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
|
using System;
using System.Diagnostics;
using Org.BouncyCastle.Math.Raw;
namespace Org.BouncyCastle.Math.EC.Custom.Sec
{
internal class SecT233Field
{
private const ulong M41 = ulong.MaxValue >> 23;
private const ulong M59 = ulong.MaxValue >> 5;
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];
zz[7] = xx[7] ^ yy[7];
}
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];
}
public static ulong[] FromBigInteger(BigInteger x)
{
ulong[] z = Nat256.FromBigInteger64(x);
Reduce23(z, 0);
return 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];
ulong x4 = xx[4], x5 = xx[5], x6 = xx[6], x7 = xx[7];
x3 ^= (x7 << 23);
x4 ^= (x7 >> 41) ^ (x7 << 33);
x5 ^= (x7 >> 31);
x2 ^= (x6 << 23);
x3 ^= (x6 >> 41) ^ (x6 << 33);
x4 ^= (x6 >> 31);
x1 ^= (x5 << 23);
x2 ^= (x5 >> 41) ^ (x5 << 33);
x3 ^= (x5 >> 31);
x0 ^= (x4 << 23);
x1 ^= (x4 >> 41) ^ (x4 << 33);
x2 ^= (x4 >> 31);
ulong t = x3 >> 41;
z[0] = x0 ^ t;
z[1] = x1 ^ (t << 10);
z[2] = x2;
z[3] = x3 & M41;
}
public static void Reduce23(ulong[] z, int zOff)
{
ulong z3 = z[zOff + 3], t = z3 >> 41;
z[zOff ] ^= t;
z[zOff + 1] ^= (t << 10);
z[zOff + 3] = z3 & M41;
}
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);
}
}
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 << 59);
zz[1] = (z1 >> 5) ^ (z2 << 54);
zz[2] = (z2 >> 10) ^ (z3 << 49);
zz[3] = (z3 >> 15) ^ (z4 << 44);
zz[4] = (z4 >> 20) ^ (z5 << 39);
zz[5] = (z5 >> 25) ^ (z6 << 34);
zz[6] = (z6 >> 30) ^ (z7 << 29);
zz[7] = (z7 >> 35);
}
protected static void ImplExpand(ulong[] x, ulong[] z)
{
ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
z[0] = x0 & M59;
z[1] = ((x0 >> 59) ^ (x1 << 5)) & M59;
z[2] = ((x1 >> 54) ^ (x2 << 10)) & M59;
z[3] = ((x2 >> 49) ^ (x3 << 15));
}
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 >> 59 == 0);
Debug.Assert(y >> 59 == 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 = 54;
do
{
j = (uint)(x >> k);
g = u[j & 7]
^ u[(j >> 3) & 7] << 3;
l ^= (g << k);
h ^= (g >> -k);
}
while ((k -= 6) > 0);
Debug.Assert(h >> 53 == 0);
z[zOff ] ^= l & M59;
z[zOff + 1] ^= (l >> 59) ^ (h << 5);
}
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);
ulong x3 = x[3];
zz[6] = Interleave.Expand32to64((uint)x3);
zz[7] = Interleave.Expand16to32((uint)(x3 >> 32));
}
}
}
|
