3 * Recover RSA parameters
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 ------------------------------------------------------*/
34 /*----- Main code ---------------------------------------------------------*/
36 /* --- @rsa_recover@ --- *
38 * Arguments: @rsa_priv *rp@ = pointer to parameter block
40 * Returns: Zero if all went well, nonzero if the parameters make no
43 * Use: Derives the full set of RSA parameters given a minimal set.
46 int rsa_recover(rsa_priv
*rp
)
48 /* --- If there is no modulus, calculate it --- */
53 rp
->n
= mp_mul(MP_NEW
, rp
->p
, rp
->q
);
56 /* --- If there are no factors, compute them --- */
58 else if (!rp
->p
|| !rp
->q
) {
60 /* --- If one is missing, use simple division to recover the other --- */
65 mp_div(&rp
->q
, &r
, rp
->n
, rp
->p
);
67 mp_div(&rp
->p
, &r
, rp
->n
, rp
->q
);
68 if (!MP_EQ(r
, MP_ZERO
)) {
75 /* --- Otherwise use the public and private moduli --- */
77 else if (!rp
->e
|| !rp
->d
)
88 /* --- Work out the appropriate exponent --- *
90 * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and
94 t
= mp_mul(MP_NEW
, rp
->e
, rp
->d
);
95 t
= mp_sub(t
, t
, MP_ONE
);
98 /* --- Set up for the exponentiation --- */
100 mpmont_create(&mm
, rp
->n
);
101 m1
= mp_sub(MP_NEW
, rp
->n
, mm
.r
);
103 /* --- Now for the main loop --- *
105 * Choose candidate integers and attempt to factor the modulus.
108 mp_build(&a
, &aw
, &aw
+ 1);
113 /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- *
115 * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration
120 z
= mpmont_mul(&mm
, z
, &a
, mm
.r2
);
121 z
= mpmont_expr(&mm
, z
, z
, t
);
122 if (MP_EQ(z
, mm
.r
) || MP_EQ(z
, m1
))
125 /* --- Now square until something interesting happens --- *
127 * Compute %$z^{2i} \bmod n$%. Eventually, I'll either get %$-1$% or
128 * %$1$%. If the former, the number is uninteresting, and I need to
129 * restart. If the latter, the previous number minus 1 has a common
134 mp
*zz
= mp_sqr(MP_NEW
, z
);
135 zz
= mpmont_reduce(&mm
, zz
, zz
);
136 if (MP_EQ(zz
, mm
.r
)) {
139 } else if (MP_EQ(zz
, m1
)) {
148 /* --- Do the factoring --- *
150 * Here's how it actually works. I've found an interesting square
151 * root of %$1 \pmod n$%. Any square root of 1 must be congruent to
152 * %$\pm 1$% modulo both %$p$% and %$q$%. Both congruent to %$1$% is
153 * boring, as is both congruent to %$-1$%. Subtracting one from the
154 * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and
155 * nobody cares which), and hence can be extracted by a GCD
160 z
= mpmont_reduce(&mm
, z
, z
);
161 z
= mp_sub(z
, z
, MP_ONE
);
163 mp_gcd(&rp
->p
, 0, 0, rp
->n
, z
);
165 mp_div(&rp
->q
, 0, rp
->n
, rp
->p
);
169 if (MP_CMP(rp
->p
, <, rp
->q
)) {
178 /* --- If %$e$% or %$d$% is missing, recalculate it --- */
180 if (!rp
->e
|| !rp
->d
) {
185 /* --- Compute %$\varphi(n)$% --- */
187 phi
= mp_sub(MP_NEW
, rp
->n
, rp
->p
);
188 phi
= mp_sub(phi
, phi
, rp
->q
);
189 phi
= mp_add(phi
, phi
, MP_ONE
);
190 p1
= mp_sub(MP_NEW
, rp
->p
, MP_ONE
);
191 q1
= mp_sub(MP_NEW
, rp
->q
, MP_ONE
);
192 mp_gcd(&g
, 0, 0, p1
, q1
);
193 mp_div(&phi
, 0, phi
, g
);
197 /* --- Recover the other exponent --- */
200 mp_gcd(&g
, 0, &rp
->d
, phi
, rp
->e
);
202 mp_gcd(&g
, 0, &rp
->e
, phi
, rp
->d
);
210 if (!MP_EQ(g
, MP_ONE
)) {
217 /* --- Compute %$q^{-1} \bmod p$% --- */
220 mp_gcd(0, 0, &rp
->q_inv
, rp
->p
, rp
->q
);
222 /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */
225 mp
*p1
= mp_sub(MP_NEW
, rp
->p
, MP_ONE
);
226 mp_div(0, &rp
->dp
, rp
->d
, p1
);
230 mp
*q1
= mp_sub(MP_NEW
, rp
->q
, MP_ONE
);
231 mp_div(0, &rp
->dq
, rp
->d
, q1
);
240 /*----- That's all, folks -------------------------------------------------*/