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
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
|
using System;
using System.Diagnostics;
using Org.BouncyCastle.Math.Raw;
namespace Org.BouncyCastle.Math.EC.Custom.Sec
{
internal class SecT193Field
{
private const ulong M01 = 1UL;
private const ulong M49 = ulong.MaxValue >> 15;
public static void Add(ulong[] x, ulong[] y, ulong[] z)
{
z[0] = x[0] ^ y[0];
z[1] = x[1] ^ y[1];
z[2] = x[2] ^ y[2];
z[3] = x[3] ^ y[3];
}
public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
{
zz[0] = xx[0] ^ yy[0];
zz[1] = xx[1] ^ yy[1];
zz[2] = xx[2] ^ yy[2];
zz[3] = xx[3] ^ yy[3];
zz[4] = xx[4] ^ yy[4];
zz[5] = xx[5] ^ yy[5];
zz[6] = xx[6] ^ yy[6];
}
public static void AddOne(ulong[] x, ulong[] z)
{
z[0] = x[0] ^ 1UL;
z[1] = x[1];
z[2] = x[2];
z[3] = x[3];
}
private static void AddTo(ulong[] x, ulong[] z)
{
z[0] ^= x[0];
z[1] ^= x[1];
z[2] ^= x[2];
z[3] ^= x[3];
}
public static ulong[] FromBigInteger(BigInteger x)
{
return Nat.FromBigInteger64(193, x);
}
public static void HalfTrace(ulong[] x, ulong[] z)
{
ulong[] tt = Nat256.CreateExt64();
Nat256.Copy64(x, z);
for (int i = 1; i < 193; i += 2)
{
ImplSquare(z, tt);
Reduce(tt, z);
ImplSquare(z, tt);
Reduce(tt, z);
AddTo(x, z);
}
}
public static void Invert(ulong[] x, ulong[] z)
{
if (Nat256.IsZero64(x))
throw new InvalidOperationException();
// Itoh-Tsujii inversion with bases { 2, 3 }
ulong[] t0 = Nat256.Create64();
ulong[] t1 = Nat256.Create64();
Square(x, t0);
// 3 | 192
SquareN(t0, 1, t1);
Multiply(t0, t1, t0);
SquareN(t1, 1, t1);
Multiply(t0, t1, t0);
// 2 | 64
SquareN(t0, 3, t1);
Multiply(t0, t1, t0);
// 2 | 32
SquareN(t0, 6, t1);
Multiply(t0, t1, t0);
// 2 | 16
SquareN(t0, 12, t1);
Multiply(t0, t1, t0);
// 2 | 8
SquareN(t0, 24, t1);
Multiply(t0, t1, t0);
// 2 | 4
SquareN(t0, 48, t1);
Multiply(t0, t1, t0);
// 2 | 2
SquareN(t0, 96, t1);
Multiply(t0, t1, z);
}
public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
{
ulong[] tt = Nat256.CreateExt64();
ImplMultiply(x, y, tt);
Reduce(tt, z);
}
public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
{
ulong[] tt = Nat256.CreateExt64();
ImplMultiply(x, y, tt);
AddExt(zz, tt, zz);
}
public static void Reduce(ulong[] xx, ulong[] z)
{
ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4], x5 = xx[5], x6 = xx[6];
x2 ^= (x6 << 63);
x3 ^= (x6 >> 1) ^ (x6 << 14);
x4 ^= (x6 >> 50);
x1 ^= (x5 << 63);
x2 ^= (x5 >> 1) ^ (x5 << 14);
x3 ^= (x5 >> 50);
x0 ^= (x4 << 63);
x1 ^= (x4 >> 1) ^ (x4 << 14);
x2 ^= (x4 >> 50);
ulong t = x3 >> 1;
z[0] = x0 ^ t ^ (t << 15);
z[1] = x1 ^ (t >> 49);
z[2] = x2;
z[3] = x3 & M01;
}
public static void Reduce63(ulong[] z, int zOff)
{
ulong z3 = z[zOff + 3], t = z3 >> 1;
z[zOff ] ^= t ^ (t << 15);
z[zOff + 1] ^= (t >> 49);
z[zOff + 3] = z3 & M01;
}
public static void Sqrt(ulong[] x, ulong[] z)
{
ulong u0, u1;
u0 = Interleave.Unshuffle(x[0]); u1 = Interleave.Unshuffle(x[1]);
ulong e0 = (u0 & 0x00000000FFFFFFFFUL) | (u1 << 32);
ulong c0 = (u0 >> 32) | (u1 & 0xFFFFFFFF00000000UL);
u0 = Interleave.Unshuffle(x[2]);
ulong e1 = (u0 & 0x00000000FFFFFFFFUL) ^ (x[3] << 32);
ulong c1 = (u0 >> 32);
z[0] = e0 ^ (c0 << 8);
z[1] = e1 ^ (c1 << 8) ^ (c0 >> 56) ^ (c0 << 33);
z[2] = (c1 >> 56) ^ (c1 << 33) ^ (c0 >> 31);
z[3] = (c1 >> 31);
}
public static void Square(ulong[] x, ulong[] z)
{
ulong[] tt = Nat256.CreateExt64();
ImplSquare(x, tt);
Reduce(tt, z);
}
public static void SquareAddToExt(ulong[] x, ulong[] zz)
{
ulong[] tt = Nat256.CreateExt64();
ImplSquare(x, tt);
AddExt(zz, tt, zz);
}
public static void SquareN(ulong[] x, int n, ulong[] z)
{
Debug.Assert(n > 0);
ulong[] tt = Nat256.CreateExt64();
ImplSquare(x, tt);
Reduce(tt, z);
while (--n > 0)
{
ImplSquare(z, tt);
Reduce(tt, z);
}
}
public static uint Trace(ulong[] x)
{
// Non-zero-trace bits: 0
return (uint)(x[0]) & 1U;
}
protected static void ImplCompactExt(ulong[] zz)
{
ulong z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4], z5 = zz[5], z6 = zz[6], z7 = zz[7];
zz[0] = z0 ^ (z1 << 49);
zz[1] = (z1 >> 15) ^ (z2 << 34);
zz[2] = (z2 >> 30) ^ (z3 << 19);
zz[3] = (z3 >> 45) ^ (z4 << 4)
^ (z5 << 53);
zz[4] = (z4 >> 60) ^ (z6 << 38)
^ (z5 >> 11);
zz[5] = (z6 >> 26) ^ (z7 << 23);
zz[6] = (z7 >> 41);
zz[7] = 0;
}
protected static void ImplExpand(ulong[] x, ulong[] z)
{
ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
z[0] = x0 & M49;
z[1] = ((x0 >> 49) ^ (x1 << 15)) & M49;
z[2] = ((x1 >> 34) ^ (x2 << 30)) & M49;
z[3] = ((x2 >> 19) ^ (x3 << 45));
}
protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
{
/*
* "Two-level seven-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
*/
ulong[] f = new ulong[4], g = new ulong[4];
ImplExpand(x, f);
ImplExpand(y, g);
ImplMulwAcc(f[0], g[0], zz, 0);
ImplMulwAcc(f[1], g[1], zz, 1);
ImplMulwAcc(f[2], g[2], zz, 2);
ImplMulwAcc(f[3], g[3], zz, 3);
// U *= (1 - t^n)
for (int i = 5; i > 0; --i)
{
zz[i] ^= zz[i - 1];
}
ImplMulwAcc(f[0] ^ f[1], g[0] ^ g[1], zz, 1);
ImplMulwAcc(f[2] ^ f[3], g[2] ^ g[3], zz, 3);
// V *= (1 - t^2n)
for (int i = 7; i > 1; --i)
{
zz[i] ^= zz[i - 2];
}
// Double-length recursion
{
ulong c0 = f[0] ^ f[2], c1 = f[1] ^ f[3];
ulong d0 = g[0] ^ g[2], d1 = g[1] ^ g[3];
ImplMulwAcc(c0 ^ c1, d0 ^ d1, zz, 3);
ulong[] t = new ulong[3];
ImplMulwAcc(c0, d0, t, 0);
ImplMulwAcc(c1, d1, t, 1);
ulong t0 = t[0], t1 = t[1], t2 = t[2];
zz[2] ^= t0;
zz[3] ^= t0 ^ t1;
zz[4] ^= t2 ^ t1;
zz[5] ^= t2;
}
ImplCompactExt(zz);
}
protected static void ImplMulwAcc(ulong x, ulong y, ulong[] z, int zOff)
{
Debug.Assert(x >> 49 == 0);
Debug.Assert(y >> 49 == 0);
ulong[] u = new ulong[8];
//u[0] = 0;
u[1] = y;
u[2] = u[1] << 1;
u[3] = u[2] ^ y;
u[4] = u[2] << 1;
u[5] = u[4] ^ y;
u[6] = u[3] << 1;
u[7] = u[6] ^ y;
uint j = (uint)x;
ulong g, h = 0, l = u[j & 7]
^ (u[(j >> 3) & 7] << 3);
int k = 36;
do
{
j = (uint)(x >> k);
g = u[j & 7]
^ u[(j >> 3) & 7] << 3
^ u[(j >> 6) & 7] << 6
^ u[(j >> 9) & 7] << 9
^ u[(j >> 12) & 7] << 12;
l ^= (g << k);
h ^= (g >> -k);
}
while ((k -= 15) > 0);
Debug.Assert(h >> 33 == 0);
z[zOff ] ^= l & M49;
z[zOff + 1] ^= (l >> 49) ^ (h << 15);
}
protected static void ImplSquare(ulong[] x, ulong[] zz)
{
Interleave.Expand64To128(x[0], zz, 0);
Interleave.Expand64To128(x[1], zz, 2);
Interleave.Expand64To128(x[2], zz, 4);
zz[6] = (x[3] & M01);
}
}
}
|
