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
|
package org.spongycastle.math.ec.custom.sec;
import java.math.BigInteger;
import org.spongycastle.math.raw.Nat;
import org.spongycastle.math.raw.Nat512;
public class SecP521R1Field
{
// 2^521 - 1
static final int[] P = new int[]{ 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x1FF };
private static final int P16 = 0x1FF;
public static void add(int[] x, int[] y, int[] z)
{
int c = Nat.add(16, x, y, z) + x[16] + y[16];
if (c > P16 || (c == P16 && Nat.eq(16, z, P)))
{
c += Nat.inc(16, z);
c &= P16;
}
z[16] = c;
}
public static void addOne(int[] x, int[] z)
{
int c = Nat.inc(16, x, z) + x[16];
if (c > P16 || (c == P16 && Nat.eq(16, z, P)))
{
c += Nat.inc(16, z);
c &= P16;
}
z[16] = c;
}
public static int[] fromBigInteger(BigInteger x)
{
int[] z = Nat.fromBigInteger(521, x);
if (Nat.eq(17, z, P))
{
Nat.zero(17, z);
}
return z;
}
public static void half(int[] x, int[] z)
{
int x16 = x[16];
int c = Nat.shiftDownBit(16, x, x16, z);
z[16] = (x16 >>> 1) | (c >>> 23);
}
public static void multiply(int[] x, int[] y, int[] z)
{
int[] tt = Nat.create(33);
implMultiply(x, y, tt);
reduce(tt, z);
}
public static void negate(int[] x, int[] z)
{
if (Nat.isZero(17, x))
{
Nat.zero(17, z);
}
else
{
Nat.sub(17, P, x, z);
}
}
public static void reduce(int[] xx, int[] z)
{
// assert xx[32] >>> 18 == 0;
int xx32 = xx[32];
int c = Nat.shiftDownBits(16, xx, 16, 9, xx32, z, 0) >>> 23;
c += xx32 >>> 9;
c += Nat.addTo(16, xx, z);
if (c > P16 || (c == P16 && Nat.eq(16, z, P)))
{
c += Nat.inc(16, z);
c &= P16;
}
z[16] = c;
}
public static void reduce23(int[] z)
{
int z16 = z[16];
int c = Nat.addWordTo(16, z16 >>> 9, z) + (z16 & P16);
if (c > P16 || (c == P16 && Nat.eq(16, z, P)))
{
c += Nat.inc(16, z);
c &= P16;
}
z[16] = c;
}
public static void square(int[] x, int[] z)
{
int[] tt = Nat.create(33);
implSquare(x, tt);
reduce(tt, z);
}
public static void squareN(int[] x, int n, int[] z)
{
// assert n > 0;
int[] tt = Nat.create(33);
implSquare(x, tt);
reduce(tt, z);
while (--n > 0)
{
implSquare(z, tt);
reduce(tt, z);
}
}
public static void subtract(int[] x, int[] y, int[] z)
{
int c = Nat.sub(16, x, y, z) + x[16] - y[16];
if (c < 0)
{
c += Nat.dec(16, z);
c &= P16;
}
z[16] = c;
}
public static void twice(int[] x, int[] z)
{
int x16 = x[16];
int c = Nat.shiftUpBit(16, x, x16 << 23, z) | (x16 << 1);
z[16] = c & P16;
}
protected static void implMultiply(int[] x, int[] y, int[] zz)
{
Nat512.mul(x, y, zz);
int x16 = x[16], y16 = y[16];
zz[32] = Nat.mul31BothAdd(16, x16, y, y16, x, zz, 16) + (x16 * y16);
}
protected static void implSquare(int[] x, int[] zz)
{
Nat512.square(x, zz);
int x16 = x[16];
zz[32] = Nat.mulWordAddTo(16, x16 << 1, x, 0, zz, 16) + (x16 * x16);
}
}
|
