2 This file is part of GNUnet.
3 (C) 2014 Christian Grothoff (and other contributing authors)
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13 General Public License for more details.
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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)
116 // determine how many operations we could allow, if the other number
117 // has the same length.
118 GNUNET_assert (NULL != (tmp1 = gcry_mpi_set_ui (NULL, 1)));
119 GNUNET_assert (NULL != (tmp2 = gcry_mpi_set_ui (NULL, 2)));
120 gcry_mpi_mul_2exp (tmp1, tmp1, GNUNET_CRYPTO_PAILLIER_BITS);
122 // count number of possible operations
123 // this would be nicer with gcry_mpi_get_nbits, however it does not return
124 // the BITLENGTH of the given MPI's value, but the bits required
125 // to represent the number as MPI.
126 for (possible_opts = -2; gcry_mpi_cmp (tmp1, m) > 0; possible_opts++) {
127 gcry_mpi_div (tmp1, NULL, tmp1, tmp2, 0);
129 gcry_mpi_release (tmp1);
130 gcry_mpi_release (tmp2);
132 if (possible_opts < 1)
135 possible_opts = (desired_ops < possible_opts)? desired_ops : possible_opts;
137 ciphertext->remaining_ops = htonl (possible_opts);
139 GNUNET_assert (0 != (n_square = gcry_mpi_new (0)));
140 GNUNET_assert (0 != (r = gcry_mpi_new (0)));
141 GNUNET_assert (0 != (g = gcry_mpi_new (0)));
142 GNUNET_assert (0 != (c = gcry_mpi_new (0)));
144 GNUNET_CRYPTO_mpi_scan_unsigned (&n, public_key, sizeof (struct GNUNET_CRYPTO_PaillierPublicKey));
146 gcry_mpi_mul (n_square, n, n);
150 gcry_mpi_randomize (r, GNUNET_CRYPTO_PAILLIER_BITS, GCRY_WEAK_RANDOM);
152 while (gcry_mpi_cmp (r, n) >= 0);
154 // c = (n+1)^m mod n^2
155 gcry_mpi_add_ui (c, n, 1);
156 gcry_mpi_powm (c, c, m, n_square);
158 gcry_mpi_powm (r, r, n, n_square);
160 gcry_mpi_mulm (c, r, c, n_square);
162 GNUNET_CRYPTO_mpi_print_unsigned (ciphertext->bits,
163 sizeof ciphertext->bits,
166 gcry_mpi_release (n_square);
167 gcry_mpi_release (r);
168 gcry_mpi_release (c);
170 return possible_opts;
175 * Decrypt a paillier ciphertext with a private key.
177 * @param private_key Private key to use for decryption.
178 * @param public_key Public key to use for encryption.
179 * @param ciphertext Ciphertext to decrypt.
180 * @param[out] m Decryption of @a ciphertext with @private_key.
183 GNUNET_CRYPTO_paillier_decrypt (const struct GNUNET_CRYPTO_PaillierPrivateKey *private_key,
184 const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
185 const struct GNUNET_CRYPTO_PaillierCiphertext *ciphertext,
194 GNUNET_assert (0 != (n_square = gcry_mpi_new (0)));
196 GNUNET_CRYPTO_mpi_scan_unsigned (&lambda, private_key->lambda, sizeof private_key->lambda);
197 GNUNET_CRYPTO_mpi_scan_unsigned (&mu, private_key->mu, sizeof private_key->mu);
198 GNUNET_CRYPTO_mpi_scan_unsigned (&n, public_key, sizeof *public_key);
199 GNUNET_CRYPTO_mpi_scan_unsigned (&c, ciphertext->bits, sizeof ciphertext->bits);
201 gcry_mpi_mul (n_square, n, n);
202 // m = c^lambda mod n^2
203 gcry_mpi_powm (m, c, lambda, n_square);
205 gcry_mpi_sub_ui (m, m, 1);
207 gcry_mpi_div (m, NULL, m, n, 0);
208 gcry_mpi_mulm (m, m, mu, n);
210 gcry_mpi_release (mu);
211 gcry_mpi_release (lambda);
212 gcry_mpi_release (n);
213 gcry_mpi_release (n_square);
214 gcry_mpi_release (c);
219 * Compute a ciphertext that represents the sum of the plaintext in @a x1 and @a x2
221 * Note that this operation can only be done a finite number of times
222 * before an overflow occurs.
224 * @param public_key Public key to use for encryption.
225 * @param c1 Paillier cipher text.
226 * @param c2 Paillier cipher text.
227 * @param[out] result Result of the homomorphic operation.
228 * @return #GNUNET_OK if the result could be computed,
229 * #GNUNET_SYSERR if no more homomorphic operations are remaining.
232 GNUNET_CRYPTO_paillier_hom_add (const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
233 const struct GNUNET_CRYPTO_PaillierCiphertext *c1,
234 const struct GNUNET_CRYPTO_PaillierCiphertext *c2,
235 struct GNUNET_CRYPTO_PaillierCiphertext *result)
244 o1 = ntohl (c1->remaining_ops);
245 o2 = ntohl (c2->remaining_ops);
246 if (0 >= o1 || 0 >= o2)
247 return GNUNET_SYSERR;
249 GNUNET_assert (0 != (c = gcry_mpi_new (0)));
251 GNUNET_CRYPTO_mpi_scan_unsigned (&a, c1->bits, sizeof c1->bits);
252 GNUNET_CRYPTO_mpi_scan_unsigned (&b, c1->bits, sizeof c2->bits);
253 GNUNET_CRYPTO_mpi_scan_unsigned (&n_square, public_key, sizeof *public_key);
254 gcry_mpi_mul (n_square, n_square, n_square);
255 gcry_mpi_mulm (c, a, b, n_square);
257 result->remaining_ops = htonl (((o2 > o1) ? o1 : o2) - 1);
258 GNUNET_CRYPTO_mpi_print_unsigned (result->bits,
261 gcry_mpi_release (a);
262 gcry_mpi_release (b);
263 gcry_mpi_release (c);
264 gcry_mpi_release (n_square);
265 return ntohl (result->remaining_ops);
270 * Get the number of remaining supported homomorphic operations.
272 * @param c Paillier cipher text.
273 * @return the number of remaining homomorphic operations
276 GNUNET_CRYPTO_paillier_hom_get_remaining (const struct GNUNET_CRYPTO_PaillierCiphertext *c)
278 GNUNET_assert (NULL != c);
279 return ntohl (c->remaining_ops);
282 /* end of crypto_paillier.c */