along with GNUnet; see the file COPYING. If not, write to the
Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.
-*/
+ */
/**
* @file util/crypto_paillier.c
#include <gcrypt.h>
#include "gnunet_util_lib.h"
+
+/**
+ * Create a freshly generated paillier public key.
+ *
+ * @param[out] public_key Where to store the public key?
+ * @param[out] private_key Where to store the private key?
+ */
+void
+GNUNET_CRYPTO_paillier_create (struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
+ struct GNUNET_CRYPTO_PaillierPrivateKey *private_key)
+{
+ gcry_mpi_t p;
+ gcry_mpi_t q;
+
+ gcry_mpi_t phi;
+ gcry_mpi_t n;
+
+ GNUNET_assert (NULL != (phi = gcry_mpi_new (0)));
+ GNUNET_assert (NULL != (n = gcry_mpi_new (0)));
+
+ p = q = NULL;
+
+ // Generate two distinct primes.
+ // The probability that the loop body
+ // is executed more than once is very low.
+ do {
+ if (NULL != p)
+ gcry_mpi_release (p);
+ if (NULL != q)
+ gcry_mpi_release (q);
+ // generate rsa modulus
+ GNUNET_assert (0 == gcry_prime_generate (&p, GNUNET_CRYPTO_PAILLIER_BITS / 2, 0, NULL, NULL, NULL,
+ GCRY_WEAK_RANDOM, 0));
+ GNUNET_assert (0 == gcry_prime_generate (&q, GNUNET_CRYPTO_PAILLIER_BITS / 2, 0, NULL, NULL, NULL,
+ GCRY_WEAK_RANDOM, 0));
+ }
+ while (0 == gcry_mpi_cmp (p, q));
+ gcry_mpi_mul (n, p, q);
+ GNUNET_CRYPTO_mpi_print_unsigned (public_key, sizeof (struct GNUNET_CRYPTO_PaillierPublicKey), n);
+
+ // compute phi(n) = (p-1)(q-1)
+ gcry_mpi_sub_ui (p, p, 1);
+ gcry_mpi_sub_ui (q, q, 1);
+ gcry_mpi_mul (phi, p, q);
+
+ // lambda equals phi(n) in the simplified key generation
+ GNUNET_CRYPTO_mpi_print_unsigned (private_key->lambda, GNUNET_CRYPTO_PAILLIER_BITS / 8, phi);
+
+ // invert phi and abuse the phi mpi to store the result ...
+ GNUNET_assert (0 != gcry_mpi_invm (phi, phi, n));
+ GNUNET_CRYPTO_mpi_print_unsigned (private_key->mu, GNUNET_CRYPTO_PAILLIER_BITS / 8, phi);
+
+ gcry_mpi_release (p);
+ gcry_mpi_release (q);
+ gcry_mpi_release (phi);
+ gcry_mpi_release (n);
+}
+
+
+/**
+ * Encrypt a plaintext with a paillier public key.
+ *
+ * @param public_key Public key to use.
+ * @param m Plaintext to encrypt.
+ * @param desired_ops How many homomorphic ops the caller intends to use
+ * @param[out] ciphertext Encrytion of @a plaintext with @a public_key.
+ * @return guaranteed number of supported homomorphic operations >= 1,
+ * or desired_ops, in case that is lower,
+ * or -1 if less than one homomorphic operation is possible
+ */
+int
+GNUNET_CRYPTO_paillier_encrypt (const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
+ const gcry_mpi_t m,
+ int desired_ops,
+ struct GNUNET_CRYPTO_PaillierCiphertext *ciphertext)
+{
+ int possible_opts;
+ gcry_mpi_t n_square;
+ gcry_mpi_t r;
+ gcry_mpi_t c;
+ gcry_mpi_t n;
+ gcry_mpi_t tmp1;
+ gcry_mpi_t tmp2;
+
+ // determine how many operations we could allow, if the other number
+ // has the same length.
+ GNUNET_assert (NULL != (tmp1 = gcry_mpi_set_ui (NULL, 1)));
+ GNUNET_assert (NULL != (tmp2 = gcry_mpi_set_ui (NULL, 2)));
+ gcry_mpi_mul_2exp (tmp1, tmp1, GNUNET_CRYPTO_PAILLIER_BITS);
+
+ // count number of possible operations
+ // this would be nicer with gcry_mpi_get_nbits, however it does not return
+ // the BITLENGTH of the given MPI's value, but the bits required
+ // to represent the number as MPI.
+ for (possible_opts = -2; gcry_mpi_cmp (tmp1, m) > 0; possible_opts++) {
+ gcry_mpi_div (tmp1, NULL, tmp1, tmp2, 0);
+ }
+ gcry_mpi_release (tmp1);
+ gcry_mpi_release (tmp2);
+
+ if (possible_opts < 1)
+ possible_opts = 0;
+ //soft-cap by caller
+ possible_opts = (desired_ops < possible_opts)? desired_ops : possible_opts;
+
+ ciphertext->remaining_ops = htonl (possible_opts);
+
+ GNUNET_assert (0 != (n_square = gcry_mpi_new (0)));
+ GNUNET_assert (0 != (r = gcry_mpi_new (0)));
+ GNUNET_assert (0 != (c = gcry_mpi_new (0)));
+
+ GNUNET_CRYPTO_mpi_scan_unsigned (&n, public_key, sizeof (struct GNUNET_CRYPTO_PaillierPublicKey));
+
+ gcry_mpi_mul (n_square, n, n);
+
+ // generate r < n
+ do {
+ gcry_mpi_randomize (r, GNUNET_CRYPTO_PAILLIER_BITS, GCRY_WEAK_RANDOM);
+ }
+ while (gcry_mpi_cmp (r, n) >= 0);
+
+ // c = (n+1)^m mod n^2
+ gcry_mpi_add_ui (c, n, 1);
+ gcry_mpi_powm (c, c, m, n_square);
+ // r <- r^n mod n^2
+ gcry_mpi_powm (r, r, n, n_square);
+ // c <- r*c mod n^2
+ gcry_mpi_mulm (c, r, c, n_square);
+
+ GNUNET_CRYPTO_mpi_print_unsigned (ciphertext->bits,
+ sizeof ciphertext->bits,
+ c);
+
+ gcry_mpi_release (n_square);
+ gcry_mpi_release (n);
+ gcry_mpi_release (r);
+ gcry_mpi_release (c);
+
+ return possible_opts;
+}
+
+
+/**
+ * Decrypt a paillier ciphertext with a private key.
+ *
+ * @param private_key Private key to use for decryption.
+ * @param public_key Public key to use for encryption.
+ * @param ciphertext Ciphertext to decrypt.
+ * @param[out] m Decryption of @a ciphertext with @private_key.
+ */
+void
+GNUNET_CRYPTO_paillier_decrypt (const struct GNUNET_CRYPTO_PaillierPrivateKey *private_key,
+ const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
+ const struct GNUNET_CRYPTO_PaillierCiphertext *ciphertext,
+ gcry_mpi_t m)
+{
+ gcry_mpi_t mu;
+ gcry_mpi_t lambda;
+ gcry_mpi_t n;
+ gcry_mpi_t n_square;
+ gcry_mpi_t c;
+
+ GNUNET_assert (0 != (n_square = gcry_mpi_new (0)));
+
+ GNUNET_CRYPTO_mpi_scan_unsigned (&lambda, private_key->lambda, sizeof private_key->lambda);
+ GNUNET_CRYPTO_mpi_scan_unsigned (&mu, private_key->mu, sizeof private_key->mu);
+ GNUNET_CRYPTO_mpi_scan_unsigned (&n, public_key, sizeof *public_key);
+ GNUNET_CRYPTO_mpi_scan_unsigned (&c, ciphertext->bits, sizeof ciphertext->bits);
+
+ gcry_mpi_mul (n_square, n, n);
+ // m = c^lambda mod n^2
+ gcry_mpi_powm (m, c, lambda, n_square);
+ // m = m - 1
+ gcry_mpi_sub_ui (m, m, 1);
+ // m <- m/n
+ gcry_mpi_div (m, NULL, m, n, 0);
+ gcry_mpi_mulm (m, m, mu, n);
+
+ gcry_mpi_release (mu);
+ gcry_mpi_release (lambda);
+ gcry_mpi_release (n);
+ gcry_mpi_release (n_square);
+ gcry_mpi_release (c);
+}
+
+
+/**
+ * Compute a ciphertext that represents the sum of the plaintext in @a x1 and @a x2
+ *
+ * Note that this operation can only be done a finite number of times
+ * before an overflow occurs.
+ *
+ * @param public_key Public key to use for encryption.
+ * @param c1 Paillier cipher text.
+ * @param c2 Paillier cipher text.
+ * @param[out] result Result of the homomorphic operation.
+ * @return #GNUNET_OK if the result could be computed,
+ * #GNUNET_SYSERR if no more homomorphic operations are remaining.
+ */
+int
+GNUNET_CRYPTO_paillier_hom_add (const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
+ const struct GNUNET_CRYPTO_PaillierCiphertext *c1,
+ const struct GNUNET_CRYPTO_PaillierCiphertext *c2,
+ struct GNUNET_CRYPTO_PaillierCiphertext *result)
+{
+ gcry_mpi_t a;
+ gcry_mpi_t b;
+ gcry_mpi_t c;
+ gcry_mpi_t n_square;
+ int32_t o1;
+ int32_t o2;
+
+ o1 = ntohl (c1->remaining_ops);
+ o2 = ntohl (c2->remaining_ops);
+ if (0 >= o1 || 0 >= o2)
+ return GNUNET_SYSERR;
+
+ GNUNET_assert (0 != (c = gcry_mpi_new (0)));
+
+ GNUNET_CRYPTO_mpi_scan_unsigned (&a, c1->bits, sizeof c1->bits);
+ GNUNET_CRYPTO_mpi_scan_unsigned (&b, c1->bits, sizeof c2->bits);
+ GNUNET_CRYPTO_mpi_scan_unsigned (&n_square, public_key, sizeof *public_key);
+ gcry_mpi_mul (n_square, n_square, n_square);
+ gcry_mpi_mulm (c, a, b, n_square);
+
+ result->remaining_ops = htonl (((o2 > o1) ? o1 : o2) - 1);
+ GNUNET_CRYPTO_mpi_print_unsigned (result->bits,
+ sizeof result->bits,
+ c);
+ gcry_mpi_release (a);
+ gcry_mpi_release (b);
+ gcry_mpi_release (c);
+ gcry_mpi_release (n_square);
+ return ntohl (result->remaining_ops);
+}
+
+
+/**
+ * Get the number of remaining supported homomorphic operations.
+ *
+ * @param c Paillier cipher text.
+ * @return the number of remaining homomorphic operations
+ */
+int
+GNUNET_CRYPTO_paillier_hom_get_remaining (const struct GNUNET_CRYPTO_PaillierCiphertext *c)
+{
+ GNUNET_assert (NULL != c);
+ return ntohl (c->remaining_ops);
+}
+
/* end of crypto_paillier.c */
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