/* mpn_sec_invert

   Contributed to the GNU project by Niels Möller

Copyright 2013 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify

it under the terms of either:

  * the GNU Lesser General Public License as published by the Free

    Software Foundation; either version 3 of the License, or (at your

    option) any later version.

or

  * the GNU General Public License as published by the Free Software

    Foundation; either version 2 of the License, or (at your option) any

    later version.

or both in parallel, as here.

The GNU MP Library 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 General Public License

for more details.

You should have received copies of the GNU General Public License and the

GNU Lesser General Public License along with the GNU MP Library.  If not,

see https://www.gnu.org/licenses/.  */

#include "gmp.h"

#include "gmp-impl.h"

#if 0

/* Currently unused. Should be resurrected once mpn_cnd_neg is

   advertised. */

static mp_size_t

mpn_cnd_neg_itch (mp_size_t n)

{

  return n;

}

#endif

/* FIXME: Ought to return carry */

static void

mpn_cnd_neg (int cnd, mp_limb_t *rp, const mp_limb_t *ap, mp_size_t n,

	     mp_ptr scratch)

{

  mpn_lshift (scratch, ap, n, 1);

  mpn_cnd_sub_n (cnd, rp, ap, scratch, n);

}

static int

mpn_sec_eq_ui (mp_srcptr ap, mp_size_t n, mp_limb_t b)

{

  mp_limb_t d;

  ASSERT (n > 0);

  d = ap[0] ^ b;

  while (--n > 0)

    d |= ap[n];

  return d == 0;

}

mp_size_t

mpn_sec_invert_itch (mp_size_t n)

{

  return 4*n;

}

/* Compute V <-- A^{-1} (mod M), in data-independent time. M must be

   odd. Returns 1 on success, and 0 on failure (i.e., if gcd (A, m) !=

   1). Inputs and outputs of size n, and no overlap allowed. The {ap,

   n} area is destroyed. For arbitrary inputs, bit_size should be

   2*n*GMP_NUMB_BITS, but if A or M are known to be smaller, e.g., if

   M = 2^521 - 1 and A < M, bit_size can be any bound on the sum of

   the bit sizes of A and M. */

int

mpn_sec_invert (mp_ptr vp, mp_ptr ap, mp_srcptr mp,

		mp_size_t n, mp_bitcnt_t bit_size,

		mp_ptr scratch)

{

  ASSERT (n > 0);

  ASSERT (bit_size > 0);

  ASSERT (mp[0] & 1);

  ASSERT (! MPN_OVERLAP_P (ap, n, vp, n));

#define bp (scratch + n)

#define up (scratch + 2*n)

#define m1hp (scratch + 3*n)

  /* Maintain

       a = u * orig_a (mod m)

       b = v * orig_a (mod m)

     and b odd at all times. Initially,

       a = a_orig, u = 1

       b = m,      v = 0

     */

  up[0] = 1;

  mpn_zero (up+1, n - 1);

  mpn_copyi (bp, mp, n);

  mpn_zero (vp, n);

  ASSERT_CARRY (mpn_rshift (m1hp, mp, n, 1));

  ASSERT_NOCARRY (mpn_sec_add_1 (m1hp, m1hp, n, 1, scratch));

  while (bit_size-- > 0)

    {

      mp_limb_t odd, swap, cy;

      /* Always maintain b odd. The logic of the iteration is as

	 follows. For a, b:

	   odd = a & 1

	   a -= odd * b

	   if (underflow from a-b)

	     {

	       b += a, assigns old a

	       a = B^n-a

	     }

	   a /= 2

	 For u, v:

	   if (underflow from a - b)

	     swap u, v

	   u -= odd * v

	   if (underflow from u - v)

	     u += m

	   u /= 2

	   if (a one bit was shifted out)

	     u += (m+1)/2

	 As long as a > 0, the quantity

	   (bitsize of a) + (bitsize of b)

	 is reduced by at least one bit per iteration, hence after (bit_size of

	 orig_a) + (bit_size of m) - 1 iterations we surely have a = 0. Then b

	 = gcd(orig_a, m) and if b = 1 then also v = orig_a^{-1} (mod m).

      */

      ASSERT (bp[0] & 1);

      odd = ap[0] & 1;

      swap = mpn_cnd_sub_n (odd, ap, ap, bp, n);

      mpn_cnd_add_n (swap, bp, bp, ap, n);

      mpn_cnd_neg (swap, ap, ap, n, scratch);

      mpn_cnd_swap (swap, up, vp, n);

      cy = mpn_cnd_sub_n (odd, up, up, vp, n);

      cy -= mpn_cnd_add_n (cy, up, up, mp, n);

      ASSERT (cy == 0);

      cy = mpn_rshift (ap, ap, n, 1);

      ASSERT (cy == 0);

      cy = mpn_rshift (up, up, n, 1);

      cy = mpn_cnd_add_n (cy, up, up, m1hp, n);

      ASSERT (cy == 0);

    }

  /* Should be all zeros, but check only extreme limbs */

  ASSERT ( (ap[0] | ap[n-1]) == 0);

  /* Check if indeed gcd == 1. */

  return mpn_sec_eq_ui (bp, n, 1);

#undef bp

#undef up

#undef m1hp

}