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
|
package org.bouncycastle.math.raw;
public abstract class Mont256
{
private static final long M = 0xFFFFFFFFL;
public static int inverse32(int x)
{
// assert (x & 1) == 1;
int z = x; // x.z == 1 mod 2**3
z *= 2 - x * z; // x.z == 1 mod 2**6
z *= 2 - x * z; // x.z == 1 mod 2**12
z *= 2 - x * z; // x.z == 1 mod 2**24
z *= 2 - x * z; // x.z == 1 mod 2**48
// assert x * z == 1;
return z;
}
public static void multAdd(int[] x, int[] y, int[] z, int[] m, int mInv32)
{
int z_8 = 0;
long y_0 = y[0] & M;
for (int i = 0; i < 8; ++i)
{
long z_0 = z[0] & M;
long x_i = x[i] & M;
long prod1 = x_i * y_0;
long carry = (prod1 & M) + z_0;
long t = ((int)carry * mInv32) & M;
long prod2 = t * (m[0] & M);
carry += (prod2 & M);
// assert (int)carry == 0;
carry = (carry >>> 32) + (prod1 >>> 32) + (prod2 >>> 32);
for (int j = 1; j < 8; ++j)
{
prod1 = x_i * (y[j] & M);
prod2 = t * (m[j] & M);
carry += (prod1 & M) + (prod2 & M) + (z[j] & M);
z[j - 1] = (int)carry;
carry = (carry >>> 32) + (prod1 >>> 32) + (prod2 >>> 32);
}
carry += (z_8 & M);
z[7] = (int)carry;
z_8 = (int)(carry >>> 32);
}
if (z_8 != 0 || Nat256.gte(z, m))
{
Nat256.sub(z, m, z);
}
}
public static void multAddXF(int[] x, int[] y, int[] z, int[] m)
{
// assert m[0] == M;
int z_8 = 0;
long y_0 = y[0] & M;
for (int i = 0; i < 8; ++i)
{
long x_i = x[i] & M;
long carry = x_i * y_0 + (z[0] & M);
long t = carry & M;
carry = (carry >>> 32) + t;
for (int j = 1; j < 8; ++j)
{
long prod1 = x_i * (y[j] & M);
long prod2 = t * (m[j] & M);
carry += (prod1 & M) + (prod2 & M) + (z[j] & M);
z[j - 1] = (int)carry;
carry = (carry >>> 32) + (prod1 >>> 32) + (prod2 >>> 32);
}
carry += (z_8 & M);
z[7] = (int)carry;
z_8 = (int)(carry >>> 32);
}
if (z_8 != 0 || Nat256.gte(z, m))
{
Nat256.sub(z, m, z);
}
}
public static void reduce(int[] z, int[] m, int mInv32)
{
for (int i = 0; i < 8; ++i)
{
int z_0 = z[0];
long t = (z_0 * mInv32) & M;
long carry = t * (m[0] & M) + (z_0 & M);
// assert (int)carry == 0;
carry >>>= 32;
for (int j = 1; j < 8; ++j)
{
carry += t * (m[j] & M) + (z[j] & M);
z[j - 1] = (int)carry;
carry >>>= 32;
}
z[7] = (int)carry;
// assert carry >>> 32 == 0;
}
if (Nat256.gte(z, m))
{
Nat256.sub(z, m, z);
}
}
public static void reduceXF(int[] z, int[] m)
{
// assert m[0] == M;
for (int i = 0; i < 8; ++i)
{
int z_0 = z[0];
long t = z_0 & M;
long carry = t;
for (int j = 1; j < 8; ++j)
{
carry += t * (m[j] & M) + (z[j] & M);
z[j - 1] = (int)carry;
carry >>>= 32;
}
z[7] = (int)carry;
// assert carry >>> 32 == 0;
}
if (Nat256.gte(z, m))
{
Nat256.sub(z, m, z);
}
}
}
|
