--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: rsa-recover.c,v 1.1 1999/12/22 15:50:45 mdw Exp $
+ *
+ * Recover RSA parameters
+ *
+ * (c) 1999 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: rsa-recover.c,v $
+ * Revision 1.1 1999/12/22 15:50:45 mdw
+ * Initial RSA support.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+#include "mpmont.h"
+#include "rsa.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @rsa_recover@ --- *
+ *
+ * Arguments: @rsa_param *rp@ = pointer to parameter block
+ *
+ * Returns: Zero if all went well, nonzero if the parameters make no
+ * sense.
+ *
+ * Use: Derives the full set of RSA parameters given a minimal set.
+ */
+
+int rsa_recover(rsa_param *rp)
+{
+ /* --- If there is no modulus, calculate it --- */
+
+ if (!rp->n) {
+ if (!rp->p || !rp->q)
+ return (-1);
+ rp->n = mp_mul(MP_NEW, rp->p, rp->q);
+ }
+
+ /* --- If there are no factors, compute them --- */
+
+ else if (!rp->p || !rp->q) {
+
+ /* --- If one is missing, use simple division to recover the other --- */
+
+ if (rp->p || rp->q) {
+ mp *r = MP_NEW;
+ if (rp->p)
+ mp_div(&rp->q, &r, rp->n, rp->p);
+ else
+ mp_div(&rp->p, &r, rp->n, rp->q);
+ if (MP_CMP(r, !=, MP_ZERO)) {
+ mp_drop(r);
+ return (-1);
+ }
+ mp_drop(r);
+ }
+
+ /* --- Otherwise use the public and private moduli --- */
+
+ else if (rp->e && rp->d) {
+ mp *t;
+ unsigned s;
+ mpscan ms;
+ mp a; mpw aw;
+ mp *m1;
+ mpmont mm;
+ int i;
+ mp *z = MP_NEW;
+
+ /* --- Work out the appropriate exponent --- *
+ *
+ * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and
+ * %$t$% is odd.
+ */
+
+ t = mp_mul(MP_NEW, rp->e, rp->d);
+ t = mp_sub(t, t, MP_ONE);
+ s = 0;
+ mp_scan(&ms, t);
+ for (;;) {
+ MP_STEP(&ms);
+ if (MP_BIT(&ms))
+ break;
+ s++;
+ }
+ t = mp_lsr(t, t, s);
+
+ /* --- Set up for the exponentiation --- */
+
+ mpmont_create(&mm, rp->n);
+ m1 = mp_sub(MP_NEW, rp->n, mm.r);
+
+ /* --- Now for the main loop --- *
+ *
+ * Choose candidate integers and attempt to factor the modulus.
+ */
+
+ mp_build(&a, &aw, &aw + 1);
+ i = 0;
+ for (;;) {
+ again:
+
+ /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- *
+ *
+ * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration
+ * is a failure.
+ */
+
+ aw = primetab[i++];
+ z = mpmont_expr(&mm, z, &a, t);
+ if (MP_CMP(z, ==, mm.r) || MP_CMP(z, ==, m1))
+ continue;
+
+ /* --- Now square until something interesting happens --- *
+ *
+ * Compute %$z^{2i} \bmod n$%. Eventually, I'll either get %$-1$% or
+ * %$1$%. If the former, the number is uninteresting, and I need to
+ * restart. If the latter, the previous number minus 1 has a common
+ * factor with %$n$%.
+ */
+
+ for (;;) {
+ mp *zz = mp_sqr(MP_NEW, z);
+ zz = mpmont_reduce(&mm, zz, zz);
+ if (MP_CMP(zz, ==, mm.r)) {
+ mp_drop(zz);
+ goto done;
+ } else if (MP_CMP(zz, ==, m1)) {
+ mp_drop(zz);
+ goto again;
+ }
+ mp_drop(z);
+ z = zz;
+ }
+ }
+
+ /* --- Do the factoring --- *
+ *
+ * Here's how it actually works. I've found an interesting square
+ * root of %$1 \pmod n$%. Any square root of 1 must be congruent to
+ * %$\pm 1$% modulo both %$p$% and %$q$%. Both congruent to %$1$% is
+ * boring, as is both congruent to %$-1$%. Subtracting one from the
+ * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and
+ * nobody cares which), and hence can be extracted by a GCD
+ * operation.
+ */
+
+ done:
+ z = mpmont_reduce(&mm, z, z);
+ z = mp_sub(z, z, MP_ONE);
+ rp->p = MP_NEW;
+ mp_gcd(&rp->p, 0, 0, rp->n, z);
+ rp->q = MP_NEW;
+ mp_div(&rp->q, 0, rp->n, rp->p);
+ mp_drop(z);
+ mp_drop(t);
+ mp_drop(m1);
+ mpmont_destroy(&mm);
+ }
+ }
+
+ /* --- If %$e$% or %$d$% is missing, recalculate it --- */
+
+ if (!rp->e || !rp->d) {
+ mp *phi;
+ mp *g = MP_NEW;
+
+ /* --- Compute %$\varphi(n)$% --- */
+
+ phi = mp_sub(MP_NEW, rp->n, rp->p);
+ phi = mp_sub(phi, phi, rp->q);
+ phi = mp_add(phi, phi, MP_ONE);
+
+ /* --- Recover the other exponent --- */
+
+ if (rp->e)
+ mp_gcd(&g, 0, &rp->d, phi, rp->e);
+ else if (rp->d)
+ mp_gcd(&g, 0, &rp->e, phi, rp->d);
+ else {
+ mp_drop(phi);
+ return (-1);
+ }
+
+ mp_drop(phi);
+ if (MP_CMP(g, !=, MP_ONE)) {
+ mp_drop(g);
+ return (-1);
+ }
+ mp_drop(g);
+ }
+
+ /* --- Compute %$q^{-1} \bmod p$% --- */
+
+ if (!rp->q_inv)
+ mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q);
+
+ /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */
+
+ if (!rp->dp) {
+ mp *p1 = mp_sub(MP_NEW, rp->p, MP_ONE);
+ mp_div(0, &rp->dp, rp->d, p1);
+ mp_drop(p1);
+ }
+ if (!rp->dq) {
+ mp *q1 = mp_sub(MP_NEW, rp->q, MP_ONE);
+ mp_div(0, &rp->dq, rp->d, q1);
+ mp_drop(q1);
+ }
+
+ /* --- Done --- */
+
+ return (0);
+}
+
+/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff