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1 | /* -*-c-*- |
2 | * |
22bab86c |
3 | * $Id: rsa-recover.c,v 1.5 2000/10/08 12:11:22 mdw Exp $ |
01898d8e |
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 $ |
22bab86c |
33 | * Revision 1.5 2000/10/08 12:11:22 mdw |
34 | * Use @MP_EQ@ instead of @MP_CMP@. |
35 | * |
b82ec4e8 |
36 | * Revision 1.4 2000/07/01 11:22:22 mdw |
37 | * Remove bad type name `rsa_param'. |
38 | * |
31cb4e2e |
39 | * Revision 1.3 2000/06/22 19:03:14 mdw |
40 | * Use the new @mp_odd@ function. |
41 | * |
f3099c16 |
42 | * Revision 1.2 2000/06/17 12:07:19 mdw |
43 | * Fix a bug in argument validation. Force %$p > q$% in output. Use |
44 | * %$\lambda(n) = \lcm(p - 1, q - 1)$% rather than the more traditional |
45 | * %$\phi(n) = (p - 1)(q - 1)$% when computing the decryption exponent. |
46 | * |
01898d8e |
47 | * Revision 1.1 1999/12/22 15:50:45 mdw |
48 | * Initial RSA support. |
49 | * |
50 | */ |
51 | |
52 | /*----- Header files ------------------------------------------------------*/ |
53 | |
54 | #include "mp.h" |
55 | #include "mpmont.h" |
56 | #include "rsa.h" |
57 | |
58 | /*----- Main code ---------------------------------------------------------*/ |
59 | |
60 | /* --- @rsa_recover@ --- * |
61 | * |
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62 | * Arguments: @rsa_priv *rp@ = pointer to parameter block |
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63 | * |
64 | * Returns: Zero if all went well, nonzero if the parameters make no |
65 | * sense. |
66 | * |
67 | * Use: Derives the full set of RSA parameters given a minimal set. |
68 | */ |
69 | |
b82ec4e8 |
70 | int rsa_recover(rsa_priv *rp) |
01898d8e |
71 | { |
72 | /* --- If there is no modulus, calculate it --- */ |
73 | |
74 | if (!rp->n) { |
75 | if (!rp->p || !rp->q) |
76 | return (-1); |
77 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
78 | } |
79 | |
80 | /* --- If there are no factors, compute them --- */ |
81 | |
82 | else if (!rp->p || !rp->q) { |
83 | |
84 | /* --- If one is missing, use simple division to recover the other --- */ |
85 | |
86 | if (rp->p || rp->q) { |
87 | mp *r = MP_NEW; |
88 | if (rp->p) |
89 | mp_div(&rp->q, &r, rp->n, rp->p); |
90 | else |
91 | mp_div(&rp->p, &r, rp->n, rp->q); |
22bab86c |
92 | if (!MP_EQ(r, MP_ZERO)) { |
01898d8e |
93 | mp_drop(r); |
94 | return (-1); |
95 | } |
96 | mp_drop(r); |
97 | } |
98 | |
99 | /* --- Otherwise use the public and private moduli --- */ |
100 | |
f3099c16 |
101 | else if (!rp->e || !rp->d) |
102 | return (-1); |
103 | else { |
01898d8e |
104 | mp *t; |
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105 | size_t s; |
01898d8e |
106 | mp a; mpw aw; |
107 | mp *m1; |
108 | mpmont mm; |
109 | int i; |
110 | mp *z = MP_NEW; |
111 | |
112 | /* --- Work out the appropriate exponent --- * |
113 | * |
114 | * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and |
115 | * %$t$% is odd. |
116 | */ |
117 | |
118 | t = mp_mul(MP_NEW, rp->e, rp->d); |
119 | t = mp_sub(t, t, MP_ONE); |
31cb4e2e |
120 | t = mp_odd(t, t, &s); |
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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); |
22bab86c |
145 | if (MP_EQ(z, mm.r) || MP_EQ(z, m1)) |
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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); |
22bab86c |
159 | if (MP_EQ(zz, mm.r)) { |
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160 | mp_drop(zz); |
161 | goto done; |
22bab86c |
162 | } else if (MP_EQ(zz, m1)) { |
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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); |
f3099c16 |
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; |
f3099c16 |
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); |
f3099c16 |
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); |
f3099c16 |
228 | mp_drop(g); |
01898d8e |
229 | return (-1); |
230 | } |
231 | |
232 | mp_drop(phi); |
22bab86c |
233 | if (!MP_EQ(g, MP_ONE)) { |
01898d8e |
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 -------------------------------------------------*/ |