ecc-256.c 5.61 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"

Niels Möller's avatar
Niels Möller committed
53 54 55 56 57
#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 */
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 */
Niels Möller's avatar
Niels Möller committed
66

Niels Möller's avatar
Niels Möller committed
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
#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,
233
  256,
Niels Möller's avatar
Niels Möller committed
234 235 236 237 238
  ECC_BMODQ_SIZE,
  USE_REDC,
  ECC_REDC_SIZE,
  ECC_PIPPENGER_K,
  ECC_PIPPENGER_C,
239

240
  ECC_ADD_JJJ_ITCH (ECC_LIMB_SIZE),
241 242 243 244
  ECC_MUL_A_ITCH (ECC_LIMB_SIZE),
  ECC_MUL_G_ITCH (ECC_LIMB_SIZE),
  ECC_J_TO_A_ITCH (ECC_LIMB_SIZE),

245 246 247 248 249
  ecc_256_modp,
  ecc_256_redc,
  USE_REDC ? ecc_256_redc : ecc_256_modp,
  ecc_256_modq,

250
  ecc_add_jjj,
251 252 253 254
  ecc_mul_a,
  ecc_mul_g,
  ecc_j_to_a,

Niels Möller's avatar
Niels Möller committed
255 256 257 258
  ecc_p,
  ecc_b,
  ecc_q,
  ecc_g,
259
  NULL,
Niels Möller's avatar
Niels Möller committed
260 261 262 263 264 265 266 267 268 269
  ecc_Bmodp,
  ecc_Bmodp_shifted,
  ecc_pp1h,
  ecc_redc_ppm1,
  ecc_unit,
  ecc_Bmodq,
  ecc_Bmodq_shifted,
  ecc_qp1h,
  ecc_table
};