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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: rsa-gen.c,v 1.2 2000/06/17 12:05:15 mdw Exp $ |
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4 | * |
5 | * RSA parameter generation |
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-gen.c,v $ |
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33 | * Revision 1.2 2000/06/17 12:05:15 mdw |
34 | * Lots of changes: |
35 | * |
36 | * * Apply limits on %$\gcd(p - 1, q - 1)$% to reduce the space of |
37 | * equivalent decryption exponents. |
38 | * |
39 | * * Force %$e = F_4 = 2^{16} + 1$% to avoid small-encryption-exponent |
40 | * attacks. |
41 | * |
42 | * * Ensure that %$p > q$% and that %$p - q$% is large to deter |
43 | * square-root-based factoring methods. |
44 | * |
45 | * * Use %$e d \equiv 1 \pmod{\lambda(n)}$%, where %$\lambda(n)$% is |
46 | * %$\lcm(p - 1, q - 1)$%, as recommended in PKCS#1, rather than the |
47 | * more usual %$\varphi(n) = (p - 1)(q - 1)$%. |
48 | * |
49 | * * Handle aborts from pgen_jump. |
50 | * |
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51 | * Revision 1.1 1999/12/22 15:50:45 mdw |
52 | * Initial RSA support. |
53 | * |
54 | */ |
55 | |
56 | /*----- Header files ------------------------------------------------------*/ |
57 | |
58 | #include <mLib/dstr.h> |
59 | |
60 | #include "grand.h" |
61 | #include "mp.h" |
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62 | #include "mpint.h" |
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63 | #include "pgen.h" |
64 | #include "rsa.h" |
65 | #include "strongprime.h" |
66 | |
67 | /*----- Main code ---------------------------------------------------------*/ |
68 | |
69 | /* --- @rsa_gen@ --- * |
70 | * |
71 | * Arguments: @rsa_param *rp@ = pointer to block to be filled in |
72 | * @unsigned nbits@ = required modulus size in bits |
73 | * @grand *r@ = random number source |
74 | * @unsigned n@ = number of attempts to make |
75 | * @pgen_proc *event@ = event handler function |
76 | * @void *ectx@ = argument for the event handler |
77 | * |
78 | * Returns: Zero if all went well, nonzero otherwise. |
79 | * |
80 | * Use: Constructs a pair of strong RSA primes and other useful RSA |
81 | * parameters. A small encryption exponent is chosen if |
82 | * possible. |
83 | */ |
84 | |
85 | int rsa_gen(rsa_param *rp, unsigned nbits, grand *r, unsigned n, |
86 | pgen_proc *event, void *ectx) |
87 | { |
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88 | pgen_gcdstepctx g; |
89 | mp *phi = MP_NEW; |
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90 | |
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91 | /* --- Bits of initialization --- */ |
92 | |
93 | rp->e = mp_fromulong(MP_NEW, 0x10001); |
94 | rp->d = MP_NEW; |
95 | |
96 | /* --- Generate strong primes %$p$% and %$q$% --- * |
97 | * |
98 | * Constrain the GCD of @q@ to ensure that overly small private exponents |
99 | * are impossible. Current results suggest that if %$d < n^{0.29}$% then |
100 | * it can be guessed fairly easily. This implementation is rather more |
101 | * conservative about that sort of thing. |
102 | */ |
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103 | |
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104 | again: |
105 | if ((rp->p = strongprime("p", MP_NEWSEC, nbits/2, r, n, event, ectx)) == 0) |
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106 | goto fail_p; |
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107 | |
108 | /* --- Do painful fiddling with GCD steppers --- */ |
109 | |
110 | { |
111 | mp *q; |
112 | rabin rb; |
113 | |
114 | if ((q = strongprime_setup("q", MP_NEWSEC, &g.jp, nbits / 2, |
115 | r, n, event, ectx)) == 0) |
116 | goto fail_q; |
117 | g.r = mp_lsr(MP_NEW, rp->p, 1); |
118 | g.g = MP_NEW; |
119 | g.max = MP_256; |
120 | q = pgen("q", q, q, event, ectx, n, pgen_gcdstep, &g, |
121 | rabin_iters(nbits/2), pgen_test, &rb); |
122 | pfilt_destroy(&g.jp); |
123 | mp_drop(g.r); |
124 | if (!q) { |
125 | mp_drop(g.g); |
126 | if (n) |
127 | goto fail_q; |
128 | mp_drop(rp->p); |
129 | goto again; |
130 | } |
131 | rp->q = q; |
132 | } |
133 | |
134 | /* --- Ensure that %$p > q$% --- * |
135 | * |
136 | * Also ensure that %$p$% and %$q$% are sufficiently different to deter |
137 | * square-root-based factoring methods. |
138 | */ |
139 | |
140 | phi = mp_sub(phi, rp->p, rp->q); |
141 | if (MP_LEN(phi) * 4 < MP_LEN(rp->p) * 3 || |
142 | MP_LEN(phi) * 4 < MP_LEN(rp->q) * 3) { |
143 | mp_drop(rp->p); |
144 | mp_drop(g.g); |
145 | if (n) |
146 | goto fail_q; |
147 | mp_drop(rp->q); |
148 | goto again; |
149 | } |
150 | |
151 | if (phi->f & MP_NEG) { |
152 | mp *z = rp->p; |
153 | rp->p = rp->q; |
154 | rp->q = z; |
155 | } |
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156 | |
157 | /* --- Work out the modulus and the CRT coefficient --- */ |
158 | |
159 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
160 | rp->q_inv = MP_NEW; mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q); |
161 | |
162 | /* --- Work out %$\varphi(n) = (p - 1)(q - 1)$% --- * |
163 | * |
164 | * Save on further multiplications by noting that %$n = pq$% is known and |
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165 | * that %$(p - 1)(q - 1) = pq - p - q + 1$%. To minimize the size of @d@ |
166 | * (useful for performance reasons, although not very because an overly |
167 | * small @d@ will be rejected for security reasons) this is then divided by |
168 | * %$\gcd(p - 1, q - 1)$%. |
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169 | */ |
170 | |
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171 | phi = mp_sub(phi, rp->n, rp->p); |
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172 | phi = mp_sub(phi, phi, rp->q); |
173 | phi = mp_add(phi, phi, MP_ONE); |
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174 | phi = mp_lsr(phi, phi, 1); |
175 | mp_div(&phi, 0, phi, g.g); |
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176 | |
177 | /* --- Decide on a public exponent --- * |
178 | * |
179 | * Simultaneously compute the private exponent. |
180 | */ |
181 | |
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182 | mp_gcd(&g.g, 0, &rp->d, phi, rp->e); |
183 | if (MP_CMP(g.g, !=, MP_ONE) && MP_LEN(rp->d) * 4 > MP_LEN(rp->n) * 3) |
184 | goto fail_e; |
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185 | |
186 | /* --- Work out exponent residues --- */ |
187 | |
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188 | rp->dp = MP_NEW; phi = mp_sub(phi, rp->p, MP_ONE); |
189 | mp_div(0, &rp->dp, rp->d, phi); |
190 | |
191 | rp->dq = MP_NEW; phi = mp_sub(phi, rp->q, MP_ONE); |
192 | mp_div(0, &rp->dq, rp->d, phi); |
193 | |
194 | /* --- Done --- */ |
195 | |
196 | mp_drop(phi); |
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197 | mp_drop(g.g); |
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198 | return (0); |
199 | |
200 | /* --- Tidy up when something goes wrong --- */ |
201 | |
202 | fail_e: |
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203 | mp_drop(g.g); |
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204 | mp_drop(phi); |
205 | mp_drop(rp->n); |
206 | mp_drop(rp->q_inv); |
207 | mp_drop(rp->q); |
208 | fail_q: |
209 | mp_drop(rp->p); |
210 | fail_p: |
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211 | mp_drop(rp->e); |
212 | if (rp->d) |
213 | mp_drop(rp->d); |
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214 | return (-1); |
215 | } |
216 | |
217 | /*----- That's all, folks -------------------------------------------------*/ |