ecc-add-jja.c 3.36 KB
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/* ecc-dup-jj.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.
 */

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/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
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#if HAVE_CONFIG_H
# include "config.h"
#endif

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

/* NOTE: Behaviour for corner cases:

   + p = 0   ==>  r = 0 (invalid except if also q = 0)

   + q = 0   ==>  r = invalid

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

   + p = q   ==>  r = 0, invalid
*/

mp_size_t
ecc_add_jja_itch (const struct ecc_curve *ecc)
{
  return ECC_ADD_JJA_ITCH (ecc->size);
}

void
ecc_add_jja (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#doubling-dbl-2001-b):

     Computation		Operation	Live variables
     
      ZZ = Z_1^2		sqr		ZZ
      H = X_2*ZZ - X_1		mul (djb: U_2)	ZZ, H
      HH = H^2			sqr		ZZ, H, HH
      ZZZ = ZZ*Z_1		mul		ZZ, H, HH, ZZZ
      Z_3 = (Z_1+H)^2-ZZ-HH	sqr		H, HH, ZZZ
      W = 2 (Y_2*ZZZ - Y_1)	mul (djb: S_2)	H, HH, W
      I = 4*HH					H, W, I
      J = H*I			mul		W, I, J
      V = X_1*I			mul		W, J, V
      X_3 = W^2-J-2*V		sqr		W, J, V
      Y_3 = W*(V-X_3)-2*Y_1*J	mul, mul
  */
#define zz  scratch
#define h  (scratch + ecc->size)
#define hh (scratch + 2*ecc->size)
#define w  (scratch + 3*ecc->size)
#define j  (scratch + 4*ecc->size)
#define v   scratch

#define x1  p
#define y1 (p + ecc->size)
#define z1 (p + 2*ecc->size)
#define x2  q
#define y2 (q + ecc->size)

  /* zz */
  ecc_modp_sqr (ecc, zz, z1);
  /* h*/
  ecc_modp_mul (ecc, h, x2, zz);
  ecc_modp_sub (ecc, h, h, x1);
  /* hh */
  ecc_modp_sqr (ecc, hh, h);
  /* Do z^3 early, store at w. */
  ecc_modp_mul (ecc, w, zz, z1);
  /* z_3, use j area for scratch */
  ecc_modp_add (ecc, r + 2*ecc->size, p + 2*ecc->size, h);
  ecc_modp_sqr (ecc, j, r + 2*ecc->size);
  ecc_modp_sub (ecc, j, j, zz);
  ecc_modp_sub (ecc, r + 2*ecc->size, j, hh);
  
  /* w */
  ecc_modp_mul (ecc, j, y2, w);
  ecc_modp_sub (ecc, w, j, y1);
  ecc_modp_mul_1 (ecc, w, w, 2);
  
  /* i replaces hh, j */
  ecc_modp_mul_1 (ecc, hh, hh, 4);
  ecc_modp_mul (ecc, j, hh, h);

  /* v */
  ecc_modp_mul (ecc, v, x1, hh);

  /* x_3, use (h, hh) as sqratch */  
  ecc_modp_sqr (ecc, h, w);
  ecc_modp_sub (ecc, r, h, j);
  ecc_modp_submul_1 (ecc, r, v, 2);

  /* y_3, use (h, hh) as sqratch */
  ecc_modp_mul (ecc, h, y1, j); /* frees j */
  ecc_modp_sub (ecc, r + ecc->size, v, r);
  ecc_modp_mul (ecc, j, r + ecc->size, w);
  ecc_modp_submul_1 (ecc, j, h, 2);
  mpn_copyi (r + ecc->size, j, ecc->size);
}