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1 | /* -*-c-*- |
2 | * |
3 | * $Id: rsa-decrypt.c,v 1.1 1999/12/22 15:50:45 mdw Exp $ |
4 | * |
5 | * RSA decryption |
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-decrypt.c,v $ |
33 | * Revision 1.1 1999/12/22 15:50:45 mdw |
34 | * Initial RSA support. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include "mp.h" |
41 | #include "mpmont.h" |
42 | #include "mprand.h" |
43 | #include "rsa.h" |
44 | |
45 | /*----- Main code ---------------------------------------------------------*/ |
46 | |
47 | /* --- @rsa_decrypt@ --- * |
48 | * |
49 | * Arguments: @rsa_param *rp@ = pointer to RSA parameters |
50 | * @mp *d@ = destination |
51 | * @mp *c@ = ciphertext message |
52 | * @grand *r@ = pointer to random number source for blinding |
53 | * |
54 | * Returns: Correctly decrypted message. |
55 | * |
56 | * Use: Performs RSA decryption, very carefully. |
57 | */ |
58 | |
59 | mp *rsa_decrypt(rsa_param *rp, mp *d, mp *c, grand *r) |
60 | { |
61 | mp *ki = MP_NEW; |
62 | |
63 | /* --- If so desired, set up a blinding constant --- * |
64 | * |
65 | * Choose a constant %$k$% relatively prime to the modulus %$m$%. Compute |
66 | * %$c' = c k^e \bmod n$%, and %$k^{-1} \bmod n$%. |
67 | */ |
68 | |
69 | c = MP_COPY(c); |
70 | if (r) { |
71 | mp *k = MP_NEW, *g = MP_NEW; |
72 | mpmont mm; |
73 | |
74 | do { |
75 | k = mprand_range(k, rp->n, r, 0); |
76 | mp_gcd(&g, 0, &ki, rp->n, k); |
77 | } while (MP_CMP(g, !=, MP_ONE)); |
78 | mpmont_create(&mm, rp->n); |
79 | k = mpmont_expr(&mm, k, k, rp->e); |
80 | c = mpmont_mul(&mm, c, c, k); |
81 | mp_drop(k); |
82 | mp_drop(g); |
83 | } |
84 | |
85 | /* --- Do the actual modular exponentiation --- * |
86 | * |
87 | * Use a slightly hacked version of the Chinese Remainder Theorem stuff. |
88 | * |
89 | * Let %$q' = q^{-1} \bmod p$%. Then note that |
90 | * %$c^d \equiv q (q'(c_p^{d_p} - c_q^{d_q}) \bmod p) + c_q^{d_q} \pmod n$% |
91 | */ |
92 | |
93 | { |
94 | mpmont mm; |
95 | mp *cp = MP_NEW, *cq = MP_NEW; |
96 | |
97 | /* --- Work out the two halves of the result --- */ |
98 | |
99 | mp_div(0, &cp, c, rp->p); |
100 | mpmont_create(&mm, rp->p); |
101 | cp = mpmont_exp(&mm, cp, cp, rp->dp); |
102 | mpmont_destroy(&mm); |
103 | |
104 | mp_div(0, &cq, c, rp->q); |
105 | mpmont_create(&mm, rp->q); |
106 | cq = mpmont_exp(&mm, cq, cq, rp->dq); |
107 | mpmont_destroy(&mm); |
108 | |
109 | /* --- Combine the halves using the result above --- */ |
110 | |
111 | d = mp_sub(d, cp, cq); |
112 | if (cp->f & MP_NEG) |
113 | d = mp_add(d, d, rp->p); |
114 | d = mp_mul(d, d, rp->q_inv); |
115 | mp_div(0, &d, d, rp->p); |
116 | |
117 | d = mp_mul(d, d, rp->q); |
118 | d = mp_add(d, d, cq); |
119 | if (MP_CMP(d, >=, rp->n)) |
120 | d = mp_sub(d, d, rp->n); |
121 | |
122 | /* --- Tidy away temporary variables --- */ |
123 | |
124 | mp_drop(cp); |
125 | mp_drop(cq); |
126 | } |
127 | |
128 | /* --- Finally, possibly remove the blinding factor --- */ |
129 | |
130 | if (ki) { |
131 | d = mp_mul(d, d, ki); |
132 | mp_div(0, &d, d, rp->n); |
133 | mp_drop(ki); |
134 | } |
135 | |
136 | /* --- Done --- */ |
137 | |
138 | mp_drop(c); |
139 | return (d); |
140 | } |
141 | |
142 | /*----- That's all, folks -------------------------------------------------*/ |