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1 | /* -*-c-*- |
2 | * |
31cb4e2e |
3 | * $Id: rsa-recover.c,v 1.3 2000/06/22 19:03:14 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 $ |
31cb4e2e |
33 | * Revision 1.3 2000/06/22 19:03:14 mdw |
34 | * Use the new @mp_odd@ function. |
35 | * |
f3099c16 |
36 | * Revision 1.2 2000/06/17 12:07:19 mdw |
37 | * Fix a bug in argument validation. Force %$p > q$% in output. Use |
38 | * %$\lambda(n) = \lcm(p - 1, q - 1)$% rather than the more traditional |
39 | * %$\phi(n) = (p - 1)(q - 1)$% when computing the decryption exponent. |
40 | * |
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41 | * Revision 1.1 1999/12/22 15:50:45 mdw |
42 | * Initial RSA support. |
43 | * |
44 | */ |
45 | |
46 | /*----- Header files ------------------------------------------------------*/ |
47 | |
48 | #include "mp.h" |
49 | #include "mpmont.h" |
50 | #include "rsa.h" |
51 | |
52 | /*----- Main code ---------------------------------------------------------*/ |
53 | |
54 | /* --- @rsa_recover@ --- * |
55 | * |
56 | * Arguments: @rsa_param *rp@ = pointer to parameter block |
57 | * |
58 | * Returns: Zero if all went well, nonzero if the parameters make no |
59 | * sense. |
60 | * |
61 | * Use: Derives the full set of RSA parameters given a minimal set. |
62 | */ |
63 | |
64 | int rsa_recover(rsa_param *rp) |
65 | { |
66 | /* --- If there is no modulus, calculate it --- */ |
67 | |
68 | if (!rp->n) { |
69 | if (!rp->p || !rp->q) |
70 | return (-1); |
71 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
72 | } |
73 | |
74 | /* --- If there are no factors, compute them --- */ |
75 | |
76 | else if (!rp->p || !rp->q) { |
77 | |
78 | /* --- If one is missing, use simple division to recover the other --- */ |
79 | |
80 | if (rp->p || rp->q) { |
81 | mp *r = MP_NEW; |
82 | if (rp->p) |
83 | mp_div(&rp->q, &r, rp->n, rp->p); |
84 | else |
85 | mp_div(&rp->p, &r, rp->n, rp->q); |
86 | if (MP_CMP(r, !=, MP_ZERO)) { |
87 | mp_drop(r); |
88 | return (-1); |
89 | } |
90 | mp_drop(r); |
91 | } |
92 | |
93 | /* --- Otherwise use the public and private moduli --- */ |
94 | |
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95 | else if (!rp->e || !rp->d) |
96 | return (-1); |
97 | else { |
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98 | mp *t; |
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99 | size_t s; |
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100 | mp a; mpw aw; |
101 | mp *m1; |
102 | mpmont mm; |
103 | int i; |
104 | mp *z = MP_NEW; |
105 | |
106 | /* --- Work out the appropriate exponent --- * |
107 | * |
108 | * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and |
109 | * %$t$% is odd. |
110 | */ |
111 | |
112 | t = mp_mul(MP_NEW, rp->e, rp->d); |
113 | t = mp_sub(t, t, MP_ONE); |
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114 | t = mp_odd(t, t, &s); |
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115 | |
116 | /* --- Set up for the exponentiation --- */ |
117 | |
118 | mpmont_create(&mm, rp->n); |
119 | m1 = mp_sub(MP_NEW, rp->n, mm.r); |
120 | |
121 | /* --- Now for the main loop --- * |
122 | * |
123 | * Choose candidate integers and attempt to factor the modulus. |
124 | */ |
125 | |
126 | mp_build(&a, &aw, &aw + 1); |
127 | i = 0; |
128 | for (;;) { |
129 | again: |
130 | |
131 | /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- * |
132 | * |
133 | * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration |
134 | * is a failure. |
135 | */ |
136 | |
137 | aw = primetab[i++]; |
138 | z = mpmont_expr(&mm, z, &a, t); |
139 | if (MP_CMP(z, ==, mm.r) || MP_CMP(z, ==, m1)) |
140 | continue; |
141 | |
142 | /* --- Now square until something interesting happens --- * |
143 | * |
144 | * Compute %$z^{2i} \bmod n$%. Eventually, I'll either get %$-1$% or |
145 | * %$1$%. If the former, the number is uninteresting, and I need to |
146 | * restart. If the latter, the previous number minus 1 has a common |
147 | * factor with %$n$%. |
148 | */ |
149 | |
150 | for (;;) { |
151 | mp *zz = mp_sqr(MP_NEW, z); |
152 | zz = mpmont_reduce(&mm, zz, zz); |
153 | if (MP_CMP(zz, ==, mm.r)) { |
154 | mp_drop(zz); |
155 | goto done; |
156 | } else if (MP_CMP(zz, ==, m1)) { |
157 | mp_drop(zz); |
158 | goto again; |
159 | } |
160 | mp_drop(z); |
161 | z = zz; |
162 | } |
163 | } |
164 | |
165 | /* --- Do the factoring --- * |
166 | * |
167 | * Here's how it actually works. I've found an interesting square |
168 | * root of %$1 \pmod n$%. Any square root of 1 must be congruent to |
169 | * %$\pm 1$% modulo both %$p$% and %$q$%. Both congruent to %$1$% is |
170 | * boring, as is both congruent to %$-1$%. Subtracting one from the |
171 | * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and |
172 | * nobody cares which), and hence can be extracted by a GCD |
173 | * operation. |
174 | */ |
175 | |
176 | done: |
177 | z = mpmont_reduce(&mm, z, z); |
178 | z = mp_sub(z, z, MP_ONE); |
179 | rp->p = MP_NEW; |
180 | mp_gcd(&rp->p, 0, 0, rp->n, z); |
181 | rp->q = MP_NEW; |
182 | mp_div(&rp->q, 0, rp->n, rp->p); |
183 | mp_drop(z); |
184 | mp_drop(t); |
185 | mp_drop(m1); |
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186 | if (MP_CMP(rp->p, <, rp->q)) { |
187 | z = rp->p; |
188 | rp->p = rp->q; |
189 | rp->q = z; |
190 | } |
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191 | mpmont_destroy(&mm); |
192 | } |
193 | } |
194 | |
195 | /* --- If %$e$% or %$d$% is missing, recalculate it --- */ |
196 | |
197 | if (!rp->e || !rp->d) { |
198 | mp *phi; |
199 | mp *g = MP_NEW; |
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200 | mp *p1, *q1; |
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201 | |
202 | /* --- Compute %$\varphi(n)$% --- */ |
203 | |
204 | phi = mp_sub(MP_NEW, rp->n, rp->p); |
205 | phi = mp_sub(phi, phi, rp->q); |
206 | phi = mp_add(phi, phi, MP_ONE); |
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207 | p1 = mp_sub(MP_NEW, rp->p, MP_ONE); |
208 | q1 = mp_sub(MP_NEW, rp->q, MP_ONE); |
209 | mp_gcd(&g, 0, 0, p1, q1); |
210 | mp_div(&phi, 0, phi, g); |
211 | mp_drop(p1); |
212 | mp_drop(q1); |
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213 | |
214 | /* --- Recover the other exponent --- */ |
215 | |
216 | if (rp->e) |
217 | mp_gcd(&g, 0, &rp->d, phi, rp->e); |
218 | else if (rp->d) |
219 | mp_gcd(&g, 0, &rp->e, phi, rp->d); |
220 | else { |
221 | mp_drop(phi); |
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222 | mp_drop(g); |
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223 | return (-1); |
224 | } |
225 | |
226 | mp_drop(phi); |
227 | if (MP_CMP(g, !=, MP_ONE)) { |
228 | mp_drop(g); |
229 | return (-1); |
230 | } |
231 | mp_drop(g); |
232 | } |
233 | |
234 | /* --- Compute %$q^{-1} \bmod p$% --- */ |
235 | |
236 | if (!rp->q_inv) |
237 | mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q); |
238 | |
239 | /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */ |
240 | |
241 | if (!rp->dp) { |
242 | mp *p1 = mp_sub(MP_NEW, rp->p, MP_ONE); |
243 | mp_div(0, &rp->dp, rp->d, p1); |
244 | mp_drop(p1); |
245 | } |
246 | if (!rp->dq) { |
247 | mp *q1 = mp_sub(MP_NEW, rp->q, MP_ONE); |
248 | mp_div(0, &rp->dq, rp->d, q1); |
249 | mp_drop(q1); |
250 | } |
251 | |
252 | /* --- Done --- */ |
253 | |
254 | return (0); |
255 | } |
256 | |
257 | /*----- That's all, folks -------------------------------------------------*/ |