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 i;
  53   size_t s;
  54   mpmont mm;
  55   mp a; mpw aw;
  56   mp *g = MP_NEW, *r = MP_NEW, *t = MP_NEW;
  57   mp *m1 = MP_NEW, *z = MP_NEW, *zz = MP_NEW;
  58   mp *phi = MP_NEW, *p1 = MP_NEW, *q1 = MP_NEW;
  59
  60   /* --- If there is no modulus, calculate it --- */
  61
  62   if (!rp->n) {
  63     if (!rp->p || !rp->q)
  64       return (-1);
  65     rp->n = mp_mul(MP_NEW, rp->p, rp->q);
  66   }
  67
  68   /* --- If there are no factors, compute them --- */
  69
  70   else if (!rp->p || !rp->q) {
  71
  72     /* --- If one is missing, use simple division to recover the other --- */
  73
  74     if (rp->p || rp->q) {
  75       if (rp->p)
  76         mp_div(&rp->q, &r, rp->n, rp->p);
  77       else
  78         mp_div(&rp->p, &r, rp->n, rp->q);
  79       if (!MP_EQ(r, MP_ZERO)) {
  80         mp_drop(r);
  81         return (-1);
  82       }
  83       mp_drop(r);
  84     }
  85
  86     /* --- Otherwise use the public and private moduli --- */
  87
  88     else if (!rp->e || !rp->d)
  89       return (-1);
  90     else {
  91
  92       /* --- Work out the appropriate exponent --- *
  93        *
  94        * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and
  95        * %$t$% is odd.
  96        */
  97
  98       t = mp_mul(t, rp->e, rp->d);
  99       t = mp_sub(t, t, MP_ONE);
 100       t = mp_odd(t, t, &s);
 101
 102       /* --- Set up for the exponentiation --- */
 103
 104       mpmont_create(&mm, rp->n);
 105       m1 = mp_sub(m1, rp->n, mm.r);
 106
 107       /* --- Now for the main loop --- *
 108        *
 109        * Choose candidate integers and attempt to factor the modulus.
 110        */
 111
 112       mp_build(&a, &aw, &aw + 1);
 113       i = 0;
 114       for (;;) {
 115       again:
 116
 117         /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- *
 118          *
 119          * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration
 120          * is a failure.
 121          */
 122
 123         aw = primetab[i++];
 124         z = mpmont_mul(&mm, z, &a, mm.r2);
 125         z = mpmont_expr(&mm, z, z, t);
 126         if (MP_EQ(z, mm.r) || MP_EQ(z, m1))
 127           continue;
 128
 129         /* --- Now square until something interesting happens --- *
 130          *
 131          * Compute %$z^{2i} \bmod n$%.  Eventually, I'll either get %$-1$% or
 132          * %$1$%.  If the former, the number is uninteresting, and I need to
 133          * restart.  If the latter, the previous number minus 1 has a common
 134          * factor with %$n$%.
 135          */
 136
 137         for (;;) {
 138           zz = mp_sqr(zz, z);
 139           zz = mpmont_reduce(&mm, zz, zz);
 140           if (MP_EQ(zz, mm.r)) {
 141             mp_drop(zz);
 142             goto done;
 143           } else if (MP_EQ(zz, m1)) {
 144             mp_drop(zz);
 145             goto again;
 146           }
 147           mp_drop(z);
 148           z = zz;
 149           zz = MP_NEW;
 150         }
 151       }
 152
 153       /* --- Do the factoring --- *
 154        *
 155        * Here's how it actually works.  I've found an interesting square
 156        * root of %$1 \pmod n$%.  Any square root of 1 must be congruent to
 157        * %$\pm 1$% modulo both %$p$% and %$q$%.  Both congruent to %$1$% is
 158        * boring, as is both congruent to %$-1$%.  Subtracting one from the
 159        * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and
 160        * nobody cares which), and hence can be extracted by a GCD
 161        * operation.
 162        */
 163
 164     done:
 165       z = mpmont_reduce(&mm, z, z);
 166       z = mp_sub(z, z, MP_ONE);
 167       rp->p = MP_NEW;
 168       mp_gcd(&rp->p, 0, 0, rp->n, z);
 169       rp->q = MP_NEW;
 170       mp_div(&rp->q, 0, rp->n, rp->p);
 171       mp_drop(z);
 172       mp_drop(t);
 173       mp_drop(m1);
 174       if (MP_CMP(rp->p, <, rp->q)) {
 175         z = rp->p;
 176         rp->p = rp->q;
 177         rp->q = z;
 178       }
 179       mpmont_destroy(&mm);
 180     }
 181   }
 182
 183   /* --- If %$e$% or %$d$% is missing, recalculate it --- */
 184
 185   if (!rp->e || !rp->d) {
 186
 187     /* --- Compute %$\varphi(n)$% --- */
 188
 189     phi = mp_sub(phi, rp->n, rp->p);
 190     phi = mp_sub(phi, phi, rp->q);
 191     phi = mp_add(phi, phi, MP_ONE);
 192     p1 = mp_sub(p1, rp->p, MP_ONE);
 193     q1 = mp_sub(q1, rp->q, MP_ONE);
 194     mp_gcd(&g, 0, 0, p1, q1);
 195     mp_div(&phi, 0, phi, g);
 196     mp_drop(p1); p1 = MP_NEW;
 197     mp_drop(q1); q1 = MP_NEW;
 198
 199     /* --- Recover the other exponent --- */
 200
 201     if (rp->e)
 202       mp_gcd(&g, 0, &rp->d, phi, rp->e);
 203     else if (rp->d)
 204       mp_gcd(&g, 0, &rp->e, phi, rp->d);
 205     else {
 206       mp_drop(phi);
 207       mp_drop(g);
 208       return (-1);
 209     }
 210
 211     mp_drop(phi);
 212     if (!MP_EQ(g, MP_ONE)) {
 213       mp_drop(g);
 214       return (-1);
 215     }
 216     mp_drop(g);
 217   }
 218
 219   /* --- Compute %$q^{-1} \bmod p$% --- */
 220
 221   if (!rp->q_inv)
 222     mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q);
 223
 224   /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */
 225
 226   if (!rp->dp) {
 227     p1 = mp_sub(p1, rp->p, MP_ONE);
 228     mp_div(0, &rp->dp, rp->d, p1);
 229     mp_drop(p1);
 230   }
 231   if (!rp->dq) {
 232     q1 = mp_sub(q1, rp->q, MP_ONE);
 233     mp_div(0, &rp->dq, rp->d, q1);
 234     mp_drop(q1);
 235   }
 236
 237   /* --- Done --- */
 238
 239   return (0);
 240 }
 241
 242 /*----- That's all, folks -------------------------------------------------*/