3 * RSA private-key operations
5 * (c) 1999 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
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.
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.
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,
28 /*----- Header files ------------------------------------------------------*/
30 #include <mLib/alloc.h>
31 #include <mLib/bits.h>
32 #include <mLib/dstr.h>
39 /*----- Public key operations ---------------------------------------------*/
41 /* --- @rsa_privcreate@ --- *
43 * Arguments: @rsa_privctx *rd@ = pointer to an RSA private key context
44 * @rsa_priv *rp@ = pointer to RSA private key
45 * @grand *r@ = pointer to random number source for blinding
49 * Use: Initializes an RSA private-key context. Keeping a context
50 * for several decryption or signing operations provides a minor
51 * performance benefit.
53 * The random number source may be null if blinding is not
54 * desired. This improves decryption speed, at the risk of
55 * permitting timing attacks.
58 void rsa_privcreate(rsa_privctx *rd, rsa_priv *rp, grand *r)
63 mpmont_create(&rd->nm, rp->n);
64 mpmont_create(&rd->pm, rp->p);
65 mpmont_create(&rd->qm, rp->q);
68 /* --- @rsa_privdestroy@ --- *
70 * Arguments: @rsa_privctx *rd@ = pointer to an RSA decryption context
74 * Use: Destroys an RSA decryption context.
77 void rsa_privdestroy(rsa_privctx *rd)
80 mpmont_destroy(&rd->nm);
81 mpmont_destroy(&rd->pm);
82 mpmont_destroy(&rd->qm);
85 /* --- @rsa_privop@ --- *
87 * Arguments: @rsa_privctx *rd@ = pointer to RSA private key context
88 * @mp *d@ = destination
89 * @mp *c@ = input message
91 * Returns: The transformed output message.
93 * Use: Performs an RSA private key operation. This function takes
94 * advantage of knowledge of the key factors in order to speed
95 * up decryption. It also blinds the ciphertext prior to
96 * decryption and unblinds it afterwards to thwart timing
100 mp *rsa_privop(rsa_privctx *rd, mp *d, mp *c)
103 rsa_priv *rp = rd->rp;
105 /* --- If so desired, set up a blinding constant --- *
107 * Choose a constant %$k$% relatively prime to the modulus %$m$%. Compute
108 * %$c' = c k^e \bmod n$%, and %$k^{-1} \bmod n$%. Don't bother with the
109 * CRT stuff here because %$e$% is chosen to be small.
114 mp *k = MP_NEWSEC, *g = MP_NEW;
117 k = mprand_range(k, rp->n, rd->r, 0);
118 mp_gcd(&g, 0, &ki, rp->n, k);
119 } while (!MP_EQ(g, MP_ONE));
120 k = mpmont_mul(&rd->nm, k, k, rd->nm.r2);
121 k = mpmont_expr(&rd->nm, k, k, rp->e);
122 c = mpmont_mul(&rd->nm, c, c, k);
127 /* --- Do the actual modular exponentiation --- *
129 * Use a slightly hacked version of the Chinese Remainder Theorem stuff.
131 * Let %$q' = q^{-1} \bmod p$%. Then note that
132 * %$c^d \equiv q (q'(c_p^{d_p} - c_q^{d_q}) \bmod p) + c_q^{d_q} \pmod n$%
136 mp *cp = MP_NEW, *cq = MP_NEW;
138 /* --- Work out the two halves of the result --- */
140 mp_div(0, &cp, c, rp->p);
141 cp = mpmont_exp(&rd->pm, cp, cp, rp->dp);
143 mp_div(0, &cq, c, rp->q);
144 cq = mpmont_exp(&rd->qm, cq, cq, rp->dq);
146 /* --- Combine the halves using the result above --- */
148 d = mp_sub(d, cp, cq);
149 mp_div(0, &d, d, rp->p);
150 d = mpmont_mul(&rd->pm, d, d, rp->q_inv);
151 d = mpmont_mul(&rd->pm, d, d, rd->pm.r2);
153 d = mp_mul(d, d, rp->q);
154 d = mp_add(d, d, cq);
155 if (MP_CMP(d, >=, rp->n))
156 d = mp_sub(d, d, rp->n);
158 /* --- Tidy away temporary variables --- */
164 /* --- Finally, possibly remove the blinding factor --- */
167 d = mpmont_mul(&rd->nm, d, d, ki);
168 d = mpmont_mul(&rd->nm, d, d, rd->nm.r2);
178 /* --- @rsa_qprivop@ --- *
180 * Arguments: @rsa_priv *rp@ = pointer to RSA parameters
181 * @mp *d@ = destination
182 * @mp *c@ = input message
183 * @grand *r@ = pointer to random number source for blinding
185 * Returns: Correctly transformed output message
187 * Use: Performs an RSA private key operation, very carefully.
190 mp *rsa_qprivop(rsa_priv *rp, mp *d, mp *c, grand *r)
193 rsa_privcreate(&rd, rp, r);
194 d = rsa_privop(&rd, d, c);
195 rsa_privdestroy(&rd);
199 /*----- Operations with padding -------------------------------------------*/
201 /* --- @rsa_sign@ --- *
203 * Arguments: @rsa_privctx *rp@ = pointer to an RSA private key context
204 * @mp *d@ = where to put the result
205 * @const void *m@ = pointer to input message
206 * @size_t msz@ = size of input message
207 * @rsa_pad *e@ = encoding procedure
208 * @void *earg@ = argument pointer for encoding procedure
210 * Returns: The signature, as a multiprecision integer, or null on
213 * Use: Computes an RSA digital signature.
216 mp *rsa_sign(rsa_privctx *rp, mp *d, const void *m, size_t msz,
217 rsa_pad *e, void *earg)
220 unsigned long nb = mp_bits(rp->rp->n);
221 size_t n = (nb + 7)/8;
222 arena *a = d && d->a ? d->a->a : arena_global;
225 d = e(d, m, msz, p, n, nb, earg);
227 return (d ? rsa_privop(rp, d, d) : 0);
230 /* --- @rsa_decrypt@ --- *
232 * Arguments: @rsa_privctx *rp@ = pointer to an RSA private key context
233 * @mp *m@ = encrypted message, as a multiprecision integer
234 * @dstr *d@ = pointer to output string
235 * @rsa_decunpad *e@ = decoding procedure
236 * @void *earg@ = argument pointer for decoding procedure
238 * Returns: The length of the output string if successful, negative on
241 * Use: Does RSA decryption.
244 int rsa_decrypt(rsa_privctx *rp, mp *m, dstr *d,
245 rsa_decunpad *e, void *earg)
247 mp *p = rsa_privop(rp, MP_NEW, m);
248 unsigned long nb = mp_bits(rp->rp->n);
249 size_t n = (nb + 7)/8;
253 rc = e(p, (octet *)d->buf + d->len, n, nb, earg);
260 /*----- That's all, folks -------------------------------------------------*/