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/* sec-modinv.c */
/* nettle, low-level cryptographics library
*
* Copyright (C) 2013 Niels Möller
*
* The nettle library is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or (at your
* option) any later version.
*
* The nettle library 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 Lesser General Public
* License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with the nettle library; see the file COPYING.LIB. If not, write to
* the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 02111-1301, USA.
*/
/* Development of Nettle's ECC support was funded by Internetfonden. */
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <assert.h>
#include "ecc-internal.h"
static void
cnd_neg (int cnd, mp_limb_t *rp, const mp_limb_t *ap, mp_size_t n)
{
mp_limb_t cy = (cnd != 0);
mp_limb_t mask = -cy;
mp_size_t i;
for (i = 0; i < n; i++)
{
mp_limb_t r = (ap[i] ^ mask) + cy;
cy = r < cy;
rp[i] = r;
}
}
static void
cnd_swap (int cnd, mp_limb_t *ap, mp_limb_t *bp, mp_size_t n)
{
mp_limb_t mask = - (mp_limb_t) (cnd != 0);
mp_size_t i;
for (i = 0; i < n; i++)
{
mp_limb_t a, b, t;
a = ap[i];
b = bp[i];
t = (a ^ b) & mask;
ap[i] = a ^ t;
bp[i] = b ^ t;
}
}
/* Compute a^{-1} mod m, with running time depending only on the size.
Also needs (m+1)/2, and m must be odd. */
void
sec_modinv (mp_limb_t *vp, mp_limb_t *ap, mp_size_t n,
const mp_limb_t *mp, const mp_limb_t *mp1h, mp_size_t bit_size,
mp_limb_t *scratch)
{
#define bp scratch
#define dp (scratch + n)
#define up (scratch + 2*n)
mp_bitcnt_t i;
/* Maintain
a = u * orig_a (mod m)
b = v * orig_a (mod m)
and b odd at all times. Initially,
a = a_orig, u = 1
b = m, v = 0
*/
assert (ap != vp);
up[0] = 1;
mpn_zero (up+1, n - 1);
mpn_copyi (bp, mp, n);
mpn_zero (vp, n);
for (i = bit_size + GMP_NUMB_BITS * n; i-- > 0; )
{
mp_limb_t odd, swap, cy;
/* Always maintain b odd. The logic of the iteration is as
follows. For a, b:
odd = a & 1
a -= odd * b
if (underflow from a-b)
{
b += a, assigns old a
a = B^n-a
}
a /= 2
For u, v:
if (underflow from a - b)
swap u, v
u -= odd * v
if (underflow from u - v)
u += m
u /= 2
if (a one bit was shifted out)
u += (m+1)/2
As long as a > 0, the quantity
(bitsize of a) + (bitsize of b)
is reduced by at least one bit per iteration, hence after
(bit_size of orig_a) + (bit_size of m) - 1 iterations we
surely have a = 0. Then b = gcd(orig_a, m) and if b = 1 then
also v = orig_a^{-1} (mod m)
*/
assert (bp[0] & 1);
odd = ap[0] & 1;
/* Which variant is fastest depends on the speed of the various
cnd_* functions. Assembly implementation would help. */
#if 1
swap = cnd_sub_n (odd, ap, bp, n);
cnd_add_n (swap, bp, ap, n);
cnd_neg (swap, ap, ap, n);
#else
swap = odd & mpn_sub_n (dp, ap, bp, n);
cnd_copy (swap, bp, ap, n);
cnd_neg (swap, dp, dp, n);
cnd_copy (odd, ap, dp, n);
#endif
#if 1
cnd_swap (swap, up, vp, n);
cy = cnd_sub_n (odd, up, vp, n);
cy -= cnd_add_n (cy, up, mp, n);
#else
cy = cnd_sub_n (odd, up, vp, n);
cnd_add_n (swap, vp, up, n);
cnd_neg (swap, up, up, n);
cnd_add_n (cy ^ swap, up, mp, n);
#endif
cy = mpn_rshift (ap, ap, n, 1);
assert (cy == 0);
cy = mpn_rshift (up, up, n, 1);
cy = cnd_add_n (cy, up, mp1h, n);
assert (cy == 0);
}
assert ( (ap[0] | ap[n-1]) == 0);
#undef bp
#undef dp
#undef up
}
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