3 * RSA parameter generation
5 * (c) 1999 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
15 * License, or (at your option) any later version.
17 * Catacomb is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
28 /*----- Header files ------------------------------------------------------*/
30 #include <mLib/dstr.h>
37 #include "strongprime.h"
39 /*----- Main code ---------------------------------------------------------*/
41 /* --- @rsa_gen@ --- *
43 * Arguments: @rsa_priv *rp@ = pointer to block to be filled in
44 * @unsigned nbits@ = required modulus size in bits
45 * @grand *r@ = random number source
46 * @unsigned n@ = number of attempts to make
47 * @pgen_proc *event@ = event handler function
48 * @void *ectx@ = argument for the event handler
50 * Returns: Zero if all went well, nonzero otherwise.
52 * Use: Constructs a pair of strong RSA primes and other useful RSA
53 * parameters. A small encryption exponent is chosen if
57 int rsa_gen(rsa_priv *rp, unsigned nbits, grand *r, unsigned n,
58 pgen_proc *event, void *ectx)
63 /* --- Bits of initialization --- */
65 rp->e = mp_fromulong(MP_NEW, 0x10001);
68 /* --- Generate strong primes %$p$% and %$q$% --- *
70 * Constrain the GCD of @q@ to ensure that overly small private exponents
71 * are impossible. Current results suggest that if %$d < n^{0.29}$% then
72 * it can be guessed fairly easily. This implementation is rather more
73 * conservative about that sort of thing.
77 if ((rp->p = strongprime("p", MP_NEWSEC, nbits/2, r, n, event, ectx)) == 0)
80 /* --- Do painful fiddling with GCD steppers --- */
86 if ((q = strongprime_setup("q", MP_NEWSEC, &g.jp, nbits / 2,
87 r, n, event, ectx)) == 0)
89 g.r = mp_lsr(MP_NEW, rp->p, 1);
92 q = pgen("q", q, q, event, ectx, n, pgen_gcdstep, &g,
93 rabin_iters(nbits/2), pgen_test, &rb);
106 /* --- Ensure that %$p > q$% --- *
108 * Also ensure that %$p$% and %$q$% are sufficiently different to deter
109 * square-root-based factoring methods.
112 phi = mp_sub(phi, rp->p, rp->q);
113 if (MP_LEN(phi) * 4 < MP_LEN(rp->p) * 3 ||
114 MP_LEN(phi) * 4 < MP_LEN(rp->q) * 3) {
129 /* --- Work out the modulus and the CRT coefficient --- */
131 rp->n = mp_mul(MP_NEW, rp->p, rp->q);
132 rp->q_inv = mp_modinv(MP_NEW, rp->q, rp->p);
134 /* --- Work out %$\varphi(n) = (p - 1)(q - 1)$% --- *
136 * Save on further multiplications by noting that %$n = pq$% is known and
137 * that %$(p - 1)(q - 1) = pq - p - q + 1$%. To minimize the size of @d@
138 * (useful for performance reasons, although not very because an overly
139 * small @d@ will be rejected for security reasons) this is then divided by
140 * %$\gcd(p - 1, q - 1)$%.
143 phi = mp_sub(phi, rp->n, rp->p);
144 phi = mp_sub(phi, phi, rp->q);
145 phi = mp_add(phi, phi, MP_ONE);
146 phi = mp_lsr(phi, phi, 1);
147 mp_div(&phi, 0, phi, g.g);
149 /* --- Decide on a public exponent --- *
151 * Simultaneously compute the private exponent.
154 mp_gcd(&g.g, 0, &rp->d, phi, rp->e);
155 if (!MP_EQ(g.g, MP_ONE) && MP_LEN(rp->d) * 4 > MP_LEN(rp->n) * 3)
158 /* --- Work out exponent residues --- */
160 rp->dp = MP_NEW; phi = mp_sub(phi, rp->p, MP_ONE);
161 mp_div(0, &rp->dp, rp->d, phi);
163 rp->dq = MP_NEW; phi = mp_sub(phi, rp->q, MP_ONE);
164 mp_div(0, &rp->dq, rp->d, phi);
172 /* --- Tidy up when something goes wrong --- */
189 /*----- That's all, folks -------------------------------------------------*/