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/* ecc-add-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 (invalid except if also q = 0)
+ q = 0 ==> r = invalid
+ p = -q ==> r = 0, correct!
+ p = q ==> r = 0, invalid
*/
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)
{
#define x1 p
#define y1 (p + ecc->p.size)
#define z1 (p + 2*ecc->p.size)
#define x2 q
#define y2 (q + ecc->p.size)
#define x3 r
#define y3 (r + ecc->p.size)
#define z3 (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
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->p.size)
#define w (scratch + 2*ecc->p.size)
#define hh zz
#define i zz
#define v zz
#define j h
#define tp (scratch + 3*ecc->p.size)
/* zz */
ecc_mod_sqr (&ecc->p, zz, z1, tp); /* zz */
/* h*/
ecc_mod_mul (&ecc->p, h, x2, zz, tp); /* zz, h */
ecc_mod_sub (&ecc->p, h, h, x1);
/* Do z^3 early, store at w. */
ecc_mod_mul (&ecc->p, w, zz, z1, tp); /* zz, h, w */
/* z_3 */
ecc_mod_add (&ecc->p, z3, z1, h);
ecc_mod_sqr (&ecc->p, z3, z3, tp);
ecc_mod_sub (&ecc->p, z3, z3, zz); /* h, w */
/* hh */
ecc_mod_sqr (&ecc->p, hh, h, tp); /* h, w, hh */
ecc_mod_sub (&ecc->p, z3, z3, hh);
/* w */
ecc_mod_mul (&ecc->p, w, y2, w, tp);
ecc_mod_sub (&ecc->p, w, w, y1);
ecc_mod_add (&ecc->p, w, w, w);
/* i replaces hh */
ecc_mod_mul_1 (&ecc->p, i, hh, 4); /* h, w, i */
/* j replaces h */
ecc_mod_mul (&ecc->p, j, i, h, tp); /* w, i, j */
/* v replaces i */
ecc_mod_mul (&ecc->p, v, x1, i, tp);
/* x_3 */
ecc_mod_sqr (&ecc->p, x3, w, tp);
ecc_mod_sub (&ecc->p, x3, x3, j);
ecc_mod_submul_1 (&ecc->p, x3, v, 2);
/* y_3 */
ecc_mod_mul (&ecc->p, j, y1, j, tp);
ecc_mod_sub (&ecc->p, y3, v, x3);
ecc_mod_mul (&ecc->p, y3, y3, w, tp);
ecc_mod_submul_1 (&ecc->p, y3, j, 2);
}
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