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public abstract Square ( ) : |
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| Résultat | ||
internal virtual ECPoint Normalize(ECFieldElement zInv)
{
switch (this.CurveCoordinateSystem)
{
case ECCurve.COORD_HOMOGENEOUS:
case ECCurve.COORD_LAMBDA_PROJECTIVE:
{
return CreateScaledPoint(zInv, zInv);
}
case ECCurve.COORD_JACOBIAN:
case ECCurve.COORD_JACOBIAN_CHUDNOVSKY:
case ECCurve.COORD_JACOBIAN_MODIFIED:
{
ECFieldElement zInv2 = zInv.Square(), zInv3 = zInv2.Multiply(zInv);
return CreateScaledPoint(zInv2, zInv3);
}
default:
{
throw new InvalidOperationException("not a projective coordinate system");
}
}
}
protected virtual ECFieldElement CalculateJacobianModifiedW(ECFieldElement Z, ECFieldElement ZSquared)
{
ECFieldElement a4 = this.Curve.A;
if (a4.IsZero || Z.IsOne)
return a4;
if (ZSquared == null)
{
ZSquared = Z.Square();
}
ECFieldElement W = ZSquared.Square();
ECFieldElement a4Neg = a4.Negate();
if (a4Neg.BitLength < a4.BitLength)
{
W = W.Multiply(a4Neg).Negate();
}
else
{
W = W.Multiply(a4);
}
return W;
}
public override ECPoint ScaleX(ECFieldElement scale)
{
if (this.IsInfinity)
return this;
switch (CurveCoordinateSystem)
{
case ECCurve.COORD_LAMBDA_AFFINE:
{
// Y is actually Lambda (X + Y/X) here
ECFieldElement X = RawXCoord, L = RawYCoord;
ECFieldElement X2 = X.Multiply(scale);
ECFieldElement L2 = L.Add(X).Divide(scale).Add(X2);
return Curve.CreateRawPoint(X, L2, RawZCoords, IsCompressed);
}
case ECCurve.COORD_LAMBDA_PROJECTIVE:
{
// Y is actually Lambda (X + Y/X) here
ECFieldElement X = RawXCoord, L = RawYCoord, Z = RawZCoords[0];
// We scale the Z coordinate also, to avoid an inversion
ECFieldElement X2 = X.Multiply(scale.Square());
ECFieldElement L2 = L.Add(X).Add(X2);
ECFieldElement Z2 = Z.Multiply(scale);
return Curve.CreateRawPoint(X, L2, new ECFieldElement[] { Z2 }, IsCompressed);
}
default:
{
return base.ScaleX(scale);
}
}
}
private ECFieldElement CheckSqrt(ECFieldElement z)
{
return z.Square().Equals(this) ? z : null;
}
private ECFieldElement CheckSqrt(ECFieldElement z)
{
return(z.Square().Equals(this) ? z : null);
}
public override ECPoint Add(ECPoint b)
{
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
int coordinateSystem = curve.CoordinateSystem;
ECFieldElement rawXCoord = base.RawXCoord;
ECFieldElement rawXCoord2 = b.RawXCoord;
int num = coordinateSystem;
switch (num)
{
case 0:
{
ECFieldElement rawYCoord = base.RawYCoord;
ECFieldElement rawYCoord2 = b.RawYCoord;
ECFieldElement eCFieldElement = rawXCoord.Add(rawXCoord2);
ECFieldElement eCFieldElement2 = rawYCoord.Add(rawYCoord2);
if (!eCFieldElement.IsZero)
{
ECFieldElement eCFieldElement3 = eCFieldElement2.Divide(eCFieldElement);
ECFieldElement eCFieldElement4 = eCFieldElement3.Square().Add(eCFieldElement3).Add(eCFieldElement).Add(curve.A);
ECFieldElement y = eCFieldElement3.Multiply(rawXCoord.Add(eCFieldElement4)).Add(eCFieldElement4).Add(rawYCoord);
return(new F2mPoint(curve, eCFieldElement4, y, base.IsCompressed));
}
if (eCFieldElement2.IsZero)
{
return(this.Twice());
}
return(curve.Infinity);
}
case 1:
{
ECFieldElement rawYCoord3 = base.RawYCoord;
ECFieldElement eCFieldElement5 = base.RawZCoords[0];
ECFieldElement rawYCoord4 = b.RawYCoord;
ECFieldElement eCFieldElement6 = b.RawZCoords[0];
bool isOne = eCFieldElement5.IsOne;
ECFieldElement eCFieldElement7 = rawYCoord4;
ECFieldElement eCFieldElement8 = rawXCoord2;
if (!isOne)
{
eCFieldElement7 = eCFieldElement7.Multiply(eCFieldElement5);
eCFieldElement8 = eCFieldElement8.Multiply(eCFieldElement5);
}
bool isOne2 = eCFieldElement6.IsOne;
ECFieldElement eCFieldElement9 = rawYCoord3;
ECFieldElement eCFieldElement10 = rawXCoord;
if (!isOne2)
{
eCFieldElement9 = eCFieldElement9.Multiply(eCFieldElement6);
eCFieldElement10 = eCFieldElement10.Multiply(eCFieldElement6);
}
ECFieldElement eCFieldElement11 = eCFieldElement7.Add(eCFieldElement9);
ECFieldElement eCFieldElement12 = eCFieldElement8.Add(eCFieldElement10);
if (!eCFieldElement12.IsZero)
{
ECFieldElement eCFieldElement13 = eCFieldElement12.Square();
ECFieldElement eCFieldElement14 = eCFieldElement13.Multiply(eCFieldElement12);
ECFieldElement b2 = isOne ? eCFieldElement6 : (isOne2 ? eCFieldElement5 : eCFieldElement5.Multiply(eCFieldElement6));
ECFieldElement eCFieldElement15 = eCFieldElement11.Add(eCFieldElement12);
ECFieldElement eCFieldElement16 = eCFieldElement15.MultiplyPlusProduct(eCFieldElement11, eCFieldElement13, curve.A).Multiply(b2).Add(eCFieldElement14);
ECFieldElement x = eCFieldElement12.Multiply(eCFieldElement16);
ECFieldElement b3 = isOne2 ? eCFieldElement13 : eCFieldElement13.Multiply(eCFieldElement6);
ECFieldElement y2 = eCFieldElement11.MultiplyPlusProduct(rawXCoord, eCFieldElement12, rawYCoord3).MultiplyPlusProduct(b3, eCFieldElement15, eCFieldElement16);
ECFieldElement eCFieldElement17 = eCFieldElement14.Multiply(b2);
return(new F2mPoint(curve, x, y2, new ECFieldElement[]
{
eCFieldElement17
}, base.IsCompressed));
}
if (eCFieldElement11.IsZero)
{
return(this.Twice());
}
return(curve.Infinity);
}
default:
if (num != 6)
{
throw new InvalidOperationException("unsupported coordinate system");
}
if (rawXCoord.IsZero)
{
if (rawXCoord2.IsZero)
{
return(curve.Infinity);
}
return(b.Add(this));
}
else
{
ECFieldElement rawYCoord5 = base.RawYCoord;
ECFieldElement eCFieldElement18 = base.RawZCoords[0];
ECFieldElement rawYCoord6 = b.RawYCoord;
ECFieldElement eCFieldElement19 = b.RawZCoords[0];
bool isOne3 = eCFieldElement18.IsOne;
ECFieldElement eCFieldElement20 = rawXCoord2;
ECFieldElement eCFieldElement21 = rawYCoord6;
if (!isOne3)
{
eCFieldElement20 = eCFieldElement20.Multiply(eCFieldElement18);
eCFieldElement21 = eCFieldElement21.Multiply(eCFieldElement18);
}
bool isOne4 = eCFieldElement19.IsOne;
ECFieldElement eCFieldElement22 = rawXCoord;
ECFieldElement eCFieldElement23 = rawYCoord5;
if (!isOne4)
{
eCFieldElement22 = eCFieldElement22.Multiply(eCFieldElement19);
eCFieldElement23 = eCFieldElement23.Multiply(eCFieldElement19);
}
ECFieldElement eCFieldElement24 = eCFieldElement23.Add(eCFieldElement21);
ECFieldElement eCFieldElement25 = eCFieldElement22.Add(eCFieldElement20);
if (!eCFieldElement25.IsZero)
{
ECFieldElement eCFieldElement27;
ECFieldElement y3;
ECFieldElement eCFieldElement29;
if (rawXCoord2.IsZero)
{
ECPoint eCPoint = this.Normalize();
rawXCoord = eCPoint.RawXCoord;
ECFieldElement yCoord = eCPoint.YCoord;
ECFieldElement b4 = rawYCoord6;
ECFieldElement eCFieldElement26 = yCoord.Add(b4).Divide(rawXCoord);
eCFieldElement27 = eCFieldElement26.Square().Add(eCFieldElement26).Add(rawXCoord).Add(curve.A);
if (eCFieldElement27.IsZero)
{
return(new F2mPoint(curve, eCFieldElement27, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement28 = eCFieldElement26.Multiply(rawXCoord.Add(eCFieldElement27)).Add(eCFieldElement27).Add(yCoord);
y3 = eCFieldElement28.Divide(eCFieldElement27).Add(eCFieldElement27);
eCFieldElement29 = curve.FromBigInteger(BigInteger.One);
}
else
{
eCFieldElement25 = eCFieldElement25.Square();
ECFieldElement eCFieldElement30 = eCFieldElement24.Multiply(eCFieldElement22);
ECFieldElement eCFieldElement31 = eCFieldElement24.Multiply(eCFieldElement20);
eCFieldElement27 = eCFieldElement30.Multiply(eCFieldElement31);
if (eCFieldElement27.IsZero)
{
return(new F2mPoint(curve, eCFieldElement27, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement32 = eCFieldElement24.Multiply(eCFieldElement25);
if (!isOne4)
{
eCFieldElement32 = eCFieldElement32.Multiply(eCFieldElement19);
}
y3 = eCFieldElement31.Add(eCFieldElement25).SquarePlusProduct(eCFieldElement32, rawYCoord5.Add(eCFieldElement18));
eCFieldElement29 = eCFieldElement32;
if (!isOne3)
{
eCFieldElement29 = eCFieldElement29.Multiply(eCFieldElement18);
}
}
return(new F2mPoint(curve, eCFieldElement27, y3, new ECFieldElement[]
{
eCFieldElement29
}, base.IsCompressed));
}
if (eCFieldElement24.IsZero)
{
return(this.Twice());
}
return(curve.Infinity);
}
break;
}
}
public override ECPoint TwicePlus(ECPoint b)
{
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this.Twice());
}
ECCurve curve = this.Curve;
ECFieldElement rawXCoord = base.RawXCoord;
if (rawXCoord.IsZero)
{
return(b);
}
int coordinateSystem = curve.CoordinateSystem;
int num = coordinateSystem;
if (num != 6)
{
return(this.Twice().Add(b));
}
ECFieldElement rawXCoord2 = b.RawXCoord;
ECFieldElement eCFieldElement = b.RawZCoords[0];
if (rawXCoord2.IsZero || !eCFieldElement.IsOne)
{
return(this.Twice().Add(b));
}
ECFieldElement rawYCoord = base.RawYCoord;
ECFieldElement eCFieldElement2 = base.RawZCoords[0];
ECFieldElement rawYCoord2 = b.RawYCoord;
ECFieldElement x = rawXCoord.Square();
ECFieldElement b2 = rawYCoord.Square();
ECFieldElement eCFieldElement3 = eCFieldElement2.Square();
ECFieldElement b3 = rawYCoord.Multiply(eCFieldElement2);
ECFieldElement b4 = curve.A.Multiply(eCFieldElement3).Add(b2).Add(b3);
ECFieldElement eCFieldElement4 = rawYCoord2.AddOne();
ECFieldElement eCFieldElement5 = curve.A.Add(eCFieldElement4).Multiply(eCFieldElement3).Add(b2).MultiplyPlusProduct(b4, x, eCFieldElement3);
ECFieldElement eCFieldElement6 = rawXCoord2.Multiply(eCFieldElement3);
ECFieldElement eCFieldElement7 = eCFieldElement6.Add(b4).Square();
if (eCFieldElement7.IsZero)
{
if (eCFieldElement5.IsZero)
{
return(b.Twice());
}
return(curve.Infinity);
}
else
{
if (eCFieldElement5.IsZero)
{
return(new F2mPoint(curve, eCFieldElement5, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement x2 = eCFieldElement5.Square().Multiply(eCFieldElement6);
ECFieldElement eCFieldElement8 = eCFieldElement5.Multiply(eCFieldElement7).Multiply(eCFieldElement3);
ECFieldElement y = eCFieldElement5.Add(eCFieldElement7).Square().MultiplyPlusProduct(b4, eCFieldElement4, eCFieldElement8);
return(new F2mPoint(curve, x2, y, new ECFieldElement[]
{
eCFieldElement8
}, base.IsCompressed));
}
}
public override ECPoint Twice()
{
if (base.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
ECFieldElement rawXCoord = base.RawXCoord;
if (rawXCoord.IsZero)
{
return(curve.Infinity);
}
int coordinateSystem = curve.CoordinateSystem;
int num = coordinateSystem;
switch (num)
{
case 0:
{
ECFieldElement rawYCoord = base.RawYCoord;
ECFieldElement eCFieldElement = rawYCoord.Divide(rawXCoord).Add(rawXCoord);
ECFieldElement x = eCFieldElement.Square().Add(eCFieldElement).Add(curve.A);
ECFieldElement y = rawXCoord.SquarePlusProduct(x, eCFieldElement.AddOne());
return(new F2mPoint(curve, x, y, base.IsCompressed));
}
case 1:
{
ECFieldElement rawYCoord2 = base.RawYCoord;
ECFieldElement eCFieldElement2 = base.RawZCoords[0];
bool isOne = eCFieldElement2.IsOne;
ECFieldElement eCFieldElement3 = isOne ? rawXCoord : rawXCoord.Multiply(eCFieldElement2);
ECFieldElement b = isOne ? rawYCoord2 : rawYCoord2.Multiply(eCFieldElement2);
ECFieldElement eCFieldElement4 = rawXCoord.Square();
ECFieldElement eCFieldElement5 = eCFieldElement4.Add(b);
ECFieldElement eCFieldElement6 = eCFieldElement3;
ECFieldElement eCFieldElement7 = eCFieldElement6.Square();
ECFieldElement eCFieldElement8 = eCFieldElement5.Add(eCFieldElement6);
ECFieldElement eCFieldElement9 = eCFieldElement8.MultiplyPlusProduct(eCFieldElement5, eCFieldElement7, curve.A);
ECFieldElement x2 = eCFieldElement6.Multiply(eCFieldElement9);
ECFieldElement y2 = eCFieldElement4.Square().MultiplyPlusProduct(eCFieldElement6, eCFieldElement9, eCFieldElement8);
ECFieldElement eCFieldElement10 = eCFieldElement6.Multiply(eCFieldElement7);
return(new F2mPoint(curve, x2, y2, new ECFieldElement[]
{
eCFieldElement10
}, base.IsCompressed));
}
default:
{
if (num != 6)
{
throw new InvalidOperationException("unsupported coordinate system");
}
ECFieldElement rawYCoord3 = base.RawYCoord;
ECFieldElement eCFieldElement11 = base.RawZCoords[0];
bool isOne2 = eCFieldElement11.IsOne;
ECFieldElement eCFieldElement12 = isOne2 ? rawYCoord3 : rawYCoord3.Multiply(eCFieldElement11);
ECFieldElement eCFieldElement13 = isOne2 ? eCFieldElement11 : eCFieldElement11.Square();
ECFieldElement a = curve.A;
ECFieldElement eCFieldElement14 = isOne2 ? a : a.Multiply(eCFieldElement13);
ECFieldElement eCFieldElement15 = rawYCoord3.Square().Add(eCFieldElement12).Add(eCFieldElement14);
if (eCFieldElement15.IsZero)
{
return(new F2mPoint(curve, eCFieldElement15, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement16 = eCFieldElement15.Square();
ECFieldElement eCFieldElement17 = isOne2 ? eCFieldElement15 : eCFieldElement15.Multiply(eCFieldElement13);
ECFieldElement b2 = curve.B;
ECFieldElement eCFieldElement19;
if (b2.BitLength < curve.FieldSize >> 1)
{
ECFieldElement eCFieldElement18 = rawYCoord3.Add(rawXCoord).Square();
ECFieldElement b3;
if (b2.IsOne)
{
b3 = eCFieldElement14.Add(eCFieldElement13).Square();
}
else
{
b3 = eCFieldElement14.SquarePlusProduct(b2, eCFieldElement13.Square());
}
eCFieldElement19 = eCFieldElement18.Add(eCFieldElement15).Add(eCFieldElement13).Multiply(eCFieldElement18).Add(b3).Add(eCFieldElement16);
if (a.IsZero)
{
eCFieldElement19 = eCFieldElement19.Add(eCFieldElement17);
}
else if (!a.IsOne)
{
eCFieldElement19 = eCFieldElement19.Add(a.AddOne().Multiply(eCFieldElement17));
}
}
else
{
ECFieldElement eCFieldElement20 = isOne2 ? rawXCoord : rawXCoord.Multiply(eCFieldElement11);
eCFieldElement19 = eCFieldElement20.SquarePlusProduct(eCFieldElement15, eCFieldElement12).Add(eCFieldElement16).Add(eCFieldElement17);
}
return(new F2mPoint(curve, eCFieldElement16, eCFieldElement19, new ECFieldElement[]
{
eCFieldElement17
}, base.IsCompressed));
}
}
}
