2 This file is part of GNUnet.
3 (C) 2014 Christian Grothoff (and other contributing authors)
5 GNUnet is free software; you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published
7 by the Free Software Foundation; either version 3, or (at your
8 option) any later version.
10 GNUnet is distributed in the hope that it will be useful, but
11 WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with GNUnet; see the file COPYING. If not, write to the
17 Free Software Foundation, Inc., 59 Temple Place - Suite 330,
18 Boston, MA 02111-1307, USA.
22 * @file util/crypto_paillier.c
23 * @brief implementation of the paillier crypto system with libgcrypt
24 * @author Florian Dold
25 * @author Christian Fuchs
29 #include "gnunet_util_lib.h"
33 * Create a freshly generated paillier public key.
35 * @param[out] public_key Where to store the public key?
36 * @param[out] private_key Where to store the private key?
39 GNUNET_CRYPTO_paillier_create (struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
40 struct GNUNET_CRYPTO_PaillierPrivateKey *private_key)
48 GNUNET_assert (NULL != (phi = gcry_mpi_new (0)));
49 GNUNET_assert (NULL != (n = gcry_mpi_new (0)));
53 // Generate two distinct primes.
54 // The probability that the loop body
55 // is executed more than once is very low.
61 // generate rsa modulus
62 GNUNET_assert (0 == gcry_prime_generate (&p, GNUNET_CRYPTO_PAILLIER_BITS / 2, 0, NULL, NULL, NULL,
63 GCRY_WEAK_RANDOM, 0));
64 GNUNET_assert (0 == gcry_prime_generate (&q, GNUNET_CRYPTO_PAILLIER_BITS / 2, 0, NULL, NULL, NULL,
65 GCRY_WEAK_RANDOM, 0));
67 while (0 == gcry_mpi_cmp (p, q));
68 gcry_mpi_mul (n, p, q);
69 GNUNET_CRYPTO_mpi_print_unsigned (public_key, sizeof (struct GNUNET_CRYPTO_PaillierPublicKey), n);
71 // compute phi(n) = (p-1)(q-1)
72 gcry_mpi_sub_ui (p, p, 1);
73 gcry_mpi_sub_ui (q, q, 1);
74 gcry_mpi_mul (phi, p, q);
76 // lambda equals phi(n) in the simplified key generation
77 GNUNET_CRYPTO_mpi_print_unsigned (private_key->lambda, GNUNET_CRYPTO_PAILLIER_BITS / 8, phi);
79 // invert phi and abuse the phi mpi to store the result ...
80 GNUNET_assert (0 != gcry_mpi_invm (phi, phi, n));
81 GNUNET_CRYPTO_mpi_print_unsigned (private_key->mu, GNUNET_CRYPTO_PAILLIER_BITS / 8, phi);
85 gcry_mpi_release (phi);
91 * Encrypt a plaintext with a paillier public key.
93 * @param public_key Public key to use.
94 * @param m Plaintext to encrypt.
95 * @param desired_ops How many homomorphic ops the caller intends to use
96 * @param[out] ciphertext Encrytion of @a plaintext with @a public_key.
97 * @return guaranteed number of supported homomorphic operations >= 1,
98 * or desired_ops, in case that is lower,
99 * or -1 if less than one homomorphic operation is possible
102 GNUNET_CRYPTO_paillier_encrypt (const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
105 struct GNUNET_CRYPTO_PaillierCiphertext *ciphertext)
115 // determine how many operations we could allow, if the other number
116 // has the same length.
117 GNUNET_assert (NULL != (tmp1 = gcry_mpi_set_ui (NULL, 1)));
118 GNUNET_assert (NULL != (tmp2 = gcry_mpi_set_ui (NULL, 2)));
119 gcry_mpi_mul_2exp (tmp1, tmp1, GNUNET_CRYPTO_PAILLIER_BITS);
121 // count number of possible operations
122 // this would be nicer with gcry_mpi_get_nbits, however it does not return
123 // the BITLENGTH of the given MPI's value, but the bits required
124 // to represent the number as MPI.
125 for (possible_opts = -2; gcry_mpi_cmp (tmp1, m) > 0; possible_opts++) {
126 gcry_mpi_div (tmp1, NULL, tmp1, tmp2, 0);
128 gcry_mpi_release (tmp1);
129 gcry_mpi_release (tmp2);
131 if (possible_opts < 1)
134 possible_opts = (desired_ops < possible_opts)? desired_ops : possible_opts;
136 ciphertext->remaining_ops = htonl (possible_opts);
138 GNUNET_assert (0 != (n_square = gcry_mpi_new (0)));
139 GNUNET_assert (0 != (r = gcry_mpi_new (0)));
140 GNUNET_assert (0 != (c = gcry_mpi_new (0)));
142 GNUNET_CRYPTO_mpi_scan_unsigned (&n, public_key, sizeof (struct GNUNET_CRYPTO_PaillierPublicKey));
144 gcry_mpi_mul (n_square, n, n);
148 gcry_mpi_randomize (r, GNUNET_CRYPTO_PAILLIER_BITS, GCRY_WEAK_RANDOM);
150 while (gcry_mpi_cmp (r, n) >= 0);
152 // c = (n+1)^m mod n^2
153 gcry_mpi_add_ui (c, n, 1);
154 gcry_mpi_powm (c, c, m, n_square);
156 gcry_mpi_powm (r, r, n, n_square);
158 gcry_mpi_mulm (c, r, c, n_square);
160 GNUNET_CRYPTO_mpi_print_unsigned (ciphertext->bits,
161 sizeof ciphertext->bits,
164 gcry_mpi_release (n_square);
165 gcry_mpi_release (n);
166 gcry_mpi_release (r);
167 gcry_mpi_release (c);
169 return possible_opts;
174 * Decrypt a paillier ciphertext with a private key.
176 * @param private_key Private key to use for decryption.
177 * @param public_key Public key to use for encryption.
178 * @param ciphertext Ciphertext to decrypt.
179 * @param[out] m Decryption of @a ciphertext with @private_key.
182 GNUNET_CRYPTO_paillier_decrypt (const struct GNUNET_CRYPTO_PaillierPrivateKey *private_key,
183 const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
184 const struct GNUNET_CRYPTO_PaillierCiphertext *ciphertext,
193 GNUNET_assert (0 != (n_square = gcry_mpi_new (0)));
195 GNUNET_CRYPTO_mpi_scan_unsigned (&lambda, private_key->lambda, sizeof private_key->lambda);
196 GNUNET_CRYPTO_mpi_scan_unsigned (&mu, private_key->mu, sizeof private_key->mu);
197 GNUNET_CRYPTO_mpi_scan_unsigned (&n, public_key, sizeof *public_key);
198 GNUNET_CRYPTO_mpi_scan_unsigned (&c, ciphertext->bits, sizeof ciphertext->bits);
200 gcry_mpi_mul (n_square, n, n);
201 // m = c^lambda mod n^2
202 gcry_mpi_powm (m, c, lambda, n_square);
204 gcry_mpi_sub_ui (m, m, 1);
206 gcry_mpi_div (m, NULL, m, n, 0);
207 gcry_mpi_mulm (m, m, mu, n);
209 gcry_mpi_release (mu);
210 gcry_mpi_release (lambda);
211 gcry_mpi_release (n);
212 gcry_mpi_release (n_square);
213 gcry_mpi_release (c);
218 * Compute a ciphertext that represents the sum of the plaintext in @a x1 and @a x2
220 * Note that this operation can only be done a finite number of times
221 * before an overflow occurs.
223 * @param public_key Public key to use for encryption.
224 * @param c1 Paillier cipher text.
225 * @param c2 Paillier cipher text.
226 * @param[out] result Result of the homomorphic operation.
227 * @return #GNUNET_OK if the result could be computed,
228 * #GNUNET_SYSERR if no more homomorphic operations are remaining.
231 GNUNET_CRYPTO_paillier_hom_add (const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
232 const struct GNUNET_CRYPTO_PaillierCiphertext *c1,
233 const struct GNUNET_CRYPTO_PaillierCiphertext *c2,
234 struct GNUNET_CRYPTO_PaillierCiphertext *result)
243 o1 = ntohl (c1->remaining_ops);
244 o2 = ntohl (c2->remaining_ops);
245 if (0 >= o1 || 0 >= o2)
246 return GNUNET_SYSERR;
248 GNUNET_assert (0 != (c = gcry_mpi_new (0)));
250 GNUNET_CRYPTO_mpi_scan_unsigned (&a, c1->bits, sizeof c1->bits);
251 GNUNET_CRYPTO_mpi_scan_unsigned (&b, c1->bits, sizeof c2->bits);
252 GNUNET_CRYPTO_mpi_scan_unsigned (&n_square, public_key, sizeof *public_key);
253 gcry_mpi_mul (n_square, n_square, n_square);
254 gcry_mpi_mulm (c, a, b, n_square);
256 result->remaining_ops = htonl (((o2 > o1) ? o1 : o2) - 1);
257 GNUNET_CRYPTO_mpi_print_unsigned (result->bits,
260 gcry_mpi_release (a);
261 gcry_mpi_release (b);
262 gcry_mpi_release (c);
263 gcry_mpi_release (n_square);
264 return ntohl (result->remaining_ops);
269 * Get the number of remaining supported homomorphic operations.
271 * @param c Paillier cipher text.
272 * @return the number of remaining homomorphic operations
275 GNUNET_CRYPTO_paillier_hom_get_remaining (const struct GNUNET_CRYPTO_PaillierCiphertext *c)
277 GNUNET_assert (NULL != c);
278 return ntohl (c->remaining_ops);
281 /* end of crypto_paillier.c */