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 it's 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 = L1Sq.Add(L1Z1);
ECFieldElement L2plus1 = L2.AddOne();
ECFieldElement A = L2plus1.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 SecT409K1Point(curve, A, curve.B, IsCompressed));
}
ECFieldElement X3 = A.Square().Multiply(X2Z1Sq);
ECFieldElement Z3 = A.Multiply(B).Multiply(Z1Sq);
ECFieldElement L3 = A.Add(B).Square().MultiplyPlusProduct(T, L2plus1, Z3);
return(new SecT409K1Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed));
}
public PreCompInfo Precompute(PreCompInfo existing)
{
WNafPreCompInfo existingWNaf = existing as WNafPreCompInfo;
int reqPreCompLen = 1 << System.Math.Max(0, m_width - 2);
if (CheckExisting(existingWNaf, reqPreCompLen, m_includeNegated))
{
return(existingWNaf);
}
ECCurve c = m_p.Curve;
ECPoint[] preComp = null, preCompNeg = null;
ECPoint twiceP = null;
if (existingWNaf != null)
{
preComp = existingWNaf.PreComp;
preCompNeg = existingWNaf.PreCompNeg;
twiceP = existingWNaf.Twice;
}
int iniPreCompLen = 0;
if (preComp == null)
{
preComp = EMPTY_POINTS;
}
else
{
iniPreCompLen = preComp.Length;
}
if (iniPreCompLen < reqPreCompLen)
{
preComp = WNafUtilities.ResizeTable(preComp, reqPreCompLen);
if (reqPreCompLen == 1)
{
preComp[0] = m_p.Normalize();
}
else
{
int curPreCompLen = iniPreCompLen;
if (curPreCompLen == 0)
{
preComp[0] = m_p;
curPreCompLen = 1;
}
ECFieldElement iso = null;
if (reqPreCompLen == 2)
{
preComp[1] = m_p.ThreeTimes();
}
else
{
ECPoint isoTwiceP = twiceP, last = preComp[curPreCompLen - 1];
if (isoTwiceP == null)
{
isoTwiceP = preComp[0].Twice();
twiceP = isoTwiceP;
/*
* For Fp curves with Jacobian projective coordinates, use a (quasi-)isomorphism
* where 'twiceP' is "affine", so that the subsequent additions are cheaper. This
* also requires scaling the initial point's X, Y coordinates, and reversing the
* isomorphism as part of the subsequent normalization.
*
* NOTE: The correctness of this optimization depends on:
* 1) additions do not use the curve's A, B coefficients.
* 2) no special cases (i.e. Q +/- Q) when calculating 1P, 3P, 5P, ...
*/
if (!twiceP.IsInfinity && ECAlgorithms.IsFpCurve(c) && c.FieldSize >= 64)
{
switch (c.CoordinateSystem)
{
case ECCurve.COORD_JACOBIAN:
case ECCurve.COORD_JACOBIAN_CHUDNOVSKY:
case ECCurve.COORD_JACOBIAN_MODIFIED:
{
iso = twiceP.GetZCoord(0);
isoTwiceP = c.CreatePoint(twiceP.XCoord.ToBigInteger(),
twiceP.YCoord.ToBigInteger());
ECFieldElement iso2 = iso.Square(), iso3 = iso2.Multiply(iso);
last = last.ScaleX(iso2).ScaleY(iso3);
if (iniPreCompLen == 0)
{
preComp[0] = last;
}
break;
}
}
}
}
while (curPreCompLen < reqPreCompLen)
{
/*
* Compute the new ECPoints for the precomputation array. The values 1, 3,
* 5, ..., 2^(width-1)-1 times p are computed
*/
preComp[curPreCompLen++] = last = last.Add(isoTwiceP);
}
}
/*
* Having oft-used operands in affine form makes operations faster.
*/
c.NormalizeAll(preComp, iniPreCompLen, reqPreCompLen - iniPreCompLen, iso);
}
}
if (m_includeNegated)
{
int pos;
if (preCompNeg == null)
{
pos = 0;
preCompNeg = new ECPoint[reqPreCompLen];
}
else
{
pos = preCompNeg.Length;
if (pos < reqPreCompLen)
{
preCompNeg = WNafUtilities.ResizeTable(preCompNeg, reqPreCompLen);
}
}
while (pos < reqPreCompLen)
{
preCompNeg[pos] = preComp[pos].Negate();
++pos;
}
}
WNafPreCompInfo result = new WNafPreCompInfo();
result.PreComp = preComp;
result.PreCompNeg = preCompNeg;
result.Twice = twiceP;
return(result);
}
public override ECPoint Add(ECPoint b)
{
if (this.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
ECFieldElement X1 = this.RawXCoord;
ECFieldElement X2 = b.RawXCoord;
if (X1.IsZero)
{
if (X2.IsZero)
{
return(curve.Infinity);
}
return(b.Add(this));
}
ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0];
ECFieldElement L2 = b.RawYCoord, Z2 = b.RawZCoords[0];
bool Z1IsOne = Z1.IsOne;
ECFieldElement U2 = X2, S2 = L2;
if (!Z1IsOne)
{
U2 = U2.Multiply(Z1);
S2 = S2.Multiply(Z1);
}
bool Z2IsOne = Z2.IsOne;
ECFieldElement U1 = X1, S1 = L1;
if (!Z2IsOne)
{
U1 = U1.Multiply(Z2);
S1 = S1.Multiply(Z2);
}
ECFieldElement A = S1.Add(S2);
ECFieldElement B = U1.Add(U2);
if (B.IsZero)
{
if (A.IsZero)
{
return(Twice());
}
return(curve.Infinity);
}
ECFieldElement X3, L3, Z3;
if (X2.IsZero)
{
// TODO This can probably be optimized quite a bit
ECPoint p = this.Normalize();
X1 = p.XCoord;
ECFieldElement Y1 = p.YCoord;
ECFieldElement Y2 = L2;
ECFieldElement L = Y1.Add(Y2).Divide(X1);
//X3 = L.Square().Add(L).Add(X1).Add(curve.A);
X3 = L.Square().Add(L).Add(X1);
if (X3.IsZero)
{
//return new SecT283K1Point(curve, X3, curve.B.sqrt(), IsCompressed);
return(new SecT283K1Point(curve, X3, curve.B, IsCompressed));
}
ECFieldElement Y3 = L.Multiply(X1.Add(X3)).Add(X3).Add(Y1);
L3 = Y3.Divide(X3).Add(X3);
Z3 = curve.FromBigInteger(BigInteger.One);
}
else
{
B = B.Square();
ECFieldElement AU1 = A.Multiply(U1);
ECFieldElement AU2 = A.Multiply(U2);
X3 = AU1.Multiply(AU2);
if (X3.IsZero)
{
//return new SecT283K1Point(curve, X3, curve.B.sqrt(), IsCompressed);
return(new SecT283K1Point(curve, X3, curve.B, IsCompressed));
}
ECFieldElement ABZ2 = A.Multiply(B);
if (!Z2IsOne)
{
ABZ2 = ABZ2.Multiply(Z2);
}
L3 = AU2.Add(B).SquarePlusProduct(ABZ2, L1.Add(Z1));
Z3 = ABZ2;
if (!Z1IsOne)
{
Z3 = Z3.Multiply(Z1);
}
}
return(new SecT283K1Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed));
}
public override ECPoint Add(ECPoint b)
{
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
ECCurve curve = Curve;
ECFieldElement rawXCoord = base.RawXCoord;
ECFieldElement rawXCoord2 = b.RawXCoord;
if (rawXCoord.IsZero)
{
if (rawXCoord2.IsZero)
{
return(curve.Infinity);
}
return(b.Add(this));
}
ECFieldElement rawYCoord = base.RawYCoord;
ECFieldElement eCFieldElement = base.RawZCoords[0];
ECFieldElement rawYCoord2 = b.RawYCoord;
ECFieldElement eCFieldElement2 = b.RawZCoords[0];
bool isOne = eCFieldElement.IsOne;
ECFieldElement eCFieldElement3 = rawXCoord2;
ECFieldElement eCFieldElement4 = rawYCoord2;
if (!isOne)
{
eCFieldElement3 = eCFieldElement3.Multiply(eCFieldElement);
eCFieldElement4 = eCFieldElement4.Multiply(eCFieldElement);
}
bool isOne2 = eCFieldElement2.IsOne;
ECFieldElement eCFieldElement5 = rawXCoord;
ECFieldElement eCFieldElement6 = rawYCoord;
if (!isOne2)
{
eCFieldElement5 = eCFieldElement5.Multiply(eCFieldElement2);
eCFieldElement6 = eCFieldElement6.Multiply(eCFieldElement2);
}
ECFieldElement eCFieldElement7 = eCFieldElement6.Add(eCFieldElement4);
ECFieldElement eCFieldElement8 = eCFieldElement5.Add(eCFieldElement3);
if (eCFieldElement8.IsZero)
{
if (eCFieldElement7.IsZero)
{
return(Twice());
}
return(curve.Infinity);
}
ECFieldElement eCFieldElement10;
ECFieldElement y;
ECFieldElement eCFieldElement12;
if (rawXCoord2.IsZero)
{
ECPoint eCPoint = Normalize();
rawXCoord = eCPoint.XCoord;
ECFieldElement yCoord = eCPoint.YCoord;
ECFieldElement b2 = rawYCoord2;
ECFieldElement eCFieldElement9 = yCoord.Add(b2).Divide(rawXCoord);
eCFieldElement10 = eCFieldElement9.Square().Add(eCFieldElement9).Add(rawXCoord)
.Add(curve.A);
if (eCFieldElement10.IsZero)
{
return(new SecT163R1Point(curve, eCFieldElement10, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement11 = eCFieldElement9.Multiply(rawXCoord.Add(eCFieldElement10)).Add(eCFieldElement10).Add(yCoord);
y = eCFieldElement11.Divide(eCFieldElement10).Add(eCFieldElement10);
eCFieldElement12 = curve.FromBigInteger(BigInteger.One);
}
else
{
eCFieldElement8 = eCFieldElement8.Square();
ECFieldElement eCFieldElement13 = eCFieldElement7.Multiply(eCFieldElement5);
ECFieldElement eCFieldElement14 = eCFieldElement7.Multiply(eCFieldElement3);
eCFieldElement10 = eCFieldElement13.Multiply(eCFieldElement14);
if (eCFieldElement10.IsZero)
{
return(new SecT163R1Point(curve, eCFieldElement10, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement15 = eCFieldElement7.Multiply(eCFieldElement8);
if (!isOne2)
{
eCFieldElement15 = eCFieldElement15.Multiply(eCFieldElement2);
}
y = eCFieldElement14.Add(eCFieldElement8).SquarePlusProduct(eCFieldElement15, rawYCoord.Add(eCFieldElement));
eCFieldElement12 = eCFieldElement15;
if (!isOne)
{
eCFieldElement12 = eCFieldElement12.Multiply(eCFieldElement);
}
}
return(new SecT163R1Point(curve, eCFieldElement10, y, new ECFieldElement[1]
{
eCFieldElement12
}, base.IsCompressed));
}
public override ECPoint Add(ECPoint b)
{
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
ECFieldElement eCFieldElement = base.RawXCoord;
ECFieldElement rawXCoord = b.RawXCoord;
if (eCFieldElement.IsZero)
{
if (rawXCoord.IsZero)
{
return(curve.Infinity);
}
return(b.Add(this));
}
else
{
ECFieldElement rawYCoord = base.RawYCoord;
ECFieldElement eCFieldElement2 = base.RawZCoords[0];
ECFieldElement rawYCoord2 = b.RawYCoord;
ECFieldElement eCFieldElement3 = b.RawZCoords[0];
bool isOne = eCFieldElement2.IsOne;
ECFieldElement eCFieldElement4 = rawXCoord;
ECFieldElement eCFieldElement5 = rawYCoord2;
if (!isOne)
{
eCFieldElement4 = eCFieldElement4.Multiply(eCFieldElement2);
eCFieldElement5 = eCFieldElement5.Multiply(eCFieldElement2);
}
bool isOne2 = eCFieldElement3.IsOne;
ECFieldElement eCFieldElement6 = eCFieldElement;
ECFieldElement eCFieldElement7 = rawYCoord;
if (!isOne2)
{
eCFieldElement6 = eCFieldElement6.Multiply(eCFieldElement3);
eCFieldElement7 = eCFieldElement7.Multiply(eCFieldElement3);
}
ECFieldElement eCFieldElement8 = eCFieldElement7.Add(eCFieldElement5);
ECFieldElement eCFieldElement9 = eCFieldElement6.Add(eCFieldElement4);
if (!eCFieldElement9.IsZero)
{
ECFieldElement eCFieldElement11;
ECFieldElement y;
ECFieldElement eCFieldElement13;
if (rawXCoord.IsZero)
{
ECPoint eCPoint = this.Normalize();
eCFieldElement = eCPoint.XCoord;
ECFieldElement yCoord = eCPoint.YCoord;
ECFieldElement b2 = rawYCoord2;
ECFieldElement eCFieldElement10 = yCoord.Add(b2).Divide(eCFieldElement);
eCFieldElement11 = eCFieldElement10.Square().Add(eCFieldElement10).Add(eCFieldElement).Add(curve.A);
if (eCFieldElement11.IsZero)
{
return(new SecT113R2Point(curve, eCFieldElement11, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement12 = eCFieldElement10.Multiply(eCFieldElement.Add(eCFieldElement11)).Add(eCFieldElement11).Add(yCoord);
y = eCFieldElement12.Divide(eCFieldElement11).Add(eCFieldElement11);
eCFieldElement13 = curve.FromBigInteger(BigInteger.One);
}
else
{
eCFieldElement9 = eCFieldElement9.Square();
ECFieldElement eCFieldElement14 = eCFieldElement8.Multiply(eCFieldElement6);
ECFieldElement eCFieldElement15 = eCFieldElement8.Multiply(eCFieldElement4);
eCFieldElement11 = eCFieldElement14.Multiply(eCFieldElement15);
if (eCFieldElement11.IsZero)
{
return(new SecT113R2Point(curve, eCFieldElement11, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement16 = eCFieldElement8.Multiply(eCFieldElement9);
if (!isOne2)
{
eCFieldElement16 = eCFieldElement16.Multiply(eCFieldElement3);
}
y = eCFieldElement15.Add(eCFieldElement9).SquarePlusProduct(eCFieldElement16, rawYCoord.Add(eCFieldElement2));
eCFieldElement13 = eCFieldElement16;
if (!isOne)
{
eCFieldElement13 = eCFieldElement13.Multiply(eCFieldElement2);
}
}
return(new SecT113R2Point(curve, eCFieldElement11, y, new ECFieldElement[]
{
eCFieldElement13
}, base.IsCompressed));
}
if (eCFieldElement8.IsZero)
{
return(this.Twice());
}
return(curve.Infinity);
}
}
public override ECPoint Add(ECPoint b)
{
ECFieldElement element13;
ECFieldElement element14;
ECFieldElement element15;
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
ECFieldElement rawXCoord = base.RawXCoord;
ECFieldElement element2 = b.RawXCoord;
if (rawXCoord.IsZero)
{
if (element2.IsZero)
{
return(curve.Infinity);
}
return(b.Add(this));
}
ECFieldElement rawYCoord = base.RawYCoord;
ECFieldElement element4 = base.RawZCoords[0];
ECFieldElement element5 = b.RawYCoord;
ECFieldElement element6 = b.RawZCoords[0];
bool isOne = element4.IsOne;
ECFieldElement element7 = element2;
ECFieldElement element8 = element5;
if (!isOne)
{
element7 = element7.Multiply(element4);
element8 = element8.Multiply(element4);
}
bool flag2 = element6.IsOne;
ECFieldElement element9 = rawXCoord;
ECFieldElement element10 = rawYCoord;
if (!flag2)
{
element9 = element9.Multiply(element6);
element10 = element10.Multiply(element6);
}
ECFieldElement element11 = element10.Add(element8);
ECFieldElement element12 = element9.Add(element7);
if (element12.IsZero)
{
if (element11.IsZero)
{
return(this.Twice());
}
return(curve.Infinity);
}
if (element2.IsZero)
{
ECPoint point = this.Normalize();
rawXCoord = point.XCoord;
ECFieldElement yCoord = point.YCoord;
ECFieldElement element17 = element5;
ECFieldElement element18 = yCoord.Add(element17).Divide(rawXCoord);
element13 = element18.Square().Add(element18).Add(rawXCoord).AddOne();
if (element13.IsZero)
{
return(new SecT283R1Point(curve, element13, curve.B.Sqrt(), base.IsCompressed));
}
element14 = element18.Multiply(rawXCoord.Add(element13)).Add(element13).Add(yCoord).Divide(element13).Add(element13);
element15 = curve.FromBigInteger(BigInteger.One);
}
else
{
element12 = element12.Square();
ECFieldElement element20 = element11.Multiply(element9);
ECFieldElement element21 = element11.Multiply(element7);
element13 = element20.Multiply(element21);
if (element13.IsZero)
{
return(new SecT283R1Point(curve, element13, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement x = element11.Multiply(element12);
if (!flag2)
{
x = x.Multiply(element6);
}
element14 = element21.Add(element12).SquarePlusProduct(x, rawYCoord.Add(element4));
element15 = x;
if (!isOne)
{
element15 = element15.Multiply(element4);
}
}
return(new SecT283R1Point(curve, element13, element14, new ECFieldElement[] { element15 }, base.IsCompressed));
}
public override ECPoint Twice()
{
if (base.IsInfinity)
{
return(this);
}
ECCurve curve = Curve;
ECFieldElement rawXCoord = base.RawXCoord;
if (rawXCoord.IsZero)
{
return(curve.Infinity);
}
ECFieldElement rawYCoord = base.RawYCoord;
ECFieldElement eCFieldElement = base.RawZCoords[0];
bool isOne = eCFieldElement.IsOne;
ECFieldElement eCFieldElement2 = isOne ? eCFieldElement : eCFieldElement.Square();
ECFieldElement eCFieldElement3 = (!isOne) ? rawYCoord.Add(eCFieldElement).Multiply(rawYCoord) : rawYCoord.Square().Add(rawYCoord);
if (eCFieldElement3.IsZero)
{
return(new SecT283K1Point(curve, eCFieldElement3, curve.B, base.IsCompressed));
}
ECFieldElement eCFieldElement4 = eCFieldElement3.Square();
ECFieldElement eCFieldElement5 = isOne ? eCFieldElement3 : eCFieldElement3.Multiply(eCFieldElement2);
ECFieldElement eCFieldElement6 = rawYCoord.Add(rawXCoord).Square();
ECFieldElement b = isOne ? eCFieldElement : eCFieldElement2.Square();
ECFieldElement y = eCFieldElement6.Add(eCFieldElement3).Add(eCFieldElement2).Multiply(eCFieldElement6)
.Add(b)
.Add(eCFieldElement4)
.Add(eCFieldElement5);
return(new SecT283K1Point(curve, eCFieldElement4, y, new ECFieldElement[1]
{
eCFieldElement5
}, base.IsCompressed));
}
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 it's 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 = curve.A.Multiply(Z1Sq).Add(L1Sq).Add(L1Z1);
ECFieldElement T = Z1Sq.Add(L1Sq).Add(L1Z1);
ECFieldElement L2plus1 = L2.AddOne();
//ECFieldElement A = curve.A.Add(L2plus1).Multiply(Z1Sq).Add(L1Sq).MultiplyPlusProduct(T, X1Sq, Z1Sq);
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, curve.B.sqrt(), withCompression);
return(new SecT571R1Point(curve, A, SecT571R1Curve.SecT571R1_B_SQRT, IsCompressed));
}
ECFieldElement X3 = A.Square().Multiply(X2Z1Sq);
ECFieldElement Z3 = A.Multiply(B).Multiply(Z1Sq);
ECFieldElement L3 = A.Add(B).Square().MultiplyPlusProduct(T, L2plus1, Z3);
return(new SecT571R1Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed));
}
