mirror of
https://github.com/yuzu-emu/mbedtls.git
synced 2024-11-22 17:15:38 +01:00
Implement RSA helper functions
This commit is contained in:
Hanno Becker
parent
a3ebec2423
commit
e2e8b8da1d
401
library/rsa.c
401
library/rsa.c
@ -71,6 +71,407 @@ static void mbedtls_zeroize( void *v, size_t n ) {
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volatile unsigned char *p = (unsigned char*)v; while( n-- ) *p++ = 0;
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}
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/*
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* Context-independent RSA helper functions.
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*
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* The following three functions
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* - mbedtls_rsa_deduce_moduli
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* - mbedtls_rsa_deduce_private
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* - mbedtls_rsa_check_params
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* are helper functions operating on the core RSA parameters
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* (represented as MPI's). They do not use the RSA context structure
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* and therefore need not be replaced when providing an alternative
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* RSA implementation.
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*
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* Their purpose is to provide common MPI operations in the context
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* of RSA that can be easily shared across multiple implementations.
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*/
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/*
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* mbedtls_rsa_deduce_moduli
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*
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* Given the modulus N=PQ and a pair of public and private
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* exponents E and D, respectively, factor N.
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*
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* Setting F := lcm(P-1,Q-1), the idea is as follows:
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*
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* (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2)
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* is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the
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* square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four
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* possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1)
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* or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime
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* factors of N.
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*
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* (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same
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* construction still applies since (-)^K is the identity on the set of
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* roots of 1 in Z/NZ.
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*
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* The public and private key primitives (-)^E and (-)^D are mutually inverse
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* bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e.
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* if and only if DE - 1 is a multiple of F, say DE - 1 = F * L.
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* Splitting L = 2^t * K with K odd, we have
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*
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* DE - 1 = FL = (F/2) * (2^(t+1)) * K,
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*
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* so (F / 2) * K is among the numbers
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*
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* (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord
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*
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* where ord is the order of 2 in (DE - 1).
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* We can therefore iterate through these numbers apply the construction
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* of (a) and (b) above to attempt to factor N.
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*
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*/
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int mbedtls_rsa_deduce_moduli( mbedtls_mpi *N, mbedtls_mpi *D, mbedtls_mpi *E,
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int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
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mbedtls_mpi *P, mbedtls_mpi *Q )
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{
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/* Implementation note:
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*
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* Space-efficiency is given preference over time-efficiency here:
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* several calculations are done in place and temporarily change
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* the values of D and E.
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*
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* Specifically, D is replaced the largest odd divisor of DE - 1
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* throughout the calculations.
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*/
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int ret = 0;
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uint16_t attempt; /* Number of current attempt */
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uint16_t iter; /* Number of squares computed in the current attempt */
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uint16_t bitlen_half; /* Half the bitsize of the modulus N */
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uint16_t order; /* Order of 2 in DE - 1 */
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mbedtls_mpi K; /* Temporary used for two purposes:
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* - During factorization attempts, stores a andom integer
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* in the range of [0,..,N]
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* - During verification, holding intermediate results.
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*/
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if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL )
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return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 ||
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mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
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mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
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mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
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mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
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{
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return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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}
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/*
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* Initializations and temporary changes
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*/
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mbedtls_mpi_init( &K );
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mbedtls_mpi_init( P );
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mbedtls_mpi_init( Q );
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/* Replace D by DE - 1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( D, D, E ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( D, D, 1 ) );
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if( ( order = mbedtls_mpi_lsb( D ) ) == 0 )
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{
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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goto cleanup;
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}
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/* After this operation, D holds the largest odd divisor
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* of DE - 1 for the original values of D and E. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( D, order ) );
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/* This is used to generate a few numbers around N / 2
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* if no PRNG is provided. */
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if( f_rng == NULL )
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bitlen_half = mbedtls_mpi_bitlen( N ) / 2;
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/*
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* Actual work
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*/
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for( attempt = 0; attempt < 30; ++attempt )
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{
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/* Generate some number in [0,N], either randomly
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* if a PRNG is given, or try numbers around N/2 */
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if( f_rng != NULL )
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{
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MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &K,
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mbedtls_mpi_size( N ),
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f_rng, p_rng ) );
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}
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else
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{
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MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &K, 1 ) ) ;
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MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &K, bitlen_half ) ) ;
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, attempt + 1 ) );
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}
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/* Check if gcd(K,N) = 1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
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if( mbedtls_mpi_cmp_int( P, 1 ) != 0 )
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continue;
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/* Go through K^X + 1, K^(2X) + 1, K^(4X) + 1, ...
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* and check whether they have nontrivial GCD with N. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, D, N,
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Q /* temporarily use Q for storing Montgomery
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* multiplication helper values */ ) );
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for( iter = 1; iter < order; ++iter )
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{
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
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if( mbedtls_mpi_cmp_int( P, 1 ) == 1 &&
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mbedtls_mpi_cmp_mpi( P, N ) == -1 )
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{
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/*
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* Have found a nontrivial divisor P of N.
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* Set Q := N / P and verify D, E.
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*/
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MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, &K, N, P ) );
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/*
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* Verify that DE - 1 is indeed a multiple of
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* lcm(P-1, Q-1), i.e. that it's a multiple of both
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* P-1 and Q-1.
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*/
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/* Restore DE - 1 and temporarily replace P, Q by P-1, Q-1. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( D, order ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( P, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( Q, Q, 1 ) );
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/* Compute DE-1 mod P-1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, D, P ) );
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if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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goto cleanup;
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}
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/* Compute DE-1 mod Q-1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, D, Q ) );
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if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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goto cleanup;
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}
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/*
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* All good, restore P, Q and D and return.
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*/
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( P, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( Q, Q, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( D, D, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( D, NULL, D, E ) );
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goto cleanup;
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}
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) );
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}
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}
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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cleanup:
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mbedtls_mpi_free( &K );
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return( ret );
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}
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/*
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* Given P, Q and the public exponent E, deduce D.
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* This is essentially a modular inversion.
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*/
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int mbedtls_rsa_deduce_private( mbedtls_mpi *P, mbedtls_mpi *Q,
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mbedtls_mpi *D, mbedtls_mpi *E )
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{
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int ret = 0;
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mbedtls_mpi K;
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if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 )
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return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
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mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ||
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mbedtls_mpi_cmp_int( E, 0 ) == 0 )
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{
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return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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}
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mbedtls_mpi_init( &K );
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/* Temporarily replace P and Q by P-1 and Q-1, respectively. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( P, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( Q, Q, 1 ) );
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/* Temporarily compute the gcd(P-1, Q-1) in D. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, P, Q ) );
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/* Compute LCM(P-1, Q-1) in K */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) );
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/* Compute modular inverse of E in LCM(P-1, Q-1) */
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MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) );
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/* Restore P and Q. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( P, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( Q, Q, 1 ) );
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/* Double-check result */
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MBEDTLS_MPI_CHK( mbedtls_rsa_check_params( NULL, P, Q, D, E, NULL, NULL ) );
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cleanup:
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mbedtls_mpi_free( &K );
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return( ret );
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}
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/*
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* Check that core RSA parameters are sane.
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*
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* Note that the inputs are not declared const and may be
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* altered on an unsuccessful run.
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*/
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int mbedtls_rsa_check_params( mbedtls_mpi *N, mbedtls_mpi *P, mbedtls_mpi *Q,
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mbedtls_mpi *D, mbedtls_mpi *E,
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int (*f_rng)(void *, unsigned char *, size_t),
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void *p_rng )
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{
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int ret = 0;
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mbedtls_mpi K;
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mbedtls_mpi_init( &K );
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/*
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* Step 1: If PRNG provided, check that P and Q are prime
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*/
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if( f_rng != NULL && P != NULL &&
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( ret = mbedtls_mpi_is_prime( P, f_rng, p_rng ) ) != 0 )
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{
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goto cleanup;
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}
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if( f_rng != NULL && Q != NULL &&
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( ret = mbedtls_mpi_is_prime( Q, f_rng, p_rng ) ) != 0 )
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{
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goto cleanup;
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}
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/*
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* Step 2: Check that N = PQ
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*/
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if( P != NULL && Q != NULL && N != NULL )
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{
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );
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if( mbedtls_mpi_cmp_mpi( &K, N ) != 0 )
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{
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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goto cleanup;
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}
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}
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/*
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* Step 3: Check that D, E are inverse modulo P-1 and Q-1
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*/
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if( P != NULL && Q != NULL && D != NULL && E != NULL )
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{
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/* Temporarily replace P, Q by P-1, Q-1. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( P, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( Q, Q, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
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/* Compute DE-1 mod P-1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) );
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if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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goto cleanup;
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}
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/* Compute DE-1 mod Q-1 */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, Q ) );
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if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
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{
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ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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goto cleanup;
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}
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/* Restore P, Q. */
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( P, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( Q, Q, 1 ) );
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}
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cleanup:
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mbedtls_mpi_free( &K );
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return( ret );
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}
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int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
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const mbedtls_mpi *D, mbedtls_mpi *DP,
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mbedtls_mpi *DQ, mbedtls_mpi *QP )
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{
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int ret = 0;
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mbedtls_mpi K;
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mbedtls_mpi_init( &K );
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if( DP != NULL )
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{
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) );
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}
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if( DQ != NULL )
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{
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MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) );
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}
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if( QP != NULL )
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{
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MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) );
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}
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cleanup:
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mbedtls_mpi_free( &K );
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return( ret );
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}
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{
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int ret = 0;
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cleanup:
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return( ret );
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}
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/*
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* Initialize an RSA context
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*/
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