/* ecc-256.c
Compile time constant (but machine dependent) tables.
Copyright (C) 2013, 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/.
*/
/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <assert.h>
#include "ecc.h"
#include "ecc-internal.h"
#if HAVE_NATIVE_ecc_256_redc
# define USE_REDC 1
#else
# define USE_REDC (ECC_REDC_SIZE != 0)
#endif
#include "ecc-256.h"
#if HAVE_NATIVE_ecc_256_redc
# define ecc_256_redc nettle_ecc_256_redc
void
ecc_256_redc (const struct ecc_modulo *p, mp_limb_t *rp);
#else /* !HAVE_NATIVE_ecc_256_redc */
# if ECC_REDC_SIZE > 0
# define ecc_256_redc ecc_pp1_redc
# elif ECC_REDC_SIZE == 0
# define ecc_256_redc NULL
# else
# error Configuration error
# endif
#endif /* !HAVE_NATIVE_ecc_256_redc */
#if ECC_BMODP_SIZE < ECC_LIMB_SIZE
#define ecc_256_modp ecc_mod
#define ecc_256_modq ecc_mod
#elif GMP_NUMB_BITS == 64
static void
ecc_256_modp (const struct ecc_modulo *p, mp_limb_t *rp)
{
mp_limb_t u1, u0;
mp_size_t n;
n = 2*p->size;
u1 = rp[--n];
u0 = rp[n-1];
/* This is not particularly fast, but should work well with assembly implementation. */
for (; n >= p->size; n--)
{
mp_limb_t q2, q1, q0, t, cy;
/* <q2, q1, q0> = v * u1 + <u1,u0>, with v = 2^32 - 1:
+---+---+
| u1| u0|
+---+---+
|-u1|
+-+-+-+
| u1|
+---+-+-+-+-+
| q2| q1| q0|
+---+---+---+
*/
q1 = u1 - (u1 > u0);
q0 = u0 - u1;
t = u1 << 32;
q0 += t;
t = (u1 >> 32) + (q0 < t) + 1;
q1 += t;
q2 = q1 < t;
/* Compute candidate remainder */
u1 = u0 + (q1 << 32) - q1;
t = -(mp_limb_t) (u1 > q0);
u1 -= t & 0xffffffff;
q1 += t;
q2 += t + (q1 < t);
assert (q2 < 2);
/*
n-1 n-2 n-3 n-4
+---+---+---+---+
| u1| u0| u low |
+---+---+---+---+
- | q1(2^96-1)|
+-------+---+
|q2(2^.)|
+-------+
We multiply by two low limbs of p, 2^96 - 1, so we could use
shifts rather than mul.
*/
t = mpn_submul_1 (rp + n - 4, p->m, 2, q1);
t += cnd_sub_n (q2, rp + n - 3, p->m, 1);
t += (-q2) & 0xffffffff;
u0 = rp[n-2];
cy = (u0 < t);
u0 -= t;
t = (u1 < cy);
u1 -= cy;
cy = cnd_add_n (t, rp + n - 4, p->m, 2);
u0 += cy;
u1 += (u0 < cy);
u1 -= (-t) & 0xffffffff;
}
rp[2] = u0;
rp[3] = u1;
}
static void
ecc_256_modq (const struct ecc_modulo *q, mp_limb_t *rp)
{
mp_limb_t u2, u1, u0;
mp_size_t n;
n = 2*q->size;
u2 = rp[--n];
u1 = rp[n-1];
/* This is not particularly fast, but should work well with assembly implementation. */
for (; n >= q->size; n--)
{
mp_limb_t q2, q1, q0, t, c1, c0;
u0 = rp[n-2];
/* <q2, q1, q0> = v * u2 + <u2,u1>, same method as above.
+---+---+
| u2| u1|
+---+---+
|-u2|
+-+-+-+
| u2|
+---+-+-+-+-+
| q2| q1| q0|
+---+---+---+
*/
q1 = u2 - (u2 > u1);
q0 = u1 - u2;
t = u2 << 32;
q0 += t;
t = (u2 >> 32) + (q0 < t) + 1;
q1 += t;
q2 = q1 < t;
/* Compute candidate remainder, <u1, u0> - <q2, q1> * (2^128 - 2^96 + 2^64 - 1)
<u1, u0> + 2^64 q2 + (2^96 - 2^64 + 1) q1 (mod 2^128)
+---+---+
| u1| u0|
+---+---+
| q2| q1|
+---+---+
|-q1|
+-+-+-+
| q1|
--+-+-+-+---+
| u2| u1|
+---+---+
*/
u2 = u1 + q2 - q1;
u1 = u0 + q1;
u2 += (u1 < q1);
u2 += (q1 << 32);
t = -(mp_limb_t) (u2 >= q0);
q1 += t;
q2 += t + (q1 < t);
u1 += t;
u2 += (t << 32) + (u1 < t);
assert (q2 < 2);
c0 = cnd_sub_n (q2, rp + n - 3, q->m, 1);
c0 += (-q2) & q->m[1];
t = mpn_submul_1 (rp + n - 4, q->m, 2, q1);
c0 += t;
c1 = c0 < t;
/* Construct underflow condition. */
c1 += (u1 < c0);
t = - (mp_limb_t) (u2 < c1);
u1 -= c0;
u2 -= c1;
/* Conditional add of p */
u1 += t;
u2 += (t<<32) + (u1 < t);
t = cnd_add_n (t, rp + n - 4, q->m, 2);
u1 += t;
u2 += (u1 < t);
}
rp[2] = u1;
rp[3] = u2;
}
#else
#error Unsupported parameters
#endif
const struct ecc_curve _nettle_secp_256r1 =
{
{
256,
ECC_LIMB_SIZE,
ECC_BMODP_SIZE,
ECC_REDC_SIZE,
ECC_MOD_INV_ITCH (ECC_LIMB_SIZE),
0,
ecc_p,
ecc_Bmodp,
ecc_Bmodp_shifted,
ecc_redc_ppm1,
ecc_pp1h,
ecc_256_modp,
USE_REDC ? ecc_256_redc : ecc_256_modp,
ecc_mod_inv,
NULL,
},
{
256,
ECC_LIMB_SIZE,
ECC_BMODQ_SIZE,
0,
ECC_MOD_INV_ITCH (ECC_LIMB_SIZE),
0,
ecc_q,
ecc_Bmodq,
ecc_Bmodq_shifted,
NULL,
ecc_qp1h,
ecc_256_modq,
ecc_256_modq,
ecc_mod_inv,
NULL,
},
USE_REDC,
ECC_PIPPENGER_K,
ECC_PIPPENGER_C,
ECC_ADD_JJJ_ITCH (ECC_LIMB_SIZE),
ECC_MUL_A_ITCH (ECC_LIMB_SIZE),
ECC_MUL_G_ITCH (ECC_LIMB_SIZE),
ECC_J_TO_A_ITCH (ECC_LIMB_SIZE),
ecc_add_jjj,
ecc_mul_a,
ecc_mul_g,
ecc_j_to_a,
ecc_b,
ecc_g,
NULL,
ecc_unit,
ecc_table
};
const struct ecc_curve *nettle_get_secp_256r1(void)
{
return &_nettle_secp_256r1;
}