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01898d8e | 1 | /* -*-c-*- |
01898d8e | 2 | * |
3 | * Recover RSA parameters | |
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 "mp.h" | |
31 | #include "mpmont.h" | |
32 | #include "rsa.h" | |
33 | ||
34 | /*----- Main code ---------------------------------------------------------*/ | |
35 | ||
36 | /* --- @rsa_recover@ --- * | |
37 | * | |
b82ec4e8 | 38 | * Arguments: @rsa_priv *rp@ = pointer to parameter block |
01898d8e | 39 | * |
40 | * Returns: Zero if all went well, nonzero if the parameters make no | |
41 | * sense. | |
42 | * | |
43 | * Use: Derives the full set of RSA parameters given a minimal set. | |
395da108 MW |
44 | * |
45 | * On failure, the parameter block might be partially filled in, | |
46 | * but the @rsa_privfree@ function will be able to free it | |
47 | * successfully. | |
01898d8e | 48 | */ |
49 | ||
b82ec4e8 | 50 | int rsa_recover(rsa_priv *rp) |
01898d8e | 51 | { |
f2d45696 MW |
52 | int i; |
53 | size_t s; | |
54 | mpmont mm; | |
55 | mp a; mpw aw; | |
56 | mp *g = MP_NEW, *r = MP_NEW, *t = MP_NEW; | |
57 | mp *m1 = MP_NEW, *z = MP_NEW, *zz = MP_NEW; | |
58 | mp *phi = MP_NEW, *p1 = MP_NEW, *q1 = MP_NEW; | |
59 | ||
01898d8e | 60 | /* --- If there is no modulus, calculate it --- */ |
61 | ||
62 | if (!rp->n) { | |
63 | if (!rp->p || !rp->q) | |
64 | return (-1); | |
65 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); | |
66 | } | |
67 | ||
68 | /* --- If there are no factors, compute them --- */ | |
69 | ||
70 | else if (!rp->p || !rp->q) { | |
71 | ||
72 | /* --- If one is missing, use simple division to recover the other --- */ | |
73 | ||
74 | if (rp->p || rp->q) { | |
01898d8e | 75 | if (rp->p) |
76 | mp_div(&rp->q, &r, rp->n, rp->p); | |
77 | else | |
78 | mp_div(&rp->p, &r, rp->n, rp->q); | |
22bab86c | 79 | if (!MP_EQ(r, MP_ZERO)) { |
01898d8e | 80 | mp_drop(r); |
81 | return (-1); | |
82 | } | |
83 | mp_drop(r); | |
84 | } | |
85 | ||
86 | /* --- Otherwise use the public and private moduli --- */ | |
87 | ||
f3099c16 | 88 | else if (!rp->e || !rp->d) |
89 | return (-1); | |
90 | else { | |
01898d8e | 91 | |
92 | /* --- Work out the appropriate exponent --- * | |
93 | * | |
94 | * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and | |
95 | * %$t$% is odd. | |
96 | */ | |
97 | ||
f2d45696 | 98 | t = mp_mul(t, rp->e, rp->d); |
01898d8e | 99 | t = mp_sub(t, t, MP_ONE); |
31cb4e2e | 100 | t = mp_odd(t, t, &s); |
01898d8e | 101 | |
102 | /* --- Set up for the exponentiation --- */ | |
103 | ||
104 | mpmont_create(&mm, rp->n); | |
f2d45696 | 105 | m1 = mp_sub(m1, rp->n, mm.r); |
01898d8e | 106 | |
107 | /* --- Now for the main loop --- * | |
108 | * | |
109 | * Choose candidate integers and attempt to factor the modulus. | |
110 | */ | |
111 | ||
112 | mp_build(&a, &aw, &aw + 1); | |
113 | i = 0; | |
e81d8d47 MW |
114 | |
115 | again: | |
116 | ||
117 | /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- * | |
118 | * | |
119 | * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration | |
120 | * is a failure. | |
121 | */ | |
122 | ||
123 | aw = primetab[i++]; | |
124 | z = mpmont_mul(&mm, z, &a, mm.r2); | |
125 | z = mpmont_expr(&mm, z, z, t); | |
126 | if (MP_EQ(z, mm.r) || MP_EQ(z, m1)) | |
127 | goto again; | |
128 | ||
129 | /* --- Now square until something interesting happens --- * | |
130 | * | |
131 | * Compute %$z^{2i} \bmod n$%. Eventually, I'll either get %$-1$% or | |
132 | * %$1$%. If the former, the number is uninteresting, and I need to | |
133 | * restart. If the latter, the previous number minus 1 has a common | |
134 | * factor with %$n$%. | |
135 | */ | |
136 | ||
01898d8e | 137 | for (;;) { |
e81d8d47 MW |
138 | zz = mp_sqr(zz, z); |
139 | zz = mpmont_reduce(&mm, zz, zz); | |
140 | if (MP_EQ(zz, mm.r)) { | |
141 | mp_drop(zz); | |
142 | goto done; | |
143 | } else if (MP_EQ(zz, m1)) { | |
144 | mp_drop(zz); | |
145 | goto again; | |
01898d8e | 146 | } |
e81d8d47 MW |
147 | mp_drop(z); |
148 | z = zz; | |
149 | zz = MP_NEW; | |
01898d8e | 150 | } |
151 | ||
152 | /* --- Do the factoring --- * | |
153 | * | |
154 | * Here's how it actually works. I've found an interesting square | |
155 | * root of %$1 \pmod n$%. Any square root of 1 must be congruent to | |
156 | * %$\pm 1$% modulo both %$p$% and %$q$%. Both congruent to %$1$% is | |
157 | * boring, as is both congruent to %$-1$%. Subtracting one from the | |
158 | * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and | |
159 | * nobody cares which), and hence can be extracted by a GCD | |
160 | * operation. | |
161 | */ | |
162 | ||
163 | done: | |
164 | z = mpmont_reduce(&mm, z, z); | |
165 | z = mp_sub(z, z, MP_ONE); | |
166 | rp->p = MP_NEW; | |
167 | mp_gcd(&rp->p, 0, 0, rp->n, z); | |
168 | rp->q = MP_NEW; | |
169 | mp_div(&rp->q, 0, rp->n, rp->p); | |
170 | mp_drop(z); | |
171 | mp_drop(t); | |
172 | mp_drop(m1); | |
f3099c16 | 173 | if (MP_CMP(rp->p, <, rp->q)) { |
174 | z = rp->p; | |
175 | rp->p = rp->q; | |
176 | rp->q = z; | |
177 | } | |
01898d8e | 178 | mpmont_destroy(&mm); |
179 | } | |
180 | } | |
181 | ||
182 | /* --- If %$e$% or %$d$% is missing, recalculate it --- */ | |
183 | ||
184 | if (!rp->e || !rp->d) { | |
01898d8e | 185 | |
186 | /* --- Compute %$\varphi(n)$% --- */ | |
187 | ||
f2d45696 | 188 | phi = mp_sub(phi, rp->n, rp->p); |
01898d8e | 189 | phi = mp_sub(phi, phi, rp->q); |
190 | phi = mp_add(phi, phi, MP_ONE); | |
f2d45696 MW |
191 | p1 = mp_sub(p1, rp->p, MP_ONE); |
192 | q1 = mp_sub(q1, rp->q, MP_ONE); | |
f3099c16 | 193 | mp_gcd(&g, 0, 0, p1, q1); |
194 | mp_div(&phi, 0, phi, g); | |
f2d45696 MW |
195 | mp_drop(p1); p1 = MP_NEW; |
196 | mp_drop(q1); q1 = MP_NEW; | |
01898d8e | 197 | |
198 | /* --- Recover the other exponent --- */ | |
199 | ||
200 | if (rp->e) | |
201 | mp_gcd(&g, 0, &rp->d, phi, rp->e); | |
202 | else if (rp->d) | |
203 | mp_gcd(&g, 0, &rp->e, phi, rp->d); | |
204 | else { | |
205 | mp_drop(phi); | |
f3099c16 | 206 | mp_drop(g); |
01898d8e | 207 | return (-1); |
208 | } | |
209 | ||
210 | mp_drop(phi); | |
22bab86c | 211 | if (!MP_EQ(g, MP_ONE)) { |
01898d8e | 212 | mp_drop(g); |
213 | return (-1); | |
214 | } | |
215 | mp_drop(g); | |
216 | } | |
217 | ||
218 | /* --- Compute %$q^{-1} \bmod p$% --- */ | |
219 | ||
220 | if (!rp->q_inv) | |
221 | mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q); | |
222 | ||
223 | /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */ | |
224 | ||
225 | if (!rp->dp) { | |
f2d45696 | 226 | p1 = mp_sub(p1, rp->p, MP_ONE); |
01898d8e | 227 | mp_div(0, &rp->dp, rp->d, p1); |
228 | mp_drop(p1); | |
229 | } | |
230 | if (!rp->dq) { | |
f2d45696 | 231 | q1 = mp_sub(q1, rp->q, MP_ONE); |
01898d8e | 232 | mp_div(0, &rp->dq, rp->d, q1); |
233 | mp_drop(q1); | |
234 | } | |
235 | ||
236 | /* --- Done --- */ | |
237 | ||
238 | return (0); | |
239 | } | |
240 | ||
241 | /*----- That's all, folks -------------------------------------------------*/ |