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1 | /* -*-c-*- |
2 | * |
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3 | * Recover RSA parameters |
4 | * |
5 | * (c) 1999 Straylight/Edgeware |
6 | */ |
7 | |
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8 | /*----- Licensing notice --------------------------------------------------* |
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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. |
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16 | * |
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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. |
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21 | * |
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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 | |
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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 | * |
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38 | * Arguments: @rsa_priv *rp@ = pointer to parameter block |
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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. |
44 | */ |
45 | |
b82ec4e8 |
46 | int rsa_recover(rsa_priv *rp) |
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47 | { |
48 | /* --- If there is no modulus, calculate it --- */ |
49 | |
50 | if (!rp->n) { |
51 | if (!rp->p || !rp->q) |
52 | return (-1); |
53 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
54 | } |
55 | |
56 | /* --- If there are no factors, compute them --- */ |
57 | |
58 | else if (!rp->p || !rp->q) { |
59 | |
60 | /* --- If one is missing, use simple division to recover the other --- */ |
61 | |
62 | if (rp->p || rp->q) { |
63 | mp *r = MP_NEW; |
64 | if (rp->p) |
65 | mp_div(&rp->q, &r, rp->n, rp->p); |
66 | else |
67 | mp_div(&rp->p, &r, rp->n, rp->q); |
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68 | if (!MP_EQ(r, MP_ZERO)) { |
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69 | mp_drop(r); |
70 | return (-1); |
71 | } |
72 | mp_drop(r); |
73 | } |
74 | |
75 | /* --- Otherwise use the public and private moduli --- */ |
76 | |
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77 | else if (!rp->e || !rp->d) |
78 | return (-1); |
79 | else { |
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80 | mp *t; |
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81 | size_t s; |
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82 | mp a; mpw aw; |
83 | mp *m1; |
84 | mpmont mm; |
85 | int i; |
86 | mp *z = MP_NEW; |
87 | |
88 | /* --- Work out the appropriate exponent --- * |
89 | * |
90 | * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and |
91 | * %$t$% is odd. |
92 | */ |
93 | |
94 | t = mp_mul(MP_NEW, rp->e, rp->d); |
95 | t = mp_sub(t, t, MP_ONE); |
31cb4e2e |
96 | t = mp_odd(t, t, &s); |
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97 | |
98 | /* --- Set up for the exponentiation --- */ |
99 | |
100 | mpmont_create(&mm, rp->n); |
101 | m1 = mp_sub(MP_NEW, rp->n, mm.r); |
102 | |
103 | /* --- Now for the main loop --- * |
104 | * |
105 | * Choose candidate integers and attempt to factor the modulus. |
106 | */ |
107 | |
108 | mp_build(&a, &aw, &aw + 1); |
109 | i = 0; |
110 | for (;;) { |
111 | again: |
112 | |
113 | /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- * |
114 | * |
115 | * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration |
116 | * is a failure. |
117 | */ |
118 | |
119 | aw = primetab[i++]; |
b0b682aa |
120 | z = mpmont_mul(&mm, z, &a, mm.r2); |
121 | z = mpmont_expr(&mm, z, z, t); |
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122 | if (MP_EQ(z, mm.r) || MP_EQ(z, m1)) |
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123 | continue; |
124 | |
125 | /* --- Now square until something interesting happens --- * |
126 | * |
127 | * Compute %$z^{2i} \bmod n$%. Eventually, I'll either get %$-1$% or |
128 | * %$1$%. If the former, the number is uninteresting, and I need to |
129 | * restart. If the latter, the previous number minus 1 has a common |
130 | * factor with %$n$%. |
131 | */ |
132 | |
133 | for (;;) { |
134 | mp *zz = mp_sqr(MP_NEW, z); |
135 | zz = mpmont_reduce(&mm, zz, zz); |
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136 | if (MP_EQ(zz, mm.r)) { |
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137 | mp_drop(zz); |
138 | goto done; |
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139 | } else if (MP_EQ(zz, m1)) { |
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140 | mp_drop(zz); |
141 | goto again; |
142 | } |
143 | mp_drop(z); |
144 | z = zz; |
145 | } |
146 | } |
147 | |
148 | /* --- Do the factoring --- * |
149 | * |
150 | * Here's how it actually works. I've found an interesting square |
151 | * root of %$1 \pmod n$%. Any square root of 1 must be congruent to |
152 | * %$\pm 1$% modulo both %$p$% and %$q$%. Both congruent to %$1$% is |
153 | * boring, as is both congruent to %$-1$%. Subtracting one from the |
154 | * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and |
155 | * nobody cares which), and hence can be extracted by a GCD |
156 | * operation. |
157 | */ |
158 | |
159 | done: |
160 | z = mpmont_reduce(&mm, z, z); |
161 | z = mp_sub(z, z, MP_ONE); |
162 | rp->p = MP_NEW; |
163 | mp_gcd(&rp->p, 0, 0, rp->n, z); |
164 | rp->q = MP_NEW; |
165 | mp_div(&rp->q, 0, rp->n, rp->p); |
166 | mp_drop(z); |
167 | mp_drop(t); |
168 | mp_drop(m1); |
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169 | if (MP_CMP(rp->p, <, rp->q)) { |
170 | z = rp->p; |
171 | rp->p = rp->q; |
172 | rp->q = z; |
173 | } |
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174 | mpmont_destroy(&mm); |
175 | } |
176 | } |
177 | |
178 | /* --- If %$e$% or %$d$% is missing, recalculate it --- */ |
179 | |
180 | if (!rp->e || !rp->d) { |
181 | mp *phi; |
182 | mp *g = MP_NEW; |
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183 | mp *p1, *q1; |
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184 | |
185 | /* --- Compute %$\varphi(n)$% --- */ |
186 | |
187 | phi = mp_sub(MP_NEW, rp->n, rp->p); |
188 | phi = mp_sub(phi, phi, rp->q); |
189 | phi = mp_add(phi, phi, MP_ONE); |
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190 | p1 = mp_sub(MP_NEW, rp->p, MP_ONE); |
191 | q1 = mp_sub(MP_NEW, rp->q, MP_ONE); |
192 | mp_gcd(&g, 0, 0, p1, q1); |
193 | mp_div(&phi, 0, phi, g); |
194 | mp_drop(p1); |
195 | mp_drop(q1); |
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196 | |
197 | /* --- Recover the other exponent --- */ |
198 | |
199 | if (rp->e) |
200 | mp_gcd(&g, 0, &rp->d, phi, rp->e); |
201 | else if (rp->d) |
202 | mp_gcd(&g, 0, &rp->e, phi, rp->d); |
203 | else { |
204 | mp_drop(phi); |
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205 | mp_drop(g); |
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206 | return (-1); |
207 | } |
208 | |
209 | mp_drop(phi); |
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210 | if (!MP_EQ(g, MP_ONE)) { |
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211 | mp_drop(g); |
212 | return (-1); |
213 | } |
214 | mp_drop(g); |
215 | } |
216 | |
217 | /* --- Compute %$q^{-1} \bmod p$% --- */ |
218 | |
219 | if (!rp->q_inv) |
220 | mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q); |
221 | |
222 | /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */ |
223 | |
224 | if (!rp->dp) { |
225 | mp *p1 = mp_sub(MP_NEW, rp->p, MP_ONE); |
226 | mp_div(0, &rp->dp, rp->d, p1); |
227 | mp_drop(p1); |
228 | } |
229 | if (!rp->dq) { |
230 | mp *q1 = mp_sub(MP_NEW, rp->q, MP_ONE); |
231 | mp_div(0, &rp->dq, rp->d, q1); |
232 | mp_drop(q1); |
233 | } |
234 | |
235 | /* --- Done --- */ |
236 | |
237 | return (0); |
238 | } |
239 | |
240 | /*----- That's all, folks -------------------------------------------------*/ |