protected virtual Curve25519Point TwiceJacobianModified(bool calculateW)
{
Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord,
Z1 = (Curve25519FieldElement)this.RawZCoords[0], W1 = GetJacobianModifiedW();
uint c;
uint[] M = Nat256.Create();
Curve25519Field.Square(X1.x, M);
c = Nat256.AddBothTo(M, M, M);
c += Nat256.AddTo(W1.x, M);
Curve25519Field.Reduce27(c, M);
uint[] _2Y1 = Nat256.Create();
Curve25519Field.Twice(Y1.x, _2Y1);
uint[] _2Y1Squared = Nat256.Create();
Curve25519Field.Multiply(_2Y1, Y1.x, _2Y1Squared);
uint[] S = Nat256.Create();
Curve25519Field.Multiply(_2Y1Squared, X1.x, S);
Curve25519Field.Twice(S, S);
uint[] _8T = Nat256.Create();
Curve25519Field.Square(_2Y1Squared, _8T);
Curve25519Field.Twice(_8T, _8T);
Curve25519FieldElement X3 = new Curve25519FieldElement(_2Y1Squared);
Curve25519Field.Square(M, X3.x);
Curve25519Field.Subtract(X3.x, S, X3.x);
Curve25519Field.Subtract(X3.x, S, X3.x);
Curve25519FieldElement Y3 = new Curve25519FieldElement(S);
Curve25519Field.Subtract(S, X3.x, Y3.x);
Curve25519Field.Multiply(Y3.x, M, Y3.x);
Curve25519Field.Subtract(Y3.x, _8T, Y3.x);
Curve25519FieldElement Z3 = new Curve25519FieldElement(_2Y1);
if (!Nat256.IsOne(Z1.x))
{
Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x);
}
Curve25519FieldElement W3 = null;
if (calculateW)
{
W3 = new Curve25519FieldElement(_8T);
Curve25519Field.Multiply(W3.x, W1.x, W3.x);
Curve25519Field.Twice(W3.x, W3.x);
}
return(new Curve25519Point(this.Curve, X3, Y3, new ECFieldElement[] { Z3, W3 }, IsCompressed));
}
public virtual bool Equals(Curve25519FieldElement other)
{
if (this == other)
{
return(true);
}
if (null == other)
{
return(false);
}
return(Nat256.Eq(x, other.x));
}
protected virtual Curve25519FieldElement GetJacobianModifiedW()
{
ECFieldElement[] ZZ = this.RawZCoords;
Curve25519FieldElement W = (Curve25519FieldElement)ZZ[1];
if (W == null)
{
// NOTE: Rarely, TwicePlus will result in the need for a lazy W1 calculation here
ZZ[1] = W = CalculateJacobianModifiedW((Curve25519FieldElement)ZZ[0], null);
}
return(W);
}
protected virtual Curve25519FieldElement CalculateJacobianModifiedW(Curve25519FieldElement Z, uint[] ZSquared)
{
Curve25519FieldElement a4 = (Curve25519FieldElement)this.Curve.A;
if (Z.IsOne)
{
return(a4);
}
Curve25519FieldElement W = new Curve25519FieldElement();
if (ZSquared == null)
{
ZSquared = W.x;
Curve25519Field.Square(Z.x, ZSquared);
}
Curve25519Field.Square(ZSquared, W.x);
Curve25519Field.Multiply(W.x, a4.x, W.x);
return(W);
}
public virtual bool Equals(Curve25519FieldElement other)
{
if (this == other)
return true;
if (null == other)
return false;
return Nat256.Eq(x, other.x);
}
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;
Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord,
Z1 = (Curve25519FieldElement)this.RawZCoords[0];
Curve25519FieldElement X2 = (Curve25519FieldElement)b.RawXCoord, Y2 = (Curve25519FieldElement)b.RawYCoord,
Z2 = (Curve25519FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat256.CreateExt();
uint[] t2 = Nat256.Create();
uint[] t3 = Nat256.Create();
uint[] t4 = Nat256.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
Curve25519Field.Square(Z1.x, S2);
U2 = t2;
Curve25519Field.Multiply(S2, X2.x, U2);
Curve25519Field.Multiply(S2, Z1.x, S2);
Curve25519Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
Curve25519Field.Square(Z2.x, S1);
U1 = tt1;
Curve25519Field.Multiply(S1, X1.x, U1);
Curve25519Field.Multiply(S1, Z2.x, S1);
Curve25519Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat256.Create();
Curve25519Field.Subtract(U1, U2, H);
uint[] R = t2;
Curve25519Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat256.IsZero(H))
{
if (Nat256.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 = Nat256.Create();
Curve25519Field.Square(H, HSquared);
uint[] G = Nat256.Create();
Curve25519Field.Multiply(HSquared, H, G);
uint[] V = t3;
Curve25519Field.Multiply(HSquared, U1, V);
Curve25519Field.Negate(G, G);
Nat256.Mul(S1, G, tt1);
c = Nat256.AddBothTo(V, V, G);
Curve25519Field.Reduce27(c, G);
Curve25519FieldElement X3 = new Curve25519FieldElement(t4);
Curve25519Field.Square(R, X3.x);
Curve25519Field.Subtract(X3.x, G, X3.x);
Curve25519FieldElement Y3 = new Curve25519FieldElement(G);
Curve25519Field.Subtract(V, X3.x, Y3.x);
Curve25519Field.MultiplyAddToExt(Y3.x, R, tt1);
Curve25519Field.Reduce(tt1, Y3.x);
Curve25519FieldElement Z3 = new Curve25519FieldElement(H);
if (!Z1IsOne)
{
Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
Curve25519Field.Multiply(Z3.x, Z2.x, Z3.x);
}
uint[] Z3Squared = (Z1IsOne && Z2IsOne) ? HSquared : null;
// TODO If the result will only be used in a subsequent addition, we don't need W3
Curve25519FieldElement W3 = CalculateJacobianModifiedW((Curve25519FieldElement)Z3, Z3Squared);
ECFieldElement[] zs = new ECFieldElement[] { Z3, W3 };
return(new Curve25519Point(curve, X3, Y3, zs, IsCompressed));
}
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;
Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord,
Z1 = (Curve25519FieldElement)this.RawZCoords[0];
Curve25519FieldElement X2 = (Curve25519FieldElement)b.RawXCoord, Y2 = (Curve25519FieldElement)b.RawYCoord,
Z2 = (Curve25519FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat256.CreateExt();
uint[] t2 = Nat256.Create();
uint[] t3 = Nat256.Create();
uint[] t4 = Nat256.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
Curve25519Field.Square(Z1.x, S2);
U2 = t2;
Curve25519Field.Multiply(S2, X2.x, U2);
Curve25519Field.Multiply(S2, Z1.x, S2);
Curve25519Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
Curve25519Field.Square(Z2.x, S1);
U1 = tt1;
Curve25519Field.Multiply(S1, X1.x, U1);
Curve25519Field.Multiply(S1, Z2.x, S1);
Curve25519Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat256.Create();
Curve25519Field.Subtract(U1, U2, H);
uint[] R = t2;
Curve25519Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat256.IsZero(H))
{
if (Nat256.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 = Nat256.Create();
Curve25519Field.Square(H, HSquared);
uint[] G = Nat256.Create();
Curve25519Field.Multiply(HSquared, H, G);
uint[] V = t3;
Curve25519Field.Multiply(HSquared, U1, V);
Curve25519Field.Negate(G, G);
Nat256.Mul(S1, G, tt1);
c = Nat256.AddBothTo(V, V, G);
Curve25519Field.Reduce27(c, G);
Curve25519FieldElement X3 = new Curve25519FieldElement(t4);
Curve25519Field.Square(R, X3.x);
Curve25519Field.Subtract(X3.x, G, X3.x);
Curve25519FieldElement Y3 = new Curve25519FieldElement(G);
Curve25519Field.Subtract(V, X3.x, Y3.x);
Curve25519Field.MultiplyAddToExt(Y3.x, R, tt1);
Curve25519Field.Reduce(tt1, Y3.x);
Curve25519FieldElement Z3 = new Curve25519FieldElement(H);
if (!Z1IsOne)
{
Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
Curve25519Field.Multiply(Z3.x, Z2.x, Z3.x);
}
uint[] Z3Squared = (Z1IsOne && Z2IsOne) ? HSquared : null;
// TODO If the result will only be used in a subsequent addition, we don't need W3
Curve25519FieldElement W3 = CalculateJacobianModifiedW((Curve25519FieldElement)Z3, Z3Squared);
ECFieldElement[] zs = new ECFieldElement[] { Z3, W3 };
return new Curve25519Point(curve, X3, Y3, zs, IsCompressed);
}
protected virtual Curve25519Point TwiceJacobianModified(bool calculateW)
{
Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord,
Z1 = (Curve25519FieldElement)this.RawZCoords[0], W1 = GetJacobianModifiedW();
uint c;
uint[] M = Nat256.Create();
Curve25519Field.Square(X1.x, M);
c = Nat256.AddBothTo(M, M, M);
c += Nat256.AddTo(W1.x, M);
Curve25519Field.Reduce27(c, M);
uint[] _2Y1 = Nat256.Create();
Curve25519Field.Twice(Y1.x, _2Y1);
uint[] _2Y1Squared = Nat256.Create();
Curve25519Field.Multiply(_2Y1, Y1.x, _2Y1Squared);
uint[] S = Nat256.Create();
Curve25519Field.Multiply(_2Y1Squared, X1.x, S);
Curve25519Field.Twice(S, S);
uint[] _8T = Nat256.Create();
Curve25519Field.Square(_2Y1Squared, _8T);
Curve25519Field.Twice(_8T, _8T);
Curve25519FieldElement X3 = new Curve25519FieldElement(_2Y1Squared);
Curve25519Field.Square(M, X3.x);
Curve25519Field.Subtract(X3.x, S, X3.x);
Curve25519Field.Subtract(X3.x, S, X3.x);
Curve25519FieldElement Y3 = new Curve25519FieldElement(S);
Curve25519Field.Subtract(S, X3.x, Y3.x);
Curve25519Field.Multiply(Y3.x, M, Y3.x);
Curve25519Field.Subtract(Y3.x, _8T, Y3.x);
Curve25519FieldElement Z3 = new Curve25519FieldElement(_2Y1);
if (!Nat256.IsOne(Z1.x))
{
Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x);
}
Curve25519FieldElement W3 = null;
if (calculateW)
{
W3 = new Curve25519FieldElement(_8T);
Curve25519Field.Multiply(W3.x, W1.x, W3.x);
Curve25519Field.Twice(W3.x, W3.x);
}
return new Curve25519Point(this.Curve, X3, Y3, new ECFieldElement[] { Z3, W3 }, IsCompressed);
}
protected virtual Curve25519FieldElement CalculateJacobianModifiedW(Curve25519FieldElement Z, uint[] ZSquared)
{
Curve25519FieldElement a4 = (Curve25519FieldElement)this.Curve.A;
if (Z.IsOne)
return a4;
Curve25519FieldElement W = new Curve25519FieldElement();
if (ZSquared == null)
{
ZSquared = W.x;
Curve25519Field.Square(Z.x, ZSquared);
}
Curve25519Field.Square(ZSquared, W.x);
Curve25519Field.Multiply(W.x, a4.x, W.x);
return W;
}