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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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4 | * |
5 | * RSA parameter generation |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
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10 | /*----- Licensing notice --------------------------------------------------* |
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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. |
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18 | * |
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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. |
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23 | * |
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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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include <mLib/dstr.h> |
33 | |
34 | #include "grand.h" |
35 | #include "mp.h" |
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36 | #include "mpint.h" |
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37 | #include "pgen.h" |
38 | #include "rsa.h" |
39 | #include "strongprime.h" |
40 | |
41 | /*----- Main code ---------------------------------------------------------*/ |
42 | |
43 | /* --- @rsa_gen@ --- * |
44 | * |
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45 | * Arguments: @rsa_priv *rp@ = pointer to block to be filled in |
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46 | * @unsigned nbits@ = required modulus size in bits |
47 | * @grand *r@ = random number source |
48 | * @unsigned n@ = number of attempts to make |
49 | * @pgen_proc *event@ = event handler function |
50 | * @void *ectx@ = argument for the event handler |
51 | * |
52 | * Returns: Zero if all went well, nonzero otherwise. |
53 | * |
54 | * Use: Constructs a pair of strong RSA primes and other useful RSA |
55 | * parameters. A small encryption exponent is chosen if |
56 | * possible. |
57 | */ |
58 | |
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59 | int rsa_gen(rsa_priv *rp, unsigned nbits, grand *r, unsigned n, |
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60 | pgen_proc *event, void *ectx) |
61 | { |
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62 | pgen_gcdstepctx g; |
63 | mp *phi = MP_NEW; |
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64 | |
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65 | /* --- Bits of initialization --- */ |
66 | |
67 | rp->e = mp_fromulong(MP_NEW, 0x10001); |
68 | rp->d = MP_NEW; |
69 | |
70 | /* --- Generate strong primes %$p$% and %$q$% --- * |
71 | * |
72 | * Constrain the GCD of @q@ to ensure that overly small private exponents |
73 | * are impossible. Current results suggest that if %$d < n^{0.29}$% then |
74 | * it can be guessed fairly easily. This implementation is rather more |
75 | * conservative about that sort of thing. |
76 | */ |
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77 | |
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78 | again: |
79 | if ((rp->p = strongprime("p", MP_NEWSEC, nbits/2, r, n, event, ectx)) == 0) |
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80 | goto fail_p; |
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81 | |
82 | /* --- Do painful fiddling with GCD steppers --- */ |
83 | |
84 | { |
85 | mp *q; |
86 | rabin rb; |
87 | |
88 | if ((q = strongprime_setup("q", MP_NEWSEC, &g.jp, nbits / 2, |
89 | r, n, event, ectx)) == 0) |
90 | goto fail_q; |
91 | g.r = mp_lsr(MP_NEW, rp->p, 1); |
92 | g.g = MP_NEW; |
93 | g.max = MP_256; |
94 | q = pgen("q", q, q, event, ectx, n, pgen_gcdstep, &g, |
95 | rabin_iters(nbits/2), pgen_test, &rb); |
96 | pfilt_destroy(&g.jp); |
97 | mp_drop(g.r); |
98 | if (!q) { |
99 | mp_drop(g.g); |
100 | if (n) |
101 | goto fail_q; |
102 | mp_drop(rp->p); |
103 | goto again; |
104 | } |
105 | rp->q = q; |
106 | } |
107 | |
108 | /* --- Ensure that %$p > q$% --- * |
109 | * |
110 | * Also ensure that %$p$% and %$q$% are sufficiently different to deter |
111 | * square-root-based factoring methods. |
112 | */ |
113 | |
114 | phi = mp_sub(phi, rp->p, rp->q); |
115 | if (MP_LEN(phi) * 4 < MP_LEN(rp->p) * 3 || |
116 | MP_LEN(phi) * 4 < MP_LEN(rp->q) * 3) { |
117 | mp_drop(rp->p); |
118 | mp_drop(g.g); |
119 | if (n) |
120 | goto fail_q; |
121 | mp_drop(rp->q); |
122 | goto again; |
123 | } |
124 | |
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125 | if (MP_NEGP(phi)) { |
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126 | mp *z = rp->p; |
127 | rp->p = rp->q; |
128 | rp->q = z; |
129 | } |
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130 | |
131 | /* --- Work out the modulus and the CRT coefficient --- */ |
132 | |
133 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
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134 | rp->q_inv = mp_modinv(MP_NEW, rp->q, rp->p); |
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135 | |
136 | /* --- Work out %$\varphi(n) = (p - 1)(q - 1)$% --- * |
137 | * |
138 | * Save on further multiplications by noting that %$n = pq$% is known and |
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139 | * that %$(p - 1)(q - 1) = pq - p - q + 1$%. To minimize the size of @d@ |
140 | * (useful for performance reasons, although not very because an overly |
141 | * small @d@ will be rejected for security reasons) this is then divided by |
142 | * %$\gcd(p - 1, q - 1)$%. |
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143 | */ |
144 | |
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145 | phi = mp_sub(phi, rp->n, rp->p); |
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146 | phi = mp_sub(phi, phi, rp->q); |
147 | phi = mp_add(phi, phi, MP_ONE); |
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148 | phi = mp_lsr(phi, phi, 1); |
149 | mp_div(&phi, 0, phi, g.g); |
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150 | |
151 | /* --- Decide on a public exponent --- * |
152 | * |
153 | * Simultaneously compute the private exponent. |
154 | */ |
155 | |
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156 | mp_gcd(&g.g, 0, &rp->d, phi, rp->e); |
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157 | if (!MP_EQ(g.g, MP_ONE) && MP_LEN(rp->d) * 4 > MP_LEN(rp->n) * 3) |
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158 | goto fail_e; |
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159 | |
160 | /* --- Work out exponent residues --- */ |
161 | |
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162 | rp->dp = MP_NEW; phi = mp_sub(phi, rp->p, MP_ONE); |
163 | mp_div(0, &rp->dp, rp->d, phi); |
164 | |
165 | rp->dq = MP_NEW; phi = mp_sub(phi, rp->q, MP_ONE); |
166 | mp_div(0, &rp->dq, rp->d, phi); |
167 | |
168 | /* --- Done --- */ |
169 | |
170 | mp_drop(phi); |
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171 | mp_drop(g.g); |
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172 | return (0); |
173 | |
174 | /* --- Tidy up when something goes wrong --- */ |
175 | |
176 | fail_e: |
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177 | mp_drop(g.g); |
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178 | mp_drop(phi); |
179 | mp_drop(rp->n); |
180 | mp_drop(rp->q_inv); |
181 | mp_drop(rp->q); |
182 | fail_q: |
183 | mp_drop(rp->p); |
184 | fail_p: |
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185 | mp_drop(rp->e); |
186 | if (rp->d) |
187 | mp_drop(rp->d); |
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188 | return (-1); |
189 | } |
190 | |
191 | /*----- That's all, folks -------------------------------------------------*/ |