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

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