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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.
*/
/* 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 (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);
}
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