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/* ecc-add-jjj.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"
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->p.size;
mp_limb_t *u1 = scratch + 2*ecc->p.size;
mp_limb_t *u2 = scratch + 3*ecc->p.size;
mp_limb_t *s1 = scratch; /* overlap z1z1 */
mp_limb_t *s2 = scratch + ecc->p.size; /* overlap z2z2 */
mp_limb_t *i = scratch + 4*ecc->p.size;
mp_limb_t *j = scratch + 5*ecc->p.size;
mp_limb_t *v = scratch + 6*ecc->p.size;
/* z1^2, z2^2, u1 = x1 x2^2, u2 = x2 z1^2 - u1 */
ecc_modp_sqr (ecc, z1z1, p + 2*ecc->p.size);
ecc_modp_sqr (ecc, z2z2, q + 2*ecc->p.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->p.size, q + 2*ecc->p.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->p.size); /* z1^3 */
ecc_modp_mul (ecc, v, z2z2, q + 2*ecc->p.size); /* z2^3 */
ecc_modp_mul (ecc, s1, p + ecc->p.size, v);
ecc_modp_mul (ecc, v, j, q + ecc->p.size);
ecc_modp_sub (ecc, s2, v, s1);
ecc_modp_mul_1 (ecc, s2, s2, 2);
/* Store z3 */
mpn_copyi (r + 2*ecc->p.size, i, ecc->p.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->p.size, i, ecc->p.size);
}
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