Example #1
0
/****************
 * RES = BASE ^ EXPO mod MOD
 */
void
gcry_mpi_powm( gcry_mpi_t res, gcry_mpi_t base, gcry_mpi_t expo, gcry_mpi_t mod)
{
    mpi_ptr_t  rp, ep, mp, bp;
    mpi_size_t esize, msize, bsize, rsize;
    int        esign, msign, bsign, rsign;
    int        esec,  msec,  bsec,  rsec;
    mpi_size_t size;
    int mod_shift_cnt;
    int negative_result;
    mpi_ptr_t mp_marker=NULL, bp_marker=NULL, ep_marker=NULL;
    mpi_ptr_t xp_marker=NULL;
    unsigned int mp_nlimbs = 0, bp_nlimbs = 0, ep_nlimbs = 0;
    unsigned int xp_nlimbs = 0;
    int assign_rp = 0;
    mpi_ptr_t tspace = NULL;
    mpi_size_t tsize=0;   /* to avoid compiler warning */
			  /* fixme: we should check that the warning is void*/

    esize = expo->nlimbs;
    msize = mod->nlimbs;
    size = 2 * msize;
    esign = expo->sign;
    msign = mod->sign;

    esec = mpi_is_secure(expo);
    msec = mpi_is_secure(mod);
    bsec = mpi_is_secure(base);
    rsec = mpi_is_secure(res);

    rp = res->d;
    ep = expo->d;

    if( !msize )
	msize = 1 / msize;	    /* provoke a signal */

    if( !esize ) {
	/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
	 * depending on if MOD equals 1.  */
	rp[0] = 1;
	res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
	res->sign = 0;
	goto leave;
    }

    /* Normalize MOD (i.e. make its most significant bit set) as required by
     * mpn_divrem.  This will make the intermediate values in the calculation
     * slightly larger, but the correct result is obtained after a final
     * reduction using the original MOD value.	*/
    mp_nlimbs = msec? msize:0;
    mp = mp_marker = mpi_alloc_limb_space(msize, msec);
    count_leading_zeros( mod_shift_cnt, mod->d[msize-1] );
    if( mod_shift_cnt )
	_gcry_mpih_lshift( mp, mod->d, msize, mod_shift_cnt );
    else
	MPN_COPY( mp, mod->d, msize );

    bsize = base->nlimbs;
    bsign = base->sign;
    if( bsize > msize ) { /* The base is larger than the module. Reduce it. */
	/* Allocate (BSIZE + 1) with space for remainder and quotient.
	 * (The quotient is (bsize - msize + 1) limbs.)  */
        bp_nlimbs = bsec ? (bsize + 1):0;
	bp = bp_marker = mpi_alloc_limb_space( bsize + 1, bsec );
	MPN_COPY( bp, base->d, bsize );
	/* We don't care about the quotient, store it above the remainder,
	 * at BP + MSIZE.  */
	_gcry_mpih_divrem( bp + msize, 0, bp, bsize, mp, msize );
	bsize = msize;
	/* Canonicalize the base, since we are going to multiply with it
	 * quite a few times.  */
	MPN_NORMALIZE( bp, bsize );
    }
    else
	bp = base->d;

    if( !bsize ) {
	res->nlimbs = 0;
	res->sign = 0;
	goto leave;
    }

    if( res->alloced < size ) {
	/* We have to allocate more space for RES.  If any of the input
	 * parameters are identical to RES, defer deallocation of the old
	 * space.  */
	if( rp == ep || rp == mp || rp == bp ) {
	    rp = mpi_alloc_limb_space( size, rsec );
	    assign_rp = 1;
	}
	else {
	    mpi_resize( res, size );
	    rp = res->d;
	}
    }
    else { /* Make BASE, EXPO and MOD not overlap with RES.  */
	if( rp == bp ) {
	    /* RES and BASE are identical.  Allocate temp. space for BASE.  */
	    assert( !bp_marker );
            bp_nlimbs = bsec? bsize:0;
	    bp = bp_marker = mpi_alloc_limb_space( bsize, bsec );
	    MPN_COPY(bp, rp, bsize);
	}
	if( rp == ep ) {
	    /* RES and EXPO are identical.  Allocate temp. space for EXPO.  */
            ep_nlimbs = esec? esize:0;
	    ep = ep_marker = mpi_alloc_limb_space( esize, esec );
	    MPN_COPY(ep, rp, esize);
	}
	if( rp == mp ) {
	    /* RES and MOD are identical.  Allocate temporary space for MOD.*/
	    assert( !mp_marker );
            mp_nlimbs = msec?msize:0;
	    mp = mp_marker = mpi_alloc_limb_space( msize, msec );
	    MPN_COPY(mp, rp, msize);
	}
    }

    MPN_COPY( rp, bp, bsize );
    rsize = bsize;
    rsign = bsign;

    {
	mpi_size_t i;
	mpi_ptr_t xp;
	int c;
	mpi_limb_t e;
	mpi_limb_t carry_limb;
	struct karatsuba_ctx karactx;

        xp_nlimbs = msec? (2 * (msize + 1)):0;
        xp = xp_marker = mpi_alloc_limb_space( 2 * (msize + 1), msec );

	memset( &karactx, 0, sizeof karactx );
	negative_result = (ep[0] & 1) && base->sign;

	i = esize - 1;
	e = ep[i];
	count_leading_zeros (c, e);
	e = (e << c) << 1;     /* shift the expo bits to the left, lose msb */
	c = BITS_PER_MPI_LIMB - 1 - c;

	/* Main loop.
	 *
	 * Make the result be pointed to alternately by XP and RP.  This
	 * helps us avoid block copying, which would otherwise be necessary
	 * with the overlap restrictions of _gcry_mpih_divmod. With 50% probability
	 * the result after this loop will be in the area originally pointed
	 * by RP (==RES->d), and with 50% probability in the area originally
	 * pointed to by XP.
	 */

	for(;;) {
	    while( c ) {
		mpi_ptr_t tp;
		mpi_size_t xsize;

		/*mpih_mul_n(xp, rp, rp, rsize);*/
		if( rsize < KARATSUBA_THRESHOLD )
		    _gcry_mpih_sqr_n_basecase( xp, rp, rsize );
		else {
		    if( !tspace ) {
			tsize = 2 * rsize;
			tspace = mpi_alloc_limb_space( tsize, 0 );
		    }
		    else if( tsize < (2*rsize) ) {
			_gcry_mpi_free_limb_space (tspace, 0);
			tsize = 2 * rsize;
			tspace = mpi_alloc_limb_space( tsize, 0 );
		    }
		    _gcry_mpih_sqr_n( xp, rp, rsize, tspace );
		}

		xsize = 2 * rsize;
		if( xsize > msize ) {
		    _gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
		    xsize = msize;
		}

		tp = rp; rp = xp; xp = tp;
		rsize = xsize;

		if( (mpi_limb_signed_t)e < 0 ) {
		    /*mpih_mul( xp, rp, rsize, bp, bsize );*/
		    if( bsize < KARATSUBA_THRESHOLD ) {
			_gcry_mpih_mul( xp, rp, rsize, bp, bsize );
		    }
		    else {
			_gcry_mpih_mul_karatsuba_case(
				     xp, rp, rsize, bp, bsize, &karactx );
		    }

		    xsize = rsize + bsize;
		    if( xsize > msize ) {
			_gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
			xsize = msize;
		    }

		    tp = rp; rp = xp; xp = tp;
		    rsize = xsize;
		}
		e <<= 1;
		c--;
	    }

	    i--;
	    if( i < 0 )
		break;
	    e = ep[i];
	    c = BITS_PER_MPI_LIMB;
	}

	/* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
	 * steps.  Adjust the result by reducing it with the original MOD.
	 *
	 * Also make sure the result is put in RES->d (where it already
	 * might be, see above).
	 */
	if( mod_shift_cnt ) {
	    carry_limb = _gcry_mpih_lshift( res->d, rp, rsize, mod_shift_cnt);
	    rp = res->d;
	    if( carry_limb ) {
		rp[rsize] = carry_limb;
		rsize++;
	    }
	}
	else {
	    MPN_COPY( res->d, rp, rsize);
	    rp = res->d;
	}

	if( rsize >= msize ) {
	    _gcry_mpih_divrem(rp + msize, 0, rp, rsize, mp, msize);
	    rsize = msize;
	}

	/* Remove any leading zero words from the result.  */
	if( mod_shift_cnt )
	    _gcry_mpih_rshift( rp, rp, rsize, mod_shift_cnt);
	MPN_NORMALIZE (rp, rsize);

	_gcry_mpih_release_karatsuba_ctx( &karactx );
    }

    if( negative_result && rsize ) {
	if( mod_shift_cnt )
	    _gcry_mpih_rshift( mp, mp, msize, mod_shift_cnt);
	_gcry_mpih_sub( rp, mp, msize, rp, rsize);
	rsize = msize;
	rsign = msign;
	MPN_NORMALIZE(rp, rsize);
    }
    res->nlimbs = rsize;
    res->sign = rsign;

  leave:
    if( assign_rp ) _gcry_mpi_assign_limb_space( res, rp, size );
    if( mp_marker ) _gcry_mpi_free_limb_space( mp_marker, mp_nlimbs );
    if( bp_marker ) _gcry_mpi_free_limb_space( bp_marker, bp_nlimbs );
    if( ep_marker ) _gcry_mpi_free_limb_space( ep_marker, ep_nlimbs );
    if( xp_marker ) _gcry_mpi_free_limb_space( xp_marker, xp_nlimbs );
    if( tspace )    _gcry_mpi_free_limb_space( tspace, 0 );
}
Example #2
0
/****************
 * RES = BASE ^ EXPO mod MOD
 */
void
gcry_mpi_powm (gcry_mpi_t res,
               gcry_mpi_t base, gcry_mpi_t expo, gcry_mpi_t mod)
{
  /* Pointer to the limbs of the arguments, their size and signs. */
  mpi_ptr_t  rp, ep, mp, bp;
  mpi_size_t esize, msize, bsize, rsize;
  int               msign, bsign, rsign;
  /* Flags telling the secure allocation status of the arguments.  */
  int        esec,  msec,  bsec;
  /* Size of the result including space for temporary values.  */
  mpi_size_t size;
  /* Helper.  */
  int mod_shift_cnt;
  int negative_result;
  mpi_ptr_t mp_marker = NULL;
  mpi_ptr_t bp_marker = NULL;
  mpi_ptr_t ep_marker = NULL;
  mpi_ptr_t xp_marker = NULL;
  unsigned int mp_nlimbs = 0;
  unsigned int bp_nlimbs = 0;
  unsigned int ep_nlimbs = 0;
  unsigned int xp_nlimbs = 0;
  mpi_ptr_t tspace = NULL;
  mpi_size_t tsize = 0;


  esize = expo->nlimbs;
  msize = mod->nlimbs;
  size = 2 * msize;
  msign = mod->sign;

  esec = mpi_is_secure(expo);
  msec = mpi_is_secure(mod);
  bsec = mpi_is_secure(base);

  rp = res->d;
  ep = expo->d;

  if (!msize)
    grub_fatal ("mpi division by zero");

  if (!esize)
    {
      /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0 depending
         on if MOD equals 1.  */
      res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
      if (res->nlimbs)
        {
          RESIZE_IF_NEEDED (res, 1);
          rp = res->d;
          rp[0] = 1;
        }
      res->sign = 0;
      goto leave;
    }

  /* Normalize MOD (i.e. make its most significant bit set) as
     required by mpn_divrem.  This will make the intermediate values
     in the calculation slightly larger, but the correct result is
     obtained after a final reduction using the original MOD value. */
  mp_nlimbs = msec? msize:0;
  mp = mp_marker = mpi_alloc_limb_space(msize, msec);
  count_leading_zeros (mod_shift_cnt, mod->d[msize-1]);
  if (mod_shift_cnt)
    _gcry_mpih_lshift (mp, mod->d, msize, mod_shift_cnt);
  else
    MPN_COPY( mp, mod->d, msize );

  bsize = base->nlimbs;
  bsign = base->sign;
  if (bsize > msize)
    {
      /* The base is larger than the module.  Reduce it.

         Allocate (BSIZE + 1) with space for remainder and quotient.
         (The quotient is (bsize - msize + 1) limbs.)  */
      bp_nlimbs = bsec ? (bsize + 1):0;
      bp = bp_marker = mpi_alloc_limb_space( bsize + 1, bsec );
      MPN_COPY ( bp, base->d, bsize );
      /* We don't care about the quotient, store it above the
       * remainder, at BP + MSIZE.  */
      _gcry_mpih_divrem( bp + msize, 0, bp, bsize, mp, msize );
      bsize = msize;
      /* Canonicalize the base, since we are going to multiply with it
	 quite a few times.  */
      MPN_NORMALIZE( bp, bsize );
    }
  else
    bp = base->d;

  if (!bsize)
    {
      res->nlimbs = 0;
      res->sign = 0;
      goto leave;
    }


  /* Make BASE, EXPO and MOD not overlap with RES.  */
  if ( rp == bp )
    {
      /* RES and BASE are identical.  Allocate temp. space for BASE.  */
      gcry_assert (!bp_marker);
      bp_nlimbs = bsec? bsize:0;
      bp = bp_marker = mpi_alloc_limb_space( bsize, bsec );
      MPN_COPY(bp, rp, bsize);
    }
  if ( rp == ep )
    {
      /* RES and EXPO are identical.  Allocate temp. space for EXPO.  */
      ep_nlimbs = esec? esize:0;
      ep = ep_marker = mpi_alloc_limb_space( esize, esec );
      MPN_COPY(ep, rp, esize);
    }
  if ( rp == mp )
    {
      /* RES and MOD are identical.  Allocate temporary space for MOD.*/
      gcry_assert (!mp_marker);
      mp_nlimbs = msec?msize:0;
      mp = mp_marker = mpi_alloc_limb_space( msize, msec );
      MPN_COPY(mp, rp, msize);
    }

  /* Copy base to the result.  */
  if (res->alloced < size)
    {
      mpi_resize (res, size);
      rp = res->d;
    }
  MPN_COPY ( rp, bp, bsize );
  rsize = bsize;
  rsign = bsign;

  /* Main processing.  */
  {
    mpi_size_t i;
    mpi_ptr_t xp;
    int c;
    mpi_limb_t e;
    mpi_limb_t carry_limb;
    struct karatsuba_ctx karactx;

    xp_nlimbs = msec? (2 * (msize + 1)):0;
    xp = xp_marker = mpi_alloc_limb_space( 2 * (msize + 1), msec );

    memset( &karactx, 0, sizeof karactx );
    negative_result = (ep[0] & 1) && base->sign;

    i = esize - 1;
    e = ep[i];
    count_leading_zeros (c, e);
    e = (e << c) << 1;     /* Shift the expo bits to the left, lose msb.  */
    c = BITS_PER_MPI_LIMB - 1 - c;

    /* Main loop.

       Make the result be pointed to alternately by XP and RP.  This
       helps us avoid block copying, which would otherwise be
       necessary with the overlap restrictions of
       _gcry_mpih_divmod. With 50% probability the result after this
       loop will be in the area originally pointed by RP (==RES->d),
       and with 50% probability in the area originally pointed to by XP. */
    for (;;)
      {
        while (c)
          {
            mpi_ptr_t tp;
            mpi_size_t xsize;

            /*mpih_mul_n(xp, rp, rp, rsize);*/
            if ( rsize < KARATSUBA_THRESHOLD )
              _gcry_mpih_sqr_n_basecase( xp, rp, rsize );
            else
              {
                if ( !tspace )
                  {
                    tsize = 2 * rsize;
                    tspace = mpi_alloc_limb_space( tsize, 0 );
                  }
                else if ( tsize < (2*rsize) )
                  {
                    _gcry_mpi_free_limb_space (tspace, 0);
                    tsize = 2 * rsize;
                    tspace = mpi_alloc_limb_space (tsize, 0 );
                  }
                _gcry_mpih_sqr_n (xp, rp, rsize, tspace);
              }

            xsize = 2 * rsize;
            if ( xsize > msize )
              {
                _gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
                xsize = msize;
              }

            tp = rp; rp = xp; xp = tp;
            rsize = xsize;

            /* To mitigate the Yarom/Falkner flush+reload cache
             * side-channel attack on the RSA secret exponent, we do
             * the multiplication regardless of the value of the
             * high-bit of E.  But to avoid this performance penalty
             * we do it only if the exponent has been stored in secure
             * memory and we can thus assume it is a secret exponent.  */
            if (esec || (mpi_limb_signed_t)e < 0)
              {
                /*mpih_mul( xp, rp, rsize, bp, bsize );*/
                if( bsize < KARATSUBA_THRESHOLD )
                  _gcry_mpih_mul ( xp, rp, rsize, bp, bsize );
                else
                  _gcry_mpih_mul_karatsuba_case (xp, rp, rsize, bp, bsize,
                                                 &karactx);

                xsize = rsize + bsize;
                if ( xsize > msize )
                  {
                    _gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
                    xsize = msize;
                  }
              }
            if ( (mpi_limb_signed_t)e < 0 )
              {
                tp = rp; rp = xp; xp = tp;
                rsize = xsize;
              }
            e <<= 1;
            c--;
          }

        i--;
        if ( i < 0 )
          break;
        e = ep[i];
        c = BITS_PER_MPI_LIMB;
      }

    /* We shifted MOD, the modulo reduction argument, left
       MOD_SHIFT_CNT steps.  Adjust the result by reducing it with the
       original MOD.

       Also make sure the result is put in RES->d (where it already
       might be, see above).  */
    if ( mod_shift_cnt )
      {
        carry_limb = _gcry_mpih_lshift( res->d, rp, rsize, mod_shift_cnt);
        rp = res->d;
        if ( carry_limb )
          {
            rp[rsize] = carry_limb;
            rsize++;
          }
      }
    else if (res->d != rp)
      {
        MPN_COPY (res->d, rp, rsize);
        rp = res->d;
      }

    if ( rsize >= msize )
      {
        _gcry_mpih_divrem(rp + msize, 0, rp, rsize, mp, msize);
        rsize = msize;
      }

    /* Remove any leading zero words from the result.  */
    if ( mod_shift_cnt )
      _gcry_mpih_rshift( rp, rp, rsize, mod_shift_cnt);
    MPN_NORMALIZE (rp, rsize);

    _gcry_mpih_release_karatsuba_ctx (&karactx );
  }

  /* Fixup for negative results.  */
  if ( negative_result && rsize )
    {
      if ( mod_shift_cnt )
        _gcry_mpih_rshift( mp, mp, msize, mod_shift_cnt);
      _gcry_mpih_sub( rp, mp, msize, rp, rsize);
      rsize = msize;
      rsign = msign;
      MPN_NORMALIZE(rp, rsize);
    }
  gcry_assert (res->d == rp);
  res->nlimbs = rsize;
  res->sign = rsign;

 leave:
  if (mp_marker)
    _gcry_mpi_free_limb_space( mp_marker, mp_nlimbs );
  if (bp_marker)
    _gcry_mpi_free_limb_space( bp_marker, bp_nlimbs );
  if (ep_marker)
    _gcry_mpi_free_limb_space( ep_marker, ep_nlimbs );
  if (xp_marker)
    _gcry_mpi_free_limb_space( xp_marker, xp_nlimbs );
  if (tspace)
    _gcry_mpi_free_limb_space( tspace, 0 );
}
Example #3
0
void
_gcry_mpi_tdiv_qr( gcry_mpi_t quot, gcry_mpi_t rem, gcry_mpi_t num, gcry_mpi_t den)
{
    mpi_ptr_t np, dp;
    mpi_ptr_t qp, rp;
    mpi_size_t nsize = num->nlimbs;
    mpi_size_t dsize = den->nlimbs;
    mpi_size_t qsize, rsize;
    mpi_size_t sign_remainder = num->sign;
    mpi_size_t sign_quotient = num->sign ^ den->sign;
    unsigned normalization_steps;
    mpi_limb_t q_limb;
    mpi_ptr_t marker[5];
    unsigned int marker_nlimbs[5];
    int markidx=0;

    /* Ensure space is enough for quotient and remainder.
     * We need space for an extra limb in the remainder, because it's
     * up-shifted (normalized) below.  */
    rsize = nsize + 1;
    mpi_resize( rem, rsize);

    qsize = rsize - dsize;	  /* qsize cannot be bigger than this.	*/
    if( qsize <= 0 ) {
	if( num != rem ) {
	    rem->nlimbs = num->nlimbs;
	    rem->sign = num->sign;
	    MPN_COPY(rem->d, num->d, nsize);
	}
	if( quot ) {
	    /* This needs to follow the assignment to rem, in case the
	     * numerator and quotient are the same.  */
	    quot->nlimbs = 0;
	    quot->sign = 0;
	}
	return;
    }

    if( quot )
	mpi_resize( quot, qsize);

    /* Read pointers here, when reallocation is finished.  */
    np = num->d;
    dp = den->d;
    rp = rem->d;

    /* Optimize division by a single-limb divisor.  */
    if( dsize == 1 ) {
	mpi_limb_t rlimb;
	if( quot ) {
	    qp = quot->d;
	    rlimb = _gcry_mpih_divmod_1( qp, np, nsize, dp[0] );
	    qsize -= qp[qsize - 1] == 0;
	    quot->nlimbs = qsize;
	    quot->sign = sign_quotient;
	}
	else
	    rlimb = _gcry_mpih_mod_1( np, nsize, dp[0] );
	rp[0] = rlimb;
	rsize = rlimb != 0?1:0;
	rem->nlimbs = rsize;
	rem->sign = sign_remainder;
	return;
    }


    if( quot ) {
	qp = quot->d;
	/* Make sure QP and NP point to different objects.  Otherwise the
	 * numerator would be gradually overwritten by the quotient limbs.  */
	if(qp == np) { /* Copy NP object to temporary space.  */
            marker_nlimbs[markidx] = nsize;
	    np = marker[markidx++] = mpi_alloc_limb_space(nsize,
							  mpi_is_secure(quot));
	    MPN_COPY(np, qp, nsize);
	}
    }
    else /* Put quotient at top of remainder. */
	qp = rp + dsize;

    count_leading_zeros( normalization_steps, dp[dsize - 1] );

    /* Normalize the denominator, i.e. make its most significant bit set by
     * shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
     * numerator the same number of steps (to keep the quotient the same!).
     */
    if( normalization_steps ) {
	mpi_ptr_t tp;
	mpi_limb_t nlimb;

	/* Shift up the denominator setting the most significant bit of
	 * the most significant word.  Use temporary storage not to clobber
	 * the original contents of the denominator.  */
        marker_nlimbs[markidx] = dsize;
	tp = marker[markidx++] = mpi_alloc_limb_space(dsize,mpi_is_secure(den));
	_gcry_mpih_lshift( tp, dp, dsize, normalization_steps );
	dp = tp;

	/* Shift up the numerator, possibly introducing a new most
	 * significant word.  Move the shifted numerator in the remainder
	 * meanwhile.  */
	nlimb = _gcry_mpih_lshift(rp, np, nsize, normalization_steps);
	if( nlimb ) {
	    rp[nsize] = nlimb;
	    rsize = nsize + 1;
	}
	else
	    rsize = nsize;
    }
    else {
	/* The denominator is already normalized, as required.	Copy it to
	 * temporary space if it overlaps with the quotient or remainder.  */
	if( dp == rp || (quot && (dp == qp))) {
	    mpi_ptr_t tp;

            marker_nlimbs[markidx] = dsize;
	    tp = marker[markidx++] = mpi_alloc_limb_space(dsize,
                                                          mpi_is_secure(den));
	    MPN_COPY( tp, dp, dsize );
	    dp = tp;
	}

	/* Move the numerator to the remainder.  */
	if( rp != np )
	    MPN_COPY(rp, np, nsize);

	rsize = nsize;
    }

    q_limb = _gcry_mpih_divrem( qp, 0, rp, rsize, dp, dsize );

    if( quot ) {
	qsize = rsize - dsize;
	if(q_limb) {
	    qp[qsize] = q_limb;
	    qsize += 1;
	}

	quot->nlimbs = qsize;
	quot->sign = sign_quotient;
    }

    rsize = dsize;
    MPN_NORMALIZE (rp, rsize);

    if( normalization_steps && rsize ) {
	_gcry_mpih_rshift(rp, rp, rsize, normalization_steps);
	rsize -= rp[rsize - 1] == 0?1:0;
    }

    rem->nlimbs = rsize;
    rem->sign	= sign_remainder;
    while( markidx )
      {
        markidx--;
	_gcry_mpi_free_limb_space (marker[markidx], marker_nlimbs[markidx]);
      }
}