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

   1 /* -*-c-*-
   2  *
   3  * $Id: rsa-recover.c,v 1.4 2000/07/01 11:22:22 mdw Exp $
   4  *
   5  * Recover RSA parameters
   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-recover.c,v $
  33  * Revision 1.4  2000/07/01 11:22:22  mdw
  34  * Remove bad type name `rsa_param'.
  35  *
  36  * Revision 1.3  2000/06/22 19:03:14  mdw
  37  * Use the new @mp_odd@ function.
  38  *
  39  * Revision 1.2  2000/06/17 12:07:19  mdw
  40  * Fix a bug in argument validation.  Force %$p > q$% in output.  Use
  41  * %$\lambda(n) = \lcm(p - 1, q - 1)$% rather than the more traditional
  42  * %$\phi(n) = (p - 1)(q - 1)$% when computing the decryption exponent.
  43  *
  44  * Revision 1.1  1999/12/22 15:50:45  mdw
  45  * Initial RSA support.
  46  *
  47  */
  48
  49 /*----- Header files ------------------------------------------------------*/
  50
  51 #include "mp.h"
  52 #include "mpmont.h"
  53 #include "rsa.h"
  54
  55 /*----- Main code ---------------------------------------------------------*/
  56
  57 /* --- @rsa_recover@ --- *
  58  *
  59  * Arguments:   @rsa_priv *rp@ = pointer to parameter block
  60  *
  61  * Returns:     Zero if all went well, nonzero if the parameters make no
  62  *              sense.
  63  *
  64  * Use:         Derives the full set of RSA parameters given a minimal set.
  65  */
  66
  67 int rsa_recover(rsa_priv *rp)
  68 {
  69   /* --- If there is no modulus, calculate it --- */
  70
  71   if (!rp->n) {
  72     if (!rp->p || !rp->q)
  73       return (-1);
  74     rp->n = mp_mul(MP_NEW, rp->p, rp->q);
  75   }
  76
  77   /* --- If there are no factors, compute them --- */
  78
  79   else if (!rp->p || !rp->q) {
  80
  81     /* --- If one is missing, use simple division to recover the other --- */
  82
  83     if (rp->p || rp->q) {
  84       mp *r = MP_NEW;
  85       if (rp->p)
  86         mp_div(&rp->q, &r, rp->n, rp->p);
  87       else
  88         mp_div(&rp->p, &r, rp->n, rp->q);
  89       if (MP_CMP(r, !=, MP_ZERO)) {
  90         mp_drop(r);
  91         return (-1);
  92       }
  93       mp_drop(r);
  94     }
  95
  96     /* --- Otherwise use the public and private moduli --- */
  97
  98     else if (!rp->e || !rp->d)
  99       return (-1);
 100     else {
 101       mp *t;
 102       size_t s;
 103       mp a; mpw aw;
 104       mp *m1;
 105       mpmont mm;
 106       int i;
 107       mp *z = MP_NEW;
 108
 109       /* --- Work out the appropriate exponent --- *
 110        *
 111        * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and
 112        * %$t$% is odd.
 113        */
 114
 115       t = mp_mul(MP_NEW, rp->e, rp->d);
 116       t = mp_sub(t, t, MP_ONE);
 117       t = mp_odd(t, t, &s);
 118
 119       /* --- Set up for the exponentiation --- */
 120
 121       mpmont_create(&mm, rp->n);
 122       m1 = mp_sub(MP_NEW, rp->n, mm.r);
 123
 124       /* --- Now for the main loop --- *
 125        *
 126        * Choose candidate integers and attempt to factor the modulus.
 127        */
 128
 129       mp_build(&a, &aw, &aw + 1);
 130       i = 0;
 131       for (;;) {
 132       again:
 133
 134         /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- *
 135          *
 136          * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration
 137          * is a failure.
 138          */
 139
 140         aw = primetab[i++];
 141         z = mpmont_expr(&mm, z, &a, t);
 142         if (MP_CMP(z, ==, mm.r) || MP_CMP(z, ==, m1))
 143           continue;
 144
 145         /* --- Now square until something interesting happens --- *
 146          *
 147          * Compute %$z^{2i} \bmod n$%.  Eventually, I'll either get %$-1$% or
 148          * %$1$%.  If the former, the number is uninteresting, and I need to
 149          * restart.  If the latter, the previous number minus 1 has a common
 150          * factor with %$n$%.
 151          */
 152
 153         for (;;) {
 154           mp *zz = mp_sqr(MP_NEW, z);
 155           zz = mpmont_reduce(&mm, zz, zz);
 156           if (MP_CMP(zz, ==, mm.r)) {
 157             mp_drop(zz);
 158             goto done;
 159           } else if (MP_CMP(zz, ==, m1)) {
 160             mp_drop(zz);
 161             goto again;
 162           }
 163           mp_drop(z);
 164           z = zz;
 165         }
 166       }
 167
 168       /* --- Do the factoring --- *
 169        *
 170        * Here's how it actually works.  I've found an interesting square
 171        * root of %$1 \pmod n$%.  Any square root of 1 must be congruent to
 172        * %$\pm 1$% modulo both %$p$% and %$q$%.  Both congruent to %$1$% is
 173        * boring, as is both congruent to %$-1$%.  Subtracting one from the
 174        * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and
 175        * nobody cares which), and hence can be extracted by a GCD
 176        * operation.
 177        */
 178
 179     done:
 180       z = mpmont_reduce(&mm, z, z);
 181       z = mp_sub(z, z, MP_ONE);
 182       rp->p = MP_NEW;
 183       mp_gcd(&rp->p, 0, 0, rp->n, z);
 184       rp->q = MP_NEW;
 185       mp_div(&rp->q, 0, rp->n, rp->p);
 186       mp_drop(z);
 187       mp_drop(t);
 188       mp_drop(m1);
 189       if (MP_CMP(rp->p, <, rp->q)) {
 190         z = rp->p;
 191         rp->p = rp->q;
 192         rp->q = z;
 193       }
 194       mpmont_destroy(&mm);
 195     }
 196   }
 197
 198   /* --- If %$e$% or %$d$% is missing, recalculate it --- */
 199
 200   if (!rp->e || !rp->d) {
 201     mp *phi;
 202     mp *g = MP_NEW;
 203     mp *p1, *q1;
 204
 205     /* --- Compute %$\varphi(n)$% --- */
 206
 207     phi = mp_sub(MP_NEW, rp->n, rp->p);
 208     phi = mp_sub(phi, phi, rp->q);
 209     phi = mp_add(phi, phi, MP_ONE);
 210     p1 = mp_sub(MP_NEW, rp->p, MP_ONE);
 211     q1 = mp_sub(MP_NEW, rp->q, MP_ONE);
 212     mp_gcd(&g, 0, 0, p1, q1);
 213     mp_div(&phi, 0, phi, g);
 214     mp_drop(p1);
 215     mp_drop(q1);
 216
 217     /* --- Recover the other exponent --- */
 218
 219     if (rp->e)
 220       mp_gcd(&g, 0, &rp->d, phi, rp->e);
 221     else if (rp->d)
 222       mp_gcd(&g, 0, &rp->e, phi, rp->d);
 223     else {
 224       mp_drop(phi);
 225       mp_drop(g);
 226       return (-1);
 227     }
 228
 229     mp_drop(phi);
 230     if (MP_CMP(g, !=, MP_ONE)) {
 231       mp_drop(g);
 232       return (-1);
 233     }
 234     mp_drop(g);
 235   }
 236
 237   /* --- Compute %$q^{-1} \bmod p$% --- */
 238
 239   if (!rp->q_inv)
 240     mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q);
 241
 242   /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */
 243
 244   if (!rp->dp) {
 245     mp *p1 = mp_sub(MP_NEW, rp->p, MP_ONE);
 246     mp_div(0, &rp->dp, rp->d, p1);
 247     mp_drop(p1);
 248   }
 249   if (!rp->dq) {
 250     mp *q1 = mp_sub(MP_NEW, rp->q, MP_ONE);
 251     mp_div(0, &rp->dq, rp->d, q1);
 252     mp_drop(q1);
 253   }
 254
 255   /* --- Done --- */
 256
 257   return (0);
 258 }
 259
 260 /*----- That's all, folks -------------------------------------------------*/