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
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
|
using System;
using Org.BouncyCastle.Math.Raw;
namespace Org.BouncyCastle.Math.EC.Custom.Sec
{
internal class SecP160R1Point
: AbstractFpPoint
{
internal SecP160R1Point(ECCurve curve, ECFieldElement x, ECFieldElement y)
: base(curve, x, y)
{
}
internal SecP160R1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs)
: base(curve, x, y, zs)
{
}
protected override ECPoint Detach()
{
return new SecP160R1Point(null, AffineXCoord, AffineYCoord);
}
public override ECPoint Add(ECPoint b)
{
if (this.IsInfinity)
return b;
if (b.IsInfinity)
return this;
if (this == b)
return Twice();
ECCurve curve = this.Curve;
SecP160R1FieldElement X1 = (SecP160R1FieldElement)this.RawXCoord, Y1 = (SecP160R1FieldElement)this.RawYCoord;
SecP160R1FieldElement X2 = (SecP160R1FieldElement)b.RawXCoord, Y2 = (SecP160R1FieldElement)b.RawYCoord;
SecP160R1FieldElement Z1 = (SecP160R1FieldElement)this.RawZCoords[0];
SecP160R1FieldElement Z2 = (SecP160R1FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat160.CreateExt();
uint[] t2 = Nat160.Create();
uint[] t3 = Nat160.Create();
uint[] t4 = Nat160.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
SecP160R1Field.Square(Z1.x, S2);
U2 = t2;
SecP160R1Field.Multiply(S2, X2.x, U2);
SecP160R1Field.Multiply(S2, Z1.x, S2);
SecP160R1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP160R1Field.Square(Z2.x, S1);
U1 = tt1;
SecP160R1Field.Multiply(S1, X1.x, U1);
SecP160R1Field.Multiply(S1, Z2.x, S1);
SecP160R1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat160.Create();
SecP160R1Field.Subtract(U1, U2, H);
uint[] R = t2;
SecP160R1Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat160.IsZero(H))
{
if (Nat160.IsZero(R))
{
// this == b, i.e. this must be doubled
return this.Twice();
}
// this == -b, i.e. the result is the point at infinity
return curve.Infinity;
}
uint[] HSquared = t3;
SecP160R1Field.Square(H, HSquared);
uint[] G = Nat160.Create();
SecP160R1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP160R1Field.Multiply(HSquared, U1, V);
SecP160R1Field.Negate(G, G);
Nat160.Mul(S1, G, tt1);
c = Nat160.AddBothTo(V, V, G);
SecP160R1Field.Reduce32(c, G);
SecP160R1FieldElement X3 = new SecP160R1FieldElement(t4);
SecP160R1Field.Square(R, X3.x);
SecP160R1Field.Subtract(X3.x, G, X3.x);
SecP160R1FieldElement Y3 = new SecP160R1FieldElement(G);
SecP160R1Field.Subtract(V, X3.x, Y3.x);
SecP160R1Field.MultiplyAddToExt(Y3.x, R, tt1);
SecP160R1Field.Reduce(tt1, Y3.x);
SecP160R1FieldElement Z3 = new SecP160R1FieldElement(H);
if (!Z1IsOne)
{
SecP160R1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP160R1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[]{ Z3 };
return new SecP160R1Point(curve, X3, Y3, zs);
}
public override ECPoint Twice()
{
if (this.IsInfinity)
return this;
ECCurve curve = this.Curve;
SecP160R1FieldElement Y1 = (SecP160R1FieldElement)this.RawYCoord;
if (Y1.IsZero)
return curve.Infinity;
SecP160R1FieldElement X1 = (SecP160R1FieldElement)this.RawXCoord, Z1 = (SecP160R1FieldElement)this.RawZCoords[0];
uint c;
uint[] t1 = Nat160.Create();
uint[] t2 = Nat160.Create();
uint[] Y1Squared = Nat160.Create();
SecP160R1Field.Square(Y1.x, Y1Squared);
uint[] T = Nat160.Create();
SecP160R1Field.Square(Y1Squared, T);
bool Z1IsOne = Z1.IsOne;
uint[] Z1Squared = Z1.x;
if (!Z1IsOne)
{
Z1Squared = t2;
SecP160R1Field.Square(Z1.x, Z1Squared);
}
SecP160R1Field.Subtract(X1.x, Z1Squared, t1);
uint[] M = t2;
SecP160R1Field.Add(X1.x, Z1Squared, M);
SecP160R1Field.Multiply(M, t1, M);
c = Nat160.AddBothTo(M, M, M);
SecP160R1Field.Reduce32(c, M);
uint[] S = Y1Squared;
SecP160R1Field.Multiply(Y1Squared, X1.x, S);
c = Nat.ShiftUpBits(5, S, 2, 0);
SecP160R1Field.Reduce32(c, S);
c = Nat.ShiftUpBits(5, T, 3, 0, t1);
SecP160R1Field.Reduce32(c, t1);
SecP160R1FieldElement X3 = new SecP160R1FieldElement(T);
SecP160R1Field.Square(M, X3.x);
SecP160R1Field.Subtract(X3.x, S, X3.x);
SecP160R1Field.Subtract(X3.x, S, X3.x);
SecP160R1FieldElement Y3 = new SecP160R1FieldElement(S);
SecP160R1Field.Subtract(S, X3.x, Y3.x);
SecP160R1Field.Multiply(Y3.x, M, Y3.x);
SecP160R1Field.Subtract(Y3.x, t1, Y3.x);
SecP160R1FieldElement Z3 = new SecP160R1FieldElement(M);
SecP160R1Field.Twice(Y1.x, Z3.x);
if (!Z1IsOne)
{
SecP160R1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
return new SecP160R1Point(curve, X3, Y3, new ECFieldElement[]{ Z3 });
}
public override ECPoint TwicePlus(ECPoint b)
{
if (this == b)
return ThreeTimes();
if (this.IsInfinity)
return b;
if (b.IsInfinity)
return Twice();
ECFieldElement Y1 = this.RawYCoord;
if (Y1.IsZero)
return b;
return Twice().Add(b);
}
public override ECPoint ThreeTimes()
{
if (this.IsInfinity || this.RawYCoord.IsZero)
return this;
// NOTE: Be careful about recursions between TwicePlus and ThreeTimes
return Twice().Add(this);
}
public override ECPoint Negate()
{
if (IsInfinity)
return this;
return new SecP160R1Point(Curve, RawXCoord, RawYCoord.Negate(), RawZCoords);
}
}
}
|
