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; }