/* * The RSA public-key cryptosystem * * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved * 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. * * This file is part of mbed TLS (https://tls.mbed.org) */ /* * The following sources were referenced in the design of this implementation * of the RSA algorithm: * * [1] A method for obtaining digital signatures and public-key cryptosystems * R Rivest, A Shamir, and L Adleman * http://people.csail.mit.edu/rivest/pubs.html#RSA78 * * [2] Handbook of Applied Cryptography - 1997, Chapter 8 * Menezes, van Oorschot and Vanstone * * [3] Malware Guard Extension: Using SGX to Conceal Cache Attacks * Michael Schwarz, Samuel Weiser, Daniel Gruss, Clémentine Maurice and * Stefan Mangard * https://arxiv.org/abs/1702.08719v2 * */ #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/oid.h" #include #if defined(MBEDTLS_PKCS1_V21) #include "mbedtls/md.h" #endif #if defined(MBEDTLS_PKCS1_V15) && !defined(__OpenBSD__) #include #endif #if defined(MBEDTLS_PLATFORM_C) #include "mbedtls/platform.h" #else #include #define mbedtls_printf printf #define mbedtls_calloc calloc #define mbedtls_free free #endif /* Implementation that should never be optimized out by the compiler */ static void mbedtls_zeroize( void *v, size_t n ) { volatile unsigned char *p = (unsigned char*)v; while( n-- ) *p++ = 0; } /* * Context-independent RSA helper functions. * * There are two classes of helper functions: * (1) Parameter-generating helpers. These are: * - mbedtls_rsa_deduce_moduli * - mbedtls_rsa_deduce_private * - mbedtls_rsa_deduce_crt * Each of these functions takes a set of core RSA parameters * and generates some other, or CRT related parameters. * (2) Parameter-checking helpers. These are: * - mbedtls_rsa_validate_params * - mbedtls_rsa_validate_crt * They take a set of core or CRT related RSA parameters * and check their validity. * * The helper functions do not use the RSA context structure * and therefore do not need to be replaced when providing * an alternative RSA implementation. * * Their main purpose is to provide common MPI operations in the context * of RSA that can be easily shared across multiple implementations. */ /* * * Given the modulus N=PQ and a pair of public and private * exponents E and D, respectively, factor N. * * 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_moduli( mbedtls_mpi const *N, mbedtls_mpi const *D, mbedtls_mpi const *E, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 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 bitlen_half; /* Half the bitsize of the modulus N */ uint16_t order; /* Order of 2 in DE - 1 */ mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */ mbedtls_mpi K; /* During factorization attempts, stores a random integer * in the range of [0,..,N] */ 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 = 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 ) ); /* This is used to generate a few numbers around N / 2 * if no PRNG is provided. */ if( f_rng == NULL ) bitlen_half = mbedtls_mpi_bitlen( N ) / 2; /* * Actual work */ for( attempt = 0; attempt < 30; ++attempt ) { /* Generate some number in [0,N], either randomly * if a PRNG is given, or try numbers around N/2 */ if( f_rng != NULL ) { MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &K, mbedtls_mpi_size( N ), f_rng, p_rng ) ); } else { MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &K, 1 ) ) ; MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &K, bitlen_half ) ) ; MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, attempt + 1 ) ); } /* 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 ) { 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 ) ); } } 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( 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 - P == 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 ) { return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); } } /* Check that DQ - Q == 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 ) { return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); } } /* Check that QP * P - 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 ) { return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); } } 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 N = PQ */ 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 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 || mbedtls_mpi_cmp_int( D, 1 ) <= 0 || mbedtls_mpi_cmp_int( E, 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 ); } /* * Default RSA interface implementation */ #if !defined(MBEDTLS_RSA_ALT) int mbedtls_rsa_import( mbedtls_rsa_context *ctx, const mbedtls_mpi *N, const mbedtls_mpi *P, const mbedtls_mpi *Q, const mbedtls_mpi *D, const mbedtls_mpi *E ) { int ret; if( ( N != NULL && ( ret = mbedtls_mpi_copy( &ctx->N, N ) ) != 0 ) || ( P != NULL && ( ret = mbedtls_mpi_copy( &ctx->P, P ) ) != 0 ) || ( Q != NULL && ( ret = mbedtls_mpi_copy( &ctx->Q, Q ) ) != 0 ) || ( D != NULL && ( ret = mbedtls_mpi_copy( &ctx->D, D ) ) != 0 ) || ( E != NULL && ( ret = mbedtls_mpi_copy( &ctx->E, E ) ) != 0 ) ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); } if( N != NULL ) ctx->len = mbedtls_mpi_size( &ctx->N ); return( 0 ); } int mbedtls_rsa_import_raw( mbedtls_rsa_context *ctx, unsigned char *N, size_t N_len, unsigned char *P, size_t P_len, unsigned char *Q, size_t Q_len, unsigned char *D, size_t D_len, unsigned char *E, size_t E_len ) { int ret; if( N != NULL ) { MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->N, N, N_len ) ); ctx->len = mbedtls_mpi_size( &ctx->N ); } if( P != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->P, P, P_len ) ); if( Q != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->Q, Q, Q_len ) ); if( D != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->D, D, D_len ) ); if( E != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->E, E, E_len ) ); cleanup: if( ret != 0 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); return( 0 ); } int mbedtls_rsa_complete( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret = 0; const int have_N = ( mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 ); const int have_P = ( mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 ); const int have_Q = ( mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 ); const int have_D = ( mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 ); const int have_E = ( mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0 ); /* * Check whether provided parameters are enough * to deduce all others. The following incomplete * parameter sets for private keys are supported: * * (1) P, Q missing. * (2) D and potentially N missing. * */ const int n_missing = have_P && have_Q && have_D && have_E; const int pq_missing = have_N && !have_P && !have_Q && have_D && have_E; const int d_missing = have_P && have_Q && !have_D && have_E; const int is_pub = have_N && !have_P && !have_Q && !have_D && have_E; /* These three alternatives are mutually exclusive */ const int is_priv = n_missing || pq_missing || d_missing; if( !is_priv && !is_pub ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); /* * Step 1: Deduce N if P, Q are provided. */ if( !have_N && have_P && have_Q ) { if( ( ret = mbedtls_mpi_mul_mpi( &ctx->N, &ctx->P, &ctx->Q ) ) != 0 ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); } ctx->len = mbedtls_mpi_size( &ctx->N ); } /* * Step 2: Deduce and verify all remaining core parameters. */ if( pq_missing ) { /* This includes sanity checking of core parameters, * so no further checks necessary. */ ret = mbedtls_rsa_deduce_moduli( &ctx->N, &ctx->D, &ctx->E, f_rng, p_rng, &ctx->P, &ctx->Q ); if( ret != 0 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); } else if( d_missing ) { #if defined(MBEDTLS_GENPRIME) /* If a PRNG is provided, check if P, Q are prime. */ if( f_rng != NULL && ( ( ret = mbedtls_mpi_is_prime( &ctx->P, f_rng, p_rng ) ) != 0 || ( ret = mbedtls_mpi_is_prime( &ctx->Q, f_rng, p_rng ) ) != 0 ) ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); } #endif /* MBEDTLS_GENPRIME */ /* Deduce private exponent. This includes double-checking of the result, * so together with the primality test above all core parameters are * guaranteed to be sane if this call succeeds. */ if( ( ret = mbedtls_rsa_deduce_private( &ctx->P, &ctx->Q, &ctx->E, &ctx->D ) ) != 0 ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); } } /* In the remaining case of a public key, there's nothing to check for. */ /* * Step 3: Deduce all additional parameters specific * to our current RSA implementaiton. */ #if !defined(MBEDTLS_RSA_NO_CRT) if( is_priv ) { ret = mbedtls_rsa_deduce_crt( &ctx->P, &ctx->Q, &ctx->D, &ctx->DP, &ctx->DQ, &ctx->QP ); if( ret != 0 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); } #endif /* MBEDTLS_RSA_NO_CRT */ /* * Step 3: Double check */ if( is_priv ) { if( ( ret = mbedtls_rsa_check_privkey( ctx ) ) != 0 ) return( ret ); } else { if( ( ret = mbedtls_rsa_check_pubkey( ctx ) ) != 0 ) return( ret ); } return( 0 ); } /* * Check if CRT parameters match RSA context. * This has to be implemented even if CRT is not used, * in order to be able to validate DER encoded RSA keys, * which always contain CRT parameters. */ int mbedtls_rsa_check_crt( const mbedtls_rsa_context *ctx, mbedtls_mpi *DP, mbedtls_mpi *DQ, mbedtls_mpi *QP ) { int ret = 0; /* Check if key is private or public */ const int is_priv = mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0; if( !is_priv ) { /* Checking optional parameters only makes sense for private keys. */ return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); } #if !defined(MBEDTLS_RSA_NO_CRT) if( ( DP != NULL && mbedtls_mpi_cmp_mpi( DP, &ctx->DP ) != 0 ) || ( DQ != NULL && mbedtls_mpi_cmp_mpi( DQ, &ctx->DQ ) != 0 ) || ( QP != NULL && mbedtls_mpi_cmp_mpi( QP, &ctx->QP ) != 0 ) ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); } #else /* MBEDTLS_RSA_NO_CRT */ if( ( ret = mbedtls_rsa_validate_crt( &ctx->P, &ctx->Q, &ctx->D, DP, DQ, QP ) ) != 0 ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); } #endif if( ret != 0 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); return( 0 ); } int mbedtls_rsa_export_raw( const mbedtls_rsa_context *ctx, unsigned char *N, size_t N_len, unsigned char *P, size_t P_len, unsigned char *Q, size_t Q_len, unsigned char *D, size_t D_len, unsigned char *E, size_t E_len ) { int ret = 0; /* Check if key is private or public */ const int is_priv = mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0; if( !is_priv ) { /* If we're trying to export private parameters for a public key, * something must be wrong. */ if( P != NULL || Q != NULL || D != NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); } if( N != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->N, N, N_len ) ); if( P != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->P, P, P_len ) ); if( Q != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->Q, Q, Q_len ) ); if( D != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->D, D, D_len ) ); if( E != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->E, E, E_len ) ); cleanup: return( ret ); } int mbedtls_rsa_export( const mbedtls_rsa_context *ctx, mbedtls_mpi *N, mbedtls_mpi *P, mbedtls_mpi *Q, mbedtls_mpi *D, mbedtls_mpi *E ) { int ret; /* Check if key is private or public */ int is_priv = mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0; if( !is_priv ) { /* If we're trying to export private parameters for a public key, * something must be wrong. */ if( P != NULL || Q != NULL || D != NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); } /* Export all requested core parameters. */ if( ( N != NULL && ( ret = mbedtls_mpi_copy( N, &ctx->N ) ) != 0 ) || ( P != NULL && ( ret = mbedtls_mpi_copy( P, &ctx->P ) ) != 0 ) || ( Q != NULL && ( ret = mbedtls_mpi_copy( Q, &ctx->Q ) ) != 0 ) || ( D != NULL && ( ret = mbedtls_mpi_copy( D, &ctx->D ) ) != 0 ) || ( E != NULL && ( ret = mbedtls_mpi_copy( E, &ctx->E ) ) != 0 ) ) { return( ret ); } return( 0 ); } /* * Export CRT parameters * This must also be implemented if CRT is not used, for being able to * write DER encoded RSA keys. The helper function mbedtls_rsa_deduce_crt * can be used in this case. */ int mbedtls_rsa_export_crt( const mbedtls_rsa_context *ctx, mbedtls_mpi *DP, mbedtls_mpi *DQ, mbedtls_mpi *QP ) { int ret; /* Check if key is private or public */ int is_priv = mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 && mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0; if( !is_priv ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); #if !defined(MBEDTLS_RSA_NO_CRT) /* Export all requested blinding parameters. */ if( ( DP != NULL && ( ret = mbedtls_mpi_copy( DP, &ctx->DP ) ) != 0 ) || ( DQ != NULL && ( ret = mbedtls_mpi_copy( DQ, &ctx->DQ ) ) != 0 ) || ( QP != NULL && ( ret = mbedtls_mpi_copy( QP, &ctx->QP ) ) != 0 ) ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); } #else if( ( ret = mbedtls_rsa_deduce_crt( &ctx->P, &ctx->Q, &ctx->D, DP, DQ, QP ) ) != 0 ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret ); } #endif return( 0 ); } /* * Initialize an RSA context */ void mbedtls_rsa_init( mbedtls_rsa_context *ctx, int padding, int hash_id ) { memset( ctx, 0, sizeof( mbedtls_rsa_context ) ); mbedtls_rsa_set_padding( ctx, padding, hash_id ); #if defined(MBEDTLS_THREADING_C) mbedtls_mutex_init( &ctx->mutex ); #endif } /* * Set padding for an existing RSA context */ void mbedtls_rsa_set_padding( mbedtls_rsa_context *ctx, int padding, int hash_id ) { ctx->padding = padding; ctx->hash_id = hash_id; } /* * Get length in bytes of RSA modulus */ size_t mbedtls_rsa_get_len( const mbedtls_rsa_context *ctx ) { return( ctx->len ); } #if defined(MBEDTLS_GENPRIME) /* * Generate an RSA keypair */ int mbedtls_rsa_gen_key( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, unsigned int nbits, int exponent ) { int ret; mbedtls_mpi H, G; if( f_rng == NULL || nbits < 128 || exponent < 3 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); if( nbits % 2 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); mbedtls_mpi_init( &H ); mbedtls_mpi_init( &G ); /* * find primes P and Q with Q < P so that: * GCD( E, (P-1)*(Q-1) ) == 1 */ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &ctx->E, exponent ) ); do { MBEDTLS_MPI_CHK( mbedtls_mpi_gen_prime( &ctx->P, nbits >> 1, 0, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_gen_prime( &ctx->Q, nbits >> 1, 0, f_rng, p_rng ) ); if( mbedtls_mpi_cmp_mpi( &ctx->P, &ctx->Q ) == 0 ) continue; MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->N, &ctx->P, &ctx->Q ) ); if( mbedtls_mpi_bitlen( &ctx->N ) != nbits ) continue; if( mbedtls_mpi_cmp_mpi( &ctx->P, &ctx->Q ) < 0 ) mbedtls_mpi_swap( &ctx->P, &ctx->Q ); /* Temporarily replace P,Q by P-1, Q-1 */ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &ctx->P, &ctx->P, 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &ctx->Q, &ctx->Q, 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &H, &ctx->P, &ctx->Q ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, &ctx->E, &H ) ); } while( mbedtls_mpi_cmp_int( &G, 1 ) != 0 ); /* Restore P,Q */ MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &ctx->P, &ctx->P, 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &ctx->Q, &ctx->Q, 1 ) ); ctx->len = mbedtls_mpi_size( &ctx->N ); /* * D = E^-1 mod ((P-1)*(Q-1)) * DP = D mod (P - 1) * DQ = D mod (Q - 1) * QP = Q^-1 mod P */ MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->D, &ctx->E, &H ) ); #if !defined(MBEDTLS_RSA_NO_CRT) MBEDTLS_MPI_CHK( mbedtls_rsa_deduce_crt( &ctx->P, &ctx->Q, &ctx->D, &ctx->DP, &ctx->DQ, &ctx->QP ) ); #endif /* MBEDTLS_RSA_NO_CRT */ /* Double-check */ MBEDTLS_MPI_CHK( mbedtls_rsa_check_privkey( ctx ) ); cleanup: mbedtls_mpi_free( &H ); mbedtls_mpi_free( &G ); if( ret != 0 ) { mbedtls_rsa_free( ctx ); return( MBEDTLS_ERR_RSA_KEY_GEN_FAILED + ret ); } return( 0 ); } #endif /* MBEDTLS_GENPRIME */ /* * Check a public RSA key */ int mbedtls_rsa_check_pubkey( const mbedtls_rsa_context *ctx ) { if( !ctx->N.p || !ctx->E.p ) return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); if( ctx->len != mbedtls_mpi_size( &ctx->N ) ) return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); if( ( ctx->N.p[0] & 1 ) == 0 || ( ctx->E.p[0] & 1 ) == 0 ) return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); if( mbedtls_mpi_bitlen( &ctx->N ) < 128 || mbedtls_mpi_bitlen( &ctx->N ) > MBEDTLS_MPI_MAX_BITS ) return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); if( mbedtls_mpi_bitlen( &ctx->E ) < 2 || mbedtls_mpi_cmp_mpi( &ctx->E, &ctx->N ) >= 0 ) return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); return( 0 ); } /* * Check a private RSA key */ int mbedtls_rsa_check_privkey( const mbedtls_rsa_context *ctx ) { if( mbedtls_rsa_check_pubkey( ctx ) != 0 || mbedtls_rsa_validate_params( &ctx->N, &ctx->P, &ctx->Q, &ctx->D, &ctx->E, NULL, NULL ) != 0 ) { return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); } #if !defined(MBEDTLS_RSA_NO_CRT) else if( mbedtls_rsa_validate_crt( &ctx->P, &ctx->Q, &ctx->D, &ctx->DP, &ctx->DQ, &ctx->QP ) != 0 ) { return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); } #endif return( 0 ); } /* * Check if contexts holding a public and private key match */ int mbedtls_rsa_check_pub_priv( const mbedtls_rsa_context *pub, const mbedtls_rsa_context *prv ) { if( mbedtls_rsa_check_pubkey( pub ) != 0 || mbedtls_rsa_check_privkey( prv ) != 0 ) { return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); } if( mbedtls_mpi_cmp_mpi( &pub->N, &prv->N ) != 0 || mbedtls_mpi_cmp_mpi( &pub->E, &prv->E ) != 0 ) { return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ); } return( 0 ); } /* * Do an RSA public key operation */ int mbedtls_rsa_public( mbedtls_rsa_context *ctx, const unsigned char *input, unsigned char *output ) { int ret; size_t olen; mbedtls_mpi T; mbedtls_mpi_init( &T ); #if defined(MBEDTLS_THREADING_C) if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 ) return( ret ); #endif MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &T, input, ctx->len ) ); if( mbedtls_mpi_cmp_mpi( &T, &ctx->N ) >= 0 ) { ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; goto cleanup; } olen = ctx->len; MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T, &T, &ctx->E, &ctx->N, &ctx->RN ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &T, output, olen ) ); cleanup: #if defined(MBEDTLS_THREADING_C) if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 ) return( MBEDTLS_ERR_THREADING_MUTEX_ERROR ); #endif mbedtls_mpi_free( &T ); if( ret != 0 ) return( MBEDTLS_ERR_RSA_PUBLIC_FAILED + ret ); return( 0 ); } /* * Generate or update blinding values, see section 10 of: * KOCHER, Paul C. Timing attacks on implementations of Diffie-Hellman, RSA, * DSS, and other systems. In : Advances in Cryptology-CRYPTO'96. Springer * Berlin Heidelberg, 1996. p. 104-113. */ static int rsa_prepare_blinding( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret, count = 0; if( ctx->Vf.p != NULL ) { /* We already have blinding values, just update them by squaring */ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->Vi, &ctx->Vi, &ctx->Vi ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->Vi, &ctx->Vi, &ctx->N ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->Vf, &ctx->Vf, &ctx->Vf ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->Vf, &ctx->Vf, &ctx->N ) ); goto cleanup; } /* Unblinding value: Vf = random number, invertible mod N */ do { if( count++ > 10 ) return( MBEDTLS_ERR_RSA_RNG_FAILED ); MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &ctx->Vf, ctx->len - 1, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &ctx->Vi, &ctx->Vf, &ctx->N ) ); } while( mbedtls_mpi_cmp_int( &ctx->Vi, 1 ) != 0 ); /* Blinding value: Vi = Vf^(-e) mod N */ MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->Vi, &ctx->Vf, &ctx->N ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &ctx->Vi, &ctx->Vi, &ctx->E, &ctx->N, &ctx->RN ) ); cleanup: return( ret ); } /* * Exponent blinding supposed to prevent side-channel attacks using multiple * traces of measurements to recover the RSA key. The more collisions are there, * the more bits of the key can be recovered. See [3]. * * Collecting n collisions with m bit long blinding value requires 2^(m-m/n) * observations on avarage. * * For example with 28 byte blinding to achieve 2 collisions the adversary has * to make 2^112 observations on avarage. * * (With the currently (as of 2017 April) known best algorithms breaking 2048 * bit RSA requires approximately as much time as trying out 2^112 random keys. * Thus in this sense with 28 byte blinding the security is not reduced by * side-channel attacks like the one in [3]) * * This countermeasure does not help if the key recovery is possible with a * single trace. */ #define RSA_EXPONENT_BLINDING 28 /* * Do an RSA private key operation */ int mbedtls_rsa_private( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, const unsigned char *input, unsigned char *output ) { int ret; size_t olen; mbedtls_mpi T, T1, T2; mbedtls_mpi P1, Q1, R; #if defined(MBEDTLS_RSA_NO_CRT) mbedtls_mpi D_blind; mbedtls_mpi *D = &ctx->D; #else mbedtls_mpi DP_blind, DQ_blind; mbedtls_mpi *DP = &ctx->DP; mbedtls_mpi *DQ = &ctx->DQ; #endif /* Sanity-check that all relevant fields are at least set, * but don't perform a full keycheck. */ if( mbedtls_mpi_cmp_int( &ctx->N, 0 ) == 0 || mbedtls_mpi_cmp_int( &ctx->P, 0 ) == 0 || mbedtls_mpi_cmp_int( &ctx->Q, 0 ) == 0 || mbedtls_mpi_cmp_int( &ctx->D, 0 ) == 0 || mbedtls_mpi_cmp_int( &ctx->E, 0 ) == 0 ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); } #if !defined(MBEDTLS_RSA_NO_CRT) if( mbedtls_mpi_cmp_int( &ctx->DP, 0 ) == 0 || mbedtls_mpi_cmp_int( &ctx->DQ, 0 ) == 0 || mbedtls_mpi_cmp_int( &ctx->QP, 0 ) == 0 ) { return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); } #endif /* MBEDTLS_RSA_NO_CRT */ mbedtls_mpi_init( &T ); mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &R ); if( f_rng != NULL ) { #if defined(MBEDTLS_RSA_NO_CRT) mbedtls_mpi_init( &D_blind ); #else mbedtls_mpi_init( &DP_blind ); mbedtls_mpi_init( &DQ_blind ); #endif } #if defined(MBEDTLS_THREADING_C) if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 ) return( ret ); #endif MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &T, input, ctx->len ) ); if( mbedtls_mpi_cmp_mpi( &T, &ctx->N ) >= 0 ) { ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; goto cleanup; } if( f_rng != NULL ) { /* * Blinding * T = T * Vi mod N */ MBEDTLS_MPI_CHK( rsa_prepare_blinding( ctx, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &T, &ctx->Vi ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &T, &ctx->N ) ); /* * Exponent blinding */ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &P1, &ctx->P, 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &Q1, &ctx->Q, 1 ) ); #if defined(MBEDTLS_RSA_NO_CRT) /* * D_blind = ( P - 1 ) * ( Q - 1 ) * R + D */ MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &R, RSA_EXPONENT_BLINDING, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &D_blind, &P1, &Q1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &D_blind, &D_blind, &R ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &D_blind, &D_blind, &ctx->D ) ); D = &D_blind; #else /* * DP_blind = ( P - 1 ) * R + DP */ MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &R, RSA_EXPONENT_BLINDING, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DP_blind, &P1, &R ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &DP_blind, &DP_blind, &ctx->DP ) ); DP = &DP_blind; /* * DQ_blind = ( Q - 1 ) * R + DQ */ MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &R, RSA_EXPONENT_BLINDING, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DQ_blind, &Q1, &R ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &DQ_blind, &DQ_blind, &ctx->DQ ) ); DQ = &DQ_blind; #endif /* MBEDTLS_RSA_NO_CRT */ } #if defined(MBEDTLS_RSA_NO_CRT) MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T, &T, D, &ctx->N, &ctx->RN ) ); #else /* * Faster decryption using the CRT * * T1 = input ^ dP mod P * T2 = input ^ dQ mod Q */ MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T1, &T, DP, &ctx->P, &ctx->RP ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T2, &T, DQ, &ctx->Q, &ctx->RQ ) ); /* * T = (T1 - T2) * (Q^-1 mod P) mod P */ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T1, &T2 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T, &ctx->QP ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &T1, &ctx->P ) ); /* * T = T2 + T * Q */ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T, &ctx->Q ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &T2, &T1 ) ); #endif /* MBEDTLS_RSA_NO_CRT */ if( f_rng != NULL ) { /* * Unblind * T = T * Vf mod N */ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &T, &ctx->Vf ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &T, &ctx->N ) ); } olen = ctx->len; MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &T, output, olen ) ); cleanup: #if defined(MBEDTLS_THREADING_C) if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 ) return( MBEDTLS_ERR_THREADING_MUTEX_ERROR ); #endif mbedtls_mpi_free( &T ); mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &R ); if( f_rng != NULL ) { #if defined(MBEDTLS_RSA_NO_CRT) mbedtls_mpi_free( &D_blind ); #else mbedtls_mpi_free( &DP_blind ); mbedtls_mpi_free( &DQ_blind ); #endif } if( ret != 0 ) return( MBEDTLS_ERR_RSA_PRIVATE_FAILED + ret ); return( 0 ); } #if defined(MBEDTLS_PKCS1_V21) /** * Generate and apply the MGF1 operation (from PKCS#1 v2.1) to a buffer. * * \param dst buffer to mask * \param dlen length of destination buffer * \param src source of the mask generation * \param slen length of the source buffer * \param md_ctx message digest context to use */ static void mgf_mask( unsigned char *dst, size_t dlen, unsigned char *src, size_t slen, mbedtls_md_context_t *md_ctx ) { unsigned char mask[MBEDTLS_MD_MAX_SIZE]; unsigned char counter[4]; unsigned char *p; unsigned int hlen; size_t i, use_len; memset( mask, 0, MBEDTLS_MD_MAX_SIZE ); memset( counter, 0, 4 ); hlen = mbedtls_md_get_size( md_ctx->md_info ); /* Generate and apply dbMask */ p = dst; while( dlen > 0 ) { use_len = hlen; if( dlen < hlen ) use_len = dlen; mbedtls_md_starts( md_ctx ); mbedtls_md_update( md_ctx, src, slen ); mbedtls_md_update( md_ctx, counter, 4 ); mbedtls_md_finish( md_ctx, mask ); for( i = 0; i < use_len; ++i ) *p++ ^= mask[i]; counter[3]++; dlen -= use_len; } mbedtls_zeroize( mask, sizeof( mask ) ); } #endif /* MBEDTLS_PKCS1_V21 */ #if defined(MBEDTLS_PKCS1_V21) /* * Implementation of the PKCS#1 v2.1 RSAES-OAEP-ENCRYPT function */ int mbedtls_rsa_rsaes_oaep_encrypt( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, const unsigned char *label, size_t label_len, size_t ilen, const unsigned char *input, unsigned char *output ) { size_t olen; int ret; unsigned char *p = output; unsigned int hlen; const mbedtls_md_info_t *md_info; mbedtls_md_context_t md_ctx; if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V21 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); if( f_rng == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); md_info = mbedtls_md_info_from_type( (mbedtls_md_type_t) ctx->hash_id ); if( md_info == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); olen = ctx->len; hlen = mbedtls_md_get_size( md_info ); /* first comparison checks for overflow */ if( ilen + 2 * hlen + 2 < ilen || olen < ilen + 2 * hlen + 2 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); memset( output, 0, olen ); *p++ = 0; /* Generate a random octet string seed */ if( ( ret = f_rng( p_rng, p, hlen ) ) != 0 ) return( MBEDTLS_ERR_RSA_RNG_FAILED + ret ); p += hlen; /* Construct DB */ mbedtls_md( md_info, label, label_len, p ); p += hlen; p += olen - 2 * hlen - 2 - ilen; *p++ = 1; memcpy( p, input, ilen ); mbedtls_md_init( &md_ctx ); if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 ) { mbedtls_md_free( &md_ctx ); return( ret ); } /* maskedDB: Apply dbMask to DB */ mgf_mask( output + hlen + 1, olen - hlen - 1, output + 1, hlen, &md_ctx ); /* maskedSeed: Apply seedMask to seed */ mgf_mask( output + 1, hlen, output + hlen + 1, olen - hlen - 1, &md_ctx ); mbedtls_md_free( &md_ctx ); return( ( mode == MBEDTLS_RSA_PUBLIC ) ? mbedtls_rsa_public( ctx, output, output ) : mbedtls_rsa_private( ctx, f_rng, p_rng, output, output ) ); } #endif /* MBEDTLS_PKCS1_V21 */ #if defined(MBEDTLS_PKCS1_V15) /* * Implementation of the PKCS#1 v2.1 RSAES-PKCS1-V1_5-ENCRYPT function */ int mbedtls_rsa_rsaes_pkcs1_v15_encrypt( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, size_t ilen, const unsigned char *input, unsigned char *output ) { size_t nb_pad, olen; int ret; unsigned char *p = output; if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); // We don't check p_rng because it won't be dereferenced here if( f_rng == NULL || input == NULL || output == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); olen = ctx->len; /* first comparison checks for overflow */ if( ilen + 11 < ilen || olen < ilen + 11 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); nb_pad = olen - 3 - ilen; *p++ = 0; if( mode == MBEDTLS_RSA_PUBLIC ) { *p++ = MBEDTLS_RSA_CRYPT; while( nb_pad-- > 0 ) { int rng_dl = 100; do { ret = f_rng( p_rng, p, 1 ); } while( *p == 0 && --rng_dl && ret == 0 ); /* Check if RNG failed to generate data */ if( rng_dl == 0 || ret != 0 ) return( MBEDTLS_ERR_RSA_RNG_FAILED + ret ); p++; } } else { *p++ = MBEDTLS_RSA_SIGN; while( nb_pad-- > 0 ) *p++ = 0xFF; } *p++ = 0; memcpy( p, input, ilen ); return( ( mode == MBEDTLS_RSA_PUBLIC ) ? mbedtls_rsa_public( ctx, output, output ) : mbedtls_rsa_private( ctx, f_rng, p_rng, output, output ) ); } #endif /* MBEDTLS_PKCS1_V15 */ /* * Add the message padding, then do an RSA operation */ int mbedtls_rsa_pkcs1_encrypt( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, size_t ilen, const unsigned char *input, unsigned char *output ) { switch( ctx->padding ) { #if defined(MBEDTLS_PKCS1_V15) case MBEDTLS_RSA_PKCS_V15: return mbedtls_rsa_rsaes_pkcs1_v15_encrypt( ctx, f_rng, p_rng, mode, ilen, input, output ); #endif #if defined(MBEDTLS_PKCS1_V21) case MBEDTLS_RSA_PKCS_V21: return mbedtls_rsa_rsaes_oaep_encrypt( ctx, f_rng, p_rng, mode, NULL, 0, ilen, input, output ); #endif default: return( MBEDTLS_ERR_RSA_INVALID_PADDING ); } } #if defined(MBEDTLS_PKCS1_V21) /* * Implementation of the PKCS#1 v2.1 RSAES-OAEP-DECRYPT function */ int mbedtls_rsa_rsaes_oaep_decrypt( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, const unsigned char *label, size_t label_len, size_t *olen, const unsigned char *input, unsigned char *output, size_t output_max_len ) { int ret; size_t ilen, i, pad_len; unsigned char *p, bad, pad_done; unsigned char buf[MBEDTLS_MPI_MAX_SIZE]; unsigned char lhash[MBEDTLS_MD_MAX_SIZE]; unsigned int hlen; const mbedtls_md_info_t *md_info; mbedtls_md_context_t md_ctx; /* * Parameters sanity checks */ if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V21 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); ilen = ctx->len; if( ilen < 16 || ilen > sizeof( buf ) ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); md_info = mbedtls_md_info_from_type( (mbedtls_md_type_t) ctx->hash_id ); if( md_info == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); hlen = mbedtls_md_get_size( md_info ); // checking for integer underflow if( 2 * hlen + 2 > ilen ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); /* * RSA operation */ ret = ( mode == MBEDTLS_RSA_PUBLIC ) ? mbedtls_rsa_public( ctx, input, buf ) : mbedtls_rsa_private( ctx, f_rng, p_rng, input, buf ); if( ret != 0 ) goto cleanup; /* * Unmask data and generate lHash */ mbedtls_md_init( &md_ctx ); if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 ) { mbedtls_md_free( &md_ctx ); goto cleanup; } /* Generate lHash */ mbedtls_md( md_info, label, label_len, lhash ); /* seed: Apply seedMask to maskedSeed */ mgf_mask( buf + 1, hlen, buf + hlen + 1, ilen - hlen - 1, &md_ctx ); /* DB: Apply dbMask to maskedDB */ mgf_mask( buf + hlen + 1, ilen - hlen - 1, buf + 1, hlen, &md_ctx ); mbedtls_md_free( &md_ctx ); /* * Check contents, in "constant-time" */ p = buf; bad = 0; bad |= *p++; /* First byte must be 0 */ p += hlen; /* Skip seed */ /* Check lHash */ for( i = 0; i < hlen; i++ ) bad |= lhash[i] ^ *p++; /* Get zero-padding len, but always read till end of buffer * (minus one, for the 01 byte) */ pad_len = 0; pad_done = 0; for( i = 0; i < ilen - 2 * hlen - 2; i++ ) { pad_done |= p[i]; pad_len += ((pad_done | (unsigned char)-pad_done) >> 7) ^ 1; } p += pad_len; bad |= *p++ ^ 0x01; /* * The only information "leaked" is whether the padding was correct or not * (eg, no data is copied if it was not correct). This meets the * recommendations in PKCS#1 v2.2: an opponent cannot distinguish between * the different error conditions. */ if( bad != 0 ) { ret = MBEDTLS_ERR_RSA_INVALID_PADDING; goto cleanup; } if( ilen - ( p - buf ) > output_max_len ) { ret = MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE; goto cleanup; } *olen = ilen - (p - buf); memcpy( output, p, *olen ); ret = 0; cleanup: mbedtls_zeroize( buf, sizeof( buf ) ); mbedtls_zeroize( lhash, sizeof( lhash ) ); return( ret ); } #endif /* MBEDTLS_PKCS1_V21 */ #if defined(MBEDTLS_PKCS1_V15) /* * Implementation of the PKCS#1 v2.1 RSAES-PKCS1-V1_5-DECRYPT function */ int mbedtls_rsa_rsaes_pkcs1_v15_decrypt( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, size_t *olen, const unsigned char *input, unsigned char *output, size_t output_max_len) { int ret; size_t ilen, pad_count = 0, i; unsigned char *p, bad, pad_done = 0; unsigned char buf[MBEDTLS_MPI_MAX_SIZE]; if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); ilen = ctx->len; if( ilen < 16 || ilen > sizeof( buf ) ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); ret = ( mode == MBEDTLS_RSA_PUBLIC ) ? mbedtls_rsa_public( ctx, input, buf ) : mbedtls_rsa_private( ctx, f_rng, p_rng, input, buf ); if( ret != 0 ) goto cleanup; p = buf; bad = 0; /* * Check and get padding len in "constant-time" */ bad |= *p++; /* First byte must be 0 */ /* This test does not depend on secret data */ if( mode == MBEDTLS_RSA_PRIVATE ) { bad |= *p++ ^ MBEDTLS_RSA_CRYPT; /* Get padding len, but always read till end of buffer * (minus one, for the 00 byte) */ for( i = 0; i < ilen - 3; i++ ) { pad_done |= ((p[i] | (unsigned char)-p[i]) >> 7) ^ 1; pad_count += ((pad_done | (unsigned char)-pad_done) >> 7) ^ 1; } p += pad_count; bad |= *p++; /* Must be zero */ } else { bad |= *p++ ^ MBEDTLS_RSA_SIGN; /* Get padding len, but always read till end of buffer * (minus one, for the 00 byte) */ for( i = 0; i < ilen - 3; i++ ) { pad_done |= ( p[i] != 0xFF ); pad_count += ( pad_done == 0 ); } p += pad_count; bad |= *p++; /* Must be zero */ } bad |= ( pad_count < 8 ); if( bad ) { ret = MBEDTLS_ERR_RSA_INVALID_PADDING; goto cleanup; } if( ilen - ( p - buf ) > output_max_len ) { ret = MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE; goto cleanup; } *olen = ilen - (p - buf); memcpy( output, p, *olen ); ret = 0; cleanup: mbedtls_zeroize( buf, sizeof( buf ) ); return( ret ); } #endif /* MBEDTLS_PKCS1_V15 */ /* * Do an RSA operation, then remove the message padding */ int mbedtls_rsa_pkcs1_decrypt( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, size_t *olen, const unsigned char *input, unsigned char *output, size_t output_max_len) { switch( ctx->padding ) { #if defined(MBEDTLS_PKCS1_V15) case MBEDTLS_RSA_PKCS_V15: return mbedtls_rsa_rsaes_pkcs1_v15_decrypt( ctx, f_rng, p_rng, mode, olen, input, output, output_max_len ); #endif #if defined(MBEDTLS_PKCS1_V21) case MBEDTLS_RSA_PKCS_V21: return mbedtls_rsa_rsaes_oaep_decrypt( ctx, f_rng, p_rng, mode, NULL, 0, olen, input, output, output_max_len ); #endif default: return( MBEDTLS_ERR_RSA_INVALID_PADDING ); } } #if defined(MBEDTLS_PKCS1_V21) /* * Implementation of the PKCS#1 v2.1 RSASSA-PSS-SIGN function */ int mbedtls_rsa_rsassa_pss_sign( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, mbedtls_md_type_t md_alg, unsigned int hashlen, const unsigned char *hash, unsigned char *sig ) { size_t olen; unsigned char *p = sig; unsigned char salt[MBEDTLS_MD_MAX_SIZE]; unsigned int slen, hlen, offset = 0; int ret; size_t msb; const mbedtls_md_info_t *md_info; mbedtls_md_context_t md_ctx; if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V21 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); if( f_rng == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); olen = ctx->len; if( md_alg != MBEDTLS_MD_NONE ) { /* Gather length of hash to sign */ md_info = mbedtls_md_info_from_type( md_alg ); if( md_info == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); hashlen = mbedtls_md_get_size( md_info ); } md_info = mbedtls_md_info_from_type( (mbedtls_md_type_t) ctx->hash_id ); if( md_info == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); hlen = mbedtls_md_get_size( md_info ); slen = hlen; if( olen < hlen + slen + 2 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); memset( sig, 0, olen ); /* Generate salt of length slen */ if( ( ret = f_rng( p_rng, salt, slen ) ) != 0 ) return( MBEDTLS_ERR_RSA_RNG_FAILED + ret ); /* Note: EMSA-PSS encoding is over the length of N - 1 bits */ msb = mbedtls_mpi_bitlen( &ctx->N ) - 1; p += olen - hlen * 2 - 2; *p++ = 0x01; memcpy( p, salt, slen ); p += slen; mbedtls_md_init( &md_ctx ); if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 ) { mbedtls_md_free( &md_ctx ); /* No need to zeroize salt: we didn't use it. */ return( ret ); } /* Generate H = Hash( M' ) */ mbedtls_md_starts( &md_ctx ); mbedtls_md_update( &md_ctx, p, 8 ); mbedtls_md_update( &md_ctx, hash, hashlen ); mbedtls_md_update( &md_ctx, salt, slen ); mbedtls_md_finish( &md_ctx, p ); mbedtls_zeroize( salt, sizeof( salt ) ); /* Compensate for boundary condition when applying mask */ if( msb % 8 == 0 ) offset = 1; /* maskedDB: Apply dbMask to DB */ mgf_mask( sig + offset, olen - hlen - 1 - offset, p, hlen, &md_ctx ); mbedtls_md_free( &md_ctx ); msb = mbedtls_mpi_bitlen( &ctx->N ) - 1; sig[0] &= 0xFF >> ( olen * 8 - msb ); p += hlen; *p++ = 0xBC; return( ( mode == MBEDTLS_RSA_PUBLIC ) ? mbedtls_rsa_public( ctx, sig, sig ) : mbedtls_rsa_private( ctx, f_rng, p_rng, sig, sig ) ); } #endif /* MBEDTLS_PKCS1_V21 */ #if defined(MBEDTLS_PKCS1_V15) /* * Implementation of the PKCS#1 v2.1 RSASSA-PKCS1-V1_5-SIGN function */ /* * Do an RSA operation to sign the message digest */ int mbedtls_rsa_rsassa_pkcs1_v15_sign( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, mbedtls_md_type_t md_alg, unsigned int hashlen, const unsigned char *hash, unsigned char *sig ) { size_t nb_pad, olen, oid_size = 0; unsigned char *p = sig; const char *oid = NULL; unsigned char *sig_try = NULL, *verif = NULL; size_t i; unsigned char diff; volatile unsigned char diff_no_optimize; int ret; if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); olen = ctx->len; nb_pad = olen - 3; if( md_alg != MBEDTLS_MD_NONE ) { const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type( md_alg ); if( md_info == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); if( mbedtls_oid_get_oid_by_md( md_alg, &oid, &oid_size ) != 0 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); nb_pad -= 10 + oid_size; hashlen = mbedtls_md_get_size( md_info ); } nb_pad -= hashlen; if( ( nb_pad < 8 ) || ( nb_pad > olen ) ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); *p++ = 0; *p++ = MBEDTLS_RSA_SIGN; memset( p, 0xFF, nb_pad ); p += nb_pad; *p++ = 0; if( md_alg == MBEDTLS_MD_NONE ) { memcpy( p, hash, hashlen ); } else { /* * DigestInfo ::= SEQUENCE { * digestAlgorithm DigestAlgorithmIdentifier, * digest Digest } * * DigestAlgorithmIdentifier ::= AlgorithmIdentifier * * Digest ::= OCTET STRING */ *p++ = MBEDTLS_ASN1_SEQUENCE | MBEDTLS_ASN1_CONSTRUCTED; *p++ = (unsigned char) ( 0x08 + oid_size + hashlen ); *p++ = MBEDTLS_ASN1_SEQUENCE | MBEDTLS_ASN1_CONSTRUCTED; *p++ = (unsigned char) ( 0x04 + oid_size ); *p++ = MBEDTLS_ASN1_OID; *p++ = oid_size & 0xFF; memcpy( p, oid, oid_size ); p += oid_size; *p++ = MBEDTLS_ASN1_NULL; *p++ = 0x00; *p++ = MBEDTLS_ASN1_OCTET_STRING; *p++ = hashlen; memcpy( p, hash, hashlen ); } if( mode == MBEDTLS_RSA_PUBLIC ) return( mbedtls_rsa_public( ctx, sig, sig ) ); /* * In order to prevent Lenstra's attack, make the signature in a * temporary buffer and check it before returning it. */ sig_try = mbedtls_calloc( 1, ctx->len ); if( sig_try == NULL ) return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); verif = mbedtls_calloc( 1, ctx->len ); if( verif == NULL ) { mbedtls_free( sig_try ); return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); } MBEDTLS_MPI_CHK( mbedtls_rsa_private( ctx, f_rng, p_rng, sig, sig_try ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_public( ctx, sig_try, verif ) ); /* Compare in constant time just in case */ for( diff = 0, i = 0; i < ctx->len; i++ ) diff |= verif[i] ^ sig[i]; diff_no_optimize = diff; if( diff_no_optimize != 0 ) { ret = MBEDTLS_ERR_RSA_PRIVATE_FAILED; goto cleanup; } memcpy( sig, sig_try, ctx->len ); cleanup: mbedtls_free( sig_try ); mbedtls_free( verif ); return( ret ); } #endif /* MBEDTLS_PKCS1_V15 */ /* * Do an RSA operation to sign the message digest */ int mbedtls_rsa_pkcs1_sign( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, mbedtls_md_type_t md_alg, unsigned int hashlen, const unsigned char *hash, unsigned char *sig ) { switch( ctx->padding ) { #if defined(MBEDTLS_PKCS1_V15) case MBEDTLS_RSA_PKCS_V15: return mbedtls_rsa_rsassa_pkcs1_v15_sign( ctx, f_rng, p_rng, mode, md_alg, hashlen, hash, sig ); #endif #if defined(MBEDTLS_PKCS1_V21) case MBEDTLS_RSA_PKCS_V21: return mbedtls_rsa_rsassa_pss_sign( ctx, f_rng, p_rng, mode, md_alg, hashlen, hash, sig ); #endif default: return( MBEDTLS_ERR_RSA_INVALID_PADDING ); } } #if defined(MBEDTLS_PKCS1_V21) /* * Implementation of the PKCS#1 v2.1 RSASSA-PSS-VERIFY function */ int mbedtls_rsa_rsassa_pss_verify_ext( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, mbedtls_md_type_t md_alg, unsigned int hashlen, const unsigned char *hash, mbedtls_md_type_t mgf1_hash_id, int expected_salt_len, const unsigned char *sig ) { int ret; size_t siglen; unsigned char *p; unsigned char result[MBEDTLS_MD_MAX_SIZE]; unsigned char zeros[8]; unsigned int hlen; size_t slen, msb; const mbedtls_md_info_t *md_info; mbedtls_md_context_t md_ctx; unsigned char buf[MBEDTLS_MPI_MAX_SIZE]; if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V21 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); siglen = ctx->len; if( siglen < 16 || siglen > sizeof( buf ) ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); ret = ( mode == MBEDTLS_RSA_PUBLIC ) ? mbedtls_rsa_public( ctx, sig, buf ) : mbedtls_rsa_private( ctx, f_rng, p_rng, sig, buf ); if( ret != 0 ) return( ret ); p = buf; if( buf[siglen - 1] != 0xBC ) return( MBEDTLS_ERR_RSA_INVALID_PADDING ); if( md_alg != MBEDTLS_MD_NONE ) { /* Gather length of hash to sign */ md_info = mbedtls_md_info_from_type( md_alg ); if( md_info == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); hashlen = mbedtls_md_get_size( md_info ); } md_info = mbedtls_md_info_from_type( mgf1_hash_id ); if( md_info == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); hlen = mbedtls_md_get_size( md_info ); slen = siglen - hlen - 1; /* Currently length of salt + padding */ memset( zeros, 0, 8 ); /* * Note: EMSA-PSS verification is over the length of N - 1 bits */ msb = mbedtls_mpi_bitlen( &ctx->N ) - 1; /* Compensate for boundary condition when applying mask */ if( msb % 8 == 0 ) { p++; siglen -= 1; } if( buf[0] >> ( 8 - siglen * 8 + msb ) ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); mbedtls_md_init( &md_ctx ); if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 ) { mbedtls_md_free( &md_ctx ); return( ret ); } mgf_mask( p, siglen - hlen - 1, p + siglen - hlen - 1, hlen, &md_ctx ); buf[0] &= 0xFF >> ( siglen * 8 - msb ); while( p < buf + siglen && *p == 0 ) p++; if( p == buf + siglen || *p++ != 0x01 ) { mbedtls_md_free( &md_ctx ); return( MBEDTLS_ERR_RSA_INVALID_PADDING ); } /* Actual salt len */ slen -= p - buf; if( expected_salt_len != MBEDTLS_RSA_SALT_LEN_ANY && slen != (size_t) expected_salt_len ) { mbedtls_md_free( &md_ctx ); return( MBEDTLS_ERR_RSA_INVALID_PADDING ); } /* * Generate H = Hash( M' ) */ mbedtls_md_starts( &md_ctx ); mbedtls_md_update( &md_ctx, zeros, 8 ); mbedtls_md_update( &md_ctx, hash, hashlen ); mbedtls_md_update( &md_ctx, p, slen ); mbedtls_md_finish( &md_ctx, result ); mbedtls_md_free( &md_ctx ); if( memcmp( p + slen, result, hlen ) == 0 ) return( 0 ); else return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); } /* * Simplified PKCS#1 v2.1 RSASSA-PSS-VERIFY function */ int mbedtls_rsa_rsassa_pss_verify( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, mbedtls_md_type_t md_alg, unsigned int hashlen, const unsigned char *hash, const unsigned char *sig ) { mbedtls_md_type_t mgf1_hash_id = ( ctx->hash_id != MBEDTLS_MD_NONE ) ? (mbedtls_md_type_t) ctx->hash_id : md_alg; return( mbedtls_rsa_rsassa_pss_verify_ext( ctx, f_rng, p_rng, mode, md_alg, hashlen, hash, mgf1_hash_id, MBEDTLS_RSA_SALT_LEN_ANY, sig ) ); } #endif /* MBEDTLS_PKCS1_V21 */ #if defined(MBEDTLS_PKCS1_V15) /* * Implementation of the PKCS#1 v2.1 RSASSA-PKCS1-v1_5-VERIFY function */ int mbedtls_rsa_rsassa_pkcs1_v15_verify( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, mbedtls_md_type_t md_alg, unsigned int hashlen, const unsigned char *hash, const unsigned char *sig ) { int ret; size_t len, siglen, asn1_len; unsigned char *p, *p0, *end; mbedtls_md_type_t msg_md_alg; const mbedtls_md_info_t *md_info; mbedtls_asn1_buf oid; unsigned char buf[MBEDTLS_MPI_MAX_SIZE]; if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); siglen = ctx->len; if( siglen < 16 || siglen > sizeof( buf ) ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); ret = ( mode == MBEDTLS_RSA_PUBLIC ) ? mbedtls_rsa_public( ctx, sig, buf ) : mbedtls_rsa_private( ctx, f_rng, p_rng, sig, buf ); if( ret != 0 ) return( ret ); p = buf; if( *p++ != 0 || *p++ != MBEDTLS_RSA_SIGN ) return( MBEDTLS_ERR_RSA_INVALID_PADDING ); while( *p != 0 ) { if( p >= buf + siglen - 1 || *p != 0xFF ) return( MBEDTLS_ERR_RSA_INVALID_PADDING ); p++; } p++; /* skip 00 byte */ /* We've read: 00 01 PS 00 where PS must be at least 8 bytes */ if( p - buf < 11 ) return( MBEDTLS_ERR_RSA_INVALID_PADDING ); len = siglen - ( p - buf ); if( len == hashlen && md_alg == MBEDTLS_MD_NONE ) { if( memcmp( p, hash, hashlen ) == 0 ) return( 0 ); else return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); } md_info = mbedtls_md_info_from_type( md_alg ); if( md_info == NULL ) return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA ); hashlen = mbedtls_md_get_size( md_info ); end = p + len; /* * Parse the ASN.1 structure inside the PKCS#1 v1.5 structure. * Insist on 2-byte length tags, to protect against variants of * Bleichenbacher's forgery attack against lax PKCS#1v1.5 verification. */ p0 = p; if( ( ret = mbedtls_asn1_get_tag( &p, end, &asn1_len, MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE ) ) != 0 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); if( p != p0 + 2 || asn1_len + 2 != len ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); p0 = p; if( ( ret = mbedtls_asn1_get_tag( &p, end, &asn1_len, MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE ) ) != 0 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); if( p != p0 + 2 || asn1_len + 6 + hashlen != len ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); p0 = p; if( ( ret = mbedtls_asn1_get_tag( &p, end, &oid.len, MBEDTLS_ASN1_OID ) ) != 0 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); if( p != p0 + 2 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); oid.p = p; p += oid.len; if( mbedtls_oid_get_md_alg( &oid, &msg_md_alg ) != 0 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); if( md_alg != msg_md_alg ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); /* * assume the algorithm parameters must be NULL */ p0 = p; if( ( ret = mbedtls_asn1_get_tag( &p, end, &asn1_len, MBEDTLS_ASN1_NULL ) ) != 0 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); if( p != p0 + 2 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); p0 = p; if( ( ret = mbedtls_asn1_get_tag( &p, end, &asn1_len, MBEDTLS_ASN1_OCTET_STRING ) ) != 0 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); if( p != p0 + 2 || asn1_len != hashlen ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); if( memcmp( p, hash, hashlen ) != 0 ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); p += hashlen; if( p != end ) return( MBEDTLS_ERR_RSA_VERIFY_FAILED ); return( 0 ); } #endif /* MBEDTLS_PKCS1_V15 */ /* * Do an RSA operation and check the message digest */ int mbedtls_rsa_pkcs1_verify( mbedtls_rsa_context *ctx, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, int mode, mbedtls_md_type_t md_alg, unsigned int hashlen, const unsigned char *hash, const unsigned char *sig ) { switch( ctx->padding ) { #if defined(MBEDTLS_PKCS1_V15) case MBEDTLS_RSA_PKCS_V15: return mbedtls_rsa_rsassa_pkcs1_v15_verify( ctx, f_rng, p_rng, mode, md_alg, hashlen, hash, sig ); #endif #if defined(MBEDTLS_PKCS1_V21) case MBEDTLS_RSA_PKCS_V21: return mbedtls_rsa_rsassa_pss_verify( ctx, f_rng, p_rng, mode, md_alg, hashlen, hash, sig ); #endif default: return( MBEDTLS_ERR_RSA_INVALID_PADDING ); } } /* * Copy the components of an RSA key */ int mbedtls_rsa_copy( mbedtls_rsa_context *dst, const mbedtls_rsa_context *src ) { int ret; dst->ver = src->ver; dst->len = src->len; MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->N, &src->N ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->E, &src->E ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->D, &src->D ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->P, &src->P ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Q, &src->Q ) ); #if !defined(MBEDTLS_RSA_NO_CRT) MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->DP, &src->DP ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->DQ, &src->DQ ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->QP, &src->QP ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RP, &src->RP ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RQ, &src->RQ ) ); #endif MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RN, &src->RN ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Vi, &src->Vi ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Vf, &src->Vf ) ); dst->padding = src->padding; dst->hash_id = src->hash_id; cleanup: if( ret != 0 ) mbedtls_rsa_free( dst ); return( ret ); } /* * Free the components of an RSA key */ void mbedtls_rsa_free( mbedtls_rsa_context *ctx ) { mbedtls_mpi_free( &ctx->Vi ); mbedtls_mpi_free( &ctx->Vf ); mbedtls_mpi_free( &ctx->RN ); mbedtls_mpi_free( &ctx->D ); mbedtls_mpi_free( &ctx->Q ); mbedtls_mpi_free( &ctx->P ); mbedtls_mpi_free( &ctx->E ); mbedtls_mpi_free( &ctx->N ); #if !defined(MBEDTLS_RSA_NO_CRT) mbedtls_mpi_free( &ctx->RQ ); mbedtls_mpi_free( &ctx->RP ); mbedtls_mpi_free( &ctx->QP ); mbedtls_mpi_free( &ctx->DQ ); mbedtls_mpi_free( &ctx->DP ); #endif /* MBEDTLS_RSA_NO_CRT */ #if defined(MBEDTLS_THREADING_C) mbedtls_mutex_free( &ctx->mutex ); #endif } #endif /* !MBEDTLS_RSA_ALT */ #if defined(MBEDTLS_SELF_TEST) #include "mbedtls/sha1.h" /* * Example RSA-1024 keypair, for test purposes */ #define KEY_LEN 128 #define RSA_N "9292758453063D803DD603D5E777D788" \ "8ED1D5BF35786190FA2F23EBC0848AEA" \ "DDA92CA6C3D80B32C4D109BE0F36D6AE" \ "7130B9CED7ACDF54CFC7555AC14EEBAB" \ "93A89813FBF3C4F8066D2D800F7C38A8" \ "1AE31942917403FF4946B0A83D3D3E05" \ "EE57C6F5F5606FB5D4BC6CD34EE0801A" \ "5E94BB77B07507233A0BC7BAC8F90F79" #define RSA_E "10001" #define RSA_D "24BF6185468786FDD303083D25E64EFC" \ "66CA472BC44D253102F8B4A9D3BFA750" \ "91386C0077937FE33FA3252D28855837" \ "AE1B484A8A9A45F7EE8C0C634F99E8CD" \ "DF79C5CE07EE72C7F123142198164234" \ "CABB724CF78B8173B9F880FC86322407" \ "AF1FEDFDDE2BEB674CA15F3E81A1521E" \ "071513A1E85B5DFA031F21ECAE91A34D" #define RSA_P "C36D0EB7FCD285223CFB5AABA5BDA3D8" \ "2C01CAD19EA484A87EA4377637E75500" \ "FCB2005C5C7DD6EC4AC023CDA285D796" \ "C3D9E75E1EFC42488BB4F1D13AC30A57" #define RSA_Q "C000DF51A7C77AE8D7C7370C1FF55B69" \ "E211C2B9E5DB1ED0BF61D0D9899620F4" \ "910E4168387E3C30AA1E00C339A79508" \ "8452DD96A9A5EA5D9DCA68DA636032AF" #define RSA_DP "C1ACF567564274FB07A0BBAD5D26E298" \ "3C94D22288ACD763FD8E5600ED4A702D" \ "F84198A5F06C2E72236AE490C93F07F8" \ "3CC559CD27BC2D1CA488811730BB5725" #define RSA_DQ "4959CBF6F8FEF750AEE6977C155579C7" \ "D8AAEA56749EA28623272E4F7D0592AF" \ "7C1F1313CAC9471B5C523BFE592F517B" \ "407A1BD76C164B93DA2D32A383E58357" #define RSA_QP "9AE7FBC99546432DF71896FC239EADAE" \ "F38D18D2B2F0E2DD275AA977E2BF4411" \ "F5A3B2A5D33605AEBBCCBA7FEB9F2D2F" \ "A74206CEC169D74BF5A8C50D6F48EA08" #define PT_LEN 24 #define RSA_PT "\xAA\xBB\xCC\x03\x02\x01\x00\xFF\xFF\xFF\xFF\xFF" \ "\x11\x22\x33\x0A\x0B\x0C\xCC\xDD\xDD\xDD\xDD\xDD" #if defined(MBEDTLS_PKCS1_V15) static int myrand( void *rng_state, unsigned char *output, size_t len ) { #if !defined(__OpenBSD__) size_t i; if( rng_state != NULL ) rng_state = NULL; for( i = 0; i < len; ++i ) output[i] = rand(); #else if( rng_state != NULL ) rng_state = NULL; arc4random_buf( output, len ); #endif /* !OpenBSD */ return( 0 ); } #endif /* MBEDTLS_PKCS1_V15 */ /* * Checkup routine */ int mbedtls_rsa_self_test( int verbose ) { int ret = 0; #if defined(MBEDTLS_PKCS1_V15) size_t len; mbedtls_rsa_context rsa; unsigned char rsa_plaintext[PT_LEN]; unsigned char rsa_decrypted[PT_LEN]; unsigned char rsa_ciphertext[KEY_LEN]; #if defined(MBEDTLS_SHA1_C) unsigned char sha1sum[20]; #endif mbedtls_mpi K; mbedtls_mpi_init( &K ); mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, 0 ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_N ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, &K, NULL, NULL, NULL, NULL ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_P ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, &K, NULL, NULL, NULL ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_Q ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, &K, NULL, NULL ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_D ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, NULL, &K, NULL ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_E ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, NULL, NULL, &K ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_complete( &rsa, NULL, NULL ) ); if( verbose != 0 ) mbedtls_printf( " RSA key validation: " ); if( mbedtls_rsa_check_pubkey( &rsa ) != 0 || mbedtls_rsa_check_privkey( &rsa ) != 0 ) { if( verbose != 0 ) mbedtls_printf( "failed\n" ); return( 1 ); } MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_DP ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_check_crt( &rsa, &K, NULL, NULL ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_DQ ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_check_crt( &rsa, NULL, &K, NULL ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_QP ) ); MBEDTLS_MPI_CHK( mbedtls_rsa_check_crt( &rsa, NULL, NULL, &K ) ); if( verbose != 0 ) mbedtls_printf( "passed\n PKCS#1 encryption : " ); memcpy( rsa_plaintext, RSA_PT, PT_LEN ); if( mbedtls_rsa_pkcs1_encrypt( &rsa, myrand, NULL, MBEDTLS_RSA_PUBLIC, PT_LEN, rsa_plaintext, rsa_ciphertext ) != 0 ) { if( verbose != 0 ) mbedtls_printf( "failed\n" ); return( 1 ); } if( verbose != 0 ) mbedtls_printf( "passed\n PKCS#1 decryption : " ); if( mbedtls_rsa_pkcs1_decrypt( &rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE, &len, rsa_ciphertext, rsa_decrypted, sizeof(rsa_decrypted) ) != 0 ) { if( verbose != 0 ) mbedtls_printf( "failed\n" ); return( 1 ); } if( memcmp( rsa_decrypted, rsa_plaintext, len ) != 0 ) { if( verbose != 0 ) mbedtls_printf( "failed\n" ); return( 1 ); } if( verbose != 0 ) mbedtls_printf( "passed\n" ); #if defined(MBEDTLS_SHA1_C) if( verbose != 0 ) mbedtls_printf( " PKCS#1 data sign : " ); mbedtls_sha1( rsa_plaintext, PT_LEN, sha1sum ); if( mbedtls_rsa_pkcs1_sign( &rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE, MBEDTLS_MD_SHA1, 0, sha1sum, rsa_ciphertext ) != 0 ) { if( verbose != 0 ) mbedtls_printf( "failed\n" ); return( 1 ); } if( verbose != 0 ) mbedtls_printf( "passed\n PKCS#1 sig. verify: " ); if( mbedtls_rsa_pkcs1_verify( &rsa, NULL, NULL, MBEDTLS_RSA_PUBLIC, MBEDTLS_MD_SHA1, 0, sha1sum, rsa_ciphertext ) != 0 ) { if( verbose != 0 ) mbedtls_printf( "failed\n" ); return( 1 ); } if( verbose != 0 ) mbedtls_printf( "passed\n" ); #endif /* MBEDTLS_SHA1_C */ if( verbose != 0 ) mbedtls_printf( "\n" ); cleanup: mbedtls_mpi_free( &K ); mbedtls_rsa_free( &rsa ); #else /* MBEDTLS_PKCS1_V15 */ ((void) verbose); #endif /* MBEDTLS_PKCS1_V15 */ return( ret ); } #endif /* MBEDTLS_SELF_TEST */ #endif /* MBEDTLS_RSA_C */