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using System;
using Org.BouncyCastle.Math.Raw;
namespace Org.BouncyCastle.Math.EC.Custom.Sec
{
internal class SecT571R1Point
: AbstractF2mPoint
{
internal SecT571R1Point(ECCurve curve, ECFieldElement x, ECFieldElement y)
: base(curve, x, y)
{
}
internal SecT571R1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs)
: base(curve, x, y, zs)
{
}
protected override ECPoint Detach()
{
return new SecT571R1Point(null, AffineXCoord, 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;
SecT571FieldElement X1 = (SecT571FieldElement)this.RawXCoord;
SecT571FieldElement X2 = (SecT571FieldElement)b.RawXCoord;
if (X1.IsZero)
{
if (X2.IsZero)
return curve.Infinity;
return b.Add(this);
}
SecT571FieldElement L1 = (SecT571FieldElement)this.RawYCoord, Z1 = (SecT571FieldElement)this.RawZCoords[0];
SecT571FieldElement L2 = (SecT571FieldElement)b.RawYCoord, Z2 = (SecT571FieldElement)b.RawZCoords[0];
ulong[] t1 = Nat576.Create64();
ulong[] t2 = Nat576.Create64();
ulong[] t3 = Nat576.Create64();
ulong[] t4 = Nat576.Create64();
ulong[] Z1Precomp = Z1.IsOne ? null : SecT571Field.PrecompMultiplicand(Z1.x);
ulong[] U2, S2;
if (Z1Precomp == null)
{
U2 = X2.x;
S2 = L2.x;
}
else
{
SecT571Field.MultiplyPrecomp(X2.x, Z1Precomp, U2 = t2);
SecT571Field.MultiplyPrecomp(L2.x, Z1Precomp, S2 = t4);
}
ulong[] Z2Precomp = Z2.IsOne ? null : SecT571Field.PrecompMultiplicand(Z2.x);
ulong[] U1, S1;
if (Z2Precomp == null)
{
U1 = X1.x;
S1 = L1.x;
}
else
{
SecT571Field.MultiplyPrecomp(X1.x, Z2Precomp, U1 = t1);
SecT571Field.MultiplyPrecomp(L1.x, Z2Precomp, S1 = t3);
}
ulong[] A = t3;
SecT571Field.Add(S1, S2, A);
ulong[] B = t4;
SecT571Field.Add(U1, U2, B);
if (Nat576.IsZero64(B))
{
if (Nat576.IsZero64(A))
return Twice();
return curve.Infinity;
}
SecT571FieldElement X3, L3, Z3;
if (X2.IsZero)
{
// TODO This can probably be optimized quite a bit
ECPoint p = this.Normalize();
X1 = (SecT571FieldElement)p.XCoord;
ECFieldElement Y1 = p.YCoord;
ECFieldElement Y2 = L2;
ECFieldElement L = Y1.Add(Y2).Divide(X1);
X3 = (SecT571FieldElement)L.Square().Add(L).Add(X1).AddOne();
if (X3.IsZero)
{
return new SecT571R1Point(curve, X3, SecT571R1Curve.SecT571R1_B_SQRT);
}
ECFieldElement Y3 = L.Multiply(X1.Add(X3)).Add(X3).Add(Y1);
L3 = (SecT571FieldElement)Y3.Divide(X3).Add(X3);
Z3 = (SecT571FieldElement)curve.FromBigInteger(BigInteger.One);
}
else
{
SecT571Field.Square(B, B);
ulong[] APrecomp = SecT571Field.PrecompMultiplicand(A);
ulong[] AU1 = t1;
ulong[] AU2 = t2;
SecT571Field.MultiplyPrecomp(U1, APrecomp, AU1);
SecT571Field.MultiplyPrecomp(U2, APrecomp, AU2);
X3 = new SecT571FieldElement(t1);
SecT571Field.Multiply(AU1, AU2, X3.x);
if (X3.IsZero)
{
return new SecT571R1Point(curve, X3, SecT571R1Curve.SecT571R1_B_SQRT);
}
Z3 = new SecT571FieldElement(t3);
SecT571Field.MultiplyPrecomp(B, APrecomp, Z3.x);
if (Z2Precomp != null)
{
SecT571Field.MultiplyPrecomp(Z3.x, Z2Precomp, Z3.x);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt = stackalloc ulong[18];
#else
ulong[] tt = Nat576.CreateExt64();
#endif
SecT571Field.Add(AU2, B, t4);
SecT571Field.SquareExt(t4, tt);
SecT571Field.Add(L1.x, Z1.x, t4);
SecT571Field.MultiplyAddToExt(t4, Z3.x, tt);
L3 = new SecT571FieldElement(t4);
SecT571Field.Reduce(tt, L3.x);
if (Z1Precomp != null)
{
SecT571Field.MultiplyPrecomp(Z3.x, Z1Precomp, Z3.x);
}
}
return new SecT571R1Point(curve, X3, L3, new ECFieldElement[] { Z3 });
}
public override ECPoint Twice()
{
if (this.IsInfinity)
return this;
ECCurve curve = this.Curve;
SecT571FieldElement X1 = (SecT571FieldElement)this.RawXCoord;
if (X1.IsZero)
{
// A point with X == 0 is its own additive inverse
return curve.Infinity;
}
SecT571FieldElement L1 = (SecT571FieldElement)this.RawYCoord, Z1 = (SecT571FieldElement)this.RawZCoords[0];
ulong[] t1 = Nat576.Create64();
ulong[] t2 = Nat576.Create64();
ulong[] Z1Precomp = Z1.IsOne ? null : SecT571Field.PrecompMultiplicand(Z1.x);
ulong[] L1Z1, Z1Sq;
if (Z1Precomp == null)
{
L1Z1 = L1.x;
Z1Sq = Z1.x;
}
else
{
SecT571Field.MultiplyPrecomp(L1.x, Z1Precomp, L1Z1 = t1);
SecT571Field.Square(Z1.x, Z1Sq = t2);
}
ulong[] T = Nat576.Create64();
SecT571Field.Square(L1.x, T);
SecT571Field.AddBothTo(L1Z1, Z1Sq, T);
if (Nat576.IsZero64(T))
{
return new SecT571R1Point(curve, new SecT571FieldElement(T), SecT571R1Curve.SecT571R1_B_SQRT);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt = stackalloc ulong[18];
#else
ulong[] tt = Nat576.CreateExt64();
#endif
SecT571Field.MultiplyAddToExt(T, L1Z1, tt);
SecT571FieldElement X3 = new SecT571FieldElement(t1);
SecT571Field.Square(T, X3.x);
SecT571FieldElement Z3 = new SecT571FieldElement(T);
if (Z1Precomp != null)
{
SecT571Field.Multiply(Z3.x, Z1Sq, Z3.x);
}
ulong[] X1Z1;
if (Z1Precomp == null)
{
X1Z1 = X1.x;
}
else
{
SecT571Field.MultiplyPrecomp(X1.x, Z1Precomp, X1Z1 = t2);
}
SecT571Field.SquareAddToExt(X1Z1, tt);
SecT571Field.Reduce(tt, t2);
SecT571Field.AddBothTo(X3.x, Z3.x, t2);
SecT571FieldElement L3 = new SecT571FieldElement(t2);
return new SecT571R1Point(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;
}
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 SecT571R1Point(curve, A, SecT571R1Curve.SecT571R1_B_SQRT);
}
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 SecT571R1Point(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 SecT571R1Point(Curve, X, L.Add(Z), new ECFieldElement[] { Z });
}
}
}
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