3 rsa.c RSA Public and Private key generation functions,
4 RSA encrypt and decrypt functions.
6 Author: Pekka Riikonen <priikone@silcnet.org>
8 Copyright (C) 1997 - 2006 Pekka Riikonen
10 This program is free software; you can redistribute it and/or modify
11 it under the terms of the GNU General Public License as published by
12 the Free Software Foundation; version 2 of the License.
14 This program is distributed in the hope that it will be useful,
15 but WITHOUT ANY WARRANTY; without even the implied warranty of
16 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 GNU General Public License for more details.
19 Created: Sat Mar 1 13:26:45 1997 pekka
21 RSA public key cryptographic algorithm used in this distribution is:
29 e relatively prime to (p-1) * (q-1)
31 d = e ^ -1 mod lcm(((p-1) * (q-1)))
38 Supports CRT (Chinese Remainder Theorem) for private key operations.
40 The SSH's (Secure Shell), PGP's (Pretty Good Privacy) and RSAREF
41 Toolkit were used as reference when coding this implementation. They
42 all were a big help for me.
44 I also suggest reading Bruce Schneier's; Applied Cryptography, Second
45 Edition, John Wiley & Sons, Inc. 1996. This book deals about RSA and
46 everything else too about cryptography.
54 o Mon Feb 12 11:20:32 EET 2001 Pekka
56 Changed RSA private exponent generation to what PKCS #1 suggests. We
57 try to find the smallest possible d by doing modinv(e, lcm(phi)) instead
58 of modinv(e, phi). Note: this is not security fix but optimization.
60 o Tue Feb 20 13:58:58 EET 2001 Pekka
62 Set key->bits in rsa_generate_key. It is the modulus length in bits.
63 The `tmplen' in encrypt, decrypt, sign and verify PKCS API functions
64 is now calculated by (key->bits + 7) / 8. It is the length of one block.
66 o Sat Mar 16 18:27:19 EET 2002 Pekka
68 Use the SilcRng sent as argument to SILC_PKCS_API_INIT in prime
71 o Sat Sep 26 19:59:48 EEST 2002 Pekka
73 Fixed double free in public key setting. Use a bit larger e as
74 starting point in key generation.
76 o Fri Dec 30 13:39:51 EET 2005 Pekka
78 Support PKCS #1 format public and private keys. Support for new
85 /* Generates RSA public and private keys. Primes p and q that are used
86 to compute the modulus n has to be generated before calling this. They
87 are then sent as argument for the function. */
89 SilcBool rsa_generate_keys(SilcUInt32 bits, SilcMPInt *p, SilcMPInt *q,
90 void **ret_public_key, void **ret_private_key)
93 RsaPrivateKey *privkey;
98 *ret_public_key = pubkey = silc_calloc(1, sizeof(*pubkey));
102 *ret_private_key = privkey = silc_calloc(1, sizeof(*privkey));
106 /* Initialize variables */
107 silc_mp_init(&privkey->n);
108 silc_mp_init(&privkey->e);
109 silc_mp_init(&privkey->d);
110 silc_mp_init(&privkey->dP);
111 silc_mp_init(&privkey->dQ);
112 silc_mp_init(&privkey->qP);
120 /* Set modulus length */
121 privkey->bits = bits;
123 /* Compute modulus, n = p * q */
124 silc_mp_mul(&privkey->n, p, q);
126 /* phi = (p - 1) * (q - 1) */
127 silc_mp_sub_ui(&pm1, p, 1);
128 silc_mp_sub_ui(&qm1, q, 1);
129 silc_mp_mul(&phi, &pm1, &qm1);
131 /* Set e, the public exponent. We try to use same public exponent
132 for all keys. Also, to make encryption faster we use small
134 silc_mp_set_ui(&privkey->e, 65533);
136 /* See if e is relatively prime to phi. gcd == greates common divisor,
137 if gcd equals 1 they are relatively prime. */
138 silc_mp_gcd(&hlp, &privkey->e, &phi);
139 if ((silc_mp_cmp_ui(&hlp, 1)) > 0) {
140 silc_mp_add_ui(&privkey->e, &privkey->e, 2);
144 /* Find d, the private exponent, e ^ -1 mod lcm(phi). */
145 silc_mp_gcd(&div, &pm1, &qm1);
146 silc_mp_div(&lcm, &phi, &div);
147 silc_mp_modinv(&privkey->d, &privkey->e, &lcm);
149 /* Optimize d with CRT. */
150 silc_mp_mod(&privkey->dP, &privkey->d, &pm1);
151 silc_mp_mod(&privkey->dQ, &privkey->d, &qm1);
152 silc_mp_modinv(&privkey->qP, q, p);
153 silc_mp_set(&privkey->p, p);
154 silc_mp_set(&privkey->q, q);
156 silc_mp_uninit(&phi);
157 silc_mp_uninit(&hlp);
158 silc_mp_uninit(&div);
159 silc_mp_uninit(&lcm);
160 silc_mp_uninit(&pm1);
161 silc_mp_uninit(&qm1);
164 silc_mp_init(&pubkey->n);
165 silc_mp_init(&pubkey->e);
166 pubkey->bits = privkey->bits;
167 silc_mp_set(&pubkey->n, &privkey->n);
168 silc_mp_set(&pubkey->e, &privkey->e);
173 /* RSA public key operation */
175 SilcBool rsa_public_operation(RsaPublicKey *key, SilcMPInt *src,
178 /* dst = src ^ e mod n */
179 silc_mp_pow_mod(dst, src, &key->e, &key->n);
183 /* RSA private key operation */
185 SilcBool rsa_private_operation(RsaPrivateKey *key, SilcMPInt *src,
192 /* dst = (src ^ dP mod p) */
193 silc_mp_pow_mod(dst, src, &key->dP, &key->p);
195 /* tmp = (src ^ dQ mod q) */
196 silc_mp_pow_mod(&tmp, src, &key->dQ, &key->q);
198 /* dst = (dst - tmp) * qP mod p */
199 silc_mp_sub(dst, dst, &tmp);
200 silc_mp_mul(dst, dst, &key->qP);
201 silc_mp_mod(dst, dst, &key->p);
203 /* dst = (q * dst) + tmp */
204 silc_mp_mul(dst, dst, &key->q);
205 silc_mp_add(dst, dst, &tmp);
207 silc_mp_uninit(&tmp);