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
|
// Copyright 2021 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Code generated by addchain. DO NOT EDIT.
package fiat
// Invert sets e = 1/x, and returns e.
//
// If x == 0, Invert returns e = 0.
func (e *P384Element) Invert(x *P384Element) *P384Element {
// Inversion is implemented as exponentiation with exponent p − 2.
// The sequence of 15 multiplications and 383 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain v0.3.0.
//
// _10 = 2*1
// _11 = 1 + _10
// _110 = 2*_11
// _111 = 1 + _110
// _111000 = _111 << 3
// _111111 = _111 + _111000
// x12 = _111111 << 6 + _111111
// x24 = x12 << 12 + x12
// x30 = x24 << 6 + _111111
// x31 = 2*x30 + 1
// x32 = 2*x31 + 1
// x63 = x32 << 31 + x31
// x126 = x63 << 63 + x63
// x252 = x126 << 126 + x126
// x255 = x252 << 3 + _111
// i397 = ((x255 << 33 + x32) << 94 + x30) << 2
// return 1 + i397
//
var z = new(P384Element).Set(e)
var t0 = new(P384Element)
var t1 = new(P384Element)
var t2 = new(P384Element)
var t3 = new(P384Element)
z.Square(x)
z.Mul(x, z)
z.Square(z)
t1.Mul(x, z)
z.Square(t1)
for s := 1; s < 3; s++ {
z.Square(z)
}
z.Mul(t1, z)
t0.Square(z)
for s := 1; s < 6; s++ {
t0.Square(t0)
}
t0.Mul(z, t0)
t2.Square(t0)
for s := 1; s < 12; s++ {
t2.Square(t2)
}
t0.Mul(t0, t2)
for s := 0; s < 6; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
t0.Square(z)
t2.Mul(x, t0)
t0.Square(t2)
t0.Mul(x, t0)
t3.Square(t0)
for s := 1; s < 31; s++ {
t3.Square(t3)
}
t2.Mul(t2, t3)
t3.Square(t2)
for s := 1; s < 63; s++ {
t3.Square(t3)
}
t2.Mul(t2, t3)
t3.Square(t2)
for s := 1; s < 126; s++ {
t3.Square(t3)
}
t2.Mul(t2, t3)
for s := 0; s < 3; s++ {
t2.Square(t2)
}
t1.Mul(t1, t2)
for s := 0; s < 33; s++ {
t1.Square(t1)
}
t0.Mul(t0, t1)
for s := 0; s < 94; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
for s := 0; s < 2; s++ {
z.Square(z)
}
z.Mul(x, z)
return e.Set(z)
}
|
