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

   1 /* -*-c-*-
   2  *
   3  * RSA parameter generation
   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 <mLib/dstr.h>
  31
  32 #include "grand.h"
  33 #include "mp.h"
  34 #include "mpint.h"
  35 #include "pgen.h"
  36 #include "rsa.h"
  37 #include "strongprime.h"
  38
  39 /*----- Main code ---------------------------------------------------------*/
  40
  41 /* --- @rsa_gen@ --- *
  42  *
  43  * Arguments:   @rsa_priv *rp@ = pointer to block to be filled in
  44  *              @unsigned nbits@ = required modulus size in bits
  45  *              @grand *r@ = random number source
  46  *              @unsigned n@ = number of attempts to make
  47  *              @pgen_proc *event@ = event handler function
  48  *              @void *ectx@ = argument for the event handler
  49  *
  50  * Returns:     Zero if all went well, nonzero otherwise.
  51  *
  52  * Use:         Constructs a pair of strong RSA primes and other useful RSA
  53  *              parameters.  A small encryption exponent is chosen if
  54  *              possible.
  55  */
  56
  57 int rsa_gen(rsa_priv *rp, unsigned nbits, grand *r, unsigned n,
  58             pgen_proc *event, void *ectx)
  59 {
  60   pgen_gcdstepctx g;
  61   mp *phi = MP_NEW;
  62
  63   /* --- Bits of initialization --- */
  64
  65   rp->e = mp_fromulong(MP_NEW, 0x10001);
  66   rp->d = MP_NEW;
  67
  68   /* --- Generate strong primes %$p$% and %$q$% --- *
  69    *
  70    * Constrain the GCD of @q@ to ensure that overly small private exponents
  71    * are impossible.  Current results suggest that if %$d < n^{0.29}$% then
  72    * it can be guessed fairly easily.  This implementation is rather more
  73    * conservative about that sort of thing.
  74    */
  75
  76 again:
  77   if ((rp->p = strongprime("p", MP_NEWSEC, nbits/2, r, n, event, ectx)) == 0)
  78     goto fail_p;
  79
  80   /* --- Do painful fiddling with GCD steppers --- *
  81    *
  82    * Also, arrange that %$q \ge \lceil 2^{N-1}/p \rceil$%, so that %$p q$%
  83    * has the right length.
  84    */
  85
  86   {
  87     mp *q;
  88     mp *t = MP_NEW, *u = MP_NEW;
  89     rabin rb;
  90
  91     if ((q = strongprime_setup("q", MP_NEWSEC, &g.jp, nbits / 2,
  92                                r, n, event, ectx)) == 0)
  93       goto fail_q;
  94     t = mp_lsl(t, MP_ONE, nbits - 1);
  95     mp_div(&t, &u, t, rp->p);
  96     if (!MP_ZEROP(u)) t = mp_add(t, t, MP_ONE);
  97     if (MP_CMP(q, <, t)) q = mp_leastcongruent(q, t, q, g.jp.m);
  98
  99     g.r = mp_lsr(MP_NEW, rp->p, 1);
 100     g.g = MP_NEW;
 101     g.max = MP_256;
 102     q = pgen("q", q, q, event, ectx, n, pgen_gcdstep, &g,
 103              rabin_iters(nbits/2), pgen_test, &rb);
 104     pfilt_destroy(&g.jp);
 105     mp_drop(g.r);
 106     if (!q) {
 107       mp_drop(g.g);
 108       if (n)
 109         goto fail_q;
 110       mp_drop(rp->p);
 111       goto again;
 112     }
 113     rp->q = q;
 114   }
 115
 116   /* --- Ensure that %$p > q$% --- *
 117    *
 118    * Also ensure that %$p$% and %$q$% are sufficiently different to deter
 119    * square-root-based factoring methods.
 120    */
 121
 122   phi = mp_sub(phi, rp->p, rp->q);
 123   if (MP_LEN(phi) * 4 < MP_LEN(rp->p) * 3 ||
 124       MP_LEN(phi) * 4 < MP_LEN(rp->q) * 3) {
 125     mp_drop(rp->p);
 126     mp_drop(g.g);
 127     if (n)
 128       goto fail_q;
 129     mp_drop(rp->q);
 130     goto again;
 131   }
 132
 133   if (MP_NEGP(phi)) {
 134     mp *z = rp->p;
 135     rp->p = rp->q;
 136     rp->q = z;
 137   }
 138
 139   /* --- Work out the modulus and the CRT coefficient --- */
 140
 141   rp->n = mp_mul(MP_NEW, rp->p, rp->q);
 142   rp->q_inv = mp_modinv(MP_NEW, rp->q, rp->p);
 143
 144   /* --- Work out %$\varphi(n) = (p - 1)(q - 1)$% --- *
 145    *
 146    * Save on further multiplications by noting that %$n = pq$% is known and
 147    * that %$(p - 1)(q - 1) = pq - p - q + 1$%.  To minimize the size of @d@
 148    * (useful for performance reasons, although not very because an overly
 149    * small @d@ will be rejected for security reasons) this is then divided by
 150    * %$\gcd(p - 1, q - 1)$%.
 151    */
 152
 153   phi = mp_sub(phi, rp->n, rp->p);
 154   phi = mp_sub(phi, phi, rp->q);
 155   phi = mp_add(phi, phi, MP_ONE);
 156   phi = mp_lsr(phi, phi, 1);
 157   mp_div(&phi, 0, phi, g.g);
 158
 159   /* --- Decide on a public exponent --- *
 160    *
 161    * Simultaneously compute the private exponent.
 162    */
 163
 164   mp_gcd(&g.g, 0, &rp->d, phi, rp->e);
 165   if (!MP_EQ(g.g, MP_ONE) && MP_LEN(rp->d) * 4 > MP_LEN(rp->n) * 3)
 166     goto fail_e;
 167
 168   /* --- Work out exponent residues --- */
 169
 170   rp->dp = MP_NEW; phi = mp_sub(phi, rp->p, MP_ONE);
 171   mp_div(0, &rp->dp, rp->d, phi);
 172
 173   rp->dq = MP_NEW; phi = mp_sub(phi, rp->q, MP_ONE);
 174   mp_div(0, &rp->dq, rp->d, phi);
 175
 176   /* --- Done --- */
 177
 178   mp_drop(phi);
 179   mp_drop(g.g);
 180   return (0);
 181
 182   /* --- Tidy up when something goes wrong --- */
 183
 184 fail_e:
 185   mp_drop(g.g);
 186   mp_drop(phi);
 187   mp_drop(rp->n);
 188   mp_drop(rp->q_inv);
 189   mp_drop(rp->q);
 190 fail_q:
 191   mp_drop(rp->p);
 192 fail_p:
 193   mp_drop(rp->e);
 194   if (rp->d)
 195     mp_drop(rp->d);
 196   return (-1);
 197 }
 198
 199 /*----- That's all, folks -------------------------------------------------*/