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-rw-r--r--pwmanager/libcrypt/cipher/elgamal.c682
1 files changed, 682 insertions, 0 deletions
diff --git a/pwmanager/libcrypt/cipher/elgamal.c b/pwmanager/libcrypt/cipher/elgamal.c
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+++ b/pwmanager/libcrypt/cipher/elgamal.c
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+/* Elgamal.c - ElGamal Public Key encryption
+ * Copyright (C) 1998, 2000, 2001, 2002, 2003 Free Software Foundation, Inc.
+ *
+ * This file is part of Libgcrypt.
+ *
+ * Libgcrypt is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser general Public License as
+ * published by the Free Software Foundation; either version 2.1 of
+ * the License, or (at your option) any later version.
+ *
+ * Libgcrypt 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 Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser 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
+ *
+ * For a description of the algorithm, see:
+ * Bruce Schneier: Applied Cryptography. John Wiley & Sons, 1996.
+ * ISBN 0-471-11709-9. Pages 476 ff.
+ */
+
+#include <config.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "g10lib.h"
+#include "mpi.h"
+#include "cipher.h"
+
+typedef struct
+{
+ gcry_mpi_t p; /* prime */
+ gcry_mpi_t g; /* group generator */
+ gcry_mpi_t y; /* g^x mod p */
+} ELG_public_key;
+
+
+typedef struct
+{
+ gcry_mpi_t p; /* prime */
+ gcry_mpi_t g; /* group generator */
+ gcry_mpi_t y; /* g^x mod p */
+ gcry_mpi_t x; /* secret exponent */
+} ELG_secret_key;
+
+
+static void test_keys (ELG_secret_key *sk, unsigned nbits);
+static gcry_mpi_t gen_k (gcry_mpi_t p, int small_k);
+static void generate (ELG_secret_key *sk, unsigned nbits, gcry_mpi_t **factors);
+static int check_secret_key (ELG_secret_key *sk);
+static void do_encrypt (gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input,
+ ELG_public_key *pkey);
+static void decrypt (gcry_mpi_t output, gcry_mpi_t a, gcry_mpi_t b,
+ ELG_secret_key *skey);
+static void sign (gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input,
+ ELG_secret_key *skey);
+static int verify (gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input,
+ ELG_public_key *pkey);
+
+
+static void (*progress_cb) (void *, const char *, int, int, int);
+static void *progress_cb_data;
+
+void
+_gcry_register_pk_elg_progress (void (*cb) (void *, const char *,
+ int, int, int),
+ void *cb_data)
+{
+ progress_cb = cb;
+ progress_cb_data = cb_data;
+}
+
+
+static void
+progress (int c)
+{
+ if (progress_cb)
+ progress_cb (progress_cb_data, "pk_elg", c, 0, 0);
+}
+
+
+/****************
+ * Michael Wiener's table on subgroup sizes to match field sizes
+ * (floating around somewhere - Fixme: need a reference)
+ */
+static unsigned int
+wiener_map( unsigned int n )
+{
+ static struct { unsigned int p_n, q_n; } t[] =
+ { /* p q attack cost */
+ { 512, 119 }, /* 9 x 10^17 */
+ { 768, 145 }, /* 6 x 10^21 */
+ { 1024, 165 }, /* 7 x 10^24 */
+ { 1280, 183 }, /* 3 x 10^27 */
+ { 1536, 198 }, /* 7 x 10^29 */
+ { 1792, 212 }, /* 9 x 10^31 */
+ { 2048, 225 }, /* 8 x 10^33 */
+ { 2304, 237 }, /* 5 x 10^35 */
+ { 2560, 249 }, /* 3 x 10^37 */
+ { 2816, 259 }, /* 1 x 10^39 */
+ { 3072, 269 }, /* 3 x 10^40 */
+ { 3328, 279 }, /* 8 x 10^41 */
+ { 3584, 288 }, /* 2 x 10^43 */
+ { 3840, 296 }, /* 4 x 10^44 */
+ { 4096, 305 }, /* 7 x 10^45 */
+ { 4352, 313 }, /* 1 x 10^47 */
+ { 4608, 320 }, /* 2 x 10^48 */
+ { 4864, 328 }, /* 2 x 10^49 */
+ { 5120, 335 }, /* 3 x 10^50 */
+ { 0, 0 }
+ };
+ int i;
+
+ for(i=0; t[i].p_n; i++ )
+ {
+ if( n <= t[i].p_n )
+ return t[i].q_n;
+ }
+ /* Not in table - use an arbitrary high number. */
+ return n / 8 + 200;
+}
+
+static void
+test_keys( ELG_secret_key *sk, unsigned nbits )
+{
+ ELG_public_key pk;
+ gcry_mpi_t test = gcry_mpi_new ( 0 );
+ gcry_mpi_t out1_a = gcry_mpi_new ( nbits );
+ gcry_mpi_t out1_b = gcry_mpi_new ( nbits );
+ gcry_mpi_t out2 = gcry_mpi_new ( nbits );
+
+ pk.p = sk->p;
+ pk.g = sk->g;
+ pk.y = sk->y;
+
+ gcry_mpi_randomize( test, nbits, GCRY_WEAK_RANDOM );
+
+ do_encrypt( out1_a, out1_b, test, &pk );
+ decrypt( out2, out1_a, out1_b, sk );
+ if( mpi_cmp( test, out2 ) )
+ log_fatal("ElGamal operation: encrypt, decrypt failed\n");
+
+ sign( out1_a, out1_b, test, sk );
+ if( !verify( out1_a, out1_b, test, &pk ) )
+ log_fatal("ElGamal operation: sign, verify failed\n");
+
+ gcry_mpi_release ( test );
+ gcry_mpi_release ( out1_a );
+ gcry_mpi_release ( out1_b );
+ gcry_mpi_release ( out2 );
+}
+
+
+/****************
+ * Generate a random secret exponent k from prime p, so that k is
+ * relatively prime to p-1. With SMALL_K set, k will be selected for
+ * better encryption performance - this must never be used signing!
+ */
+static gcry_mpi_t
+gen_k( gcry_mpi_t p, int small_k )
+{
+ gcry_mpi_t k = mpi_alloc_secure( 0 );
+ gcry_mpi_t temp = mpi_alloc( mpi_get_nlimbs(p) );
+ gcry_mpi_t p_1 = mpi_copy(p);
+ unsigned int orig_nbits = mpi_get_nbits(p);
+ unsigned int nbits, nbytes;
+ char *rndbuf = NULL;
+
+ if (small_k)
+ {
+ /* Using a k much lesser than p is sufficient for encryption and
+ * it greatly improves the encryption performance. We use
+ * Wiener's table and add a large safety margin. */
+ nbits = wiener_map( orig_nbits ) * 3 / 2;
+ if( nbits >= orig_nbits )
+ BUG();
+ }
+ else
+ nbits = orig_nbits;
+
+
+ nbytes = (nbits+7)/8;
+ if( DBG_CIPHER )
+ log_debug("choosing a random k ");
+ mpi_sub_ui( p_1, p, 1);
+ for(;;)
+ {
+ if( !rndbuf || nbits < 32 )
+ {
+ gcry_free(rndbuf);
+ rndbuf = gcry_random_bytes_secure( nbytes, GCRY_STRONG_RANDOM );
+ }
+ else
+ {
+ /* Change only some of the higher bits. We could improve
+ this by directly requesting more memory at the first call
+ to get_random_bytes() and use this the here maybe it is
+ easier to do this directly in random.c Anyway, it is
+ highly inlikely that we will ever reach this code. */
+ char *pp = gcry_random_bytes_secure( 4, GCRY_STRONG_RANDOM );
+ memcpy( rndbuf, pp, 4 );
+ gcry_free(pp);
+ }
+ _gcry_mpi_set_buffer( k, rndbuf, nbytes, 0 );
+
+ for(;;)
+ {
+ if( !(mpi_cmp( k, p_1 ) < 0) ) /* check: k < (p-1) */
+ {
+ if( DBG_CIPHER )
+ progress('+');
+ break; /* no */
+ }
+ if( !(mpi_cmp_ui( k, 0 ) > 0) ) /* check: k > 0 */
+ {
+ if( DBG_CIPHER )
+ progress('-');
+ break; /* no */
+ }
+ if (gcry_mpi_gcd( temp, k, p_1 ))
+ goto found; /* okay, k is relative prime to (p-1) */
+ mpi_add_ui( k, k, 1 );
+ if( DBG_CIPHER )
+ progress('.');
+ }
+ }
+ found:
+ gcry_free(rndbuf);
+ if( DBG_CIPHER )
+ progress('\n');
+ mpi_free(p_1);
+ mpi_free(temp);
+
+ return k;
+}
+
+/****************
+ * Generate a key pair with a key of size NBITS
+ * Returns: 2 structures filles 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;
+ gcry_mpi_t temp;
+ unsigned int qbits;
+ unsigned int xbits;
+ byte *rndbuf;
+
+ p_min1 = gcry_mpi_new ( nbits );
+ temp = 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;
+
+ /* Now we can test our keys (this should never fail!) */
+ test_keys( sk, nbits - 64 );
+
+ gcry_mpi_release ( p_min1 );
+ gcry_mpi_release ( temp );
+}
+
+
+/****************
+ * 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;
+}
+
+
+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);
+}
+
+
+
+
+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);
+}
+
+
+/****************
+ * Make an Elgamal signature out of INPUT
+ */
+
+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);
+}
+
+
+/****************
+ * 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;
+}
+
+/*********************************************
+ ************** interface ******************
+ *********************************************/
+
+gcry_err_code_t
+_gcry_elg_generate (int algo, unsigned nbits, unsigned long dummy,
+ gcry_mpi_t *skey, gcry_mpi_t **retfactors)
+{
+ ELG_secret_key sk;
+
+ generate (&sk, nbits, retfactors);
+ skey[0] = sk.p;
+ skey[1] = sk.g;
+ skey[2] = sk.y;
+ skey[3] = sk.x;
+
+ return GPG_ERR_NO_ERROR;
+}
+
+
+gcry_err_code_t
+_gcry_elg_check_secret_key (int algo, gcry_mpi_t *skey)
+{
+ gcry_err_code_t err = GPG_ERR_NO_ERROR;
+ ELG_secret_key sk;
+
+ if ((! skey[0]) || (! skey[1]) || (! skey[2]) || (! skey[3]))
+ err = GPG_ERR_BAD_MPI;
+ else
+ {
+ sk.p = skey[0];
+ sk.g = skey[1];
+ sk.y = skey[2];
+ sk.x = skey[3];
+
+ if (! check_secret_key (&sk))
+ err = GPG_ERR_BAD_SECKEY;
+ }
+
+ return err;
+}
+
+
+gcry_err_code_t
+_gcry_elg_encrypt (int algo, gcry_mpi_t *resarr,
+ gcry_mpi_t data, gcry_mpi_t *pkey, int flags)
+{
+ gcry_err_code_t err = GPG_ERR_NO_ERROR;
+ ELG_public_key pk;
+
+ if ((! data) || (! pkey[0]) || (! pkey[1]) || (! pkey[2]))
+ err = GPG_ERR_BAD_MPI;
+ else
+ {
+ pk.p = pkey[0];
+ pk.g = pkey[1];
+ pk.y = pkey[2];
+ resarr[0] = mpi_alloc (mpi_get_nlimbs (pk.p));
+ resarr[1] = mpi_alloc (mpi_get_nlimbs (pk.p));
+ do_encrypt (resarr[0], resarr[1], data, &pk);
+ }
+ return err;
+}
+
+
+gcry_err_code_t
+_gcry_elg_decrypt (int algo, gcry_mpi_t *result,
+ gcry_mpi_t *data, gcry_mpi_t *skey, int flags)
+{
+ gcry_err_code_t err = GPG_ERR_NO_ERROR;
+ ELG_secret_key sk;
+
+ if ((! data[0]) || (! data[1])
+ || (! skey[0]) || (! skey[1]) || (! skey[2]) || (! skey[3]))
+ err = GPG_ERR_BAD_MPI;
+ else
+ {
+ sk.p = skey[0];
+ sk.g = skey[1];
+ sk.y = skey[2];
+ sk.x = skey[3];
+ *result = mpi_alloc_secure (mpi_get_nlimbs (sk.p));
+ decrypt (*result, data[0], data[1], &sk);
+ }
+ return err;
+}
+
+
+gcry_err_code_t
+_gcry_elg_sign (int algo, gcry_mpi_t *resarr, gcry_mpi_t data, gcry_mpi_t *skey)
+{
+ gcry_err_code_t err = GPG_ERR_NO_ERROR;
+ ELG_secret_key sk;
+
+ if ((! data)
+ || (! skey[0]) || (! skey[1]) || (! skey[2]) || (! skey[3]))
+ err = GPG_ERR_BAD_MPI;
+ else
+ {
+ sk.p = skey[0];
+ sk.g = skey[1];
+ sk.y = skey[2];
+ sk.x = skey[3];
+ resarr[0] = mpi_alloc (mpi_get_nlimbs (sk.p));
+ resarr[1] = mpi_alloc (mpi_get_nlimbs (sk.p));
+ sign (resarr[0], resarr[1], data, &sk);
+ }
+
+ return err;
+}
+
+gcry_err_code_t
+_gcry_elg_verify (int algo, gcry_mpi_t hash, gcry_mpi_t *data, gcry_mpi_t *pkey,
+ int (*cmp) (void *, gcry_mpi_t), void *opaquev)
+{
+ gcry_err_code_t err = GPG_ERR_NO_ERROR;
+ ELG_public_key pk;
+
+ if ((! data[0]) || (! data[1]) || (! hash)
+ || (! pkey[0]) || (! pkey[1]) || (! pkey[2]))
+ err = GPG_ERR_BAD_MPI;
+ else
+ {
+ pk.p = pkey[0];
+ pk.g = pkey[1];
+ pk.y = pkey[2];
+ if (! verify (data[0], data[1], hash, &pk))
+ err = GPG_ERR_BAD_SIGNATURE;
+ }
+
+ return err;
+}
+
+
+unsigned int
+_gcry_elg_get_nbits (int algo, gcry_mpi_t *pkey)
+{
+ return mpi_get_nbits (pkey[0]);
+}
+
+static char *elg_names[] =
+ {
+ "elg",
+ "openpgp-elg",
+ "openpgp-elg-sig",
+ NULL,
+ };
+
+
+gcry_pk_spec_t _gcry_pubkey_spec_elg =
+ {
+ "ELG", elg_names,
+ "pgy", "pgyx", "ab", "rs", "pgy",
+ GCRY_PK_USAGE_SIGN | GCRY_PK_USAGE_ENCR,
+ _gcry_elg_generate,
+ _gcry_elg_check_secret_key,
+ _gcry_elg_encrypt,
+ _gcry_elg_decrypt,
+ _gcry_elg_sign,
+ _gcry_elg_verify,
+ _gcry_elg_get_nbits,
+ };