/* ecc-dup-jj.c

   Copyright (C) 2013 Niels Möller

   This file is part of GNU Nettle.

   GNU Nettle 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.

   GNU Nettle 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 this program.  If

   not, see http://www.gnu.org/licenses/.

*/

/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */

#if HAVE_CONFIG_H

# include "config.h"

#endif

#include "ecc.h"

#include "ecc-internal.h"

/* NOTE: Behaviour for corner cases:

   + p = 0  ==>  r = 0, correct!

*/

void

ecc_dup_jj (const struct ecc_curve *ecc,

      mp_limb_t *r, const mp_limb_t *p,

      mp_limb_t *scratch)

{

#define x1 p

#define y1 (p + ecc->p.size)

#define z1 (p + 2*ecc->p.size)

#define x2 r

#define y2 (r + ecc->p.size)

#define z2 (r + 2*ecc->p.size)

  /* Formulas (from djb,

     http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b):

     Computation      Operation Live variables

     delta = z^2      sqr   delta

     gamma = y^2      sqr   delta, gamma

     z' = (y+z)^2-gamma-delta   sqr   delta, gamma

     alpha = 3*(x-delta)*(x+delta)  mul   gamma, beta, alpha

     beta = x*gamma     mul   gamma, beta, alpha

     x' = alpha^2-8*beta    sqr   gamma, beta, alpha

     y' = alpha*(4*beta-x')-8*gamma^2 mul, sqr

  */

#define gamma scratch

#define delta (scratch + ecc->p.size)

#define alpha delta

#define beta (scratch + 2*ecc->p.size)

#define sum  (scratch + 3*ecc->p.size)

  ecc_mod_sqr (&ecc->p, gamma, y1, gamma);  /* x, y, z, gamma */

  ecc_mod_sqr (&ecc->p, delta, z1, delta);  /* x, y, z, gamma, delta */

  ecc_mod_add (&ecc->p, sum, z1, y1);    /* x, gamma, delta, s */

  ecc_mod_sqr (&ecc->p, sum, sum, y2);    /* Can use y-z as scratch */

  ecc_mod_sub (&ecc->p, z2, sum, delta);  /* x, z, gamma, delta */

  ecc_mod_sub (&ecc->p, z2, z2, gamma);

  ecc_mod_mul (&ecc->p, beta, x1, gamma, beta);  /* x, z, gamma, delta, beta */

  ecc_mod_add (&ecc->p, sum, x1, delta);  /* x, sum, z', gamma, delta, beta */

  ecc_mod_sub (&ecc->p, delta, x1, delta);  /* sum, z', gamma, delta, beta */

  /* This multiplication peaks the storage need; can use x-y for scratch. */

  ecc_mod_mul (&ecc->p, alpha, sum, delta, x2);  /* z', gamma, alpha, beta */

  ecc_mod_mul_1 (&ecc->p, alpha, alpha, 3);

  ecc_mod_mul_1 (&ecc->p, y2, beta, 4);

  /* From now on, can use beta as scratch. */

  ecc_mod_sqr (&ecc->p, x2, alpha, beta);  /* alpha^2 */

  ecc_mod_submul_1 (&ecc->p, x2, y2, 2); /*  alpha^2 - 8 beta */

  ecc_mod_sub (&ecc->p, y2, y2, x2);    /* 4 beta - x' */

  ecc_mod_mul (&ecc->p, y2, y2, alpha, beta);

  ecc_mod_sqr (&ecc->p, gamma, gamma, beta);

  ecc_mod_submul_1 (&ecc->p, y2, gamma, 8);

}