-
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
package curve25519
import (
"crypto/elliptic"
"math/big"
"sync"
)
var cv25519 cv25519Curve
type cv25519Curve struct {
*elliptic.CurveParams
}
func copyReverse(dst []byte, src []byte) {
// Curve 25519 multiplication functions expect scalars in reverse
// order than PGP. To keep the curve25519Curve type consistent
// with other curves, we reverse it here.
for i, j := 0, len(src)-1; j >= 0 && i < len(dst); i, j = i+1, j-1 {
dst[i] = src[j]
}
}
func copyTruncate(dst []byte, src []byte) {
lenDst, lenSrc := len(dst), len(src)
if lenDst == lenSrc {
copy(dst, src)
} else if lenDst > lenSrc {
copy(dst[lenDst-lenSrc:lenDst], src)
} else if lenDst < lenSrc {
copy(dst, src[:lenDst])
}
}
func (cv25519Curve) ScalarMult(x1, y1 *big.Int, scalar []byte) (x, y *big.Int) {
// Assume y1 is 0 with cv25519.
var dst [32]byte
var x1Bytes [32]byte
var scalarBytes [32]byte
copyTruncate(x1Bytes[:], x1.Bytes())
copyReverse(scalarBytes[:], scalar)
scalarMult(&dst, &scalarBytes, &x1Bytes)
x = new(big.Int).SetBytes(dst[:])
y = new(big.Int)
return x, y
}
func (cv25519Curve) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
var dst [32]byte
var scalarBytes [32]byte
copyReverse(scalarBytes[:], scalar[:32])
scalarMult(&dst, &scalarBytes, &basePoint)
x = new(big.Int).SetBytes(dst[:])
y = new(big.Int)
return x, y
}
func (cv25519Curve) IsOnCurve(bigX, bigY *big.Int) bool {
return bigY.Sign() == 0 // bigY == 0 ?
}
// More information about 0x40 point format:
// https://tools.ietf.org/html/draft-koch-eddsa-for-openpgp-00#section-3
// In addition to uncompressed point format described here:
// https://tools.ietf.org/html/rfc6637#section-6
func (cv25519Curve) MarshalType40(x, y *big.Int) []byte {
byteLen := 32
ret := make([]byte, 1+byteLen)
ret[0] = 0x40
xBytes := x.Bytes()
copyTruncate(ret[1:], xBytes)
return ret
}
func (cv25519Curve) UnmarshalType40(data []byte) (x, y *big.Int) {
if len(data) != 1+32 {
return nil, nil
}
if data[0] != 0x40 {
return nil, nil
}
x = new(big.Int).SetBytes(data[1:])
// Any x is a valid curve point.
return x, new(big.Int)
}
// ToCurve25519 casts given elliptic.Curve type to Curve25519 type, or
// returns nil, false if cast was unsuccessful.
func ToCurve25519(cv elliptic.Curve) (cv25519Curve, bool) {
cv2, ok := cv.(cv25519Curve)
return cv2, ok
}
func initCv25519() {
cv25519.CurveParams = &elliptic.CurveParams{Name: "Curve 25519"}
// Some code relies on these parameters being available for
// checking Curve coordinate length. They should not be used
// directly for any calculations.
cv25519.P, _ = new(big.Int).SetString("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed", 16)
cv25519.N, _ = new(big.Int).SetString("1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed", 16)
cv25519.Gx, _ = new(big.Int).SetString("9", 16)
cv25519.Gy, _ = new(big.Int).SetString("20ae19a1b8a086b4e01edd2c7748d14c923d4d7e6d7c61b229e9c5a27eced3d9", 16)
cv25519.BitSize = 256
}
var initonce sync.Once
// Cv25519 returns a Curve which (partially) implements Cv25519. Only
// ScalarMult and ScalarBaseMult are valid for this curve. Add and
// Double should not be used.
func Cv25519() elliptic.Curve {
initonce.Do(initCv25519)
return cv25519
}
func (curve cv25519Curve) Params() *elliptic.CurveParams {
return curve.CurveParams
}