ecc-256.c 5.25 KB
Newer Older
1
/* ecc-256.c
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

   Compile time constant (but machine dependent) tables.

   Copyright (C) 2013 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/.
*/
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
42
43

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

#include <assert.h>

#include "ecc-internal.h"

44
45
46
47
48
#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
49
50
51

#include "ecc-256.h"

Niels Möller's avatar
Niels Möller committed
52
53
54
55
56
57
58
59
#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

Niels Möller's avatar
Niels Möller committed
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
#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,
231
232
233
234
235
236

  ecc_256_modp,
  ecc_256_redc,
  USE_REDC ? ecc_256_redc : ecc_256_modp,
  ecc_256_modq,

Niels Möller's avatar
Niels Möller committed
237
238
239
240
241
  ecc_p,
  ecc_b,
  ecc_q,
  ecc_g,
  ecc_redc_g,
242
  NULL,
Niels Möller's avatar
Niels Möller committed
243
244
245
246
247
248
249
250
251
252
  ecc_Bmodp,
  ecc_Bmodp_shifted,
  ecc_pp1h,
  ecc_redc_ppm1,
  ecc_unit,
  ecc_Bmodq,
  ecc_Bmodq_shifted,
  ecc_qp1h,
  ecc_table
};