01898d8e |
1 | /* -*-c-*- |
01898d8e |
2 | * |
3 | * RSA parameter generation |
4 | * |
5 | * (c) 1999 Straylight/Edgeware |
6 | */ |
7 | |
45c0fd36 |
8 | /*----- Licensing notice --------------------------------------------------* |
01898d8e |
9 | * |
10 | * This file is part of Catacomb. |
11 | * |
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. |
45c0fd36 |
16 | * |
01898d8e |
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. |
45c0fd36 |
21 | * |
01898d8e |
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, |
25 | * MA 02111-1307, USA. |
26 | */ |
27 | |
01898d8e |
28 | /*----- Header files ------------------------------------------------------*/ |
29 | |
30 | #include <mLib/dstr.h> |
31 | |
32 | #include "grand.h" |
33 | #include "mp.h" |
bb2e2fd8 |
34 | #include "mpint.h" |
01898d8e |
35 | #include "pgen.h" |
36 | #include "rsa.h" |
37 | #include "strongprime.h" |
38 | |
39 | /*----- Main code ---------------------------------------------------------*/ |
40 | |
41 | /* --- @rsa_gen@ --- * |
42 | * |
b82ec4e8 |
43 | * Arguments: @rsa_priv *rp@ = pointer to block to be filled in |
01898d8e |
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 |
49 | * |
50 | * Returns: Zero if all went well, nonzero otherwise. |
51 | * |
52 | * Use: Constructs a pair of strong RSA primes and other useful RSA |
53 | * parameters. A small encryption exponent is chosen if |
54 | * possible. |
55 | */ |
56 | |
b82ec4e8 |
57 | int rsa_gen(rsa_priv *rp, unsigned nbits, grand *r, unsigned n, |
01898d8e |
58 | pgen_proc *event, void *ectx) |
59 | { |
bb2e2fd8 |
60 | pgen_gcdstepctx g; |
61 | mp *phi = MP_NEW; |
01898d8e |
62 | |
bb2e2fd8 |
63 | /* --- Bits of initialization --- */ |
64 | |
65 | rp->e = mp_fromulong(MP_NEW, 0x10001); |
66 | rp->d = MP_NEW; |
67 | |
68 | /* --- Generate strong primes %$p$% and %$q$% --- * |
69 | * |
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. |
74 | */ |
01898d8e |
75 | |
bb2e2fd8 |
76 | again: |
77 | if ((rp->p = strongprime("p", MP_NEWSEC, nbits/2, r, n, event, ectx)) == 0) |
01898d8e |
78 | goto fail_p; |
bb2e2fd8 |
79 | |
80 | /* --- Do painful fiddling with GCD steppers --- */ |
81 | |
82 | { |
83 | mp *q; |
84 | rabin rb; |
85 | |
86 | if ((q = strongprime_setup("q", MP_NEWSEC, &g.jp, nbits / 2, |
87 | r, n, event, ectx)) == 0) |
88 | goto fail_q; |
89 | g.r = mp_lsr(MP_NEW, rp->p, 1); |
90 | g.g = MP_NEW; |
91 | g.max = MP_256; |
92 | q = pgen("q", q, q, event, ectx, n, pgen_gcdstep, &g, |
93 | rabin_iters(nbits/2), pgen_test, &rb); |
94 | pfilt_destroy(&g.jp); |
95 | mp_drop(g.r); |
96 | if (!q) { |
97 | mp_drop(g.g); |
98 | if (n) |
99 | goto fail_q; |
100 | mp_drop(rp->p); |
101 | goto again; |
102 | } |
103 | rp->q = q; |
104 | } |
105 | |
106 | /* --- Ensure that %$p > q$% --- * |
107 | * |
108 | * Also ensure that %$p$% and %$q$% are sufficiently different to deter |
109 | * square-root-based factoring methods. |
110 | */ |
111 | |
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) { |
115 | mp_drop(rp->p); |
116 | mp_drop(g.g); |
117 | if (n) |
118 | goto fail_q; |
119 | mp_drop(rp->q); |
120 | goto again; |
121 | } |
122 | |
a69a3efd |
123 | if (MP_NEGP(phi)) { |
bb2e2fd8 |
124 | mp *z = rp->p; |
125 | rp->p = rp->q; |
126 | rp->q = z; |
127 | } |
01898d8e |
128 | |
129 | /* --- Work out the modulus and the CRT coefficient --- */ |
130 | |
131 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
b817bfc6 |
132 | rp->q_inv = mp_modinv(MP_NEW, rp->q, rp->p); |
01898d8e |
133 | |
134 | /* --- Work out %$\varphi(n) = (p - 1)(q - 1)$% --- * |
135 | * |
136 | * Save on further multiplications by noting that %$n = pq$% is known and |
bb2e2fd8 |
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 | * %$\gcd(p - 1, q - 1)$%. |
01898d8e |
141 | */ |
142 | |
bb2e2fd8 |
143 | phi = mp_sub(phi, rp->n, rp->p); |
01898d8e |
144 | phi = mp_sub(phi, phi, rp->q); |
145 | phi = mp_add(phi, phi, MP_ONE); |
bb2e2fd8 |
146 | phi = mp_lsr(phi, phi, 1); |
147 | mp_div(&phi, 0, phi, g.g); |
01898d8e |
148 | |
149 | /* --- Decide on a public exponent --- * |
150 | * |
151 | * Simultaneously compute the private exponent. |
152 | */ |
153 | |
bb2e2fd8 |
154 | mp_gcd(&g.g, 0, &rp->d, phi, rp->e); |
22bab86c |
155 | if (!MP_EQ(g.g, MP_ONE) && MP_LEN(rp->d) * 4 > MP_LEN(rp->n) * 3) |
bb2e2fd8 |
156 | goto fail_e; |
01898d8e |
157 | |
158 | /* --- Work out exponent residues --- */ |
159 | |
01898d8e |
160 | rp->dp = MP_NEW; phi = mp_sub(phi, rp->p, MP_ONE); |
161 | mp_div(0, &rp->dp, rp->d, phi); |
162 | |
163 | rp->dq = MP_NEW; phi = mp_sub(phi, rp->q, MP_ONE); |
164 | mp_div(0, &rp->dq, rp->d, phi); |
165 | |
166 | /* --- Done --- */ |
167 | |
168 | mp_drop(phi); |
bb2e2fd8 |
169 | mp_drop(g.g); |
01898d8e |
170 | return (0); |
171 | |
172 | /* --- Tidy up when something goes wrong --- */ |
173 | |
174 | fail_e: |
bb2e2fd8 |
175 | mp_drop(g.g); |
01898d8e |
176 | mp_drop(phi); |
177 | mp_drop(rp->n); |
178 | mp_drop(rp->q_inv); |
179 | mp_drop(rp->q); |
180 | fail_q: |
181 | mp_drop(rp->p); |
182 | fail_p: |
bb2e2fd8 |
183 | mp_drop(rp->e); |
184 | if (rp->d) |
185 | mp_drop(rp->d); |
01898d8e |
186 | return (-1); |
187 | } |
188 | |
189 | /*----- That's all, folks -------------------------------------------------*/ |