/* ecc-add-jjj.c */

/* nettle, low-level cryptographics library
 *
 * Copyright (C) 2013 Niels Möller
 *  
 * The nettle library is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or (at your
 * option) any later version.
 * 
 * The nettle 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 Lesser General Public
 * License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with the nettle library; see the file COPYING.LIB.  If not, write to
 * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
 * MA 02111-1301, USA.
 */

/* Development of Nettle's ECC support was funded by Internetfonden. */

#if HAVE_CONFIG_H
# include "config.h"
#endif

#include "ecc.h"
#include "ecc-internal.h"

mp_size_t
ecc_add_jjj_itch (const struct ecc_curve *ecc)
{
  /* Needs 8 * ecc->size */
  return ECC_ADD_JJJ_ITCH (ecc->size);
}

void
ecc_add_jjj (const struct ecc_curve *ecc,
	     mp_limb_t *r, const mp_limb_t *p, const mp_limb_t *q,
	     mp_limb_t *scratch)
{
  /* Formulas, from djb,
     http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl:

     Computation		Operation	Live variables

      Z1Z1 = Z1^2		sqr		Z1Z1
      Z2Z2 = Z2^2		sqr		Z1Z1, Z2Z2
      U1 = X1*Z2Z2		mul		Z1Z1, Z2Z2, U1
      U2 = X2*Z1Z1		mul		Z1Z1, Z2Z2, U1, U2
      H = U2-U1					Z1Z1, Z2Z2, U1, H
      Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2)*H sqr, mul	Z1Z1, Z2Z2, U1, H
      S1 = Y1*Z2*Z2Z2		mul, mul	Z1Z1, U1, H, S1
      S2 = Y2*Z1*Z1Z1		mul, mul	U1, H, S1, S2
      W = 2*(S2-S1)	(djb: r)		U1, H, S1, W
      I = (2*H)^2		sqr		U1, H, S1, W, I
      J = H*I			mul		U1, S1, W, J, V
      V = U1*I			mul		S1, W, J, V
      X3 = W^2-J-2*V		sqr		S1, W, J, V
      Y3 = W*(V-X3)-2*S1*J	mul, mul
  */
  mp_limb_t *z1z1 = scratch;
  mp_limb_t *z2z2 = scratch + ecc->size;
  mp_limb_t *u1   = scratch + 2*ecc->size;
  mp_limb_t *u2   = scratch + 3*ecc->size;
  mp_limb_t *s1   = scratch; /* overlap z1z1 */
  mp_limb_t *s2   = scratch + ecc->size; /* overlap z2z2 */
  mp_limb_t *i    = scratch + 4*ecc->size;
  mp_limb_t *j    = scratch + 5*ecc->size;
  mp_limb_t *v    = scratch + 6*ecc->size;

  /* z1^2, z2^2, u1 = x1 x2^2, u2 = x2 z1^2 - u1 */
  ecc_modp_sqr (ecc, z1z1, p + 2*ecc->size);
  ecc_modp_sqr (ecc, z2z2, q + 2*ecc->size);
  ecc_modp_mul (ecc, u1, p, z2z2);
  ecc_modp_mul (ecc, u2, q, z1z1);
  ecc_modp_sub (ecc, u2, u2, u1);  /* Store h in u2 */

  /* z3, use i, j, v as scratch, result at i. */
  ecc_modp_add (ecc, i, p + 2*ecc->size, q + 2*ecc->size);
  ecc_modp_sqr (ecc, v, i);
  ecc_modp_sub (ecc, v, v, z1z1);
  ecc_modp_sub (ecc, v, v, z2z2);
  ecc_modp_mul (ecc, i, v, u2);
  /* Delayed write, to support in-place operation. */

  /* s1 = y1 z2^3, s2 = y2 z1^3, scratch at j and v */
  ecc_modp_mul (ecc, j, z1z1, p + 2*ecc->size); /* z1^3 */
  ecc_modp_mul (ecc, v, z2z2, q + 2*ecc->size); /* z2^3 */
  ecc_modp_mul (ecc, s1, p + ecc->size, v);
  ecc_modp_mul (ecc, v, j, q + ecc->size);
  ecc_modp_sub (ecc, s2, v, s1);
  ecc_modp_mul_1 (ecc, s2, s2, 2);

  /* Store z3 */
  mpn_copyi (r + 2*ecc->size, i, ecc->size);

  /* i, j, v */
  ecc_modp_sqr (ecc, i, u2);
  ecc_modp_mul_1 (ecc, i, i, 4);
  ecc_modp_mul (ecc, j, u2, i);
  ecc_modp_mul (ecc, v, u1, i);

  /* now, u1, u2 and i are free for reuse .*/
  /* x3, use u1, u2 as scratch */
  ecc_modp_sqr (ecc, u1, s2);
  ecc_modp_sub (ecc, r, u1, j);
  ecc_modp_submul_1 (ecc, r, v, 2);

  /* y3 */
  ecc_modp_mul (ecc, u1, s1, j); /* Frees j */
  ecc_modp_sub (ecc, u2, v, r);  /* Frees v */
  ecc_modp_mul (ecc, i, s2, u2);
  ecc_modp_submul_1 (ecc, i, u1, 2);
  mpn_copyi (r + ecc->size, i, ecc->size);
}