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eucrypt_ch5_rsa_keys    1 /*
eucrypt_ch5_rsa_keys    2  * An implementation of TMSR RSA
eucrypt_ch5_rsa_keys    3  * S.MG, 2018
eucrypt_ch5_rsa_keys    4  */
eucrypt_ch5_rsa_keys    5 
eucrypt_ch5_rsa_keys    6 #include "smg_rsa.h"
eucrypt_ch5_rsa_keys    7 #include <assert.h>
eucrypt_ch5_rsa_keys    8 
eucrypt_ch5_rsa_keys    9 void gen_keypair( RSA_secret_key *sk ) {
eucrypt_ch5_rsa_keys   10 	/* precondition: sk is not null */
eucrypt_ch5_rsa_keys   11 	assert(sk != NULL);
eucrypt_ch5_rsa_keys   12 
eucrypt_ch5_rsa_keys   13 	/* precondition: enough memory allocated, corresponding to key size */
eucrypt_ch5_rsa_keys   14 	int noctets_pq = KEY_LENGTH_OCTETS / 2;
eucrypt_ch5_rsa_keys   15 	unsigned int nlimbs_pq = mpi_nlimb_hint_from_nbytes( noctets_pq);
eucrypt_ch5_rsa_keys   16 	unsigned int nlimbs_n = mpi_nlimb_hint_from_nbytes( KEY_LENGTH_OCTETS);
eucrypt_ch5_rsa_keys   17 	assert( mpi_get_alloced( sk->n) >= nlimbs_n);
eucrypt_ch5_rsa_keys   18 	assert( mpi_get_alloced( sk->p) >= nlimbs_pq);
eucrypt_ch5_rsa_keys   19 	assert( mpi_get_alloced( sk->q) >= nlimbs_pq);
eucrypt_ch5_rsa_keys   20 
eucrypt_ch5_rsa_keys   21 	/* helper variables for calculating Euler's totient phi=(p-1)*(q-1) */
eucrypt_ch5_rsa_keys   22 	MPI p_minus1 = mpi_alloc(nlimbs_pq);
eucrypt_ch5_rsa_keys   23 	MPI q_minus1 = mpi_alloc(nlimbs_pq);
eucrypt_ch5_rsa_keys   24 	MPI phi = mpi_alloc(nlimbs_n);
eucrypt_ch5_rsa_keys   25 
eucrypt_ch5_rsa_keys   26 	/* generate 2 random primes, p and q*/
eucrypt_ch5_rsa_keys   27 	/* gen_random_prime sets top 2 bits to 1 so p*q will have KEY_LENGTH bits */
eucrypt_ch5_rsa_keys   28 	/* in the extremely unlikely case that p = q, discard and generate again */
eucrypt_ch5_rsa_keys   29 	do {
eucrypt_ch5_rsa_keys   30 		gen_random_prime( noctets_pq, sk->p);
eucrypt_ch5_rsa_keys   31 		gen_random_prime( noctets_pq, sk->q);
eucrypt_ch5_rsa_keys   32 	} while ( mpi_cmp( sk->p, sk->q) == 0);
eucrypt_ch5_rsa_keys   33 
eucrypt_ch5_rsa_keys   34 	/* swap if needed, to ensure p < q for calculating u */
eucrypt_ch5_rsa_keys   35 	if ( mpi_cmp( sk->p, sk->q) > 0)
eucrypt_ch5_rsa_keys   36 		mpi_swap( sk->p, sk->q);
eucrypt_ch5_rsa_keys   37 
eucrypt_ch5_rsa_keys   38 	/* calculate helper for Chinese Remainder Theorem:
eucrypt_ch5_rsa_keys   39 			u = p ^ -1 ( mod q )
eucrypt_ch5_rsa_keys   40 		 this is used to speed-up decryption.
eucrypt_ch5_rsa_keys   41 	*/
eucrypt_ch5_rsa_keys   42 	mpi_invm( sk->u, sk->p, sk->q);
eucrypt_ch5_rsa_keys   43 
eucrypt_ch5_rsa_keys   44 	/* calculate modulus n = p * q */
eucrypt_ch5_rsa_keys   45 	mpi_mul( sk->n, sk->p, sk->q);
eucrypt_ch5_rsa_keys   46 
eucrypt_ch5_rsa_keys   47 	/* calculate Euler totient: phi = (p-1)*(q-1) */
eucrypt_ch5_rsa_keys   48 	mpi_sub_ui( p_minus1, sk->p, 1);
eucrypt_ch5_rsa_keys   49 	mpi_sub_ui( q_minus1, sk->q, 1);
eucrypt_ch5_rsa_keys   50 	mpi_mul( phi, p_minus1, q_minus1);
eucrypt_ch5_rsa_keys   51 
eucrypt_ch5_rsa_keys   52 	/* choose random prime e, public exponent, with 3 < e < phi */
eucrypt_ch5_rsa_keys   53 	/* because e is prime, gcd(e, phi) is always 1 so no need to check it */
eucrypt_ch5_rsa_keys   54 	do {
eucrypt_ch5_rsa_keys   55 		gen_random_prime( noctets_pq, sk->e);
eucrypt_ch5_rsa_keys   56 	} while ( (mpi_cmp_ui(sk->e, 3) < 0) || (mpi_cmp(sk->e, phi) > 0));
eucrypt_ch5_rsa_keys   57 
eucrypt_ch5_rsa_keys   58 	/* calculate private exponent d, 1 < d < phi, where e * d = 1 mod phi */
eucrypt_ch5_rsa_keys   59 	mpi_invm( sk->d, sk->e, phi);
eucrypt_ch5_rsa_keys   60 
eucrypt_ch5_rsa_keys   61 	/*	tidy up: free locally allocated memory for helper variables */
eucrypt_ch5_rsa_keys   62 	mpi_free(phi);
eucrypt_ch5_rsa_keys   63 	mpi_free(p_minus1);
eucrypt_ch5_rsa_keys   64 	mpi_free(q_minus1);
eucrypt_ch5_rsa_keys   65 }
eucrypt_ch5_rsa_keys   66 
eucrypt_ch5_rsa_keys   67 void public_rsa( MPI output, MPI input, RSA_public_key *pk ) {
eucrypt_ch5_rsa_keys   68 
eucrypt_ch5_rsa_keys   69 	/* mpi_powm can't handle output and input being same */
eucrypt_ch5_rsa_keys   70 	assert (output != input);
eucrypt_ch5_rsa_keys   71 
eucrypt_ch5_rsa_keys   72 	mpi_powm( output, input, pk->e, pk->n );
eucrypt_ch5_rsa_keys   73 }
eucrypt_ch5_rsa_keys   74 
eucrypt_ch5_rsa_keys   75 void secret_rsa( MPI output, MPI input, RSA_secret_key *skey ) {
eucrypt_ch5_rsa_keys   76 	/* at its simplest, this would be input ^ d (mod n), hence:
eucrypt_ch5_rsa_keys   77 	 *    mpi_powm( output, input, skey->d, skey->n );
eucrypt_ch5_rsa_keys   78 	 * for faster decryption though, we'll use CRT and Garner's algorithm, hence:
eucrypt_ch5_rsa_keys   79 	 *        u = p ^ (-1) (mod q) , already calculated and stored in skey
eucrypt_ch5_rsa_keys   80 	 *       dp = d mod (p-1)
eucrypt_ch5_rsa_keys   81 	 *       dq = d mod (q-1)
eucrypt_ch5_rsa_keys   82 	 *       m1 = input ^ dp (mod p)
eucrypt_ch5_rsa_keys   83 	 *       m2 = input ^ dq (mod q)
eucrypt_ch5_rsa_keys   84 	 *        h = u * (m2 - m1) mod q
eucrypt_ch5_rsa_keys   85 	 *   output = m1 + h * p
eucrypt_ch5_rsa_keys   86    * Note that same CRT speed up isn't available for encryption because at 
eucrypt_ch5_rsa_keys   87 encryption time not enough information is available (only e and n are known).
eucrypt_ch5_rsa_keys   88 	 */
eucrypt_ch5_rsa_keys   89 
eucrypt_ch5_rsa_keys   90 	/* allocate memory for all local, helper MPIs */
eucrypt_ch5_rsa_keys   91 	MPI p_minus1 = mpi_alloc( mpi_get_nlimbs( skey->p) );
eucrypt_ch5_rsa_keys   92 	MPI q_minus1 = mpi_alloc( mpi_get_nlimbs( skey->q) );
eucrypt_ch5_rsa_keys   93 	int nlimbs   = mpi_get_nlimbs( skey->n ) + 1;
eucrypt_ch5_rsa_keys   94 	MPI dp       = mpi_alloc( nlimbs );
eucrypt_ch5_rsa_keys   95 	MPI dq       = mpi_alloc( nlimbs );
eucrypt_ch5_rsa_keys   96 	MPI m1       = mpi_alloc( nlimbs );
eucrypt_ch5_rsa_keys   97 	MPI m2       = mpi_alloc( nlimbs );
eucrypt_ch5_rsa_keys   98 	MPI h        = mpi_alloc( nlimbs );
eucrypt_ch5_rsa_keys   99 
eucrypt_ch5_rsa_keys  100 	/* p_minus1 = p - 1 */
eucrypt_ch5_rsa_keys  101 	mpi_sub_ui( p_minus1, skey->p, 1 );
eucrypt_ch5_rsa_keys  102 
eucrypt_ch5_rsa_keys  103 	/* dp = d mod (p - 1) aka remainder of d / (p - 1) */
eucrypt_ch5_rsa_keys  104 	mpi_fdiv_r( dp, skey->d, p_minus1 );
eucrypt_ch5_rsa_keys  105 
eucrypt_ch5_rsa_keys  106 	/* m1 = input ^ dp (mod p) */
eucrypt_ch5_rsa_keys  107 	mpi_powm( m1, input, dp, skey->p );
eucrypt_ch5_rsa_keys  108 
eucrypt_ch5_rsa_keys  109 	/* q_minus1 = q - 1 */
eucrypt_ch5_rsa_keys  110 	mpi_sub_ui( q_minus1, skey->q, 1 );
eucrypt_ch5_rsa_keys  111 
eucrypt_ch5_rsa_keys  112 	/* dq = d mod (q - 1) aka remainder of d / (q - 1) */
eucrypt_ch5_rsa_keys  113 	mpi_fdiv_r( dq, skey->d, q_minus1 );
eucrypt_ch5_rsa_keys  114 
eucrypt_ch5_rsa_keys  115 	/* m2 = input ^ dq (mod q) */
eucrypt_ch5_rsa_keys  116 	mpi_powm( m2, input, dq, skey->q );
eucrypt_ch5_rsa_keys  117 
eucrypt_ch5_rsa_keys  118 	/* h = u * ( m2 - m1 ) mod q */
eucrypt_ch5_rsa_keys  119 	mpi_sub( h, m2, m1 );
eucrypt_ch5_rsa_keys  120 	if ( mpi_is_neg( h ) )
eucrypt_ch5_rsa_keys  121 		mpi_add ( h, h, skey->q );
eucrypt_ch5_rsa_keys  122 	mpi_mulm( h, skey->u, h, skey->q );
eucrypt_ch5_rsa_keys  123 
eucrypt_ch5_rsa_keys  124 	/* output = m1 + h * p */
eucrypt_ch5_rsa_keys  125 	mpi_mul ( h, h, skey->p );
eucrypt_ch5_rsa_keys  126 	mpi_add ( output, m1, h );
eucrypt_ch5_rsa_keys  127 
eucrypt_ch5_rsa_keys  128 	/* tidy up */
eucrypt_ch5_rsa_keys  129 	mpi_free ( p_minus1 );
eucrypt_ch5_rsa_keys  130 	mpi_free ( q_minus1 );
eucrypt_ch5_rsa_keys  131 	mpi_free ( dp );
eucrypt_ch5_rsa_keys  132 	mpi_free ( dq );
eucrypt_ch5_rsa_keys  133 	mpi_free ( m1 );
eucrypt_ch5_rsa_keys  134 	mpi_free ( m2 );
eucrypt_ch5_rsa_keys  135 	mpi_free ( h );
eucrypt_ch5_rsa_keys  136 
eucrypt_ch5_rsa_keys  137 }
eucrypt_ch5_rsa_keys  138