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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: rsa-priv.c,v 1.2 2000/10/08 12:11:22 mdw Exp $ |
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4 | * |
5 | * RSA private-key operations |
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-priv.c,v $ |
22bab86c |
33 | * Revision 1.2 2000/10/08 12:11:22 mdw |
34 | * Use @MP_EQ@ instead of @MP_CMP@. |
35 | * |
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36 | * Revision 1.1 2000/07/01 11:23:20 mdw |
37 | * Renamed from `rsa-decrypt', since the name was no longer appropriate. |
38 | * Add functions for doing padded RSA decryption and signing. |
39 | * |
40 | * --- Previous lives as rsa-decrypt.c --- |
41 | * |
42 | * Revision 1.2 2000/06/17 11:57:56 mdw |
43 | * Improve bulk performance by making better use of Montgomery |
44 | * multiplication and separating out initialization and finalization from |
45 | * the main code. |
46 | * |
47 | * Revision 1.1 1999/12/22 15:50:45 mdw |
48 | * Initial RSA support. |
49 | * |
50 | */ |
51 | |
52 | /*----- Header files ------------------------------------------------------*/ |
53 | |
54 | #include <mLib/alloc.h> |
55 | #include <mLib/bits.h> |
56 | #include <mLib/dstr.h> |
57 | |
58 | #include "mp.h" |
59 | #include "mpmont.h" |
60 | #include "mprand.h" |
61 | #include "rsa.h" |
62 | |
63 | /*----- Public key operations ---------------------------------------------*/ |
64 | |
65 | /* --- @rsa_privcreate@ --- * |
66 | * |
67 | * Arguments: @rsa_privctx *rd@ = pointer to an RSA private key context |
68 | * @rsa_priv *rp@ = pointer to RSA private key |
69 | * @grand *r@ = pointer to random number source for blinding |
70 | * |
71 | * Returns: --- |
72 | * |
73 | * Use: Initializes an RSA private-key context. Keeping a context |
74 | * for several decryption or signing operations provides a minor |
75 | * performance benefit. |
76 | * |
77 | * The random number source may be null if blinding is not |
78 | * desired. This improves decryption speed, at the risk of |
79 | * permitting timing attacks. |
80 | */ |
81 | |
82 | void rsa_privcreate(rsa_privctx *rd, rsa_priv *rp, grand *r) |
83 | { |
84 | rd->rp = rp; |
85 | rd->r = r; |
86 | if (r) |
87 | mpmont_create(&rd->nm, rp->n); |
88 | mpmont_create(&rd->pm, rp->p); |
89 | mpmont_create(&rd->qm, rp->q); |
90 | } |
91 | |
92 | /* --- @rsa_privdestroy@ --- * |
93 | * |
94 | * Arguments: @rsa_privctx *rd@ = pointer to an RSA decryption context |
95 | * |
96 | * Returns: --- |
97 | * |
98 | * Use: Destroys an RSA decryption context. |
99 | */ |
100 | |
101 | void rsa_privdestroy(rsa_privctx *rd) |
102 | { |
103 | if (rd->r) |
104 | mpmont_destroy(&rd->nm); |
105 | mpmont_destroy(&rd->pm); |
106 | mpmont_destroy(&rd->qm); |
107 | } |
108 | |
109 | /* --- @rsa_privop@ --- * |
110 | * |
111 | * Arguments: @rsa_privctx *rd@ = pointer to RSA private key context |
112 | * @mp *d@ = destination |
113 | * @mp *c@ = input message |
114 | * |
115 | * Returns: The transformed output message. |
116 | * |
117 | * Use: Performs an RSA private key operation. This function takes |
118 | * advantage of knowledge of the key factors in order to speed |
119 | * up decryption. It also blinds the ciphertext prior to |
120 | * decryption and unblinds it afterwards to thwart timing |
121 | * attacks. |
122 | */ |
123 | |
124 | mp *rsa_privop(rsa_privctx *rd, mp *d, mp *c) |
125 | { |
126 | mp *ki = MP_NEW; |
127 | rsa_priv *rp = rd->rp; |
128 | |
129 | /* --- If so desired, set up a blinding constant --- * |
130 | * |
131 | * Choose a constant %$k$% relatively prime to the modulus %$m$%. Compute |
132 | * %$c' = c k^e \bmod n$%, and %$k^{-1} \bmod n$%. Don't bother with the |
133 | * CRT stuff here because %$e$% is chosen to be small. |
134 | */ |
135 | |
136 | c = MP_COPY(c); |
137 | if (rd->r) { |
138 | mp *k = MP_NEWSEC, *g = MP_NEW; |
139 | |
140 | do { |
141 | k = mprand_range(k, rp->n, rd->r, 0); |
142 | mp_gcd(&g, 0, &ki, rp->n, k); |
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143 | } while (!MP_EQ(g, MP_ONE)); |
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144 | k = mpmont_expr(&rd->nm, k, k, rp->e); |
145 | c = mpmont_mul(&rd->nm, c, c, k); |
146 | mp_drop(k); |
147 | mp_drop(g); |
148 | } |
149 | |
150 | /* --- Do the actual modular exponentiation --- * |
151 | * |
152 | * Use a slightly hacked version of the Chinese Remainder Theorem stuff. |
153 | * |
154 | * Let %$q' = q^{-1} \bmod p$%. Then note that |
155 | * %$c^d \equiv q (q'(c_p^{d_p} - c_q^{d_q}) \bmod p) + c_q^{d_q} \pmod n$% |
156 | */ |
157 | |
158 | { |
159 | mp *cp = MP_NEW, *cq = MP_NEW; |
160 | |
161 | /* --- Work out the two halves of the result --- */ |
162 | |
163 | mp_div(0, &cp, c, rp->p); |
164 | cp = mpmont_exp(&rd->pm, cp, cp, rp->dp); |
165 | |
166 | mp_div(0, &cq, c, rp->q); |
167 | cq = mpmont_exp(&rd->qm, cq, cq, rp->dq); |
168 | |
169 | /* --- Combine the halves using the result above --- */ |
170 | |
171 | d = mp_sub(d, cp, cq); |
172 | mp_div(0, &d, d, rp->p); |
173 | d = mpmont_mul(&rd->pm, d, d, rp->q_inv); |
174 | d = mpmont_mul(&rd->pm, d, d, rd->pm.r2); |
175 | |
176 | d = mp_mul(d, d, rp->q); |
177 | d = mp_add(d, d, cq); |
178 | if (MP_CMP(d, >=, rp->n)) |
179 | d = mp_sub(d, d, rp->n); |
180 | |
181 | /* --- Tidy away temporary variables --- */ |
182 | |
183 | mp_drop(cp); |
184 | mp_drop(cq); |
185 | } |
186 | |
187 | /* --- Finally, possibly remove the blinding factor --- */ |
188 | |
189 | if (ki) { |
190 | d = mpmont_mul(&rd->nm, d, d, ki); |
191 | d = mpmont_mul(&rd->nm, d, d, rd->nm.r2); |
192 | mp_drop(ki); |
193 | } |
194 | |
195 | /* --- Done --- */ |
196 | |
197 | mp_drop(c); |
198 | return (d); |
199 | } |
200 | |
201 | /* --- @rsa_qprivop@ --- * |
202 | * |
203 | * Arguments: @rsa_priv *rp@ = pointer to RSA parameters |
204 | * @mp *d@ = destination |
205 | * @mp *c@ = input message |
206 | * @grand *r@ = pointer to random number source for blinding |
207 | * |
208 | * Returns: Correctly transformed output message |
209 | * |
210 | * Use: Performs an RSA private key operation, very carefully. |
211 | */ |
212 | |
213 | mp *rsa_qprivop(rsa_priv *rp, mp *d, mp *c, grand *r) |
214 | { |
215 | rsa_privctx rd; |
216 | rsa_privcreate(&rd, rp, r); |
217 | d = rsa_privop(&rd, d, c); |
218 | rsa_privdestroy(&rd); |
219 | return (d); |
220 | } |
221 | |
222 | /*----- Operations with padding -------------------------------------------*/ |
223 | |
224 | /* --- @rsa_sign@ --- * |
225 | * |
226 | * Arguments: @rsa_privctx *rp@ = pointer to an RSA private key context |
227 | * @const void *m@ = pointer to input message |
228 | * @size_t sz@ = size of input message |
229 | * @dstr *d@ = pointer to output string |
230 | * @rsa_encodeproc e@ = encoding procedure |
231 | * @void *earg@ = argument pointer for encoding procedure |
232 | * |
233 | * Returns: The length of the output string if successful, negative on |
234 | * failure. |
235 | * |
236 | * Use: Computes an RSA digital signature. |
237 | */ |
238 | |
239 | int rsa_sign(rsa_privctx *rp, const void *m, size_t sz, |
240 | dstr *d, rsa_encodeproc e, void *earg) |
241 | { |
242 | mp *x; |
243 | size_t n = mp_octets(rp->rp->n); |
244 | octet *p; |
245 | int rc; |
246 | |
247 | /* --- Sort out some space --- */ |
248 | |
249 | dstr_ensure(d, n); |
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250 | p = (octet *)d->buf + d->len; |
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251 | p[0] = 0; |
252 | |
253 | /* --- Do the packing --- */ |
254 | |
255 | if ((rc = e(m, sz, p, n, earg)) < 0) |
256 | return (rc); |
257 | |
258 | /* --- Do the encryption --- */ |
259 | |
260 | x = mp_loadb(MP_NEWSEC, p, n); |
261 | x = rsa_privop(rp, x, x); |
262 | mp_storeb(x, p, n); |
263 | d->len += n; |
264 | mp_drop(x); |
265 | return (n); |
266 | } |
267 | |
268 | /* --- @rsa_decrypt@ --- * |
269 | * |
270 | * Arguments: @rsa_privctx *rp@ = pointer to an RSA private key context |
271 | * @const void *m@ = pointer to input message |
272 | * @size_t sz@ = size of input message |
273 | * @dstr *d@ = pointer to output string |
274 | * @rsa_decodeproc e@ = decoding procedure |
275 | * @void *earg@ = argument pointer for decoding procedure |
276 | * |
277 | * Returns: The length of the output string if successful, negative on |
278 | * failure. |
279 | * |
280 | * Use: Does RSA signature verification. |
281 | */ |
282 | |
283 | int rsa_decrypt(rsa_privctx *rp, const void *m, size_t sz, |
284 | dstr *d, rsa_decodeproc e, void *earg) |
285 | { |
286 | mp *x; |
287 | size_t n = mp_octets(rp->rp->n); |
288 | octet *p; |
289 | int rc; |
290 | |
291 | /* --- Do the exponentiation --- */ |
292 | |
293 | p = x_alloc(d->a, n); |
294 | x = mp_loadb(MP_NEW, m, sz); |
295 | x = rsa_privop(rp, x, x); |
296 | mp_storeb(x, p, n); |
297 | mp_drop(x); |
298 | |
299 | /* --- Do the decoding --- */ |
300 | |
301 | rc = e(p, n, d, earg); |
302 | x_free(d->a, p); |
303 | return (rc); |
304 | } |
305 | |
306 | /*----- That's all, folks -------------------------------------------------*/ |