git.distorted.org.uk Git - u/mdw/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
  46 int rsa_recover(rsa_priv *rp)
  47 {
  48   /* --- If there is no modulus, calculate it --- */
  49
  50   if (!rp->n) {
  51     if (!rp->p || !rp->q)
  52       return (-1);
  53     rp->n = mp_mul(MP_NEW, rp->p, rp->q);
  54   }
  55
  56   /* --- If there are no factors, compute them --- */
  57
  58   else if (!rp->p || !rp->q) {
  59
  60     /* --- If one is missing, use simple division to recover the other --- */
  61
  62     if (rp->p || rp->q) {
  63       mp *r = MP_NEW;
  64       if (rp->p)
  65         mp_div(&rp->q, &r, rp->n, rp->p);
  66       else
  67         mp_div(&rp->p, &r, rp->n, rp->q);
  68       if (!MP_EQ(r, MP_ZERO)) {
  69         mp_drop(r);
  70         return (-1);
  71       }
  72       mp_drop(r);
  73     }
  74
  75     /* --- Otherwise use the public and private moduli --- */
  76
  77     else if (!rp->e || !rp->d)
  78       return (-1);
  79     else {
  80       mp *t;
  81       size_t s;
  82       mp a; mpw aw;
  83       mp *m1;
  84       mpmont mm;
  85       int i;
  86       mp *z = MP_NEW;
  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(MP_NEW, 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       mpmont_create(&mm, rp->n);
 101       m1 = mp_sub(MP_NEW, 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       for (;;) {
 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         aw = primetab[i++];
 120         z = mpmont_mul(&mm, z, &a, mm.r2);
 121         z = mpmont_expr(&mm, z, z, t);
 122         if (MP_EQ(z, mm.r) || MP_EQ(z, m1))
 123           continue;
 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           mp *zz = mp_sqr(MP_NEW, z);
 135           zz = mpmont_reduce(&mm, zz, zz);
 136           if (MP_EQ(zz, mm.r)) {
 137             mp_drop(zz);
 138             goto done;
 139           } else if (MP_EQ(zz, m1)) {
 140             mp_drop(zz);
 141             goto again;
 142           }
 143           mp_drop(z);
 144           z = zz;
 145         }
 146       }
 147
 148       /* --- Do the factoring --- *
 149        *
 150        * Here's how it actually works.  I've found an interesting square
 151        * root of %$1 \pmod n$%.  Any square root of 1 must be congruent to
 152        * %$\pm 1$% modulo both %$p$% and %$q$%.  Both congruent to %$1$% is
 153        * boring, as is both congruent to %$-1$%.  Subtracting one from the
 154        * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and
 155        * nobody cares which), and hence can be extracted by a GCD
 156        * operation.
 157        */
 158
 159     done:
 160       z = mpmont_reduce(&mm, z, z);
 161       z = mp_sub(z, z, MP_ONE);
 162       rp->p = MP_NEW;
 163       mp_gcd(&rp->p, 0, 0, rp->n, z);
 164       rp->q = MP_NEW;
 165       mp_div(&rp->q, 0, rp->n, rp->p);
 166       mp_drop(z);
 167       mp_drop(t);
 168       mp_drop(m1);
 169       if (MP_CMP(rp->p, <, rp->q)) {
 170         z = rp->p;
 171         rp->p = rp->q;
 172         rp->q = z;
 173       }
 174       mpmont_destroy(&mm);
 175     }
 176   }
 177
 178   /* --- If %$e$% or %$d$% is missing, recalculate it --- */
 179
 180   if (!rp->e || !rp->d) {
 181     mp *phi;
 182     mp *g = MP_NEW;
 183     mp *p1, *q1;
 184
 185     /* --- Compute %$\varphi(n)$% --- */
 186
 187     phi = mp_sub(MP_NEW, rp->n, rp->p);
 188     phi = mp_sub(phi, phi, rp->q);
 189     phi = mp_add(phi, phi, MP_ONE);
 190     p1 = mp_sub(MP_NEW, rp->p, MP_ONE);
 191     q1 = mp_sub(MP_NEW, rp->q, MP_ONE);
 192     mp_gcd(&g, 0, 0, p1, q1);
 193     mp_div(&phi, 0, phi, g);
 194     mp_drop(p1);
 195     mp_drop(q1);
 196
 197     /* --- Recover the other exponent --- */
 198
 199     if (rp->e)
 200       mp_gcd(&g, 0, &rp->d, phi, rp->e);
 201     else if (rp->d)
 202       mp_gcd(&g, 0, &rp->e, phi, rp->d);
 203     else {
 204       mp_drop(phi);
 205       mp_drop(g);
 206       return (-1);
 207     }
 208
 209     mp_drop(phi);
 210     if (!MP_EQ(g, MP_ONE)) {
 211       mp_drop(g);
 212       return (-1);
 213     }
 214     mp_drop(g);
 215   }
 216
 217   /* --- Compute %$q^{-1} \bmod p$% --- */
 218
 219   if (!rp->q_inv)
 220     mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q);
 221
 222   /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */
 223
 224   if (!rp->dp) {
 225     mp *p1 = mp_sub(MP_NEW, rp->p, MP_ONE);
 226     mp_div(0, &rp->dp, rp->d, p1);
 227     mp_drop(p1);
 228   }
 229   if (!rp->dq) {
 230     mp *q1 = mp_sub(MP_NEW, rp->q, MP_ONE);
 231     mp_div(0, &rp->dq, rp->d, q1);
 232     mp_drop(q1);
 233   }
 234
 235   /* --- Done --- */
 236
 237   return (0);
 238 }
 239
 240 /*----- That's all, folks -------------------------------------------------*/