2 This file is part of GNUnet.
3 (C) 2014 Christian Grothoff (and other contributing authors)
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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
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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.
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16 along with GNUnet; see the file COPYING. If not, write to the
17 Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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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 (GNUNET_CRYPTO_PAILLIER_BITS)));
49 GNUNET_assert (NULL != (n = gcry_mpi_new (GNUNET_CRYPTO_PAILLIER_BITS)));
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));
66 } while (0 == gcry_mpi_cmp (p, q));
67 gcry_mpi_mul (n, p, q);
68 GNUNET_CRYPTO_mpi_print_unsigned (public_key, sizeof (struct GNUNET_CRYPTO_PaillierPublicKey), n);
70 // compute phi(n) = (p-1)(q-1)
71 gcry_mpi_sub_ui (p, p, 1);
72 gcry_mpi_sub_ui (q, q, 1);
73 gcry_mpi_mul (phi, p, q);
75 // lambda equals phi(n) in the simplified key generation
76 GNUNET_CRYPTO_mpi_print_unsigned (private_key->lambda, GNUNET_CRYPTO_PAILLIER_BITS / 8, phi);
78 // invert phi and abuse the phi mpi to store the result ...
79 GNUNET_assert (0 != gcry_mpi_invm (phi, phi, n));
80 GNUNET_CRYPTO_mpi_print_unsigned (private_key->mu, GNUNET_CRYPTO_PAILLIER_BITS / 8, phi);
84 gcry_mpi_release (phi);
90 * Encrypt a plaintext with a paillier public key.
92 * @param public_key Public key to use.
93 * @param m Plaintext to encrypt.
94 * @param[out] ciphertext Encrytion of @a plaintext with @a public_key.
95 * @return guaranteed number of supported homomorphic operations >= 1, -1 for failure
98 GNUNET_CRYPTO_paillier_encrypt (const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
100 struct GNUNET_CRYPTO_PaillierCiphertext *ciphertext)
109 // determine how many operations we could allow, if the other number
110 // has the same length.
111 length = gcry_mpi_get_nbits(m);
112 if (length >= GNUNET_CRYPTO_PAILLIER_BITS)
115 ciphertext->remaining_ops = ntohl(pow(2,(GNUNET_CRYPTO_PAILLIER_BITS-length-1)));
117 GNUNET_assert (0 != (n_square = gcry_mpi_new (0)));
118 GNUNET_assert (0 != (r = gcry_mpi_new (0)));
119 GNUNET_assert (0 != (g = gcry_mpi_new (0)));
120 GNUNET_assert (0 != (c = gcry_mpi_new (0)));
122 GNUNET_CRYPTO_mpi_scan_unsigned (&n, public_key, sizeof (struct GNUNET_CRYPTO_PaillierPublicKey));
124 gcry_mpi_mul (n_square, n, n);
129 gcry_mpi_randomize (r, GNUNET_CRYPTO_PAILLIER_BITS, GCRY_WEAK_RANDOM);
131 while (gcry_mpi_cmp (r, n) >= 0);
133 // c = (n+1)^m mod n^2
134 gcry_mpi_add_ui (c, n, 1);
135 gcry_mpi_powm (c, c, m, n_square);
137 gcry_mpi_powm (r, r, n, n_square);
139 gcry_mpi_mulm (c, r, c, n_square);
141 GNUNET_CRYPTO_mpi_print_unsigned (ciphertext->bits,
142 sizeof ciphertext->bits,
145 gcry_mpi_release (n_square);
146 gcry_mpi_release (r);
147 gcry_mpi_release (c);
149 return pow(2,(GNUNET_CRYPTO_PAILLIER_BITS-length-1));
154 * Decrypt a paillier ciphertext with a private key.
156 * @param private_key Private key to use for decryption.
157 * @param public_key Public key to use for encryption.
158 * @param ciphertext Ciphertext to decrypt.
159 * @param[out] m Decryption of @a ciphertext with @private_key.
162 GNUNET_CRYPTO_paillier_decrypt (const struct GNUNET_CRYPTO_PaillierPrivateKey *private_key,
163 const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
164 const struct GNUNET_CRYPTO_PaillierCiphertext *ciphertext,
173 GNUNET_assert (0 != (n_square = gcry_mpi_new (0)));
175 GNUNET_CRYPTO_mpi_scan_unsigned (&lambda, private_key->lambda, sizeof private_key->lambda);
176 GNUNET_CRYPTO_mpi_scan_unsigned (&mu, private_key->mu, sizeof private_key->mu);
177 GNUNET_CRYPTO_mpi_scan_unsigned (&n, public_key, sizeof *public_key);
178 GNUNET_CRYPTO_mpi_scan_unsigned (&c, ciphertext, sizeof *ciphertext);
180 gcry_mpi_mul (n_square, n, n);
181 // m = c^lambda mod n^2
182 gcry_mpi_powm (m, c, lambda, n_square);
184 gcry_mpi_sub_ui (m, m, 1);
186 gcry_mpi_div (m, NULL, m, n, 0);
187 gcry_mpi_mulm (m, m, mu, n);
189 gcry_mpi_release (mu);
190 gcry_mpi_release (lambda);
191 gcry_mpi_release (n);
192 gcry_mpi_release (n_square);
193 gcry_mpi_release (c);
198 * Compute a ciphertext that represents the sum of the plaintext in @a x1 and @a x2
200 * Note that this operation can only be done a finite number of times
201 * before an overflow occurs.
203 * @param public_key Public key to use for encryption.
204 * @param c1 Paillier cipher text.
205 * @param c2 Paillier cipher text.
206 * @param[out] result Result of the homomorphic operation.
207 * @return #GNUNET_OK if the result could be computed,
208 * #GNUNET_SYSERR if no more homomorphic operations are remaining.
211 GNUNET_CRYPTO_paillier_hom_add (const struct GNUNET_CRYPTO_PaillierPublicKey *public_key,
212 const struct GNUNET_CRYPTO_PaillierCiphertext *c1,
213 const struct GNUNET_CRYPTO_PaillierCiphertext *c2,
214 struct GNUNET_CRYPTO_PaillierCiphertext *result)
221 if (0 == c1->remaining_ops || 0 == c2->remaining_ops)
222 return GNUNET_SYSERR;
224 GNUNET_assert (0 != (c = gcry_mpi_new (0)));
226 GNUNET_CRYPTO_mpi_scan_unsigned (&a, c1->bits, sizeof c1->bits);
227 GNUNET_CRYPTO_mpi_scan_unsigned (&b, c1->bits, sizeof c2->bits);
228 GNUNET_CRYPTO_mpi_scan_unsigned (&n_square, public_key, sizeof *public_key);
229 gcry_mpi_mul(n_square, n_square,n_square);
230 gcry_mpi_mulm(c,a,b,n_square);
232 result->remaining_ops = (c1->remaining_ops > c2->remaining_ops) ? c2->remaining_ops : c1->remaining_ops;
233 GNUNET_CRYPTO_mpi_print_unsigned (result->bits,
236 gcry_mpi_release (a);
237 gcry_mpi_release (b);
238 gcry_mpi_release (c);
239 gcry_mpi_release (n_square);
244 /* end of crypto_paillier.c */