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
|
using System;
using Org.BouncyCastle.Math.EC.Abc;
namespace Org.BouncyCastle.Math.EC.Multiplier
{
/**
* Class implementing the WTNAF (Window
* <code>τ</code>-adic Non-Adjacent Form) algorithm.
*/
public class WTauNafMultiplier
: AbstractECMultiplier
{
/**
* Multiplies a {@link org.bouncycastle.math.ec.F2mPoint F2mPoint}
* by <code>k</code> using the reduced <code>τ</code>-adic NAF (RTNAF)
* method.
* @param p The F2mPoint to multiply.
* @param k The integer by which to multiply <code>k</code>.
* @return <code>p</code> multiplied by <code>k</code>.
*/
protected override ECPoint MultiplyPositive(ECPoint point, BigInteger k)
{
if (!(point is F2mPoint))
throw new ArgumentException("Only F2mPoint can be used in WTauNafMultiplier");
F2mPoint p = (F2mPoint)point;
F2mCurve curve = (F2mCurve)p.Curve;
int m = curve.M;
sbyte a = (sbyte) curve.A.ToBigInteger().IntValue;
sbyte mu = curve.GetMu();
BigInteger[] s = curve.GetSi();
ZTauElement rho = Tnaf.PartModReduction(k, m, a, s, mu, (sbyte)10);
return MultiplyWTnaf(p, rho, curve.GetPreCompInfo(p), a, mu);
}
/**
* Multiplies a {@link org.bouncycastle.math.ec.F2mPoint F2mPoint}
* by an element <code>λ</code> of <code><b>Z</b>[τ]</code> using
* the <code>τ</code>-adic NAF (TNAF) method.
* @param p The F2mPoint to multiply.
* @param lambda The element <code>λ</code> of
* <code><b>Z</b>[τ]</code> of which to compute the
* <code>[τ]</code>-adic NAF.
* @return <code>p</code> multiplied by <code>λ</code>.
*/
private F2mPoint MultiplyWTnaf(F2mPoint p, ZTauElement lambda,
PreCompInfo preCompInfo, sbyte a, sbyte mu)
{
ZTauElement[] alpha = (a == 0) ? Tnaf.Alpha0 : Tnaf.Alpha1;
BigInteger tw = Tnaf.GetTw(mu, Tnaf.Width);
sbyte[]u = Tnaf.TauAdicWNaf(mu, lambda, Tnaf.Width,
BigInteger.ValueOf(Tnaf.Pow2Width), tw, alpha);
return MultiplyFromWTnaf(p, u, preCompInfo);
}
/**
* Multiplies a {@link org.bouncycastle.math.ec.F2mPoint F2mPoint}
* by an element <code>λ</code> of <code><b>Z</b>[τ]</code>
* using the window <code>τ</code>-adic NAF (TNAF) method, given the
* WTNAF of <code>λ</code>.
* @param p The F2mPoint to multiply.
* @param u The the WTNAF of <code>λ</code>..
* @return <code>λ * p</code>
*/
private static F2mPoint MultiplyFromWTnaf(F2mPoint p, sbyte[] u, PreCompInfo preCompInfo)
{
F2mCurve curve = (F2mCurve)p.Curve;
sbyte a = (sbyte)curve.A.ToBigInteger().IntValue;
F2mPoint[] pu;
if ((preCompInfo == null) || !(preCompInfo is WTauNafPreCompInfo))
{
pu = Tnaf.GetPreComp(p, a);
WTauNafPreCompInfo pre = new WTauNafPreCompInfo();
pre.PreComp = pu;
curve.SetPreCompInfo(p, pre);
}
else
{
pu = ((WTauNafPreCompInfo)preCompInfo).PreComp;
}
// q = infinity
F2mPoint q = (F2mPoint)curve.Infinity;
for (int i = u.Length - 1; i >= 0; i--)
{
q = Tnaf.Tau(q);
sbyte ui = u[i];
if (ui != 0)
{
if (ui > 0)
{
q = q.AddSimple(pu[ui]);
}
else
{
// u[i] < 0
q = q.SubtractSimple(pu[-ui]);
}
}
}
return q;
}
}
}
|
