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/* ecc-eh-to-a.c
Copyright (C) 2014 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/.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include "ecc.h"
#include "ecc-internal.h"
mp_size_t
ecc_eh_to_a_itch (const struct ecc_curve *ecc)
{
/* Needs 2*ecc->size + scratch for ecc_modq_inv */
return ECC_EH_TO_A_ITCH (ecc->size);
}
/* Convert from homogeneous coordinates on the Edwards curve to affine
coordinates on the corresponding Montgomery curve. */
void
ecc_eh_to_a (const struct ecc_curve *ecc,
int flags,
mp_limb_t *r, const mp_limb_t *p,
mp_limb_t *scratch)
{
#define izp scratch
#define sp (scratch + ecc->size)
#define tp (scratch + 2*ecc->size)
#define xp r
#define yp (r + ecc->size)
#define up p
#define vp (p + ecc->size)
#define wp (p + 2*ecc->size)
/* x = (v+1)/(v-1), y = t x / u (with t = sqrt(b+2))
In homogeneous coordinates,
X = (W + V) U
Y = t (W + V) W
Z = (W - V) U
*/
/* FIXME: Simplify for common case that only x-coordinate is wanted. */
mp_limb_t cy;
ecc_modp_sub (ecc, izp, wp, vp);
/* FIXME: For the infinity point, this subtraction gives zero (mod
p), which isn't invertible. For curve25519, the desired output is
x = 0, which we get if the modular inversion function returns 0
in this case. Need to check that modular inversion really returns
0. */
ecc_modp_mul (ecc, izp + ecc->size, izp, up);
/* Needs 3*size scratch */
ecc_modp_inv (ecc, izp, izp + ecc->size, izp + 2*ecc->size);
ecc_modp_add (ecc, sp, wp, vp);
ecc_modp_mul (ecc, tp, sp, up);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, izp);
cy = mpn_sub_n (xp, tp, ecc->p, ecc->size);
cnd_copy (cy, xp, tp, ecc->size);
if (flags & 2)
/* Skip y coordinate */
return;
ecc_modp_add (ecc, sp, wp, vp); /* FIXME: Redundant */
ecc_modp_mul (ecc, tp, sp, wp);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, ecc->edwards_root);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, izp);
cy = mpn_sub_n (yp, tp, ecc->p, ecc->size);
cnd_copy (cy, yp, tp, ecc->size);
}
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