_mpi_is_prime_ext( P, 50, f_rng, p_rng ) ) != 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+\r
+ if( f_rng != NULL && Q != NULL &&\r
+ ( ret = mbedtls_mpi_is_prime_ext( Q, 50, f_rng, p_rng ) ) != 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+#else\r
+ ((void) f_rng);\r
+ ((void) p_rng);\r
+#endif /* MBEDTLS_GENPRIME */\r
+\r
+ /*\r
+ * Step 2: Check that 1 < N = P * Q\r
+ */\r
+\r
+ if( P != NULL && Q != NULL && N != NULL )\r
+ {\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );\r
+ if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 ||\r
+ mbedtls_mpi_cmp_mpi( &K, N ) != 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+ }\r
+\r
+ /*\r
+ * Step 3: Check and 1 < D, E < N if present.\r
+ */\r
+\r
+ if( N != NULL && D != NULL && E != NULL )\r
+ {\r
+ if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||\r
+ mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||\r
+ mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||\r
+ mbedtls_mpi_cmp_mpi( E, N ) >= 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+ }\r
+\r
+ /*\r
+ * Step 4: Check that D, E are inverse modulo P-1 and Q-1\r
+ */\r
+\r
+ if( P != NULL && Q != NULL && D != NULL && E != NULL )\r
+ {\r
+ if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||\r
+ mbedtls_mpi_cmp_int( Q, 1 ) <= 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+\r
+ /* Compute DE-1 mod P-1 */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );\r
+ if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+\r
+ /* Compute DE-1 mod Q-1 */\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );\r
+ if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )\r
+ {\r
+ ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ goto cleanup;\r
+ }\r
+ }\r
+\r
+cleanup:\r
+\r
+ mbedtls_mpi_free( &K );\r
+ mbedtls_mpi_free( &L );\r
+\r
+ /* Wrap MPI error codes by RSA check failure error code */\r
+ if( ret != 0 && ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED )\r
+ {\r
+ ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;\r
+ }\r
+\r
+ return( ret );\r
+}\r
+\r
+int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,\r
+ const mbedtls_mpi *D, mbedtls_mpi *DP,\r
+ mbedtls_mpi *DQ, mbedtls_mpi *QP )\r
+{\r
+ int ret = 0;\r
+ mbedtls_mpi K;\r
+ mbedtls_mpi_init( &K );\r
+\r
+ /* DP = D mod P-1 */\r
+ if( DP != NULL )\r
+ {\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) );\r
+ }\r
+\r
+ /* DQ = D mod Q-1 */\r
+ if( DQ != NULL )\r
+ {\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) );\r
+ }\r
+\r
+ /* QP = Q^{-1} mod P */\r
+ if( QP != NULL )\r
+ {\r
+ MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) );\r
+ }\r
+\r
+cleanup:\r
+ mbedtls_mpi_free( &K );\r
+\r
+ return( ret );\r
+}\r
+\r
+#endif /* MBEDTLS_RSA_C */\r
projects / freertos / blobdiff