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 - 2007 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.
80 /* Generates RSA public and private keys. Primes p and q that are used
81 to compute the modulus n has to be generated before calling this. They
82 are then sent as argument for the function. */
84 SilcBool silc_rsa_generate_keys(SilcUInt32 bits, SilcMPInt *p, SilcMPInt *q,
85 void **ret_public_key, void **ret_private_key)
88 RsaPrivateKey *privkey;
93 *ret_public_key = pubkey = silc_calloc(1, sizeof(*pubkey));
97 *ret_private_key = privkey = silc_calloc(1, sizeof(*privkey));
101 /* Initialize variables */
102 silc_mp_init(&privkey->n);
103 silc_mp_init(&privkey->e);
104 silc_mp_init(&privkey->d);
105 silc_mp_init(&privkey->dP);
106 silc_mp_init(&privkey->dQ);
107 silc_mp_init(&privkey->qP);
115 /* Set modulus length */
116 privkey->bits = bits;
118 /* Compute modulus, n = p * q */
119 silc_mp_mul(&privkey->n, p, q);
121 /* phi = (p - 1) * (q - 1) */
122 silc_mp_sub_ui(&pm1, p, 1);
123 silc_mp_sub_ui(&qm1, q, 1);
124 silc_mp_mul(&phi, &pm1, &qm1);
126 /* Set e, the public exponent. We try to use same public exponent
127 for all keys. Also, to make encryption faster we use small
129 silc_mp_set_ui(&privkey->e, 65533);
131 /* See if e is relatively prime to phi. gcd == greates common divisor,
132 if gcd equals 1 they are relatively prime. */
133 silc_mp_gcd(&hlp, &privkey->e, &phi);
134 if ((silc_mp_cmp_ui(&hlp, 1)) > 0) {
135 silc_mp_add_ui(&privkey->e, &privkey->e, 2);
139 /* Find d, the private exponent, e ^ -1 mod lcm(phi). */
140 silc_mp_gcd(&div, &pm1, &qm1);
141 silc_mp_div(&lcm, &phi, &div);
142 silc_mp_modinv(&privkey->d, &privkey->e, &lcm);
144 /* Optimize d with CRT. */
145 silc_mp_mod(&privkey->dP, &privkey->d, &pm1);
146 silc_mp_mod(&privkey->dQ, &privkey->d, &qm1);
147 silc_mp_modinv(&privkey->qP, q, p);
148 silc_mp_set(&privkey->p, p);
149 silc_mp_set(&privkey->q, q);
151 silc_mp_uninit(&phi);
152 silc_mp_uninit(&hlp);
153 silc_mp_uninit(&div);
154 silc_mp_uninit(&lcm);
155 silc_mp_uninit(&pm1);
156 silc_mp_uninit(&qm1);
159 silc_mp_init(&pubkey->n);
160 silc_mp_init(&pubkey->e);
161 pubkey->bits = privkey->bits;
162 silc_mp_set(&pubkey->n, &privkey->n);
163 silc_mp_set(&pubkey->e, &privkey->e);
168 /* RSA public key operation */
170 SilcBool silc_rsa_public_operation(RsaPublicKey *key, SilcMPInt *src,
173 /* dst = src ^ e mod n */
174 silc_mp_pow_mod(dst, src, &key->e, &key->n);
178 /* RSA private key operation */
180 SilcBool silc_rsa_private_operation(RsaPrivateKey *key, SilcMPInt *src,
187 /* dst = (src ^ dP mod p) */
188 silc_mp_pow_mod(dst, src, &key->dP, &key->p);
190 /* tmp = (src ^ dQ mod q) */
191 silc_mp_pow_mod(&tmp, src, &key->dQ, &key->q);
193 /* dst = (dst - tmp) * qP mod p */
194 silc_mp_sub(dst, dst, &tmp);
195 silc_mp_mul(dst, dst, &key->qP);
196 silc_mp_mod(dst, dst, &key->p);
198 /* dst = (q * dst) + tmp */
199 silc_mp_mul(dst, dst, &key->q);
200 silc_mp_add(dst, dst, &tmp);
202 silc_mp_uninit(&tmp);