/* rsa.c - RSA function
* Copyright (C) 1997, 1998, 1999 by Werner Koch (dd9jn)
* Copyright (C) 2000, 2001 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* GnuPG is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
/* This code uses an algorithm protected by U.S. Patent #4,405,829
which expires on September 20, 2000. The patent holder placed that
patent into the public domain on Sep 6th, 2000.
*/
#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "util.h"
#include "mpi.h"
#include "cipher.h"
#include "rsa.h"
typedef struct {
MPI n; /* modulus */
MPI e; /* exponent */
} RSA_public_key;
typedef struct {
MPI n; /* public modulus */
MPI e; /* public exponent */
MPI d; /* exponent */
MPI p; /* prime p. */
MPI q; /* prime q. */
MPI u; /* inverse of p mod q. */
} RSA_secret_key;
static void test_keys( RSA_secret_key *sk, unsigned nbits );
static void generate( RSA_secret_key *sk, unsigned nbits );
static int check_secret_key( RSA_secret_key *sk );
static void public(MPI output, MPI input, RSA_public_key *skey );
static void secret(MPI output, MPI input, RSA_secret_key *skey );
static void
test_keys( RSA_secret_key *sk, unsigned nbits )
{
RSA_public_key pk;
MPI test = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
MPI out1 = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
MPI out2 = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
pk.n = sk->n;
pk.e = sk->e;
{ char *p = get_random_bits( nbits, 0, 0 );
mpi_set_buffer( test, p, (nbits+7)/8, 0 );
m_free(p);
}
public( out1, test, &pk );
secret( out2, out1, sk );
if( mpi_cmp( test, out2 ) )
log_fatal("RSA operation: public, secret failed\n");
secret( out1, test, sk );
public( out2, out1, &pk );
if( mpi_cmp( test, out2 ) )
log_fatal("RSA operation: secret, public failed\n");
mpi_free( test );
mpi_free( out1 );
mpi_free( out2 );
}
/****************
* Generate a key pair with a key of size NBITS
* Returns: 2 structures filled with all needed values
*/
static void
generate( RSA_secret_key *sk, unsigned nbits )
{
MPI p, q; /* the two primes */
MPI d; /* the private key */
MPI u;
MPI t1, t2;
MPI n; /* the public key */
MPI e; /* the exponent */
MPI phi; /* helper: (p-1)(q-1) */
MPI g;
MPI f;
/* make sure that nbits is even so that we generate p, q of equal size */
if ( (nbits&1) )
nbits++;
n = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
p = q = NULL;
do {
/* select two (very secret) primes */
if (p)
mpi_free (p);
if (q)
mpi_free (q);
p = generate_secret_prime( nbits / 2 );
q = generate_secret_prime( nbits / 2 );
if( mpi_cmp( p, q ) > 0 ) /* p shall be smaller than q (for calc of u)*/
mpi_swap(p,q);
/* calculate the modulus */
mpi_mul( n, p, q );
} while ( mpi_get_nbits(n) != nbits );
/* calculate Euler totient: phi = (p-1)(q-1) */
t1 = mpi_alloc_secure( mpi_get_nlimbs(p) );
t2 = mpi_alloc_secure( mpi_get_nlimbs(p) );
phi = mpi_alloc_secure( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
g = mpi_alloc_secure( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
f = mpi_alloc_secure( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
mpi_sub_ui( t1, p, 1 );
mpi_sub_ui( t2, q, 1 );
mpi_mul( phi, t1, t2 );
mpi_gcd(g, t1, t2);
mpi_fdiv_q(f, phi, g);
/* find an public exponent.
We use 41 as this is quite fast and more secure than the
commonly used 17. Benchmarking the RSA verify function
with a 1024 bit key yields (2001-11-08):
e=17 0.54 ms
e=41 0.75 ms
e=257 0.95 ms
e=65537 1.80 ms
*/
e = mpi_alloc( (32+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
mpi_set_ui( e, 41);
if( !mpi_gcd(t1, e, phi) ) {
mpi_set_ui( e, 257);
if( !mpi_gcd(t1, e, phi) ) {
mpi_set_ui( e, 65537);
while( !mpi_gcd(t1, e, phi) ) /* (while gcd is not 1) */
mpi_add_ui( e, e, 2);
}
}
/* calculate the secret key d = e^1 mod phi */
d = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
mpi_invm(d, e, f );
/* calculate the inverse of p and q (used for chinese remainder theorem)*/
u = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
mpi_invm(u, p, q );
if( DBG_CIPHER ) {
log_mpidump(" p= ", p );
log_mpidump(" q= ", q );
log_mpidump("phi= ", phi );
log_mpidump(" g= ", g );
log_mpidump(" f= ", f );
log_mpidump(" n= ", n );
log_mpidump(" e= ", e );
log_mpidump(" d= ", d );
log_mpidump(" u= ", u );
}
mpi_free(t1);
mpi_free(t2);
mpi_free(phi);
mpi_free(f);
mpi_free(g);
sk->n = n;
sk->e = e;
sk->p = p;
sk->q = q;
sk->d = d;
sk->u = u;
/* now we can test our keys (this should never fail!) */
test_keys( sk, nbits - 64 );
}
/****************
* Test wether the secret key is valid.
* Returns: true if this is a valid key.
*/
static int
check_secret_key( RSA_secret_key *sk )
{
int rc;
MPI temp = mpi_alloc( mpi_get_nlimbs(sk->p)*2 );
mpi_mul(temp, sk->p, sk->q );
rc = mpi_cmp( temp, sk->n );
mpi_free(temp);
return !rc;
}
/****************
* Public key operation. Encrypt INPUT with PKEY and put result into OUTPUT.
*
* c = m^e mod n
*
* Where c is OUTPUT, m is INPUT and e,n are elements of PKEY.
*/
static void
public(MPI output, MPI input, RSA_public_key *pkey )
{
if( output == input ) { /* powm doesn't like output and input the same */
MPI x = mpi_alloc( mpi_get_nlimbs(input)*2 );
mpi_powm( x, input, pkey->e, pkey->n );
mpi_set(output, x);
mpi_free(x);
}
else
mpi_powm( output, input, pkey->e, pkey->n );
}
#if 0
static void
stronger_key_check ( RSA_secret_key *skey )
{
MPI t = mpi_alloc_secure ( 0 );
MPI t1 = mpi_alloc_secure ( 0 );
MPI t2 = mpi_alloc_secure ( 0 );
MPI phi = mpi_alloc_secure ( 0 );
/* check that n == p * q */
mpi_mul( t, skey->p, skey->q);
if (mpi_cmp( t, skey->n) )
log_info ( "RSA Oops: n != p * q\n" );
/* check that p is less than q */
if( mpi_cmp( skey->p, skey->q ) > 0 )
log_info ("RSA Oops: p >= q\n");
/* check that e divides neither p-1 nor q-1 */
mpi_sub_ui(t, skey->p, 1 );
mpi_fdiv_r(t, t, skey->e );
if ( !mpi_cmp_ui( t, 0) )
log_info ( "RSA Oops: e divides p-1\n" );
mpi_sub_ui(t, skey->q, 1 );
mpi_fdiv_r(t, t, skey->e );
if ( !mpi_cmp_ui( t, 0) )
log_info ( "RSA Oops: e divides q-1\n" );
/* check that d is correct */
mpi_sub_ui( t1, skey->p, 1 );
mpi_sub_ui( t2, skey->q, 1 );
mpi_mul( phi, t1, t2 );
mpi_gcd(t, t1, t2);
mpi_fdiv_q(t, phi, t);
mpi_invm(t, skey->e, t );
if ( mpi_cmp(t, skey->d ) )
log_info ( "RSA Oops: d is wrong\n");
/* check for crrectness of u */
mpi_invm(t, skey->p, skey->q );
if ( mpi_cmp(t, skey->u ) )
log_info ( "RSA Oops: u is wrong\n");
log_info ( "RSA secret key check finished\n");
mpi_free (t);
mpi_free (t1);
mpi_free (t2);
mpi_free (phi);
}
#endif
/****************
* Secret key operation. Encrypt INPUT with SKEY and put result into OUTPUT.
*
* m = c^d mod n
*
* Or faster:
*
* m1 = c ^ (d mod (p-1)) mod p
* m2 = c ^ (d mod (q-1)) mod q
* h = u * (m2 - m1) mod q
* m = m1 + h * p
*
* Where m is OUTPUT, c is INPUT and d,n,p,q,u are elements of SKEY.
*/
static void
secret(MPI output, MPI input, RSA_secret_key *skey )
{
#if 0
mpi_powm( output, input, skey->d, skey->n );
#else
MPI m1 = mpi_alloc_secure( mpi_get_nlimbs(skey->n)+1 );
MPI m2 = mpi_alloc_secure( mpi_get_nlimbs(skey->n)+1 );
MPI h = mpi_alloc_secure( mpi_get_nlimbs(skey->n)+1 );
/* m1 = c ^ (d mod (p-1)) mod p */
mpi_sub_ui( h, skey->p, 1 );
mpi_fdiv_r( h, skey->d, h );
mpi_powm( m1, input, h, skey->p );
/* m2 = c ^ (d mod (q-1)) mod q */
mpi_sub_ui( h, skey->q, 1 );
mpi_fdiv_r( h, skey->d, h );
mpi_powm( m2, input, h, skey->q );
/* h = u * ( m2 - m1 ) mod q */
mpi_sub( h, m2, m1 );
if ( mpi_is_neg( h ) )
mpi_add ( h, h, skey->q );
mpi_mulm( h, skey->u, h, skey->q );
/* m = m2 + h * p */
mpi_mul ( h, h, skey->p );
mpi_add ( output, m1, h );
/* ready */
mpi_free ( h );
mpi_free ( m1 );
mpi_free ( m2 );
#endif
}
/*********************************************
************** interface ******************
*********************************************/
int
rsa_generate( int algo, unsigned nbits, MPI *skey, MPI **retfactors )
{
RSA_secret_key sk;
if( !is_RSA(algo) )
return G10ERR_PUBKEY_ALGO;
generate( &sk, nbits );
skey[0] = sk.n;
skey[1] = sk.e;
skey[2] = sk.d;
skey[3] = sk.p;
skey[4] = sk.q;
skey[5] = sk.u;
/* make an empty list of factors */
*retfactors = m_alloc_clear( 1 * sizeof **retfactors );
return 0;
}
int
rsa_check_secret_key( int algo, MPI *skey )
{
RSA_secret_key sk;
if( !is_RSA(algo) )
return G10ERR_PUBKEY_ALGO;
sk.n = skey[0];
sk.e = skey[1];
sk.d = skey[2];
sk.p = skey[3];
sk.q = skey[4];
sk.u = skey[5];
if( !check_secret_key( &sk ) )
return G10ERR_BAD_SECKEY;
return 0;
}
int
rsa_encrypt( int algo, MPI *resarr, MPI data, MPI *pkey )
{
RSA_public_key pk;
if( algo != 1 && algo != 2 )
return G10ERR_PUBKEY_ALGO;
pk.n = pkey[0];
pk.e = pkey[1];
resarr[0] = mpi_alloc( mpi_get_nlimbs( pk.n ) );
public( resarr[0], data, &pk );
return 0;
}
int
rsa_decrypt( int algo, MPI *result, MPI *data, MPI *skey )
{
RSA_secret_key sk;
if( algo != 1 && algo != 2 )
return G10ERR_PUBKEY_ALGO;
sk.n = skey[0];
sk.e = skey[1];
sk.d = skey[2];
sk.p = skey[3];
sk.q = skey[4];
sk.u = skey[5];
*result = mpi_alloc_secure( mpi_get_nlimbs( sk.n ) );
secret( *result, data[0], &sk );
return 0;
}
int
rsa_sign( int algo, MPI *resarr, MPI data, MPI *skey )
{
RSA_secret_key sk;
if( algo != 1 && algo != 3 )
return G10ERR_PUBKEY_ALGO;
sk.n = skey[0];
sk.e = skey[1];
sk.d = skey[2];
sk.p = skey[3];
sk.q = skey[4];
sk.u = skey[5];
resarr[0] = mpi_alloc( mpi_get_nlimbs( sk.n ) );
secret( resarr[0], data, &sk );
return 0;
}
int
rsa_verify( int algo, MPI hash, MPI *data, MPI *pkey,
int (*cmp)(void *opaque, MPI tmp), void *opaquev )
{
RSA_public_key pk;
MPI result;
int rc;
if( algo != 1 && algo != 3 )
return G10ERR_PUBKEY_ALGO;
pk.n = pkey[0];
pk.e = pkey[1];
result = mpi_alloc( (160+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB);
public( result, data[0], &pk );
/*rc = (*cmp)( opaquev, result );*/
rc = mpi_cmp( result, hash )? G10ERR_BAD_SIGN:0;
mpi_free(result);
return rc;
}
unsigned int
rsa_get_nbits( int algo, MPI *pkey )
{
if( !is_RSA(algo) )
return 0;
return mpi_get_nbits( pkey[0] );
}
/****************
* Return some information about the algorithm. We need algo here to
* distinguish different flavors of the algorithm.
* Returns: A pointer to string describing the algorithm or NULL if
* the ALGO is invalid.
* Usage: Bit 0 set : allows signing
* 1 set : allows encryption
*/
const char *
rsa_get_info( int algo,
int *npkey, int *nskey, int *nenc, int *nsig, int *r_usage )
{
*npkey = 2;
*nskey = 6;
*nenc = 1;
*nsig = 1;
switch( algo ) {
case 1: *r_usage = PUBKEY_USAGE_SIG | PUBKEY_USAGE_ENC; return "RSA";
case 2: *r_usage = PUBKEY_USAGE_ENC; return "RSA-E";
case 3: *r_usage = PUBKEY_USAGE_SIG; return "RSA-S";
default:*r_usage = 0; return NULL;
}
}