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132 lines
3.5 KiB
C
132 lines
3.5 KiB
C
/* ecc-add-jj.c
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Copyright (C) 2013 Niels Möller
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This file is part of GNU Nettle.
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GNU Nettle is free software: you can redistribute it and/or
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modify it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free
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Software Foundation; either version 2 of the License, or (at your
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option) any later version.
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or both in parallel, as here.
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GNU Nettle is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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You should have received copies of the GNU General Public License and
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the GNU Lesser General Public License along with this program. If
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not, see http://www.gnu.org/licenses/.
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*/
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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
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# include "config.h"
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#endif
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#include "ecc.h"
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#include "ecc-internal.h"
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/* NOTE: Behaviour for corner cases:
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+ p = 0 ==> r = 0 (invalid except if also q = 0)
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+ q = 0 ==> r = invalid
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+ p = -q ==> r = 0, correct!
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+ p = q ==> r = 0, invalid
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*/
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void
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ecc_add_jja (const struct ecc_curve *ecc,
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mp_limb_t *r, const mp_limb_t *p, const mp_limb_t *q,
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mp_limb_t *scratch)
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{
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#define x1 p
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#define y1 (p + ecc->p.size)
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#define z1 (p + 2*ecc->p.size)
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#define x2 q
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#define y2 (q + ecc->p.size)
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#define x3 r
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#define y3 (r + ecc->p.size)
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#define z3 (r + 2*ecc->p.size)
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/* Formulas, from djb,
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http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b):
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Computation Operation Live variables
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ZZ = Z_1^2 sqr ZZ
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H = X_2*ZZ - X_1 mul (djb: U_2) ZZ, H
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HH = H^2 sqr ZZ, H, HH
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ZZZ = ZZ*Z_1 mul ZZ, H, HH, ZZZ
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Z_3 = (Z_1+H)^2-ZZ-HH sqr H, HH, ZZZ
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W = 2 (Y_2*ZZZ - Y_1) mul (djb: S_2) H, HH, W
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I = 4*HH H, W, I
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J = H*I mul W, I, J
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V = X_1*I mul W, J, V
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X_3 = W^2-J-2*V sqr W, J, V
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Y_3 = W*(V-X_3)-2*Y_1*J mul, mul
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*/
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#define zz scratch
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#define h (scratch + ecc->p.size)
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#define w (scratch + 2*ecc->p.size)
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#define hh zz
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#define i zz
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#define v zz
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#define j h
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#define tp (scratch + 3*ecc->p.size)
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/* zz */
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ecc_mod_sqr (&ecc->p, zz, z1, tp); /* zz */
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/* h*/
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ecc_mod_mul (&ecc->p, h, x2, zz, tp); /* zz, h */
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ecc_mod_sub (&ecc->p, h, h, x1);
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/* Do z^3 early, store at w. */
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ecc_mod_mul (&ecc->p, w, zz, z1, tp); /* zz, h, w */
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/* z_3 */
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ecc_mod_add (&ecc->p, z3, z1, h);
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ecc_mod_sqr (&ecc->p, z3, z3, tp);
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ecc_mod_sub (&ecc->p, z3, z3, zz); /* h, w */
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/* hh */
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ecc_mod_sqr (&ecc->p, hh, h, tp); /* h, w, hh */
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ecc_mod_sub (&ecc->p, z3, z3, hh);
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/* w */
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ecc_mod_mul (&ecc->p, w, y2, w, tp);
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ecc_mod_sub (&ecc->p, w, w, y1);
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ecc_mod_add (&ecc->p, w, w, w);
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/* i replaces hh */
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ecc_mod_mul_1 (&ecc->p, i, hh, 4); /* h, w, i */
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/* j replaces h */
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ecc_mod_mul (&ecc->p, j, i, h, tp); /* w, i, j */
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/* v replaces i */
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ecc_mod_mul (&ecc->p, v, x1, i, tp);
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/* x_3 */
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ecc_mod_sqr (&ecc->p, x3, w, tp);
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ecc_mod_sub (&ecc->p, x3, x3, j);
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ecc_mod_submul_1 (&ecc->p, x3, v, 2);
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/* y_3 */
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ecc_mod_mul (&ecc->p, j, y1, j, tp);
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ecc_mod_sub (&ecc->p, y3, v, x3);
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ecc_mod_mul (&ecc->p, y3, y3, w, tp);
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ecc_mod_submul_1 (&ecc->p, y3, j, 2);
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}
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