ecc-256.c 6.04 KB
Newer Older
1
/* ecc-256.c
2 3 4

   Compile time constant (but machine dependent) tables.

5
   Copyright (C) 2013, 2014 Niels Möller
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

   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/.
*/
Niels Möller's avatar
Niels Möller committed
33

34
/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
Niels Möller's avatar
Niels Möller committed
35 36 37 38 39 40 41

#if HAVE_CONFIG_H
# include "config.h"
#endif

#include <assert.h>

42
#include "ecc.h"
Niels Möller's avatar
Niels Möller committed
43 44
#include "ecc-internal.h"

45 46 47 48 49
#if HAVE_NATIVE_ecc_256_redc
# define USE_REDC 1
#else
# define USE_REDC (ECC_REDC_SIZE != 0)
#endif
Niels Möller's avatar
Niels Möller committed
50 51 52

#include "ecc-256.h"

53 54 55
#if HAVE_NATIVE_ecc_256_redc
# define ecc_256_redc nettle_ecc_256_redc
void
56
ecc_256_redc (const struct ecc_modulo *p, mp_limb_t *rp);
57
#else /* !HAVE_NATIVE_ecc_256_redc */
58 59 60 61 62 63 64 65
# 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 */
66

Niels Möller's avatar
Niels Möller committed
67
#if ECC_BMODP_SIZE < ECC_LIMB_SIZE
68 69
#define ecc_256_modp ecc_mod
#define ecc_256_modq ecc_mod
Niels Möller's avatar
Niels Möller committed
70 71 72
#elif GMP_NUMB_BITS == 64

static void
73
ecc_256_modp (const struct ecc_modulo *p, mp_limb_t *rp)
Niels Möller's avatar
Niels Möller committed
74 75 76 77
{
  mp_limb_t u1, u0;
  mp_size_t n;

78
  n = 2*p->size;
Niels Möller's avatar
Niels Möller committed
79 80 81 82
  u1 = rp[--n];
  u0 = rp[n-1];

  /* This is not particularly fast, but should work well with assembly implementation. */
83
  for (; n >= p->size; n--)
Niels Möller's avatar
Niels Möller committed
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
    {
      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);

116 117 118 119 120 121 122 123 124 125 126 127 128
      /*
	 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.
      */
129 130
      t = mpn_submul_1 (rp + n - 4, p->m, 2, q1);
      t += cnd_sub_n (q2, rp + n - 3, p->m, 1);
Niels Möller's avatar
Niels Möller committed
131 132 133 134 135 136 137
      t += (-q2) & 0xffffffff;

      u0 = rp[n-2];
      cy = (u0 < t);
      u0 -= t;
      t = (u1 < cy);
      u1 -= cy;
138 139 140 141

      cy = cnd_add_n (t, rp + n - 4, p->m, 2);
      u0 += cy;
      u1 += (u0 < cy);
Niels Möller's avatar
Niels Möller committed
142 143 144 145 146 147 148
      u1 -= (-t) & 0xffffffff;
    }
  rp[2] = u0;
  rp[3] = u1;
}

static void
149
ecc_256_modq (const struct ecc_modulo *q, mp_limb_t *rp)
Niels Möller's avatar
Niels Möller committed
150 151 152 153
{
  mp_limb_t u2, u1, u0;
  mp_size_t n;

154
  n = 2*q->size;
Niels Möller's avatar
Niels Möller committed
155 156 157 158
  u2 = rp[--n];
  u1 = rp[n-1];

  /* This is not particularly fast, but should work well with assembly implementation. */
159
  for (; n >= q->size; n--)
Niels Möller's avatar
Niels Möller committed
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
    {
      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);

213 214 215
      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);
Niels Möller's avatar
Niels Möller committed
216 217 218 219 220 221 222 223 224 225 226 227
      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;
228
      u2 += (t<<32) + (u1 < t);
Niels Möller's avatar
Niels Möller committed
229

230
      t = cnd_add_n (t, rp + n - 4, q->m, 2);
Niels Möller's avatar
Niels Möller committed
231 232 233 234 235 236 237 238 239 240 241 242 243
      u1 += t;
      u2 += (u1 < t);
    }
  rp[2] = u1;
  rp[3] = u2;
}
      
#else
#error Unsupported parameters
#endif

const struct ecc_curve nettle_secp_256r1 =
{
244 245 246 247 248
  {
    256,
    ECC_LIMB_SIZE,    
    ECC_BMODP_SIZE,
    ECC_REDC_SIZE,
249
    ECC_MOD_INV_ITCH (ECC_LIMB_SIZE),
250
    0,
251

252 253 254 255
    ecc_p,
    ecc_Bmodp,
    ecc_Bmodp_shifted,
    ecc_redc_ppm1,
256 257

    ecc_pp1h,
258 259
    ecc_256_modp,
    USE_REDC ? ecc_256_redc : ecc_256_modp,
260
    ecc_mod_inv,
261
    NULL,
262 263 264 265 266 267
  },
  {
    256,
    ECC_LIMB_SIZE,    
    ECC_BMODQ_SIZE,
    0,
268
    ECC_MOD_INV_ITCH (ECC_LIMB_SIZE),
269
    0,
270

271 272 273 274
    ecc_q,
    ecc_Bmodq,
    ecc_Bmodq_shifted,
    NULL,
275 276
    ecc_qp1h,

277 278
    ecc_256_modq,
    ecc_256_modq,
279
    ecc_mod_inv,
280
    NULL,
281 282
  },

Niels Möller's avatar
Niels Möller committed
283 284 285
  USE_REDC,
  ECC_PIPPENGER_K,
  ECC_PIPPENGER_C,
286

287
  ECC_ADD_JJJ_ITCH (ECC_LIMB_SIZE),
288 289 290 291
  ECC_MUL_A_ITCH (ECC_LIMB_SIZE),
  ECC_MUL_G_ITCH (ECC_LIMB_SIZE),
  ECC_J_TO_A_ITCH (ECC_LIMB_SIZE),

292
  ecc_add_jjj,
293 294 295 296
  ecc_mul_a,
  ecc_mul_g,
  ecc_j_to_a,

Niels Möller's avatar
Niels Möller committed
297 298
  ecc_b,
  ecc_g,
299
  NULL,
Niels Möller's avatar
Niels Möller committed
300 301 302
  ecc_unit,
  ecc_table
};