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
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
|
using System;
using Org.BouncyCastle.Math.Raw;
namespace Org.BouncyCastle.Math.EC.Custom.Sec
{
internal class SecT163K1Point
: AbstractF2mPoint
{
internal SecT163K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y)
: base(curve, x, y)
{
}
internal SecT163K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs)
: base(curve, x, y, zs)
{
}
protected override ECPoint Detach()
{
return new SecT163K1Point(null, this.AffineXCoord, this.AffineYCoord);
}
public override ECFieldElement YCoord
{
get
{
ECFieldElement X = RawXCoord, L = RawYCoord;
if (this.IsInfinity || X.IsZero)
return L;
// Y is actually Lambda (X + Y/X) here; convert to affine value on the fly
ECFieldElement Y = L.Add(X).Multiply(X);
ECFieldElement Z = RawZCoords[0];
if (!Z.IsOne)
{
Y = Y.Divide(Z);
}
return Y;
}
}
protected internal override bool CompressionYTilde
{
get
{
ECFieldElement X = this.RawXCoord;
if (X.IsZero)
return false;
ECFieldElement Y = this.RawYCoord;
// Y is actually Lambda (X + Y/X) here
return Y.TestBitZero() != X.TestBitZero();
}
}
public override ECPoint Add(ECPoint b)
{
if (this.IsInfinity)
return b;
if (b.IsInfinity)
return this;
ECCurve curve = this.Curve;
SecT163FieldElement X1 = (SecT163FieldElement)this.RawXCoord;
SecT163FieldElement X2 = (SecT163FieldElement)b.RawXCoord;
if (X1.IsZero)
{
if (X2.IsZero)
return curve.Infinity;
return b.Add(this);
}
SecT163FieldElement L1 = (SecT163FieldElement)this.RawYCoord, Z1 = (SecT163FieldElement)this.RawZCoords[0];
SecT163FieldElement L2 = (SecT163FieldElement)b.RawYCoord, Z2 = (SecT163FieldElement)b.RawZCoords[0];
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt0 = stackalloc ulong[6];
#else
ulong[] tt0 = Nat192.CreateExt64();
#endif
ulong[] t1 = Nat192.Create64();
ulong[] t2 = Nat192.Create64();
ulong[] t3 = Nat192.Create64();
bool Z1IsOne = Z1.IsOne;
if (Z1IsOne)
{
Nat192.Copy64(X2.x, t1); // U2
Nat192.Copy64(L2.x, t2); // S2
}
else
{
SecT163Field.Multiply(X2.x, Z1.x, t1); // U2
SecT163Field.Multiply(L2.x, Z1.x, t2); // S2
}
bool Z2IsOne = Z2.IsOne;
if (Z2IsOne)
{
Nat192.Copy64(X1.x, t3); // U1
Nat192.Copy64(L1.x, tt0); // S1
}
else
{
SecT163Field.Multiply(X1.x, Z2.x, t3); // U1
SecT163Field.Multiply(L1.x, Z2.x, tt0); // S1
}
SecT163Field.AddTo(tt0, t2); // A
SecT163Field.Add(t3, t1, tt0); // B
if (Nat192.IsZero64(tt0))
{
if (Nat192.IsZero64(t2))
return Twice();
return curve.Infinity;
}
if (X2.IsZero)
{
// TODO This can probably be optimized quite a bit
ECPoint p = this.Normalize();
X1 = (SecT163FieldElement)p.XCoord;
ECFieldElement Y1 = p.YCoord;
ECFieldElement Y2 = L2;
ECFieldElement L = Y1.Add(Y2).Divide(X1);
ECFieldElement X3 = L.Square().Add(L).Add(X1);
if (X3.IsZero)
return new SecT163K1Point(curve, X3, curve.B);
ECFieldElement Y3 = L.Multiply(X1.Add(X3)).Add(X3).Add(Y1);
ECFieldElement L3 = Y3.Divide(X3).Add(X3);
ECFieldElement Z3 = curve.FromBigInteger(BigInteger.One);
return new SecT163K1Point(curve, X3, L3, new ECFieldElement[]{ Z3 });
}
SecT163Field.Square(tt0, tt0);
SecT163Field.Multiply(t3, t2, t3); // AU1
SecT163Field.Multiply(t1, t2, t1); // AU2
ulong[] _X3 = t3;
SecT163Field.Multiply(_X3, t1, _X3);
if (Nat192.IsZero64(_X3))
return new SecT163K1Point(curve, new SecT163FieldElement(_X3), curve.B);
ulong[] _Z3 = t2;
SecT163Field.Multiply(_Z3, tt0, _Z3); // ABZ2
if (!Z2IsOne)
{
SecT163Field.Multiply(_Z3, Z2.x, _Z3);
}
ulong[] _L3 = t1;
SecT163Field.AddTo(tt0, _L3);
SecT163Field.SquareExt(_L3, tt0);
SecT163Field.Add(L1.x, Z1.x, _L3);
SecT163Field.MultiplyAddToExt(_Z3, _L3, tt0);
SecT163Field.Reduce(tt0, _L3);
if (!Z1IsOne)
{
SecT163Field.Multiply(_Z3, Z1.x, _Z3);
}
return new SecT163K1Point(curve, new SecT163FieldElement(_X3), new SecT163FieldElement(_L3),
new ECFieldElement[]{ new SecT163FieldElement(_Z3) });
}
public override ECPoint Twice()
{
if (this.IsInfinity)
{
return this;
}
ECCurve curve = this.Curve;
ECFieldElement X1 = this.RawXCoord;
if (X1.IsZero)
{
// A point with X == 0 is its own additive inverse
return curve.Infinity;
}
ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0];
bool Z1IsOne = Z1.IsOne;
ECFieldElement L1Z1 = Z1IsOne ? L1 : L1.Multiply(Z1);
ECFieldElement Z1Sq = Z1IsOne ? Z1 : Z1.Square();
ECFieldElement T = L1.Square().Add(L1Z1).Add(Z1Sq);
if (T.IsZero)
{
return new SecT163K1Point(curve, T, curve.B);
}
ECFieldElement X3 = T.Square();
ECFieldElement Z3 = Z1IsOne ? T : T.Multiply(Z1Sq);
ECFieldElement t1 = L1.Add(X1).Square();
ECFieldElement L3 = t1.Add(T).Add(Z1Sq).Multiply(t1).Add(X3);
return new SecT163K1Point(curve, X3, L3, new ECFieldElement[] { Z3 });
}
public override ECPoint TwicePlus(ECPoint b)
{
if (this.IsInfinity)
return b;
if (b.IsInfinity)
return Twice();
ECCurve curve = this.Curve;
ECFieldElement X1 = this.RawXCoord;
if (X1.IsZero)
{
// A point with X == 0 is its own additive inverse
return b;
}
// NOTE: TwicePlus() only optimized for lambda-affine argument
ECFieldElement X2 = b.RawXCoord, Z2 = b.RawZCoords[0];
if (X2.IsZero || !Z2.IsOne)
{
return Twice().Add(b);
}
ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0];
ECFieldElement L2 = b.RawYCoord;
ECFieldElement X1Sq = X1.Square();
ECFieldElement L1Sq = L1.Square();
ECFieldElement Z1Sq = Z1.Square();
ECFieldElement L1Z1 = L1.Multiply(Z1);
ECFieldElement T = Z1Sq.Add(L1Sq).Add(L1Z1);
ECFieldElement A = L2.Multiply(Z1Sq).Add(L1Sq).MultiplyPlusProduct(T, X1Sq, Z1Sq);
ECFieldElement X2Z1Sq = X2.Multiply(Z1Sq);
ECFieldElement B = X2Z1Sq.Add(T).Square();
if (B.IsZero)
{
if (A.IsZero)
return b.Twice();
return curve.Infinity;
}
if (A.IsZero)
{
return new SecT163K1Point(curve, A, curve.B);
}
ECFieldElement X3 = A.Square().Multiply(X2Z1Sq);
ECFieldElement Z3 = A.Multiply(B).Multiply(Z1Sq);
ECFieldElement L3 = A.Add(B).Square().MultiplyPlusProduct(T, L2.AddOne(), Z3);
return new SecT163K1Point(curve, X3, L3, new ECFieldElement[] { Z3 });
}
public override ECPoint Negate()
{
if (this.IsInfinity)
return this;
ECFieldElement X = this.RawXCoord;
if (X.IsZero)
return this;
// L is actually Lambda (X + Y/X) here
ECFieldElement L = this.RawYCoord, Z = this.RawZCoords[0];
return new SecT163K1Point(Curve, X, L.Add(Z), new ECFieldElement[] { Z });
}
}
}
|
