/****************
* We do not need to use the strongest RNG because we gain no extra
* security from it - The prime number is public and we could also
* offer the factors for those who are willing to check that it is
* indeed a strong prime. With ALL_FACTORS set to true all afcors of
* prime-1 are returned in FACTORS.
*
* mode 0: Standard
* 1: Make sure that at least one factor is of size qbits.
*/
static gcry_err_code_t
prime_generate_internal (int mode,
gcry_mpi_t *prime_generated, unsigned int pbits,
unsigned int qbits, gcry_mpi_t g,
gcry_mpi_t **ret_factors,
gcry_random_level_t randomlevel, unsigned int flags,
int all_factors,
gcry_prime_check_func_t cb_func, void *cb_arg)
{
gcry_err_code_t err = 0;
gcry_mpi_t *factors_new = NULL; /* Factors to return to the
caller. */
gcry_mpi_t *factors = NULL; /* Current factors. */
gcry_mpi_t *pool = NULL; /* Pool of primes. */
unsigned char *perms = NULL; /* Permutations of POOL. */
gcry_mpi_t q_factor = NULL; /* Used if QBITS is non-zero. */
unsigned int fbits = 0; /* Length of prime factors. */
unsigned int n = 0; /* Number of factors. */
unsigned int m = 0; /* Number of primes in pool. */
gcry_mpi_t q = NULL; /* First prime factor. */
gcry_mpi_t prime = NULL; /* Prime candidate. */
unsigned int nprime = 0; /* Bits of PRIME. */
unsigned int req_qbits; /* The original QBITS value. */
gcry_mpi_t val_2; /* For check_prime(). */
unsigned int is_secret = (flags & GCRY_PRIME_FLAG_SECRET);
unsigned int count1 = 0, count2 = 0;
unsigned int i = 0, j = 0;
if (pbits < 48)
return GPG_ERR_INV_ARG;
/* If QBITS is not given, assume a reasonable value. */
if (!qbits)
qbits = pbits / 3;
req_qbits = qbits;
/* Find number of needed prime factors. */
for (n = 1; (pbits - qbits - 1) / n >= qbits; n++)
;
n--;
val_2 = mpi_alloc_set_ui (2);
if ((! n) || ((mode == 1) && (n < 2)))
{
err = GPG_ERR_INV_ARG;
goto leave;
}
if (mode == 1)
{
n--;
fbits = (pbits - 2 * req_qbits -1) / n;
qbits = pbits - req_qbits - n * fbits;
}
else
{
fbits = (pbits - req_qbits -1) / n;
qbits = pbits - n * fbits;
}
if (DBG_CIPHER)
log_debug ("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n",
pbits, req_qbits, qbits, fbits, n);
prime = gcry_mpi_new (pbits);
/* Generate first prime factor. */
q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL);
if (mode == 1)
q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL);
/* Allocate an array to hold the factors + 2 for later usage. */
factors = gcry_calloc (n + 2, sizeof (*factors));
if (!factors)
{
err = gpg_err_code_from_errno (errno);
goto leave;
}
/* Make a pool of 3n+5 primes (this is an arbitrary value). */
m = n * 3 + 5;
if (mode == 1) /* Need some more (for e.g. DSA). */
m += 5;
if (m < 25)
m = 25;
pool = gcry_calloc (m , sizeof (*pool));
if (! pool)
{
err = gpg_err_code_from_errno (errno);
goto leave;
}
/* Permutate over the pool of primes. */
do
{
next_try:
if (! perms)
{
/* Allocate new primes. */
for(i = 0; i < m; i++)
{
mpi_free (pool[i]);
pool[i] = NULL;
}
/* Init m_out_of_n(). */
perms = gcry_calloc (1, m);
if (! perms)
{
err = gpg_err_code_from_errno (errno);
goto leave;
}
for(i = 0; i < n; i++)
{
perms[i] = 1;
pool[i] = gen_prime (fbits, is_secret,
randomlevel, NULL, NULL);
factors[i] = pool[i];
}
}
else
{
m_out_of_n ((char*)perms, n, m);
for (i = j = 0; (i < m) && (j < n); i++)
if (perms[i])
{
if(! pool[i])
pool[i] = gen_prime (fbits, 0, 1, NULL, NULL);
factors[j++] = pool[i];
}
if (i == n)
{
gcry_free (perms);
perms = NULL;
progress ('!');
goto next_try; /* Allocate new primes. */
}
}
/* Generate next prime candidate:
p = 2 * q [ * q_factor] * factor_0 * factor_1 * ... * factor_n + 1.
*/
mpi_set (prime, q);
mpi_mul_ui (prime, prime, 2);
if (mode == 1)
mpi_mul (prime, prime, q_factor);
for(i = 0; i < n; i++)
mpi_mul (prime, prime, factors[i]);
mpi_add_ui (prime, prime, 1);
nprime = mpi_get_nbits (prime);
if (nprime < pbits)
{
if (++count1 > 20)
{
count1 = 0;
qbits++;
progress('>');
mpi_free (q);
q = gen_prime (qbits, 0, 0, NULL, NULL);
goto next_try;
}
}
else
count1 = 0;
if (nprime > pbits)
{
if (++count2 > 20)
{
count2 = 0;
qbits--;
progress('<');
mpi_free (q);
q = gen_prime (qbits, 0, 0, NULL, NULL);
goto next_try;
}
}
else
count2 = 0;
}
while (! ((nprime == pbits) && check_prime (prime, val_2, cb_func, cb_arg)));
if (DBG_CIPHER)
{
progress ('\n');
log_mpidump ("prime : ", prime);
log_mpidump ("factor q: ", q);
if (mode == 1)
log_mpidump ("factor q0: ", q_factor);
for (i = 0; i < n; i++)
log_mpidump ("factor pi: ", factors[i]);
log_debug ("bit sizes: prime=%u, q=%u",
mpi_get_nbits (prime), mpi_get_nbits (q));
if (mode == 1)
log_debug (", q0=%u", mpi_get_nbits (q_factor));
for (i = 0; i < n; i++)
log_debug (", p%d=%u", i, mpi_get_nbits (factors[i]));
progress('\n');
}
if (ret_factors)
{
/* Caller wants the factors. */
factors_new = gcry_calloc (n + 4, sizeof (*factors_new));
if (! factors_new)
{
err = gpg_err_code_from_errno (errno);
goto leave;
}
if (all_factors)
{
i = 0;
factors_new[i++] = gcry_mpi_set_ui (NULL, 2);
factors_new[i++] = mpi_copy (q);
if (mode == 1)
factors_new[i++] = mpi_copy (q_factor);
for(j=0; j < n; j++)
factors_new[i++] = mpi_copy (factors[j]);
}
else
{
i = 0;
if (mode == 1)
{
factors_new[i++] = mpi_copy (q_factor);
for (; i <= n; i++)
factors_new[i] = mpi_copy (factors[i]);
}
else
for (; i < n; i++ )
factors_new[i] = mpi_copy (factors[i]);
}
}
if (g)
{
/* Create a generator (start with 3). */
gcry_mpi_t tmp = mpi_alloc (mpi_get_nlimbs (prime));
gcry_mpi_t b = mpi_alloc (mpi_get_nlimbs (prime));
gcry_mpi_t pmin1 = mpi_alloc (mpi_get_nlimbs (prime));
if (mode == 1)
err = GPG_ERR_NOT_IMPLEMENTED;
else
{
factors[n] = q;
factors[n + 1] = mpi_alloc_set_ui (2);
mpi_sub_ui (pmin1, prime, 1);
mpi_set_ui (g, 2);
do
{
mpi_add_ui (g, g, 1);
if (DBG_CIPHER)
{
log_debug ("checking g:");
gcry_mpi_dump (g);
log_printf ("\n");
}
else
progress('^');
for (i = 0; i < n + 2; i++)
{
mpi_fdiv_q (tmp, pmin1, factors[i]);
/* No mpi_pow(), but it is okay to use this with mod
prime. */
gcry_mpi_powm (b, g, tmp, prime);
if (! mpi_cmp_ui (b, 1))
break;
}
if (DBG_CIPHER)
progress('\n');
}
while (i < n + 2);
mpi_free (factors[n+1]);
mpi_free (tmp);
mpi_free (b);
mpi_free (pmin1);
}
}
if (! DBG_CIPHER)
progress ('\n');
leave:
if (pool)
{
for(i = 0; i < m; i++)
mpi_free (pool[i]);
gcry_free (pool);
}
if (factors)
gcry_free (factors); /* Factors are shallow copies. */
if (perms)
gcry_free (perms);
mpi_free (val_2);
mpi_free (q);
mpi_free (q_factor);
if (! err)
{
*prime_generated = prime;
if (ret_factors)
*ret_factors = factors_new;
}
else
{
if (factors_new)
{
for (i = 0; factors_new[i]; i++)
mpi_free (factors_new[i]);
gcry_free (factors_new);
}
mpi_free (prime);
}
return err;
}
/****************
* We do not need to use the strongest RNG because we gain no extra
* security from it - The prime number is public and we could also
* offer the factors for those who are willing to check that it is
* indeed a strong prime.
*
* mode 0: Standard
* 1: Make sure that at least one factor is of size qbits.
*/
MPI
generate_elg_prime( int mode, unsigned pbits, unsigned qbits,
MPI g, MPI **ret_factors )
{
int n; /* number of factors */
int m; /* number of primes in pool */
unsigned fbits; /* length of prime factors */
MPI *factors; /* current factors */
MPI *pool; /* pool of primes */
MPI q; /* first prime factor (variable)*/
MPI prime; /* prime test value */
MPI q_factor; /* used for mode 1 */
byte *perms = NULL;
int i, j;
int count1, count2;
unsigned nprime;
unsigned req_qbits = qbits; /* the requested q bits size */
MPI val_2 = mpi_alloc_set_ui( 2 );
/* find number of needed prime factors */
for(n=1; (pbits - qbits - 1) / n >= qbits; n++ )
;
n--;
if( !n || (mode==1 && n < 2) )
log_fatal("can't gen prime with pbits=%u qbits=%u\n", pbits, qbits );
if( mode == 1 ) {
n--;
fbits = (pbits - 2*req_qbits -1) / n;
qbits = pbits - req_qbits - n*fbits;
}
else {
fbits = (pbits - req_qbits -1) / n;
qbits = pbits - n*fbits;
}
if( DBG_CIPHER )
log_debug("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n",
pbits, req_qbits, qbits, fbits, n );
prime = mpi_alloc( (pbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB );
q = gen_prime( qbits, 0, 0 );
q_factor = mode==1? gen_prime( req_qbits, 0, 0 ) : NULL;
/* allocate an array to hold the factors + 2 for later usage */
factors = m_alloc_clear( (n+2) * sizeof *factors );
/* make a pool of 3n+5 primes (this is an arbitrary value) */
m = n*3+5;
if( mode == 1 )
m += 5; /* need some more for DSA */
if( m < 25 )
m = 25;
pool = m_alloc_clear( m * sizeof *pool );
/* permutate over the pool of primes */
count1=count2=0;
do {
next_try:
if( !perms ) {
/* allocate new primes */
for(i=0; i < m; i++ ) {
mpi_free(pool[i]);
pool[i] = NULL;
}
/* init m_out_of_n() */
perms = m_alloc_clear( m );
for(i=0; i < n; i++ ) {
perms[i] = 1;
pool[i] = gen_prime( fbits, 0, 0 );
factors[i] = pool[i];
}
}
else {
m_out_of_n( perms, n, m );
for(i=j=0; i < m && j < n ; i++ )
if( perms[i] ) {
if( !pool[i] )
pool[i] = gen_prime( fbits, 0, 0 );
factors[j++] = pool[i];
}
if( i == n ) {
m_free(perms); perms = NULL;
progress('!');
goto next_try; /* allocate new primes */
}
}
mpi_set( prime, q );
mpi_mul_ui( prime, prime, 2 );
if( mode == 1 )
mpi_mul( prime, prime, q_factor );
for(i=0; i < n; i++ )
mpi_mul( prime, prime, factors[i] );
mpi_add_ui( prime, prime, 1 );
nprime = mpi_get_nbits(prime);
if( nprime < pbits ) {
if( ++count1 > 20 ) {
count1 = 0;
qbits++;
progress('>');
mpi_free (q);
q = gen_prime( qbits, 0, 0 );
goto next_try;
}
}
else
count1 = 0;
if( nprime > pbits ) {
if( ++count2 > 20 ) {
count2 = 0;
qbits--;
progress('<');
mpi_free (q);
q = gen_prime( qbits, 0, 0 );
goto next_try;
}
}
else
count2 = 0;
} while( !(nprime == pbits && check_prime( prime, val_2 )) );
if( DBG_CIPHER ) {
progress('\n');
log_mpidump( "prime : ", prime );
log_mpidump( "factor q: ", q );
if( mode == 1 )
log_mpidump( "factor q0: ", q_factor );
for(i=0; i < n; i++ )
log_mpidump( "factor pi: ", factors[i] );
log_debug("bit sizes: prime=%u, q=%u", mpi_get_nbits(prime), mpi_get_nbits(q) );
if( mode == 1 )
fprintf(stderr, ", q0=%u", mpi_get_nbits(q_factor) );
for(i=0; i < n; i++ )
fprintf(stderr, ", p%d=%u", i, mpi_get_nbits(factors[i]) );
progress('\n');
}
if( ret_factors ) { /* caller wants the factors */
*ret_factors = m_alloc_clear( (n+2) * sizeof **ret_factors);
i = 0;
if( mode == 1 ) {
(*ret_factors)[i++] = mpi_copy( q_factor );
for(; i <= n; i++ )
(*ret_factors)[i] = mpi_copy( factors[i] );
}
else {
for(; i < n; i++ )
(*ret_factors)[i] = mpi_copy( factors[i] );
}
}
if( g ) { /* create a generator (start with 3)*/
MPI tmp = mpi_alloc( mpi_get_nlimbs(prime) );
MPI b = mpi_alloc( mpi_get_nlimbs(prime) );
MPI pmin1 = mpi_alloc( mpi_get_nlimbs(prime) );
if( mode == 1 )
BUG(); /* not yet implemented */
factors[n] = q;
factors[n+1] = mpi_alloc_set_ui(2);
mpi_sub_ui( pmin1, prime, 1 );
mpi_set_ui(g,2);
do {
mpi_add_ui(g, g, 1);
if( DBG_CIPHER ) {
log_debug("checking g: ");
mpi_print( stderr, g, 1 );
}
else
progress('^');
for(i=0; i < n+2; i++ ) {
/*fputc('~', stderr);*/
mpi_fdiv_q(tmp, pmin1, factors[i] );
/* (no mpi_pow(), but it is okay to use this with mod prime) */
mpi_powm(b, g, tmp, prime );
if( !mpi_cmp_ui(b, 1) )
break;
}
if( DBG_CIPHER )
progress('\n');
} while( i < n+2 );
mpi_free(factors[n+1]);
mpi_free(tmp);
mpi_free(b);
mpi_free(pmin1);
}
if( !DBG_CIPHER )
progress('\n');
m_free( factors ); /* (factors are shallow copies) */
for(i=0; i < m; i++ )
mpi_free( pool[i] );
m_free( pool );
m_free(perms);
mpi_free(val_2);
mpi_free(q);
return prime;
}