1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
|
/* ecc-256.c.c */
/* Compile time constant (but machine dependent) tables. */
/* 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 the .SE Internet Fund. */
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <assert.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_curve *ecc, mp_limb_t *rp);
#else /* !HAVE_NATIVE_ecc_256_redc */
# define ecc_256_redc ecc_generic_redc
#endif
#if ECC_BMODP_SIZE < ECC_LIMB_SIZE
#define ecc_256_modp ecc_generic_modp
#define ecc_256_modq ecc_generic_modq
#elif GMP_NUMB_BITS == 64
static void
ecc_256_modp (const struct ecc_curve *ecc, mp_limb_t *rp)
{
mp_limb_t u1, u0;
mp_size_t n;
n = 2*ecc->size;
u1 = rp[--n];
u0 = rp[n-1];
/* This is not particularly fast, but should work well with assembly implementation. */
for (; n >= ecc->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);
/* 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, ecc->p, 2, q1);
t += cnd_sub_n (q2, rp + n - 3, ecc->p, 1);
t += (-q2) & 0xffffffff;
u0 = rp[n-2];
cy = (u0 < t);
u0 -= t;
t = (u1 < cy);
u1 -= cy;
u1 += cnd_add_n (t, rp + n - 4, ecc->p, 3);
u1 -= (-t) & 0xffffffff;
}
rp[2] = u0;
rp[3] = u1;
}
static void
ecc_256_modq (const struct ecc_curve *ecc, mp_limb_t *rp)
{
mp_limb_t u2, u1, u0;
mp_size_t n;
n = 2*ecc->size;
u2 = rp[--n];
u1 = rp[n-1];
/* This is not particularly fast, but should work well with assembly implementation. */
for (; n >= ecc->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, ecc->q, 1);
c0 += (-q2) & ecc->q[1];
t = mpn_submul_1 (rp + n - 4, ecc->q, 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) + (u0 < t);
t = cnd_add_n (t, rp + n - 4, ecc->q, 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_BMODQ_SIZE,
USE_REDC,
ECC_REDC_SIZE,
ECC_PIPPENGER_K,
ECC_PIPPENGER_C,
ecc_p,
ecc_b,
ecc_q,
ecc_g,
ecc_redc_g,
ecc_256_modp,
ecc_256_redc,
USE_REDC ? ecc_256_redc : ecc_256_modp,
ecc_256_modq,
ecc_Bmodp,
ecc_Bmodp_shifted,
ecc_pp1h,
ecc_redc_ppm1,
ecc_unit,
ecc_Bmodq,
ecc_Bmodq_shifted,
ecc_qp1h,
ecc_table
};
|