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1 | /* -*-c-*- |
2 | * |
b817bfc6 |
3 | * $Id: rsa-recover.c,v 1.7 2004/04/08 01:36:15 mdw Exp $ |
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4 | * |
5 | * Recover RSA parameters |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
01898d8e |
30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "mp.h" |
33 | #include "mpmont.h" |
34 | #include "rsa.h" |
35 | |
36 | /*----- Main code ---------------------------------------------------------*/ |
37 | |
38 | /* --- @rsa_recover@ --- * |
39 | * |
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40 | * Arguments: @rsa_priv *rp@ = pointer to parameter block |
01898d8e |
41 | * |
42 | * Returns: Zero if all went well, nonzero if the parameters make no |
43 | * sense. |
44 | * |
45 | * Use: Derives the full set of RSA parameters given a minimal set. |
46 | */ |
47 | |
b82ec4e8 |
48 | int rsa_recover(rsa_priv *rp) |
01898d8e |
49 | { |
50 | /* --- If there is no modulus, calculate it --- */ |
51 | |
52 | if (!rp->n) { |
53 | if (!rp->p || !rp->q) |
54 | return (-1); |
55 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
56 | } |
57 | |
58 | /* --- If there are no factors, compute them --- */ |
59 | |
60 | else if (!rp->p || !rp->q) { |
61 | |
62 | /* --- If one is missing, use simple division to recover the other --- */ |
63 | |
64 | if (rp->p || rp->q) { |
65 | mp *r = MP_NEW; |
66 | if (rp->p) |
67 | mp_div(&rp->q, &r, rp->n, rp->p); |
68 | else |
69 | mp_div(&rp->p, &r, rp->n, rp->q); |
22bab86c |
70 | if (!MP_EQ(r, MP_ZERO)) { |
01898d8e |
71 | mp_drop(r); |
72 | return (-1); |
73 | } |
74 | mp_drop(r); |
75 | } |
76 | |
77 | /* --- Otherwise use the public and private moduli --- */ |
78 | |
f3099c16 |
79 | else if (!rp->e || !rp->d) |
80 | return (-1); |
81 | else { |
01898d8e |
82 | mp *t; |
31cb4e2e |
83 | size_t s; |
01898d8e |
84 | mp a; mpw aw; |
85 | mp *m1; |
86 | mpmont mm; |
87 | int i; |
88 | mp *z = MP_NEW; |
89 | |
90 | /* --- Work out the appropriate exponent --- * |
91 | * |
92 | * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and |
93 | * %$t$% is odd. |
94 | */ |
95 | |
96 | t = mp_mul(MP_NEW, rp->e, rp->d); |
97 | t = mp_sub(t, t, MP_ONE); |
31cb4e2e |
98 | t = mp_odd(t, t, &s); |
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99 | |
100 | /* --- Set up for the exponentiation --- */ |
101 | |
102 | mpmont_create(&mm, rp->n); |
103 | m1 = mp_sub(MP_NEW, rp->n, mm.r); |
104 | |
105 | /* --- Now for the main loop --- * |
106 | * |
107 | * Choose candidate integers and attempt to factor the modulus. |
108 | */ |
109 | |
110 | mp_build(&a, &aw, &aw + 1); |
111 | i = 0; |
112 | for (;;) { |
113 | again: |
114 | |
115 | /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- * |
116 | * |
117 | * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration |
118 | * is a failure. |
119 | */ |
120 | |
121 | aw = primetab[i++]; |
b0b682aa |
122 | z = mpmont_mul(&mm, z, &a, mm.r2); |
123 | z = mpmont_expr(&mm, z, z, t); |
22bab86c |
124 | if (MP_EQ(z, mm.r) || MP_EQ(z, m1)) |
01898d8e |
125 | continue; |
126 | |
127 | /* --- Now square until something interesting happens --- * |
128 | * |
129 | * Compute %$z^{2i} \bmod n$%. Eventually, I'll either get %$-1$% or |
130 | * %$1$%. If the former, the number is uninteresting, and I need to |
131 | * restart. If the latter, the previous number minus 1 has a common |
132 | * factor with %$n$%. |
133 | */ |
134 | |
135 | for (;;) { |
136 | mp *zz = mp_sqr(MP_NEW, z); |
137 | zz = mpmont_reduce(&mm, zz, zz); |
22bab86c |
138 | if (MP_EQ(zz, mm.r)) { |
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139 | mp_drop(zz); |
140 | goto done; |
22bab86c |
141 | } else if (MP_EQ(zz, m1)) { |
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142 | mp_drop(zz); |
143 | goto again; |
144 | } |
145 | mp_drop(z); |
146 | z = zz; |
147 | } |
148 | } |
149 | |
150 | /* --- Do the factoring --- * |
151 | * |
152 | * Here's how it actually works. I've found an interesting square |
153 | * root of %$1 \pmod n$%. Any square root of 1 must be congruent to |
154 | * %$\pm 1$% modulo both %$p$% and %$q$%. Both congruent to %$1$% is |
155 | * boring, as is both congruent to %$-1$%. Subtracting one from the |
156 | * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and |
157 | * nobody cares which), and hence can be extracted by a GCD |
158 | * operation. |
159 | */ |
160 | |
161 | done: |
162 | z = mpmont_reduce(&mm, z, z); |
163 | z = mp_sub(z, z, MP_ONE); |
164 | rp->p = MP_NEW; |
165 | mp_gcd(&rp->p, 0, 0, rp->n, z); |
166 | rp->q = MP_NEW; |
167 | mp_div(&rp->q, 0, rp->n, rp->p); |
168 | mp_drop(z); |
169 | mp_drop(t); |
170 | mp_drop(m1); |
f3099c16 |
171 | if (MP_CMP(rp->p, <, rp->q)) { |
172 | z = rp->p; |
173 | rp->p = rp->q; |
174 | rp->q = z; |
175 | } |
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176 | mpmont_destroy(&mm); |
177 | } |
178 | } |
179 | |
180 | /* --- If %$e$% or %$d$% is missing, recalculate it --- */ |
181 | |
182 | if (!rp->e || !rp->d) { |
183 | mp *phi; |
184 | mp *g = MP_NEW; |
f3099c16 |
185 | mp *p1, *q1; |
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186 | |
187 | /* --- Compute %$\varphi(n)$% --- */ |
188 | |
189 | phi = mp_sub(MP_NEW, rp->n, rp->p); |
190 | phi = mp_sub(phi, phi, rp->q); |
191 | phi = mp_add(phi, phi, MP_ONE); |
f3099c16 |
192 | p1 = mp_sub(MP_NEW, rp->p, MP_ONE); |
193 | q1 = mp_sub(MP_NEW, rp->q, MP_ONE); |
194 | mp_gcd(&g, 0, 0, p1, q1); |
195 | mp_div(&phi, 0, phi, g); |
196 | mp_drop(p1); |
197 | mp_drop(q1); |
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198 | |
199 | /* --- Recover the other exponent --- */ |
200 | |
201 | if (rp->e) |
202 | mp_gcd(&g, 0, &rp->d, phi, rp->e); |
203 | else if (rp->d) |
204 | mp_gcd(&g, 0, &rp->e, phi, rp->d); |
205 | else { |
206 | mp_drop(phi); |
f3099c16 |
207 | mp_drop(g); |
01898d8e |
208 | return (-1); |
209 | } |
210 | |
211 | mp_drop(phi); |
22bab86c |
212 | if (!MP_EQ(g, MP_ONE)) { |
01898d8e |
213 | mp_drop(g); |
214 | return (-1); |
215 | } |
216 | mp_drop(g); |
217 | } |
218 | |
219 | /* --- Compute %$q^{-1} \bmod p$% --- */ |
220 | |
221 | if (!rp->q_inv) |
222 | mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q); |
223 | |
224 | /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */ |
225 | |
226 | if (!rp->dp) { |
227 | mp *p1 = mp_sub(MP_NEW, rp->p, MP_ONE); |
228 | mp_div(0, &rp->dp, rp->d, p1); |
229 | mp_drop(p1); |
230 | } |
231 | if (!rp->dq) { |
232 | mp *q1 = mp_sub(MP_NEW, rp->q, MP_ONE); |
233 | mp_div(0, &rp->dq, rp->d, q1); |
234 | mp_drop(q1); |
235 | } |
236 | |
237 | /* --- Done --- */ |
238 | |
239 | return (0); |
240 | } |
241 | |
242 | /*----- That's all, folks -------------------------------------------------*/ |