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/* nettle, low-level cryptographics library
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* Copyright (C) 2013 Niels Möller
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* The nettle library is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or (at your
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* option) any later version.
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* The nettle library is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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* License for more details.
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* You should have received a copy of the GNU Lesser General Public License
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* along with the nettle library; see the file COPYING.LIB. If not, write to
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* the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
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#include "ecc-internal.h"
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ecc_add_jjj_itch (const struct ecc_curve *ecc)
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/* Needs 8 * ecc->size */
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return ECC_ADD_JJJ_ITCH (ecc->size);
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ecc_add_jjj (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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/* Formulas, from djb,
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http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl:
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Computation Operation Live variables
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Z2Z2 = Z2^2 sqr Z1Z1, Z2Z2
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U1 = X1*Z2Z2 mul Z1Z1, Z2Z2, U1
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U2 = X2*Z1Z1 mul Z1Z1, Z2Z2, U1, U2
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H = U2-U1 Z1Z1, Z2Z2, U1, H
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Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2)*H sqr, mul Z1Z1, Z2Z2, U1, H
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S1 = Y1*Z2*Z2Z2 mul, mul Z1Z1, U1, H, S1
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S2 = Y2*Z1*Z1Z1 mul, mul U1, H, S1, S2
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W = 2*(S2-S1) (djb: r) U1, H, S1, W
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I = (2*H)^2 sqr U1, H, S1, W, I
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J = H*I mul U1, S1, W, J, V
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V = U1*I mul S1, W, J, V
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X3 = W^2-J-2*V sqr S1, W, J, V
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Y3 = W*(V-X3)-2*S1*J mul, mul
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mp_limb_t *z1z1 = scratch;
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mp_limb_t *z2z2 = scratch + ecc->size;
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mp_limb_t *u1 = scratch + 2*ecc->size;
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mp_limb_t *u2 = scratch + 3*ecc->size;
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mp_limb_t *s1 = scratch; /* overlap z1z1 */
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mp_limb_t *s2 = scratch + ecc->size; /* overlap z2z2 */
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mp_limb_t *i = scratch + 4*ecc->size;
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mp_limb_t *j = scratch + 5*ecc->size;
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mp_limb_t *v = scratch + 6*ecc->size;
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/* z1^2, z2^2, u1 = x1 x2^2, u2 = x2 z1^2 - u1 */
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ecc_modp_sqr (ecc, z1z1, p + 2*ecc->size);
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ecc_modp_sqr (ecc, z2z2, q + 2*ecc->size);
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ecc_modp_mul (ecc, u1, p, z2z2);
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ecc_modp_mul (ecc, u2, q, z1z1);
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ecc_modp_sub (ecc, u2, u2, u1); /* Store h in u2 */
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/* z3, use i, j, v as scratch, result at i. */
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ecc_modp_add (ecc, i, p + 2*ecc->size, q + 2*ecc->size);
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ecc_modp_sqr (ecc, v, i);
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ecc_modp_sub (ecc, v, v, z1z1);
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ecc_modp_sub (ecc, v, v, z2z2);
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ecc_modp_mul (ecc, i, v, u2);
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/* Delayed write, to support in-place operation. */
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/* s1 = y1 z2^3, s2 = y2 z1^3, scratch at j and v */
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ecc_modp_mul (ecc, j, z1z1, p + 2*ecc->size); /* z1^3 */
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ecc_modp_mul (ecc, v, z2z2, q + 2*ecc->size); /* z2^3 */
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ecc_modp_mul (ecc, s1, p + ecc->size, v);
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ecc_modp_mul (ecc, v, j, q + ecc->size);
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ecc_modp_sub (ecc, s2, v, s1);
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ecc_modp_mul_1 (ecc, s2, s2, 2);
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mpn_copyi (r + 2*ecc->size, i, ecc->size);
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ecc_modp_sqr (ecc, i, u2);
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ecc_modp_mul_1 (ecc, i, i, 4);
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ecc_modp_mul (ecc, j, u2, i);
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ecc_modp_mul (ecc, v, u1, i);
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/* now, u1, u2 and i are free for reuse .*/
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/* x3, use u1, u2 as scratch */
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ecc_modp_sqr (ecc, u1, s2);
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ecc_modp_sub (ecc, r, u1, j);
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ecc_modp_submul_1 (ecc, r, v, 2);
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ecc_modp_mul (ecc, u1, s1, j); /* Frees j */
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ecc_modp_sub (ecc, u2, v, r); /* Frees v */
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ecc_modp_mul (ecc, i, s2, u2);
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ecc_modp_submul_1 (ecc, i, u1, 2);
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mpn_copyi (r + ecc->size, i, ecc->size);
added
removed
ecc-add-jjj.c
