static void
do_encrypt(gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_public_key *pkey )
{
gcry_mpi_t k;
/* Note: maybe we should change the interface, so that it
* is possible to check that input is < p and return an
* error code.
*/
k = gen_k( pkey->p, 1 );
gcry_mpi_powm( a, pkey->g, k, pkey->p );
/* b = (y^k * input) mod p
* = ((y^k mod p) * (input mod p)) mod p
* and because input is < p
* = ((y^k mod p) * input) mod p
*/
gcry_mpi_powm( b, pkey->y, k, pkey->p );
gcry_mpi_mulm( b, b, input, pkey->p );
#if 0
if( DBG_CIPHER )
{
log_mpidump("elg encrypted y= ", pkey->y);
log_mpidump("elg encrypted p= ", pkey->p);
log_mpidump("elg encrypted k= ", k);
log_mpidump("elg encrypted M= ", input);
log_mpidump("elg encrypted a= ", a);
log_mpidump("elg encrypted b= ", b);
}
#endif
mpi_free(k);
}
int32_t ZrtpDH::computeSecretKey(uint8_t *pubKeyBytes, uint8_t *secret) {
int32_t length = getDhSize();
gcryptCtx* tmpCtx = static_cast<gcryptCtx*>(ctx);
gcry_mpi_t pubKeyOther;
gcry_mpi_t sec = gcry_mpi_new(0);
gcry_mpi_scan(&pubKeyOther, GCRYMPI_FMT_USG, pubKeyBytes, length, NULL);
if (pkType == DH2K) {
gcry_mpi_powm(sec, pubKeyOther, tmpCtx->privKey, bnP2048);
}
else if (pkType == DH3K) {
gcry_mpi_powm(sec, pubKeyOther, tmpCtx->privKey, bnP3072);
}
else {
// gcry_mpi_powm(sec, pubKeyOther, tmpCtx->privKey, bnP4096);
return 0;
}
gcry_mpi_release(pubKeyOther);
size_t result;
gcry_mpi_print(GCRYMPI_FMT_USG, secret, length, &result, sec);
gcry_mpi_release(sec);
return result;
}
int main(int argc, char *argv[]) {
gcry_mpi_t g,p,M,N,pw,t1,t2;
size_t scanned;
int iterations, keySize;
g = gcry_mpi_new(0);
p = gcry_mpi_new(0);
M = gcry_mpi_new(0);
N = gcry_mpi_new(0);
pw = gcry_mpi_new(0);
t1 = gcry_mpi_new(0);
t2 = gcry_mpi_new(0);
/* MODP_2048 */
const char* pString = "00FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF";
const char* gString = "2";
/* password */
const char* pwd = "My$Very=Secure;Password";
const char* salt = "abcdefghijklmno";
iterations = 1000;
keySize = 32;
/* read p and g */
gcry_mpi_scan(&g, GCRYMPI_FMT_HEX, gString, 0, &scanned);
gcry_mpi_scan(&p, GCRYMPI_FMT_HEX, pString, 0, &scanned);
/* hash password */
char* result = calloc(keySize, sizeof(char));
gcry_kdf_derive(pwd, strlen(pwd), GCRY_KDF_PBKDF2, GCRY_MD_SHA256, salt, strlen(salt), iterations, keySize, result);
gcry_mpi_scan(&pw, GCRYMPI_FMT_STD, result, strlen((const char*)result), &scanned);
/* create M and N */
gen_rand(t1, p);
gen_rand(t2, p);
gcry_mpi_powm(M, g, t1, p);
gcry_mpi_powm(N, g, t2, p);
/* run test ... */
struct spake_session client = spake_init(0, g, p, M, N, pw, keySize); /* client */
struct spake_session server = spake_init(1, g, p, M, N, pw, keySize); /* server */
spake_next(&client, server.X);
spake_next(&server, client.X);
print_key(client.k, keySize, "k1");
print_key(server.k, keySize, "k2");
if (strncmp(client.k, server.k, keySize) == 0)
printf("Successful SPAKE session :)\n");
else
printf("Sorry, error in SPAKE session :(\n");
return 0;
}
/****************
* Returns true if the signature composed of A and B is valid.
*/
static int
verify(gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_public_key *pkey )
{
int rc;
gcry_mpi_t t1;
gcry_mpi_t t2;
gcry_mpi_t base[4];
gcry_mpi_t ex[4];
if( !(mpi_cmp_ui( a, 0 ) > 0 && mpi_cmp( a, pkey->p ) < 0) )
return 0; /* assertion 0 < a < p failed */
t1 = mpi_alloc( mpi_get_nlimbs(a) );
t2 = mpi_alloc( mpi_get_nlimbs(a) );
#if 0
/* t1 = (y^a mod p) * (a^b mod p) mod p */
gcry_mpi_powm( t1, pkey->y, a, pkey->p );
gcry_mpi_powm( t2, a, b, pkey->p );
mpi_mulm( t1, t1, t2, pkey->p );
/* t2 = g ^ input mod p */
gcry_mpi_powm( t2, pkey->g, input, pkey->p );
rc = !mpi_cmp( t1, t2 );
#elif 0
/* t1 = (y^a mod p) * (a^b mod p) mod p */
base[0] = pkey->y; ex[0] = a;
base[1] = a; ex[1] = b;
base[2] = NULL; ex[2] = NULL;
mpi_mulpowm( t1, base, ex, pkey->p );
/* t2 = g ^ input mod p */
gcry_mpi_powm( t2, pkey->g, input, pkey->p );
rc = !mpi_cmp( t1, t2 );
#else
/* t1 = g ^ - input * y ^ a * a ^ b mod p */
mpi_invm(t2, pkey->g, pkey->p );
base[0] = t2 ; ex[0] = input;
base[1] = pkey->y; ex[1] = a;
base[2] = a; ex[2] = b;
base[3] = NULL; ex[3] = NULL;
mpi_mulpowm( t1, base, ex, pkey->p );
rc = !mpi_cmp_ui( t1, 1 );
#endif
mpi_free(t1);
mpi_free(t2);
return rc;
}
/* Choose a random value x and calculate e = g^x mod p. Returns e and
if ret_x is not NULL x. */
static gcry_mpi_t
calc_dh_secret (gcry_mpi_t gex_g, gcry_mpi_t gex_p, gcry_mpi_t * ret_x)
{
gcry_mpi_t e, g, x, prime;
size_t n = sizeof diffie_hellman_group1_prime;
if (gex_p)
prime = gcry_mpi_copy (gex_p);
else if (gcry_mpi_scan (&prime, GCRYMPI_FMT_STD,
diffie_hellman_group1_prime, n, NULL))
abort ();
/*_gsti_dump_mpi( "prime=", prime );*/
if (gex_g)
g = gcry_mpi_copy (gex_g);
else
g = gcry_mpi_set_ui (NULL, 2);
/* FIXME: we n bits for the private exponent,
where n is 2*derrived_key_material */
x = gcry_mpi_snew (200);
gcry_mpi_randomize (x, 200, GCRY_STRONG_RANDOM);
n = gcry_mpi_get_nbits (prime);
e = gcry_mpi_new (n+1);
gcry_mpi_powm (e, g, x, prime);
if (ret_x)
*ret_x = x;
else
gcry_mpi_release (x);
gcry_mpi_release (g);
gcry_mpi_release (prime);
return e;
}
static void
do_powm ( const char *n_str, const char *e_str, const char *m_str)
{
gcry_mpi_t e, n, msg, cip;
gcry_error_t err;
int i;
err = gcry_mpi_scan (&n, GCRYMPI_FMT_HEX, n_str, 0, 0);
if (err) BUG ();
err = gcry_mpi_scan (&e, GCRYMPI_FMT_HEX, e_str, 0, 0);
if (err) BUG ();
err = gcry_mpi_scan (&msg, GCRYMPI_FMT_HEX, m_str, 0, 0);
if (err) BUG ();
cip = gcry_mpi_new (0);
start_timer ();
for (i=0; i < 1000; i++)
gcry_mpi_powm (cip, msg, e, n);
stop_timer ();
printf (" %s", elapsed_time ()); fflush (stdout);
/* { */
/* char *buf; */
/* if (gcry_mpi_aprint (GCRYMPI_FMT_HEX, (void**)&buf, NULL, cip)) */
/* BUG (); */
/* printf ("result: %s\n", buf); */
/* gcry_free (buf); */
/* } */
gcry_mpi_release (cip);
gcry_mpi_release (msg);
gcry_mpi_release (n);
gcry_mpi_release (e);
}
int32_t ZrtpDH::generatePublicKey()
{
gcryptCtx* tmpCtx = static_cast<gcryptCtx*>(ctx);
tmpCtx->pubKey = gcry_mpi_new(0);
if (pkType == DH2K) {
gcry_mpi_powm(tmpCtx->pubKey, two, tmpCtx->privKey, bnP2048);
}
else if (pkType == DH3K) {
gcry_mpi_powm(tmpCtx->pubKey, two, tmpCtx->privKey, bnP3072);
}
else {
// gcry_mpi_powm(tmpCtx->pubKey, two, tmpCtx->privKey, bnP4096);
return 0;
}
return 1;
}
/****************
* Test whether the secret key is valid.
* Returns: if this is a valid key.
*/
static int
check_secret_key( ELG_secret_key *sk )
{
int rc;
gcry_mpi_t y = mpi_alloc( mpi_get_nlimbs(sk->y) );
gcry_mpi_powm( y, sk->g, sk->x, sk->p );
rc = !mpi_cmp( y, sk->y );
mpi_free( y );
return rc;
}
GkmDataResult
gkm_data_der_read_private_key_dsa_parts (const guchar *keydata, gsize n_keydata,
const guchar *params, gsize n_params,
gcry_sexp_t *s_key)
{
gcry_mpi_t p, q, g, y, x;
GkmDataResult ret = GKM_DATA_UNRECOGNIZED;
int res;
GNode *asn_params = NULL;
GNode *asn_key = NULL;
p = q = g = y = x = NULL;
asn_params = egg_asn1x_create_and_decode (pk_asn1_tab, "DSAParameters", params, n_params);
asn_key = egg_asn1x_create_and_decode (pk_asn1_tab, "DSAPrivatePart", keydata, n_keydata);
if (!asn_params || !asn_key)
goto done;
ret = GKM_DATA_FAILURE;
if (!gkm_data_asn1_read_mpi (egg_asn1x_node (asn_params, "p", NULL), &p) ||
!gkm_data_asn1_read_mpi (egg_asn1x_node (asn_params, "q", NULL), &q) ||
!gkm_data_asn1_read_mpi (egg_asn1x_node (asn_params, "g", NULL), &g))
goto done;
if (!gkm_data_asn1_read_mpi (asn_key, &x))
goto done;
/* Now we calculate y */
y = gcry_mpi_snew (1024);
gcry_mpi_powm (y, g, x, p);
res = gcry_sexp_build (s_key, NULL, SEXP_PRIVATE_DSA, p, q, g, y, x);
if (res)
goto done;
g_assert (*s_key);
ret = GKM_DATA_SUCCESS;
done:
egg_asn1x_destroy (asn_key);
egg_asn1x_destroy (asn_params);
gcry_mpi_release (p);
gcry_mpi_release (q);
gcry_mpi_release (g);
gcry_mpi_release (y);
gcry_mpi_release (x);
if (ret == GKM_DATA_FAILURE)
g_message ("invalid DSA key");
return ret;
}
void FSPRG_Seek(void *state, uint64_t epoch, const void *msk, const void *seed, size_t seedlen) {
gcry_mpi_t p, q, n, x, xp, xq, kp, kq, xm;
uint16_t secpar;
initialize_libgcrypt();
secpar = read_secpar(msk + 0);
p = mpi_import(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8);
q = mpi_import(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8);
n = gcry_mpi_new(0);
gcry_mpi_mul(n, p, q);
x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
CRT_decompose(&xp, &xq, x, p, q); /* split (mod n) into (mod p) and (mod q) using CRT */
kp = twopowmodphi(epoch, p); /* compute 2^epoch (mod phi(p)) */
kq = twopowmodphi(epoch, q); /* compute 2^epoch (mod phi(q)) */
gcry_mpi_powm(xp, xp, kp, p); /* compute x^(2^epoch) (mod p) */
gcry_mpi_powm(xq, xq, kq, q); /* compute x^(2^epoch) (mod q) */
CRT_compose(&xm, xp, xq, p, q); /* combine (mod p) and (mod q) to (mod n) using CRT */
store_secpar(state + 0, secpar);
mpi_export(state + 2 + 0 * secpar / 8, secpar / 8, n);
mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, xm);
uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
gcry_mpi_release(p);
gcry_mpi_release(q);
gcry_mpi_release(n);
gcry_mpi_release(x);
gcry_mpi_release(xp);
gcry_mpi_release(xq);
gcry_mpi_release(kp);
gcry_mpi_release(kq);
gcry_mpi_release(xm);
}
unsigned char* modPow(unsigned char* x, unsigned char* y, unsigned char* z){
size_t scanned;
unsigned char *result;
gcry_mpi_t a = gcry_mpi_new(0);
gcry_mpi_t b = gcry_mpi_new(0);
gcry_mpi_t c = gcry_mpi_new(0);
gcry_mpi_scan(&a, GCRYMPI_FMT_HEX, x, 0, &scanned);
gcry_mpi_scan(&b, GCRYMPI_FMT_HEX, y, 0, &scanned);
gcry_mpi_scan(&c, GCRYMPI_FMT_HEX, z, 0, &scanned);
gcry_mpi_powm(a, a, b, c);
gcry_mpi_aprint(GCRYMPI_FMT_HEX, &result, NULL, a);
return result;
}
static bigint_t
wrap_gcry_mpi_powm (bigint_t w, const bigint_t b, const bigint_t e,
const bigint_t m)
{
if (w == NULL)
w = _gnutls_mpi_alloc_like (m);
if (w == NULL)
return NULL;
gcry_mpi_powm (w, b, e, m);
return w;
}
/****************
* Returns: true if this may be a prime
*/
static int
check_prime( gcry_mpi_t prime, gcry_mpi_t val_2,
gcry_prime_check_func_t cb_func, void *cb_arg)
{
int i;
unsigned int x;
unsigned int count=0;
/* Check against small primes. */
for (i=0; (x = small_prime_numbers[i]); i++ )
{
if ( mpi_divisible_ui( prime, x ) )
return 0;
}
/* A quick Fermat test. */
{
gcry_mpi_t result = mpi_alloc_like( prime );
gcry_mpi_t pminus1 = mpi_alloc_like( prime );
mpi_sub_ui( pminus1, prime, 1);
gcry_mpi_powm( result, val_2, pminus1, prime );
mpi_free( pminus1 );
if ( mpi_cmp_ui( result, 1 ) )
{
/* Is composite. */
mpi_free( result );
progress('.');
return 0;
}
mpi_free( result );
}
if (!cb_func || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_MAYBE_PRIME, prime))
{
/* Perform stronger tests. */
if ( is_prime( prime, 5, &count ) )
{
if (!cb_func
|| cb_func (cb_arg, GCRY_PRIME_CHECK_AT_GOT_PRIME, prime))
return 1; /* Probably a prime. */
}
}
progress('.');
return 0;
}
gpointer
egg_dh_gen_secret (gcry_mpi_t peer, gcry_mpi_t priv,
gcry_mpi_t prime, gsize *bytes)
{
gcry_error_t gcry;
guchar *value;
gsize n_value;
gcry_mpi_t k;
gint bits;
g_return_val_if_fail (peer, NULL);
g_return_val_if_fail (priv, NULL);
g_return_val_if_fail (prime, NULL);
bits = gcry_mpi_get_nbits (prime);
g_return_val_if_fail (bits >= 0, NULL);
k = gcry_mpi_snew (bits);
g_return_val_if_fail (k, NULL);
gcry_mpi_powm (k, peer, priv, prime);
/* Write out the secret */
gcry = gcry_mpi_print (GCRYMPI_FMT_USG, NULL, 0, &n_value, k);
g_return_val_if_fail (gcry == 0, NULL);
value = egg_secure_alloc (n_value);
gcry = gcry_mpi_print (GCRYMPI_FMT_USG, value, n_value, &n_value, k);
g_return_val_if_fail (gcry == 0, NULL);
#if DEBUG_DH_SECRET
g_printerr ("DH SECRET: ");
gcry_mpi_dump (k);
gcry_mpi_release (k);
#endif
*bytes = n_value;
#if DEBUG_DH_SECRET
gcry_mpi_scan (&k, GCRYMPI_FMT_USG, value, bytes, NULL);
g_printerr ("RAW SECRET: ");
gcry_mpi_dump (k);
gcry_mpi_release (k);
#endif
return value;
}
static gcry_mpi_t
calc_dh_key (gcry_mpi_t gex_p, gcry_mpi_t f, gcry_mpi_t x)
{
gcry_mpi_t k, prime;
size_t n = sizeof diffie_hellman_group1_prime;
if (gex_p)
prime = gcry_mpi_copy (gex_p);
else if (gcry_mpi_scan (&prime, GCRYMPI_FMT_STD,
diffie_hellman_group1_prime, n, NULL))
abort ();
n = gcry_mpi_get_nbits (prime);
k = gcry_mpi_snew (n+1);
gcry_mpi_powm (k, f, x, prime);
gcry_mpi_release (prime);
return k;
}
gboolean
egg_dh_gen_pair (gcry_mpi_t prime, gcry_mpi_t base, guint bits,
gcry_mpi_t *pub, gcry_mpi_t *priv)
{
guint pbits;
g_return_val_if_fail (prime, FALSE);
g_return_val_if_fail (base, FALSE);
g_return_val_if_fail (pub, FALSE);
g_return_val_if_fail (priv, FALSE);
pbits = gcry_mpi_get_nbits (prime);
g_return_val_if_fail (pbits > 1, FALSE);
if (bits == 0) {
bits = pbits;
} else if (bits > pbits) {
g_return_val_if_reached (FALSE);
}
/*
* Generate a strong random number of bits, and not zero.
* gcry_mpi_randomize bumps up to the next byte. Since we
* need to have a value less than half of prime, we make sure
* we bump down.
*/
*priv = gcry_mpi_snew (bits);
g_return_val_if_fail (*priv, FALSE);
while (gcry_mpi_cmp_ui (*priv, 0) == 0)
gcry_mpi_randomize (*priv, bits, GCRY_STRONG_RANDOM);
/* Secret key value must be less than half of p */
if (gcry_mpi_get_nbits (*priv) > bits)
gcry_mpi_clear_highbit (*priv, bits);
if (gcry_mpi_get_nbits (*priv) > pbits - 1)
gcry_mpi_clear_highbit (*priv, pbits - 1);
g_assert (gcry_mpi_cmp (prime, *priv) > 0);
*pub = gcry_mpi_new (gcry_mpi_get_nbits (*priv));
g_return_val_if_fail (*pub, FALSE);
gcry_mpi_powm (*pub, base, *priv, prime);
return TRUE;
}
static gboolean
dsa_subject_public_key_from_private (GNode *key_asn,
const GckAttribute *ap,
const GckAttribute *aq,
const GckAttribute *ag,
const GckAttribute *ax)
{
gcry_mpi_t mp, mq, mg, mx, my;
size_t n_buffer;
gcry_error_t gcry;
unsigned char *buffer;
gcry = gcry_mpi_scan (&mp, GCRYMPI_FMT_USG, ap->value, ap->length, NULL);
g_return_val_if_fail (gcry == 0, FALSE);
gcry = gcry_mpi_scan (&mq, GCRYMPI_FMT_USG, aq->value, aq->length, NULL);
g_return_val_if_fail (gcry == 0, FALSE);
gcry = gcry_mpi_scan (&mg, GCRYMPI_FMT_USG, ag->value, ag->length, NULL);
g_return_val_if_fail (gcry == 0, FALSE);
gcry = gcry_mpi_scan (&mx, GCRYMPI_FMT_USG, ax->value, ax->length, NULL);
g_return_val_if_fail (gcry == 0, FALSE);
/* Calculate the public part from the private */
my = gcry_mpi_snew (gcry_mpi_get_nbits (mx));
g_return_val_if_fail (my, FALSE);
gcry_mpi_powm (my, mg, mx, mp);
gcry = gcry_mpi_aprint (GCRYMPI_FMT_STD, &buffer, &n_buffer, my);
g_return_val_if_fail (gcry == 0, FALSE);
egg_asn1x_take_integer_as_raw (key_asn, g_bytes_new_with_free_func (buffer, n_buffer,
gcry_free, buffer));
gcry_mpi_release (mp);
gcry_mpi_release (mq);
gcry_mpi_release (mg);
gcry_mpi_release (mx);
gcry_mpi_release (my);
return TRUE;
}
static void
decrypt(gcry_mpi_t output, gcry_mpi_t a, gcry_mpi_t b, ELG_secret_key *skey )
{
gcry_mpi_t t1 = mpi_alloc_secure( mpi_get_nlimbs( skey->p ) );
/* output = b/(a^x) mod p */
gcry_mpi_powm( t1, a, skey->x, skey->p );
mpi_invm( t1, t1, skey->p );
mpi_mulm( output, b, t1, skey->p );
#if 0
if( DBG_CIPHER )
{
log_mpidump("elg decrypted x= ", skey->x);
log_mpidump("elg decrypted p= ", skey->p);
log_mpidump("elg decrypted a= ", a);
log_mpidump("elg decrypted b= ", b);
log_mpidump("elg decrypted M= ", output);
}
#endif
mpi_free(t1);
}
static void
sign(gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_secret_key *skey )
{
gcry_mpi_t k;
gcry_mpi_t t = mpi_alloc( mpi_get_nlimbs(a) );
gcry_mpi_t inv = mpi_alloc( mpi_get_nlimbs(a) );
gcry_mpi_t p_1 = mpi_copy(skey->p);
/*
* b = (t * inv) mod (p-1)
* b = (t * inv(k,(p-1),(p-1)) mod (p-1)
* b = (((M-x*a) mod (p-1)) * inv(k,(p-1),(p-1))) mod (p-1)
*
*/
mpi_sub_ui(p_1, p_1, 1);
k = gen_k( skey->p, 0 /* no small K ! */ );
gcry_mpi_powm( a, skey->g, k, skey->p );
mpi_mul(t, skey->x, a );
mpi_subm(t, input, t, p_1 );
mpi_invm(inv, k, p_1 );
mpi_mulm(b, t, inv, p_1 );
#if 0
if( DBG_CIPHER )
{
log_mpidump("elg sign p= ", skey->p);
log_mpidump("elg sign g= ", skey->g);
log_mpidump("elg sign y= ", skey->y);
log_mpidump("elg sign x= ", skey->x);
log_mpidump("elg sign k= ", k);
log_mpidump("elg sign M= ", input);
log_mpidump("elg sign a= ", a);
log_mpidump("elg sign b= ", b);
}
#endif
mpi_free(k);
mpi_free(t);
mpi_free(inv);
mpi_free(p_1);
}
void* mod_exp(void* mod_exp_operands)
{
struct mod_exp_operands* op = (struct mod_exp_operands*) mod_exp_operands;
unsigned long int g = op->g;
unsigned long int e = op->e;
unsigned long int n = op->n;
unsigned long int ans;
gcry_mpi_t ans_mpi = gcry_mpi_new(10);
gcry_mpi_t g_mpi = gcry_mpi_new(10);
gcry_mpi_t e_mpi = gcry_mpi_new(10);
gcry_mpi_t n_mpi = gcry_mpi_new(10);
printf("Value of g: %lu\n",g);
g_mpi = gcry_mpi_set_ui(g_mpi, g);
printf("Value of e: %lu\n",e);
e_mpi = gcry_mpi_set_ui(e_mpi, e);
printf("Value of n: %lu\n",n);
n_mpi = gcry_mpi_set_ui(n_mpi, n);
gcry_mpi_powm(ans_mpi, g_mpi,e_mpi,n_mpi);
}
/* Generate a key pair with a key of size NBITS not using a random
value for the secret key but the one given as X. This is useful to
implement a passphrase based decryption for a public key based
encryption. It has appliactions in backup systems.
Returns: A structure filled with all needed values and an array
with n-1 factors of (p-1). */
static gcry_err_code_t
generate_using_x (ELG_secret_key *sk, unsigned int nbits, gcry_mpi_t x,
gcry_mpi_t **ret_factors )
{
gcry_mpi_t p; /* The prime. */
gcry_mpi_t p_min1; /* The prime minus 1. */
gcry_mpi_t g; /* The generator. */
gcry_mpi_t y; /* g^x mod p. */
unsigned int qbits;
unsigned int xbits;
sk->p = NULL;
sk->g = NULL;
sk->y = NULL;
sk->x = NULL;
/* Do a quick check to see whether X is suitable. */
xbits = mpi_get_nbits (x);
if ( xbits < 64 || xbits >= nbits )
return GPG_ERR_INV_VALUE;
p_min1 = gcry_mpi_new ( nbits );
qbits = wiener_map ( nbits );
if ( (qbits & 1) ) /* Better have an even one. */
qbits++;
g = mpi_alloc (1);
p = _gcry_generate_elg_prime ( 0, nbits, qbits, g, ret_factors );
mpi_sub_ui (p_min1, p, 1);
if (DBG_CIPHER)
log_debug ("using a supplied x of size %u", xbits );
if ( !(mpi_cmp_ui ( x, 0 ) > 0 && mpi_cmp ( x, p_min1 ) <0 ) )
{
gcry_mpi_release ( p_min1 );
gcry_mpi_release ( p );
gcry_mpi_release ( g );
return GPG_ERR_INV_VALUE;
}
y = gcry_mpi_new (nbits);
gcry_mpi_powm ( y, g, x, p );
if ( DBG_CIPHER )
{
progress ('\n');
log_mpidump ("elg p= ", p );
log_mpidump ("elg g= ", g );
log_mpidump ("elg y= ", y );
log_mpidump ("elg x= ", x );
}
/* Copy the stuff to the key structures */
sk->p = p;
sk->g = g;
sk->y = y;
sk->x = gcry_mpi_copy (x);
gcry_mpi_release ( p_min1 );
/* Now we can test our keys. */
if ( test_keys ( sk, nbits - 64, 1 ) )
{
gcry_mpi_release ( sk->p ); sk->p = NULL;
gcry_mpi_release ( sk->g ); sk->g = NULL;
gcry_mpi_release ( sk->y ); sk->y = NULL;
gcry_mpi_release ( sk->x ); sk->x = NULL;
return GPG_ERR_BAD_SECKEY;
}
return 0;
}
/****************
* Generate a key pair with a key of size NBITS
* Returns: 2 structures filled with all needed values
* and an array with n-1 factors of (p-1)
*/
static void
generate ( ELG_secret_key *sk, unsigned int nbits, gcry_mpi_t **ret_factors )
{
gcry_mpi_t p; /* the prime */
gcry_mpi_t p_min1;
gcry_mpi_t g;
gcry_mpi_t x; /* the secret exponent */
gcry_mpi_t y;
unsigned int qbits;
unsigned int xbits;
byte *rndbuf;
p_min1 = gcry_mpi_new ( nbits );
qbits = wiener_map( nbits );
if( qbits & 1 ) /* better have a even one */
qbits++;
g = mpi_alloc(1);
p = _gcry_generate_elg_prime( 0, nbits, qbits, g, ret_factors );
mpi_sub_ui(p_min1, p, 1);
/* Select a random number which has these properties:
* 0 < x < p-1
* This must be a very good random number because this is the
* secret part. The prime is public and may be shared anyway,
* so a random generator level of 1 is used for the prime.
*
* I don't see a reason to have a x of about the same size
* as the p. It should be sufficient to have one about the size
* of q or the later used k plus a large safety margin. Decryption
* will be much faster with such an x.
*/
xbits = qbits * 3 / 2;
if( xbits >= nbits )
BUG();
x = gcry_mpi_snew ( xbits );
if( DBG_CIPHER )
log_debug("choosing a random x of size %u", xbits );
rndbuf = NULL;
do
{
if( DBG_CIPHER )
progress('.');
if( rndbuf )
{ /* Change only some of the higher bits */
if( xbits < 16 ) /* should never happen ... */
{
gcry_free(rndbuf);
rndbuf = gcry_random_bytes_secure( (xbits+7)/8,
GCRY_VERY_STRONG_RANDOM );
}
else
{
char *r = gcry_random_bytes_secure( 2,
GCRY_VERY_STRONG_RANDOM );
memcpy(rndbuf, r, 2 );
gcry_free(r);
}
}
else
{
rndbuf = gcry_random_bytes_secure( (xbits+7)/8,
GCRY_VERY_STRONG_RANDOM );
}
_gcry_mpi_set_buffer( x, rndbuf, (xbits+7)/8, 0 );
mpi_clear_highbit( x, xbits+1 );
}
while( !( mpi_cmp_ui( x, 0 )>0 && mpi_cmp( x, p_min1 )<0 ) );
gcry_free(rndbuf);
y = gcry_mpi_new (nbits);
gcry_mpi_powm( y, g, x, p );
if( DBG_CIPHER )
{
progress('\n');
log_mpidump("elg p= ", p );
log_mpidump("elg g= ", g );
log_mpidump("elg y= ", y );
log_mpidump("elg x= ", x );
}
/* Copy the stuff to the key structures */
sk->p = p;
sk->g = g;
sk->y = y;
sk->x = x;
gcry_mpi_release ( p_min1 );
/* Now we can test our keys (this should never fail!) */
test_keys ( sk, nbits - 64, 0 );
}
/* Find a generator for PRIME where the factorization of (prime-1) is
in the NULL terminated array FACTORS. Return the generator as a
newly allocated MPI in R_G. If START_G is not NULL, use this as s
atart for the search. Returns 0 on success.*/
gcry_error_t
gcry_prime_group_generator (gcry_mpi_t *r_g,
gcry_mpi_t prime, gcry_mpi_t *factors,
gcry_mpi_t start_g)
{
gcry_mpi_t tmp = gcry_mpi_new (0);
gcry_mpi_t b = gcry_mpi_new (0);
gcry_mpi_t pmin1 = gcry_mpi_new (0);
gcry_mpi_t g = start_g? gcry_mpi_copy (start_g) : gcry_mpi_set_ui (NULL, 3);
int first = 1;
int i, n;
if (!factors || !r_g || !prime)
return gpg_error (GPG_ERR_INV_ARG);
*r_g = NULL;
for (n=0; factors[n]; n++)
;
if (n < 2)
return gpg_error (GPG_ERR_INV_ARG);
/* Extra sanity check - usually disabled. */
/* mpi_set (tmp, factors[0]); */
/* for(i = 1; i < n; i++) */
/* mpi_mul (tmp, tmp, factors[i]); */
/* mpi_add_ui (tmp, tmp, 1); */
/* if (mpi_cmp (prime, tmp)) */
/* return gpg_error (GPG_ERR_INV_ARG); */
gcry_mpi_sub_ui (pmin1, prime, 1);
do
{
if (first)
first = 0;
else
gcry_mpi_add_ui (g, g, 1);
if (DBG_CIPHER)
{
log_debug ("checking g:");
gcry_mpi_dump (g);
log_debug ("\n");
}
else
progress('^');
for (i = 0; i < n; i++)
{
mpi_fdiv_q (tmp, pmin1, factors[i]);
gcry_mpi_powm (b, g, tmp, prime);
if (! mpi_cmp_ui (b, 1))
break;
}
if (DBG_CIPHER)
progress('\n');
}
while (i < n);
gcry_mpi_release (tmp);
gcry_mpi_release (b);
gcry_mpi_release (pmin1);
*r_g = g;
return 0;
}
/*
* Return true if n is probably a prime
*/
static int
is_prime (gcry_mpi_t n, int steps, unsigned int *count)
{
gcry_mpi_t x = mpi_alloc( mpi_get_nlimbs( n ) );
gcry_mpi_t y = mpi_alloc( mpi_get_nlimbs( n ) );
gcry_mpi_t z = mpi_alloc( mpi_get_nlimbs( n ) );
gcry_mpi_t nminus1 = mpi_alloc( mpi_get_nlimbs( n ) );
gcry_mpi_t a2 = mpi_alloc_set_ui( 2 );
gcry_mpi_t q;
unsigned i, j, k;
int rc = 0;
unsigned nbits = mpi_get_nbits( n );
mpi_sub_ui( nminus1, n, 1 );
/* Find q and k, so that n = 1 + 2^k * q . */
q = mpi_copy ( nminus1 );
k = mpi_trailing_zeros ( q );
mpi_tdiv_q_2exp (q, q, k);
for (i=0 ; i < steps; i++ )
{
++*count;
if( !i )
{
mpi_set_ui( x, 2 );
}
else
{
gcry_mpi_randomize( x, nbits, GCRY_WEAK_RANDOM );
/* Make sure that the number is smaller than the prime and
keep the randomness of the high bit. */
if ( mpi_test_bit ( x, nbits-2) )
{
mpi_set_highbit ( x, nbits-2); /* Clear all higher bits. */
}
else
{
mpi_set_highbit( x, nbits-2 );
mpi_clear_bit( x, nbits-2 );
}
assert ( mpi_cmp( x, nminus1 ) < 0 && mpi_cmp_ui( x, 1 ) > 0 );
}
gcry_mpi_powm ( y, x, q, n);
if ( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) )
{
for ( j=1; j < k && mpi_cmp( y, nminus1 ); j++ )
{
gcry_mpi_powm(y, y, a2, n);
if( !mpi_cmp_ui( y, 1 ) )
goto leave; /* Not a prime. */
}
if (mpi_cmp( y, nminus1 ) )
goto leave; /* Not a prime. */
}
progress('+');
}
rc = 1; /* May be a prime. */
leave:
mpi_free( x );
mpi_free( y );
mpi_free( z );
mpi_free( nminus1 );
mpi_free( q );
mpi_free( a2 );
return rc;
}
static gcry_mpi_t
gen_prime (unsigned int nbits, int secret, int randomlevel,
int (*extra_check)(void *, gcry_mpi_t), void *extra_check_arg)
{
gcry_mpi_t prime, ptest, pminus1, val_2, val_3, result;
int i;
unsigned int x, step;
unsigned int count1, count2;
int *mods;
/* if ( DBG_CIPHER ) */
/* log_debug ("generate a prime of %u bits ", nbits ); */
if (nbits < 16)
log_fatal ("can't generate a prime with less than %d bits\n", 16);
mods = gcry_xmalloc( no_of_small_prime_numbers * sizeof *mods );
/* Make nbits fit into gcry_mpi_t implementation. */
val_2 = mpi_alloc_set_ui( 2 );
val_3 = mpi_alloc_set_ui( 3);
prime = secret? gcry_mpi_snew ( nbits ): gcry_mpi_new ( nbits );
result = mpi_alloc_like( prime );
pminus1= mpi_alloc_like( prime );
ptest = mpi_alloc_like( prime );
count1 = count2 = 0;
for (;;)
{ /* try forvever */
int dotcount=0;
/* generate a random number */
gcry_mpi_randomize( prime, nbits, randomlevel );
/* Set high order bit to 1, set low order bit to 1. If we are
generating a secret prime we are most probably doing that
for RSA, to make sure that the modulus does have the
requested key size we set the 2 high order bits. */
mpi_set_highbit (prime, nbits-1);
if (secret)
mpi_set_bit (prime, nbits-2);
mpi_set_bit(prime, 0);
/* Calculate all remainders. */
for (i=0; (x = small_prime_numbers[i]); i++ )
mods[i] = mpi_fdiv_r_ui(NULL, prime, x);
/* Now try some primes starting with prime. */
for(step=0; step < 20000; step += 2 )
{
/* Check against all the small primes we have in mods. */
count1++;
for (i=0; (x = small_prime_numbers[i]); i++ )
{
while ( mods[i] + step >= x )
mods[i] -= x;
if ( !(mods[i] + step) )
break;
}
if ( x )
continue; /* Found a multiple of an already known prime. */
mpi_add_ui( ptest, prime, step );
/* Do a fast Fermat test now. */
count2++;
mpi_sub_ui( pminus1, ptest, 1);
gcry_mpi_powm( result, val_2, pminus1, ptest );
if ( !mpi_cmp_ui( result, 1 ) )
{
/* Not composite, perform stronger tests */
if (is_prime(ptest, 5, &count2 ))
{
if (!mpi_test_bit( ptest, nbits-1-secret ))
{
progress('\n');
log_debug ("overflow in prime generation\n");
break; /* Stop loop, continue with a new prime. */
}
if (extra_check && extra_check (extra_check_arg, ptest))
{
/* The extra check told us that this prime is
not of the caller's taste. */
progress ('/');
}
else
{
/* Got it. */
mpi_free(val_2);
mpi_free(val_3);
mpi_free(result);
mpi_free(pminus1);
mpi_free(prime);
gcry_free(mods);
return ptest;
}
}
}
if (++dotcount == 10 )
{
progress('.');
dotcount = 0;
}
}
progress(':'); /* restart with a new random value */
}
}
/****************
* 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;
}
static void
gen_prime (gcry_mpi_t * ptest, unsigned int nbits, struct GNUNET_HashCode * hc)
{
/* Note: 2 is not included because it can be tested more easily by
* looking at bit 0. The last entry in this list is marked by a zero */
static const uint16_t small_prime_numbers[] = {
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
4957, 4967, 4969, 4973, 4987, 4993, 4999,
0
};
#define DIM(v) (sizeof(v)/sizeof((v)[0]))
static int no_of_small_prime_numbers = DIM (small_prime_numbers) - 1;
gcry_mpi_t prime, pminus1, val_2, val_3, result;
unsigned int i;
unsigned int step;
unsigned int mods[no_of_small_prime_numbers];
gcry_mpi_t tmp;
gcry_mpi_t sp;
GNUNET_assert (nbits >= 16);
/* Make nbits fit into mpz_t implementation. */
val_2 = gcry_mpi_set_ui (NULL, 2);
val_3 = gcry_mpi_set_ui (NULL, 3);
prime = gcry_mpi_snew (0);
result = gcry_mpi_new (0);
pminus1 = gcry_mpi_new (0);
*ptest = gcry_mpi_new (0);
tmp = gcry_mpi_new (0);
sp = gcry_mpi_new (0);
while (1)
{
/* generate a random number */
mpz_randomize (prime, nbits, hc);
/* Set high order bit to 1, set low order bit to 1. If we are
* generating a secret prime we are most probably doing that
* for RSA, to make sure that the modulus does have the
* requested key size we set the 2 high order bits. */
gcry_mpi_set_bit (prime, nbits - 1);
gcry_mpi_set_bit (prime, nbits - 2);
gcry_mpi_set_bit (prime, 0);
/* Calculate all remainders. */
for (i = 0; i < no_of_small_prime_numbers; i++)
{
size_t written;
gcry_mpi_set_ui (sp, small_prime_numbers[i]);
gcry_mpi_div (NULL, tmp, prime, sp, -1);
mods[i] = 0;
written = sizeof (unsigned int);
GNUNET_assert (0 ==
gcry_mpi_print (GCRYMPI_FMT_USG,
(unsigned char *) &mods[i], written,
&written, tmp));
adjust ((unsigned char *) &mods[i], written, sizeof (unsigned int));
mods[i] = ntohl (mods[i]);
}
/* Now try some primes starting with prime. */
for (step = 0; step < 20000; step += 2)
{
/* Check against all the small primes we have in mods. */
for (i = 0; i < no_of_small_prime_numbers; i++)
{
uint16_t x = small_prime_numbers[i];
while (mods[i] + step >= x)
mods[i] -= x;
if (!(mods[i] + step))
break;
}
if (i < no_of_small_prime_numbers)
continue; /* Found a multiple of an already known prime. */
gcry_mpi_add_ui (*ptest, prime, step);
if (!gcry_mpi_test_bit (*ptest, nbits - 2))
break;
/* Do a fast Fermat test now. */
gcry_mpi_sub_ui (pminus1, *ptest, 1);
gcry_mpi_powm (result, val_2, pminus1, *ptest);
if ((!gcry_mpi_cmp_ui (result, 1)) && (is_prime (*ptest, 5, hc)))
{
/* Got it. */
gcry_mpi_release (sp);
gcry_mpi_release (tmp);
gcry_mpi_release (val_2);
gcry_mpi_release (val_3);
gcry_mpi_release (result);
gcry_mpi_release (pminus1);
gcry_mpi_release (prime);
return;
}
}
}
}
int
irc_sasl_dh (const char *data_base64,
unsigned char **public_bin, unsigned char **secret_bin,
int *length_key)
{
char *data;
unsigned char *ptr_data;
int length_data, size, num_bits_prime_number, rc;
size_t num_written;
gcry_mpi_t data_prime_number, data_generator_number, data_server_pub_key;
gcry_mpi_t pub_key, priv_key, secret_mpi;
rc = 0;
data = NULL;
data_prime_number = NULL;
data_generator_number = NULL;
data_server_pub_key = NULL;
pub_key = NULL;
priv_key = NULL;
secret_mpi = NULL;
/* decode data */
data = malloc (strlen (data_base64) + 1);
length_data = weechat_string_decode_base64 (data_base64, data);
ptr_data = (unsigned char *)data;
/* extract prime number */
size = ntohs ((((unsigned int)ptr_data[1]) << 8) | ptr_data[0]);
ptr_data += 2;
length_data -= 2;
if (size > length_data)
goto dhend;
data_prime_number = gcry_mpi_new (size * 8);
gcry_mpi_scan (&data_prime_number, GCRYMPI_FMT_USG, ptr_data, size, NULL);
num_bits_prime_number = gcry_mpi_get_nbits (data_prime_number);
ptr_data += size;
length_data -= size;
/* extract generator number */
size = ntohs ((((unsigned int)ptr_data[1]) << 8) | ptr_data[0]);
ptr_data += 2;
length_data -= 2;
if (size > length_data)
goto dhend;
data_generator_number = gcry_mpi_new (size * 8);
gcry_mpi_scan (&data_generator_number, GCRYMPI_FMT_USG, ptr_data, size, NULL);
ptr_data += size;
length_data -= size;
/* extract server-generated public key */
size = ntohs ((((unsigned int)ptr_data[1]) << 8) | ptr_data[0]);
ptr_data += 2;
length_data -= 2;
if (size > length_data)
goto dhend;
data_server_pub_key = gcry_mpi_new (size * 8);
gcry_mpi_scan (&data_server_pub_key, GCRYMPI_FMT_USG, ptr_data, size, NULL);
/* generate keys */
pub_key = gcry_mpi_new (num_bits_prime_number);
priv_key = gcry_mpi_new (num_bits_prime_number);
gcry_mpi_randomize (priv_key, num_bits_prime_number, GCRY_STRONG_RANDOM);
/* pub_key = (g ^ priv_key) % p */
gcry_mpi_powm (pub_key, data_generator_number, priv_key, data_prime_number);
/* compute secret_bin */
*length_key = num_bits_prime_number / 8;
*secret_bin = malloc (*length_key);
secret_mpi = gcry_mpi_new (num_bits_prime_number);
/* secret_mpi = (y ^ priv_key) % p */
gcry_mpi_powm (secret_mpi, data_server_pub_key, priv_key, data_prime_number);
gcry_mpi_print (GCRYMPI_FMT_USG, *secret_bin, *length_key,
&num_written, secret_mpi);
/* create public_bin */
*public_bin = malloc (*length_key);
gcry_mpi_print (GCRYMPI_FMT_USG, *public_bin, *length_key,
&num_written, pub_key);
rc = 1;
dhend:
if (data)
free (data);
if (data_prime_number)
gcry_mpi_release (data_prime_number);
if (data_generator_number)
gcry_mpi_release (data_generator_number);
if (data_server_pub_key)
gcry_mpi_release (data_server_pub_key);
if (pub_key)
gcry_mpi_release (pub_key);
if (priv_key)
gcry_mpi_release (priv_key);
if (secret_mpi)
gcry_mpi_release (secret_mpi);
return rc;
}
nuts_mpi_t nuts_mpi_powm(const nuts_mpi_t b, const nuts_mpi_t e, const nuts_mpi_t m) {
gcry_mpi_t w = gcry_mpi_new(0);
gcry_mpi_powm(w, b->mpi, e->mpi, m->mpi);
return nuts_mpi_alloc(w);
}
/**
* Return true if n is probably a prime
*/
static int
is_prime (gcry_mpi_t n, int steps, struct GNUNET_HashCode * hc)
{
gcry_mpi_t x;
gcry_mpi_t y;
gcry_mpi_t z;
gcry_mpi_t nminus1;
gcry_mpi_t a2;
gcry_mpi_t q;
unsigned int i, j, k;
int rc = 0;
unsigned int nbits;
x = gcry_mpi_new (0);
y = gcry_mpi_new (0);
z = gcry_mpi_new (0);
nminus1 = gcry_mpi_new (0);
a2 = gcry_mpi_set_ui (NULL, 2);
nbits = gcry_mpi_get_nbits (n);
gcry_mpi_sub_ui (nminus1, n, 1);
/* Find q and k, so that n = 1 + 2^k * q . */
q = gcry_mpi_set (NULL, nminus1);
k = mpz_trailing_zeroes (q);
mpz_tdiv_q_2exp (q, q, k);
for (i = 0; i < steps; i++)
{
if (!i)
{
gcry_mpi_set_ui (x, 2);
}
else
{
mpz_randomize (x, nbits - 1, hc);
GNUNET_assert (gcry_mpi_cmp (x, nminus1) < 0);
GNUNET_assert (gcry_mpi_cmp_ui (x, 1) > 0);
}
gcry_mpi_powm (y, x, q, n);
if (gcry_mpi_cmp_ui (y, 1) && gcry_mpi_cmp (y, nminus1))
{
for (j = 1; j < k && gcry_mpi_cmp (y, nminus1); j++)
{
gcry_mpi_powm (y, y, a2, n);
if (!gcry_mpi_cmp_ui (y, 1))
goto leave; /* Not a prime. */
}
if (gcry_mpi_cmp (y, nminus1))
goto leave; /* Not a prime. */
}
}
rc = 1; /* May be a prime. */
leave:
gcry_mpi_release (x);
gcry_mpi_release (y);
gcry_mpi_release (z);
gcry_mpi_release (nminus1);
gcry_mpi_release (q);
gcry_mpi_release (a2);
return rc;
}
