public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat128.IsZero(y) || Nat128.IsOne(y))
{
return(this);
}
uint[] array = Nat128.Create();
SecP128R1Field.Square(y, array);
SecP128R1Field.Multiply(array, y, array);
uint[] array2 = Nat128.Create();
SecP128R1Field.SquareN(array, 2, array2);
SecP128R1Field.Multiply(array2, array, array2);
uint[] array3 = Nat128.Create();
SecP128R1Field.SquareN(array2, 4, array3);
SecP128R1Field.Multiply(array3, array2, array3);
uint[] array4 = array2;
SecP128R1Field.SquareN(array3, 2, array4);
SecP128R1Field.Multiply(array4, array, array4);
uint[] z = array;
SecP128R1Field.SquareN(array4, 10, z);
SecP128R1Field.Multiply(z, array4, z);
uint[] array5 = array3;
SecP128R1Field.SquareN(z, 10, array5);
SecP128R1Field.Multiply(array5, array4, array5);
uint[] array6 = array4;
SecP128R1Field.Square(array5, array6);
SecP128R1Field.Multiply(array6, y, array6);
uint[] z2 = array6;
SecP128R1Field.SquareN(z2, 95, z2);
uint[] array7 = array5;
SecP128R1Field.Square(z2, array7);
return((!Nat128.Eq(y, array7)) ? null : new SecP128R1FieldElement(z2));
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat128.IsZero(x) || Nat128.IsOne(x))
{
return(this);
}
uint[] z = Nat128.Create();
SecP128R1Field.Square(x, z);
SecP128R1Field.Multiply(z, x, z);
uint[] numArray3 = Nat128.Create();
SecP128R1Field.SquareN(z, 2, numArray3);
SecP128R1Field.Multiply(numArray3, z, numArray3);
uint[] numArray4 = Nat128.Create();
SecP128R1Field.SquareN(numArray3, 4, numArray4);
SecP128R1Field.Multiply(numArray4, numArray3, numArray4);
uint[] numArray5 = numArray3;
SecP128R1Field.SquareN(numArray4, 2, numArray5);
SecP128R1Field.Multiply(numArray5, z, numArray5);
uint[] numArray6 = z;
SecP128R1Field.SquareN(numArray5, 10, numArray6);
SecP128R1Field.Multiply(numArray6, numArray5, numArray6);
uint[] numArray7 = numArray4;
SecP128R1Field.SquareN(numArray6, 10, numArray7);
SecP128R1Field.Multiply(numArray7, numArray5, numArray7);
uint[] numArray8 = numArray5;
SecP128R1Field.Square(numArray7, numArray8);
SecP128R1Field.Multiply(numArray8, x, numArray8);
uint[] numArray9 = numArray8;
SecP128R1Field.SquareN(numArray9, 0x5f, numArray9);
uint[] numArray10 = numArray7;
SecP128R1Field.Square(numArray9, numArray10);
return(!Nat128.Eq(x, numArray10) ? null : new SecP128R1FieldElement(numArray9));
}
public static void Negate(uint[] x, uint[] z)
{
if (Nat128.IsZero(x))
{
Nat128.Zero(z);
return;
}
Nat128.Sub(SecP128R1Field.P, x, z);
}
public static void Negate(uint[] x, uint[] z)
{
if (Nat128.IsZero(x))
{
Nat128.Zero(z);
}
else
{
Nat128.Sub(P, x, z);
}
}
// D.1.4 91
/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
/*
* Raise this element to the exponent 2^126 - 2^95
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 31 1s } { 95 0s }
*
* Therefore we need an addition chain containing 31 (the length of the repunit) We use:
* 1, 2, 4, 8, 10, 20, 30, [31]
*/
uint[] x1 = this.x;
if (Nat128.IsZero(x1) || Nat128.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat128.Create();
SecP128R1Field.Square(x1, x2);
SecP128R1Field.Multiply(x2, x1, x2);
uint[] x4 = Nat128.Create();
SecP128R1Field.SquareN(x2, 2, x4);
SecP128R1Field.Multiply(x4, x2, x4);
uint[] x8 = Nat128.Create();
SecP128R1Field.SquareN(x4, 4, x8);
SecP128R1Field.Multiply(x8, x4, x8);
uint[] x10 = x4;
SecP128R1Field.SquareN(x8, 2, x10);
SecP128R1Field.Multiply(x10, x2, x10);
uint[] x20 = x2;
SecP128R1Field.SquareN(x10, 10, x20);
SecP128R1Field.Multiply(x20, x10, x20);
uint[] x30 = x8;
SecP128R1Field.SquareN(x20, 10, x30);
SecP128R1Field.Multiply(x30, x10, x30);
uint[] x31 = x10;
SecP128R1Field.Square(x30, x31);
SecP128R1Field.Multiply(x31, x1, x31);
uint[] t1 = x31;
SecP128R1Field.SquareN(t1, 95, t1);
uint[] t2 = x30;
SecP128R1Field.Square(t1, t2);
return(Nat128.Eq(x1, t2) ? new SecP128R1FieldElement(t1) : null);
}
public override ECPoint Add(ECPoint b)
{
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
if (this == b)
{
return(Twice());
}
ECCurve curve = Curve;
SecP128R1FieldElement secP128R1FieldElement = (SecP128R1FieldElement)base.RawXCoord;
SecP128R1FieldElement secP128R1FieldElement2 = (SecP128R1FieldElement)base.RawYCoord;
SecP128R1FieldElement secP128R1FieldElement3 = (SecP128R1FieldElement)b.RawXCoord;
SecP128R1FieldElement secP128R1FieldElement4 = (SecP128R1FieldElement)b.RawYCoord;
SecP128R1FieldElement secP128R1FieldElement5 = (SecP128R1FieldElement)base.RawZCoords[0];
SecP128R1FieldElement secP128R1FieldElement6 = (SecP128R1FieldElement)b.RawZCoords[0];
uint[] array = Nat128.CreateExt();
uint[] array2 = Nat128.Create();
uint[] array3 = Nat128.Create();
uint[] array4 = Nat128.Create();
bool isOne = secP128R1FieldElement5.IsOne;
uint[] array5;
uint[] array6;
if (isOne)
{
array5 = secP128R1FieldElement3.x;
array6 = secP128R1FieldElement4.x;
}
else
{
array6 = array3;
SecP128R1Field.Square(secP128R1FieldElement5.x, array6);
array5 = array2;
SecP128R1Field.Multiply(array6, secP128R1FieldElement3.x, array5);
SecP128R1Field.Multiply(array6, secP128R1FieldElement5.x, array6);
SecP128R1Field.Multiply(array6, secP128R1FieldElement4.x, array6);
}
bool isOne2 = secP128R1FieldElement6.IsOne;
uint[] array7;
uint[] array8;
if (isOne2)
{
array7 = secP128R1FieldElement.x;
array8 = secP128R1FieldElement2.x;
}
else
{
array8 = array4;
SecP128R1Field.Square(secP128R1FieldElement6.x, array8);
array7 = array;
SecP128R1Field.Multiply(array8, secP128R1FieldElement.x, array7);
SecP128R1Field.Multiply(array8, secP128R1FieldElement6.x, array8);
SecP128R1Field.Multiply(array8, secP128R1FieldElement2.x, array8);
}
uint[] array9 = Nat128.Create();
SecP128R1Field.Subtract(array7, array5, array9);
uint[] array10 = array2;
SecP128R1Field.Subtract(array8, array6, array10);
if (Nat128.IsZero(array9))
{
if (Nat128.IsZero(array10))
{
return(Twice());
}
return(curve.Infinity);
}
uint[] array11 = array3;
SecP128R1Field.Square(array9, array11);
uint[] array12 = Nat128.Create();
SecP128R1Field.Multiply(array11, array9, array12);
uint[] array13 = array3;
SecP128R1Field.Multiply(array11, array7, array13);
SecP128R1Field.Negate(array12, array12);
Nat128.Mul(array8, array12, array);
uint x = Nat128.AddBothTo(array13, array13, array12);
SecP128R1Field.Reduce32(x, array12);
SecP128R1FieldElement secP128R1FieldElement7 = new SecP128R1FieldElement(array4);
SecP128R1Field.Square(array10, secP128R1FieldElement7.x);
SecP128R1Field.Subtract(secP128R1FieldElement7.x, array12, secP128R1FieldElement7.x);
SecP128R1FieldElement secP128R1FieldElement8 = new SecP128R1FieldElement(array12);
SecP128R1Field.Subtract(array13, secP128R1FieldElement7.x, secP128R1FieldElement8.x);
SecP128R1Field.MultiplyAddToExt(secP128R1FieldElement8.x, array10, array);
SecP128R1Field.Reduce(array, secP128R1FieldElement8.x);
SecP128R1FieldElement secP128R1FieldElement9 = new SecP128R1FieldElement(array9);
if (!isOne)
{
SecP128R1Field.Multiply(secP128R1FieldElement9.x, secP128R1FieldElement5.x, secP128R1FieldElement9.x);
}
if (!isOne2)
{
SecP128R1Field.Multiply(secP128R1FieldElement9.x, secP128R1FieldElement6.x, secP128R1FieldElement9.x);
}
ECFieldElement[] zs = new ECFieldElement[1] {
secP128R1FieldElement9
};
return(new SecP128R1Point(curve, secP128R1FieldElement7, secP128R1FieldElement8, zs, base.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;
SecP128R1FieldElement X1 = (SecP128R1FieldElement)this.RawXCoord, Y1 = (SecP128R1FieldElement)this.RawYCoord;
SecP128R1FieldElement X2 = (SecP128R1FieldElement)b.RawXCoord, Y2 = (SecP128R1FieldElement)b.RawYCoord;
SecP128R1FieldElement Z1 = (SecP128R1FieldElement)this.RawZCoords[0];
SecP128R1FieldElement Z2 = (SecP128R1FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat128.CreateExt();
uint[] t2 = Nat128.Create();
uint[] t3 = Nat128.Create();
uint[] t4 = Nat128.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
SecP128R1Field.Square(Z1.x, S2);
U2 = t2;
SecP128R1Field.Multiply(S2, X2.x, U2);
SecP128R1Field.Multiply(S2, Z1.x, S2);
SecP128R1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP128R1Field.Square(Z2.x, S1);
U1 = tt1;
SecP128R1Field.Multiply(S1, X1.x, U1);
SecP128R1Field.Multiply(S1, Z2.x, S1);
SecP128R1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat128.Create();
SecP128R1Field.Subtract(U1, U2, H);
uint[] R = t2;
SecP128R1Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat128.IsZero(H))
{
if (Nat128.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 = t3;
SecP128R1Field.Square(H, HSquared);
uint[] G = Nat128.Create();
SecP128R1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP128R1Field.Multiply(HSquared, U1, V);
SecP128R1Field.Negate(G, G);
Nat128.Mul(S1, G, tt1);
c = Nat128.AddBothTo(V, V, G);
SecP128R1Field.Reduce32(c, G);
SecP128R1FieldElement X3 = new SecP128R1FieldElement(t4);
SecP128R1Field.Square(R, X3.x);
SecP128R1Field.Subtract(X3.x, G, X3.x);
SecP128R1FieldElement Y3 = new SecP128R1FieldElement(G);
SecP128R1Field.Subtract(V, X3.x, Y3.x);
SecP128R1Field.MultiplyAddToExt(Y3.x, R, tt1);
SecP128R1Field.Reduce(tt1, Y3.x);
SecP128R1FieldElement Z3 = new SecP128R1FieldElement(H);
if (!Z1IsOne)
{
SecP128R1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP128R1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return(new SecP128R1Point(curve, X3, Y3, zs, IsCompressed));
}
public override ECPoint Add(ECPoint b)
{
uint[] numArray5;
uint[] numArray6;
uint[] numArray7;
uint[] numArray8;
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
if (this == b)
{
return(this.Twice());
}
ECCurve curve = this.Curve;
SecP128R1FieldElement rawXCoord = (SecP128R1FieldElement)base.RawXCoord;
SecP128R1FieldElement rawYCoord = (SecP128R1FieldElement)base.RawYCoord;
SecP128R1FieldElement element3 = (SecP128R1FieldElement)b.RawXCoord;
SecP128R1FieldElement element4 = (SecP128R1FieldElement)b.RawYCoord;
SecP128R1FieldElement element5 = (SecP128R1FieldElement)base.RawZCoords[0];
SecP128R1FieldElement element6 = (SecP128R1FieldElement)b.RawZCoords[0];
uint[] zz = Nat128.CreateExt();
uint[] numArray2 = Nat128.Create();
uint[] numArray3 = Nat128.Create();
uint[] x = Nat128.Create();
bool isOne = element5.IsOne;
if (isOne)
{
numArray5 = element3.x;
numArray6 = element4.x;
}
else
{
numArray6 = numArray3;
SecP128R1Field.Square(element5.x, numArray6);
numArray5 = numArray2;
SecP128R1Field.Multiply(numArray6, element3.x, numArray5);
SecP128R1Field.Multiply(numArray6, element5.x, numArray6);
SecP128R1Field.Multiply(numArray6, element4.x, numArray6);
}
bool flag2 = element6.IsOne;
if (flag2)
{
numArray7 = rawXCoord.x;
numArray8 = rawYCoord.x;
}
else
{
numArray8 = x;
SecP128R1Field.Square(element6.x, numArray8);
numArray7 = zz;
SecP128R1Field.Multiply(numArray8, rawXCoord.x, numArray7);
SecP128R1Field.Multiply(numArray8, element6.x, numArray8);
SecP128R1Field.Multiply(numArray8, rawYCoord.x, numArray8);
}
uint[] z = Nat128.Create();
SecP128R1Field.Subtract(numArray7, numArray5, z);
uint[] numArray10 = numArray2;
SecP128R1Field.Subtract(numArray8, numArray6, numArray10);
if (Nat128.IsZero(z))
{
if (Nat128.IsZero(numArray10))
{
return(this.Twice());
}
return(curve.Infinity);
}
uint[] numArray11 = numArray3;
SecP128R1Field.Square(z, numArray11);
uint[] numArray12 = Nat128.Create();
SecP128R1Field.Multiply(numArray11, z, numArray12);
uint[] numArray13 = numArray3;
SecP128R1Field.Multiply(numArray11, numArray7, numArray13);
SecP128R1Field.Negate(numArray12, numArray12);
Nat128.Mul(numArray8, numArray12, zz);
SecP128R1Field.Reduce32(Nat128.AddBothTo(numArray13, numArray13, numArray12), numArray12);
SecP128R1FieldElement element7 = new SecP128R1FieldElement(x);
SecP128R1Field.Square(numArray10, element7.x);
SecP128R1Field.Subtract(element7.x, numArray12, element7.x);
SecP128R1FieldElement y = new SecP128R1FieldElement(numArray12);
SecP128R1Field.Subtract(numArray13, element7.x, y.x);
SecP128R1Field.MultiplyAddToExt(y.x, numArray10, zz);
SecP128R1Field.Reduce(zz, y.x);
SecP128R1FieldElement element9 = new SecP128R1FieldElement(z);
if (!isOne)
{
SecP128R1Field.Multiply(element9.x, element5.x, element9.x);
}
if (!flag2)
{
SecP128R1Field.Multiply(element9.x, element6.x, element9.x);
}
ECFieldElement[] zs = new ECFieldElement[] { element9 };
return(new SecP128R1Point(curve, element7, y, zs, base.IsCompressed));
}