mdw@git.distorted.org.uk Git - catacomb/blob - pub/rsa-recover.c

   1 /* -*-c-*-
   2  *
   3  * Recover RSA parameters
   4  *
   5  * (c) 1999 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  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.
  16  *
  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.
  21  *
  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,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Header files ------------------------------------------------------*/
  29
  30 #include "mp.h"
  31 #include "mpmont.h"
  32 #include "rsa.h"
  33
  34 /*----- Main code ---------------------------------------------------------*/
  35
  36 /* --- @rsa_recover@ --- *
  37  *
  38  * Arguments:   @rsa_priv *rp@ = pointer to parameter block
  39  *
  40  * Returns:     Zero if all went well, nonzero if the parameters make no
  41  *              sense.
  42  *
  43  * Use:         Derives the full set of RSA parameters given a minimal set.
  44  *
  45  *              On failure, the parameter block might be partially filled in,
  46  *              but the @rsa_privfree@ function will be able to free it
  47  *              successfully.
  48  */
  49
  50 int rsa_recover(rsa_priv *rp)
  51 {
  52   int rc = -1;
  53   int i;
  54   size_t s;
  55   mpmont mm;
  56   mp a; mpw aw;
  57   mp *g = MP_NEW, *r = MP_NEW, *t = MP_NEW, *zt;
  58   mp *m1 = MP_NEW, *z = MP_NEW, *zz = MP_NEW;
  59   mp *phi = MP_NEW, *p1 = MP_NEW, *q1 = MP_NEW;
  60
  61   mm.r = 0;
  62
  63   /* --- If there is no modulus, calculate it --- */
  64
  65   if (!rp->n) {
  66     if (!rp->p || !rp->q) goto out;
  67     rp->n = mp_mul(MP_NEW, rp->p, rp->q);
  68   }
  69
  70   /* --- If there are no factors, compute them --- */
  71
  72   else if (!rp->p || !rp->q) {
  73
  74     /* --- If one is missing, use simple division to recover the other --- */
  75
  76     if (rp->p || rp->q) {
  77       if (rp->p) mp_div(&rp->q, &r, rp->n, rp->p);
  78       else mp_div(&rp->p, &r, rp->n, rp->q);
  79       if (!MP_EQ(r, MP_ZERO)) goto out;
  80     }
  81
  82     /* --- Otherwise use the public and private moduli --- */
  83
  84     else if (!rp->e || !rp->d)
  85       goto out;
  86     else {
  87
  88       /* --- Work out the appropriate exponent --- *
  89        *
  90        * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and
  91        * %$t$% is odd.
  92        */
  93
  94       t = mp_mul(t, rp->e, rp->d);
  95       t = mp_sub(t, t, MP_ONE);
  96       t = mp_odd(t, t, &s);
  97
  98       /* --- Set up for the exponentiation --- */
  99
 100       if (mpmont_create(&mm, rp->n)) goto out;
 101       m1 = mp_sub(m1, rp->n, mm.r);
 102
 103       /* --- Now for the main loop --- *
 104        *
 105        * Choose candidate integers and attempt to factor the modulus.
 106        */
 107
 108       mp_build(&a, &aw, &aw + 1);
 109       i = 0;
 110
 111     again:
 112
 113       /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- *
 114        *
 115        * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration
 116        * is a failure.
 117        */
 118
 119       if (i > NPRIME) goto out;
 120       aw = primetab[i++];
 121       z = mpmont_mul(&mm, z, &a, mm.r2);
 122       z = mpmont_expr(&mm, z, z, t);
 123       if (MP_EQ(z, mm.r) || MP_EQ(z, m1)) goto again;
 124
 125       /* --- Now square until something interesting happens --- *
 126        *
 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
 130        * factor with %$n$%.
 131        */
 132
 133       for (;;) {
 134         zz = mp_sqr(zz, z);
 135         zz = mpmont_reduce(&mm, zz, zz);
 136         if (MP_EQ(zz, mm.r)) goto done;
 137         else if (MP_EQ(zz, m1)) goto again;
 138         zt = z; z = zz; zz = zt;
 139       }
 140
 141       /* --- Do the factoring --- *
 142        *
 143        * Here's how it actually works.  I've found an interesting square
 144        * root of %$1 \pmod n$%.  Any square root of 1 must be congruent to
 145        * %$\pm 1$% modulo both %$p$% and %$q$%.  Both congruent to %$1$% is
 146        * boring, as is both congruent to %$-1$%.  Subtracting one from the
 147        * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and
 148        * nobody cares which), and hence can be extracted by a GCD
 149        * operation.
 150        */
 151
 152     done:
 153       z = mpmont_reduce(&mm, z, z);
 154       z = mp_sub(z, z, MP_ONE);
 155       mp_gcd(&rp->p, 0, 0, rp->n, z);
 156       mp_div(&rp->q, 0, rp->n, rp->p);
 157       if (MP_CMP(rp->p, <, rp->q))
 158         { zt = rp->p; rp->p = rp->q; rp->q = zt; }
 159     }
 160   }
 161
 162   /* --- If %$e$% or %$d$% is missing, recalculate it --- */
 163
 164   if (!rp->e || !rp->d) {
 165
 166     /* --- Compute %$\varphi(n)$% --- */
 167
 168     phi = mp_sub(phi, rp->n, rp->p);
 169     phi = mp_sub(phi, phi, rp->q);
 170     phi = mp_add(phi, phi, MP_ONE);
 171     p1 = mp_sub(p1, rp->p, MP_ONE);
 172     q1 = mp_sub(q1, rp->q, MP_ONE);
 173     mp_gcd(&g, 0, 0, p1, q1);
 174     mp_div(&phi, 0, phi, g);
 175
 176     /* --- Recover the other exponent --- */
 177
 178     if (rp->e) mp_gcd(&g, 0, &rp->d, phi, rp->e);
 179     else if (rp->d) mp_gcd(&g, 0, &rp->e, phi, rp->d);
 180     else goto out;
 181     if (!MP_EQ(g, MP_ONE)) goto out;
 182   }
 183
 184   /* --- Compute %$q^{-1} \bmod p$% --- */
 185
 186   if (!rp->q_inv) {
 187     mp_gcd(&g, 0, &rp->q_inv, rp->p, rp->q);
 188     if (!MP_EQ(g, MP_ONE)) goto out;
 189   }
 190
 191   /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */
 192
 193   if (!rp->dp) {
 194     p1 = mp_sub(p1, rp->p, MP_ONE);
 195     mp_div(0, &rp->dp, rp->d, p1);
 196   }
 197   if (!rp->dq) {
 198     q1 = mp_sub(q1, rp->q, MP_ONE);
 199     mp_div(0, &rp->dq, rp->d, q1);
 200   }
 201
 202   /* --- Done --- */
 203
 204   rc = 0;
 205 out:
 206   mp_drop(g); mp_drop(r); mp_drop(t);
 207   mp_drop(m1); mp_drop(z); mp_drop(zz);
 208   mp_drop(phi); mp_drop(p1); mp_drop(q1);
 209   if (mm.r) mpmont_destroy(&mm);
 210   return (rc);
 211 }
 212
 213 /*----- That's all, folks -------------------------------------------------*/