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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: rsa-recover.c,v 1.2 2000/06/17 12:07:19 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 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: rsa-recover.c,v $ |
f3099c16 |
33 | * Revision 1.2 2000/06/17 12:07:19 mdw |
34 | * Fix a bug in argument validation. Force %$p > q$% in output. Use |
35 | * %$\lambda(n) = \lcm(p - 1, q - 1)$% rather than the more traditional |
36 | * %$\phi(n) = (p - 1)(q - 1)$% when computing the decryption exponent. |
37 | * |
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38 | * Revision 1.1 1999/12/22 15:50:45 mdw |
39 | * Initial RSA support. |
40 | * |
41 | */ |
42 | |
43 | /*----- Header files ------------------------------------------------------*/ |
44 | |
45 | #include "mp.h" |
46 | #include "mpmont.h" |
47 | #include "rsa.h" |
48 | |
49 | /*----- Main code ---------------------------------------------------------*/ |
50 | |
51 | /* --- @rsa_recover@ --- * |
52 | * |
53 | * Arguments: @rsa_param *rp@ = pointer to parameter block |
54 | * |
55 | * Returns: Zero if all went well, nonzero if the parameters make no |
56 | * sense. |
57 | * |
58 | * Use: Derives the full set of RSA parameters given a minimal set. |
59 | */ |
60 | |
61 | int rsa_recover(rsa_param *rp) |
62 | { |
63 | /* --- If there is no modulus, calculate it --- */ |
64 | |
65 | if (!rp->n) { |
66 | if (!rp->p || !rp->q) |
67 | return (-1); |
68 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
69 | } |
70 | |
71 | /* --- If there are no factors, compute them --- */ |
72 | |
73 | else if (!rp->p || !rp->q) { |
74 | |
75 | /* --- If one is missing, use simple division to recover the other --- */ |
76 | |
77 | if (rp->p || rp->q) { |
78 | mp *r = MP_NEW; |
79 | if (rp->p) |
80 | mp_div(&rp->q, &r, rp->n, rp->p); |
81 | else |
82 | mp_div(&rp->p, &r, rp->n, rp->q); |
83 | if (MP_CMP(r, !=, MP_ZERO)) { |
84 | mp_drop(r); |
85 | return (-1); |
86 | } |
87 | mp_drop(r); |
88 | } |
89 | |
90 | /* --- Otherwise use the public and private moduli --- */ |
91 | |
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92 | else if (!rp->e || !rp->d) |
93 | return (-1); |
94 | else { |
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95 | mp *t; |
96 | unsigned s; |
97 | mpscan ms; |
98 | mp a; mpw aw; |
99 | mp *m1; |
100 | mpmont mm; |
101 | int i; |
102 | mp *z = MP_NEW; |
103 | |
104 | /* --- Work out the appropriate exponent --- * |
105 | * |
106 | * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and |
107 | * %$t$% is odd. |
108 | */ |
109 | |
110 | t = mp_mul(MP_NEW, rp->e, rp->d); |
111 | t = mp_sub(t, t, MP_ONE); |
112 | s = 0; |
113 | mp_scan(&ms, t); |
114 | for (;;) { |
115 | MP_STEP(&ms); |
116 | if (MP_BIT(&ms)) |
117 | break; |
118 | s++; |
119 | } |
120 | t = mp_lsr(t, t, s); |
121 | |
122 | /* --- Set up for the exponentiation --- */ |
123 | |
124 | mpmont_create(&mm, rp->n); |
125 | m1 = mp_sub(MP_NEW, rp->n, mm.r); |
126 | |
127 | /* --- Now for the main loop --- * |
128 | * |
129 | * Choose candidate integers and attempt to factor the modulus. |
130 | */ |
131 | |
132 | mp_build(&a, &aw, &aw + 1); |
133 | i = 0; |
134 | for (;;) { |
135 | again: |
136 | |
137 | /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- * |
138 | * |
139 | * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration |
140 | * is a failure. |
141 | */ |
142 | |
143 | aw = primetab[i++]; |
144 | z = mpmont_expr(&mm, z, &a, t); |
145 | if (MP_CMP(z, ==, mm.r) || MP_CMP(z, ==, m1)) |
146 | continue; |
147 | |
148 | /* --- Now square until something interesting happens --- * |
149 | * |
150 | * Compute %$z^{2i} \bmod n$%. Eventually, I'll either get %$-1$% or |
151 | * %$1$%. If the former, the number is uninteresting, and I need to |
152 | * restart. If the latter, the previous number minus 1 has a common |
153 | * factor with %$n$%. |
154 | */ |
155 | |
156 | for (;;) { |
157 | mp *zz = mp_sqr(MP_NEW, z); |
158 | zz = mpmont_reduce(&mm, zz, zz); |
159 | if (MP_CMP(zz, ==, mm.r)) { |
160 | mp_drop(zz); |
161 | goto done; |
162 | } else if (MP_CMP(zz, ==, m1)) { |
163 | mp_drop(zz); |
164 | goto again; |
165 | } |
166 | mp_drop(z); |
167 | z = zz; |
168 | } |
169 | } |
170 | |
171 | /* --- Do the factoring --- * |
172 | * |
173 | * Here's how it actually works. I've found an interesting square |
174 | * root of %$1 \pmod n$%. Any square root of 1 must be congruent to |
175 | * %$\pm 1$% modulo both %$p$% and %$q$%. Both congruent to %$1$% is |
176 | * boring, as is both congruent to %$-1$%. Subtracting one from the |
177 | * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and |
178 | * nobody cares which), and hence can be extracted by a GCD |
179 | * operation. |
180 | */ |
181 | |
182 | done: |
183 | z = mpmont_reduce(&mm, z, z); |
184 | z = mp_sub(z, z, MP_ONE); |
185 | rp->p = MP_NEW; |
186 | mp_gcd(&rp->p, 0, 0, rp->n, z); |
187 | rp->q = MP_NEW; |
188 | mp_div(&rp->q, 0, rp->n, rp->p); |
189 | mp_drop(z); |
190 | mp_drop(t); |
191 | mp_drop(m1); |
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192 | if (MP_CMP(rp->p, <, rp->q)) { |
193 | z = rp->p; |
194 | rp->p = rp->q; |
195 | rp->q = z; |
196 | } |
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197 | mpmont_destroy(&mm); |
198 | } |
199 | } |
200 | |
201 | /* --- If %$e$% or %$d$% is missing, recalculate it --- */ |
202 | |
203 | if (!rp->e || !rp->d) { |
204 | mp *phi; |
205 | mp *g = MP_NEW; |
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206 | mp *p1, *q1; |
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207 | |
208 | /* --- Compute %$\varphi(n)$% --- */ |
209 | |
210 | phi = mp_sub(MP_NEW, rp->n, rp->p); |
211 | phi = mp_sub(phi, phi, rp->q); |
212 | phi = mp_add(phi, phi, MP_ONE); |
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213 | p1 = mp_sub(MP_NEW, rp->p, MP_ONE); |
214 | q1 = mp_sub(MP_NEW, rp->q, MP_ONE); |
215 | mp_gcd(&g, 0, 0, p1, q1); |
216 | mp_div(&phi, 0, phi, g); |
217 | mp_drop(p1); |
218 | mp_drop(q1); |
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219 | |
220 | /* --- Recover the other exponent --- */ |
221 | |
222 | if (rp->e) |
223 | mp_gcd(&g, 0, &rp->d, phi, rp->e); |
224 | else if (rp->d) |
225 | mp_gcd(&g, 0, &rp->e, phi, rp->d); |
226 | else { |
227 | mp_drop(phi); |
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228 | mp_drop(g); |
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229 | return (-1); |
230 | } |
231 | |
232 | mp_drop(phi); |
233 | if (MP_CMP(g, !=, MP_ONE)) { |
234 | mp_drop(g); |
235 | return (-1); |
236 | } |
237 | mp_drop(g); |
238 | } |
239 | |
240 | /* --- Compute %$q^{-1} \bmod p$% --- */ |
241 | |
242 | if (!rp->q_inv) |
243 | mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q); |
244 | |
245 | /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */ |
246 | |
247 | if (!rp->dp) { |
248 | mp *p1 = mp_sub(MP_NEW, rp->p, MP_ONE); |
249 | mp_div(0, &rp->dp, rp->d, p1); |
250 | mp_drop(p1); |
251 | } |
252 | if (!rp->dq) { |
253 | mp *q1 = mp_sub(MP_NEW, rp->q, MP_ONE); |
254 | mp_div(0, &rp->dq, rp->d, q1); |
255 | mp_drop(q1); |
256 | } |
257 | |
258 | /* --- Done --- */ |
259 | |
260 | return (0); |
261 | } |
262 | |
263 | /*----- That's all, folks -------------------------------------------------*/ |