Compute square roots in a prime field.

[u/mdw/catacomb] / rsa-decrypt.c

/* -*-c-*-
 *
 * $Id: rsa-decrypt.c,v 1.2 2000/06/17 11:57:56 mdw Exp $
 *
 * RSA decryption
 *
 * (c) 1999 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------* 
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 * 
 * Catacomb is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 * 
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

/*----- Revision history --------------------------------------------------* 
 *
 * $Log: rsa-decrypt.c,v $
 * Revision 1.2  2000/06/17 11:57:56  mdw
 * Improve bulk performance by making better use of Montgomery
 * multiplication and separating out initialization and finalization from
 * the main code.
 *
 * Revision 1.1  1999/12/22 15:50:45  mdw
 * Initial RSA support.
 *
 */

/*----- Header files ------------------------------------------------------*/

#include "mp.h"
#include "mpmont.h"
#include "mprand.h"
#include "rsa.h"

/*----- Main code ---------------------------------------------------------*/

/* --- @rsa_deccreate@ --- *
 *
 * Arguments:	@rsa_decctx *rd@ = pointer to an RSA decryption context
 *		@rsa_priv *rp@ = pointer to RSA private key
 *		@grand *r@ = pointer to random number source for blinding
 *
 * Returns:	---
 *
 * Use:		Initializes an RSA decryption context.  Keeping a context
 *		for several decryption or signing operations provides a minor
 *		performance benefit.
 *
 *		The random number source may be null if blinding is not
 *		desired.  This improves decryption speed, at the risk of
 *		permitting timing attacks.
 */

void rsa_deccreate(rsa_decctx *rd, rsa_param *rp, grand *r)
{
  rd->rp = rp;
  rd->r = r;
  if (r)
    mpmont_create(&rd->nm, rp->n);
  mpmont_create(&rd->pm, rp->p);
  mpmont_create(&rd->qm, rp->q);
}

/* --- @rsa_decdestroy@ --- *
 *
 * Arguments:	@rsa_decctx *rd@ = pointer to an RSA decryption context
 *
 * Returns:	---
 *
 * Use:		Destroys an RSA decryption context.
 */

void rsa_decdestroy(rsa_decctx *rd)
{
  if (rd->r)
    mpmont_destroy(&rd->nm);
  mpmont_destroy(&rd->pm);
  mpmont_destroy(&rd->qm);
}

/* --- @rsa_dec@ --- *
 *
 * Arguments:	@rsa_decctx *rd@ = pointer to RSA decryption context
 *		@mp *d@ = destination
 *		@mp *c@ = ciphertext message
 *
 * Returns:	The recovered plaintext message.
 *
 * Use:		Performs RSA decryption.  This function takes advantage of
 *		knowledge of the key factors in order to speed up
 *		decryption.  It also blinds the ciphertext prior to
 *		decryption and unblinds it afterwards to thwart timing
 *		attacks.
 */

mp *rsa_dec(rsa_decctx *rd, mp *d, mp *c)
{
  mp *ki = MP_NEW;
  rsa_param *rp = rd->rp;

  /* --- If so desired, set up a blinding constant --- *
   *
   * Choose a constant %$k$% relatively prime to the modulus %$m$%.  Compute
   * %$c' = c k^e \bmod n$%, and %$k^{-1} \bmod n$%.  Don't bother with the
   * CRT stuff here because %$e$% is chosen to be small.
   */

  c = MP_COPY(c);
  if (rd->r) {
    mp *k = MP_NEWSEC, *g = MP_NEW;

    do {
      k = mprand_range(k, rp->n, rd->r, 0);
      mp_gcd(&g, 0, &ki, rp->n, k);
    } while (MP_CMP(g, !=, MP_ONE));
    k = mpmont_expr(&rd->nm, k, k, rp->e);
    c = mpmont_mul(&rd->nm, c, c, k);
    mp_drop(k);
    mp_drop(g);
  }

  /* --- Do the actual modular exponentiation --- *
   *
   * Use a slightly hacked version of the Chinese Remainder Theorem stuff.
   *
   * Let %$q' = q^{-1} \bmod p$%.  Then note that
   * %$c^d \equiv q (q'(c_p^{d_p} - c_q^{d_q}) \bmod p) + c_q^{d_q} \pmod n$%
   */

  {
    mp *cp = MP_NEW, *cq = MP_NEW;

    /* --- Work out the two halves of the result --- */

    mp_div(0, &cp, c, rp->p);
    cp = mpmont_exp(&rd->pm, cp, cp, rp->dp);

    mp_div(0, &cq, c, rp->q);
    cq = mpmont_exp(&rd->qm, cq, cq, rp->dq);

    /* --- Combine the halves using the result above --- */

    d = mp_sub(d, cp, cq);
    mp_div(0, &d, d, rp->p);
    d = mpmont_mul(&rd->pm, d, d, rp->q_inv);
    d = mpmont_mul(&rd->pm, d, d, rd->pm.r2);

    d = mp_mul(d, d, rp->q);
    d = mp_add(d, d, cq);
    if (MP_CMP(d, >=, rp->n))
      d = mp_sub(d, d, rp->n);

    /* --- Tidy away temporary variables --- */

    mp_drop(cp);
    mp_drop(cq);
  }

  /* --- Finally, possibly remove the blinding factor --- */

  if (ki) {
    d = mpmont_mul(&rd->nm, d, d, ki);
    d = mpmont_mul(&rd->nm, d, d, rd->nm.r2);
    mp_drop(ki);
  }

  /* --- Done --- */

  mp_drop(c);
  return (d);
}

/* --- @rsa_decrypt@ --- *
 *
 * Arguments:	@rsa_param *rp@ = pointer to RSA parameters
 *		@mp *d@ = destination
 *		@mp *c@ = ciphertext message
 *		@grand *r@ = pointer to random number source for blinding
 *
 * Returns:	Correctly decrypted message.
 *
 * Use:		Performs RSA decryption, very carefully.
 */

mp *rsa_decrypt(rsa_param *rp, mp *d, mp *c, grand *r)
{
  rsa_decctx rd;
  rsa_deccreate(&rd, rp, r);
  d = rsa_dec(&rd, d, c);
  rsa_decdestroy(&rd);
  return (d);
}

/*----- That's all, folks -------------------------------------------------*/