public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat192.IsZero(x) || Nat192.IsOne(x))
{
return(this);
}
uint[] z = Nat192.Create();
uint[] numArray3 = Nat192.Create();
SecP192R1Field.Square(x, z);
SecP192R1Field.Multiply(z, x, z);
SecP192R1Field.SquareN(z, 2, numArray3);
SecP192R1Field.Multiply(numArray3, z, numArray3);
SecP192R1Field.SquareN(numArray3, 4, z);
SecP192R1Field.Multiply(z, numArray3, z);
SecP192R1Field.SquareN(z, 8, numArray3);
SecP192R1Field.Multiply(numArray3, z, numArray3);
SecP192R1Field.SquareN(numArray3, 0x10, z);
SecP192R1Field.Multiply(z, numArray3, z);
SecP192R1Field.SquareN(z, 0x20, numArray3);
SecP192R1Field.Multiply(numArray3, z, numArray3);
SecP192R1Field.SquareN(numArray3, 0x40, z);
SecP192R1Field.Multiply(z, numArray3, z);
SecP192R1Field.SquareN(z, 0x3e, z);
SecP192R1Field.Square(z, numArray3);
return(!Nat192.Eq(x, numArray3) ? null : new SecP192R1FieldElement(z));
}
public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat192.IsZero(y) || Nat192.IsOne(y))
{
return(this);
}
uint[] array = Nat192.Create();
uint[] array2 = Nat192.Create();
SecP192R1Field.Square(y, array);
SecP192R1Field.Multiply(array, y, array);
SecP192R1Field.SquareN(array, 2, array2);
SecP192R1Field.Multiply(array2, array, array2);
SecP192R1Field.SquareN(array2, 4, array);
SecP192R1Field.Multiply(array, array2, array);
SecP192R1Field.SquareN(array, 8, array2);
SecP192R1Field.Multiply(array2, array, array2);
SecP192R1Field.SquareN(array2, 16, array);
SecP192R1Field.Multiply(array, array2, array);
SecP192R1Field.SquareN(array, 32, array2);
SecP192R1Field.Multiply(array2, array, array2);
SecP192R1Field.SquareN(array2, 64, array);
SecP192R1Field.Multiply(array, array2, array);
SecP192R1Field.SquareN(array, 62, array);
SecP192R1Field.Square(array, array2);
return((!Nat192.Eq(y, array2)) ? null : new SecP192R1FieldElement(array));
}
public static void Negate(uint[] x, uint[] z)
{
if (Nat192.IsZero(x))
{
Nat192.Zero(z);
return;
}
Nat192.Sub(SecP192K1Field.P, x, z);
}
public static void Negate(uint[] x, uint[] z)
{
if (Nat192.IsZero(x))
{
Nat192.Zero(z);
}
else
{
Nat192.Sub(P, x, z);
}
}
public override ECFieldElement Sqrt()
{
uint[] y = this.x;
if (Nat192.IsZero(y) || Nat192.IsOne(y))
{
return(this);
}
uint[] array = Nat192.Create();
SecP192K1Field.Square(y, array);
SecP192K1Field.Multiply(array, y, array);
uint[] array2 = Nat192.Create();
SecP192K1Field.Square(array, array2);
SecP192K1Field.Multiply(array2, y, array2);
uint[] array3 = Nat192.Create();
SecP192K1Field.SquareN(array2, 3, array3);
SecP192K1Field.Multiply(array3, array2, array3);
uint[] array4 = array3;
SecP192K1Field.SquareN(array3, 2, array4);
SecP192K1Field.Multiply(array4, array, array4);
uint[] array5 = array;
SecP192K1Field.SquareN(array4, 8, array5);
SecP192K1Field.Multiply(array5, array4, array5);
uint[] array6 = array4;
SecP192K1Field.SquareN(array5, 3, array6);
SecP192K1Field.Multiply(array6, array2, array6);
uint[] array7 = Nat192.Create();
SecP192K1Field.SquareN(array6, 16, array7);
SecP192K1Field.Multiply(array7, array5, array7);
uint[] array8 = array5;
SecP192K1Field.SquareN(array7, 35, array8);
SecP192K1Field.Multiply(array8, array7, array8);
uint[] z = array7;
SecP192K1Field.SquareN(array8, 70, z);
SecP192K1Field.Multiply(z, array8, z);
uint[] array9 = array8;
SecP192K1Field.SquareN(z, 19, array9);
SecP192K1Field.Multiply(array9, array6, array9);
uint[] z2 = array9;
SecP192K1Field.SquareN(z2, 20, z2);
SecP192K1Field.Multiply(z2, array6, z2);
SecP192K1Field.SquareN(z2, 4, z2);
SecP192K1Field.Multiply(z2, array2, z2);
SecP192K1Field.SquareN(z2, 6, z2);
SecP192K1Field.Multiply(z2, array2, z2);
SecP192K1Field.Square(z2, z2);
uint[] array10 = array2;
SecP192K1Field.Square(z2, array10);
if (!Nat192.Eq(y, array10))
{
return(null);
}
return(new SecP192K1FieldElement(z2));
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat192.IsZero(x) || Nat192.IsOne(x))
{
return(this);
}
uint[] z = Nat192.Create();
SecP192K1Field.Square(x, z);
SecP192K1Field.Multiply(z, x, z);
uint[] numArray3 = Nat192.Create();
SecP192K1Field.Square(z, numArray3);
SecP192K1Field.Multiply(numArray3, x, numArray3);
uint[] numArray4 = Nat192.Create();
SecP192K1Field.SquareN(numArray3, 3, numArray4);
SecP192K1Field.Multiply(numArray4, numArray3, numArray4);
uint[] numArray5 = numArray4;
SecP192K1Field.SquareN(numArray4, 2, numArray5);
SecP192K1Field.Multiply(numArray5, z, numArray5);
uint[] numArray6 = z;
SecP192K1Field.SquareN(numArray5, 8, numArray6);
SecP192K1Field.Multiply(numArray6, numArray5, numArray6);
uint[] numArray7 = numArray5;
SecP192K1Field.SquareN(numArray6, 3, numArray7);
SecP192K1Field.Multiply(numArray7, numArray3, numArray7);
uint[] numArray8 = Nat192.Create();
SecP192K1Field.SquareN(numArray7, 0x10, numArray8);
SecP192K1Field.Multiply(numArray8, numArray6, numArray8);
uint[] numArray9 = numArray6;
SecP192K1Field.SquareN(numArray8, 0x23, numArray9);
SecP192K1Field.Multiply(numArray9, numArray8, numArray9);
uint[] numArray10 = numArray8;
SecP192K1Field.SquareN(numArray9, 70, numArray10);
SecP192K1Field.Multiply(numArray10, numArray9, numArray10);
uint[] numArray11 = numArray9;
SecP192K1Field.SquareN(numArray10, 0x13, numArray11);
SecP192K1Field.Multiply(numArray11, numArray7, numArray11);
uint[] numArray12 = numArray11;
SecP192K1Field.SquareN(numArray12, 20, numArray12);
SecP192K1Field.Multiply(numArray12, numArray7, numArray12);
SecP192K1Field.SquareN(numArray12, 4, numArray12);
SecP192K1Field.Multiply(numArray12, numArray3, numArray12);
SecP192K1Field.SquareN(numArray12, 6, numArray12);
SecP192K1Field.Multiply(numArray12, numArray3, numArray12);
SecP192K1Field.Square(numArray12, numArray12);
uint[] numArray13 = numArray3;
SecP192K1Field.Square(numArray12, numArray13);
return(!Nat192.Eq(x, numArray13) ? null : new SecP192K1FieldElement(numArray12));
}
/**
* 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 2^190 - 2^62
uint[] x1 = this.x;
if (Nat192.IsZero(x1) || Nat192.IsOne(x1))
{
return(this);
}
uint[] t1 = Nat192.Create();
uint[] t2 = Nat192.Create();
SecP192R1Field.Square(x1, t1);
SecP192R1Field.Multiply(t1, x1, t1);
SecP192R1Field.SquareN(t1, 2, t2);
SecP192R1Field.Multiply(t2, t1, t2);
SecP192R1Field.SquareN(t2, 4, t1);
SecP192R1Field.Multiply(t1, t2, t1);
SecP192R1Field.SquareN(t1, 8, t2);
SecP192R1Field.Multiply(t2, t1, t2);
SecP192R1Field.SquareN(t2, 16, t1);
SecP192R1Field.Multiply(t1, t2, t1);
SecP192R1Field.SquareN(t1, 32, t2);
SecP192R1Field.Multiply(t2, t1, t2);
SecP192R1Field.SquareN(t2, 64, t1);
SecP192R1Field.Multiply(t1, t2, t1);
SecP192R1Field.SquareN(t1, 62, t1);
SecP192R1Field.Square(t1, t2);
return(Nat192.Eq(x1, t2) ? new SecP192R1FieldElement(t1) : null);
}
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;
SecP192K1FieldElement X1 = (SecP192K1FieldElement)this.RawXCoord, Y1 = (SecP192K1FieldElement)this.RawYCoord;
SecP192K1FieldElement X2 = (SecP192K1FieldElement)b.RawXCoord, Y2 = (SecP192K1FieldElement)b.RawYCoord;
SecP192K1FieldElement Z1 = (SecP192K1FieldElement)this.RawZCoords[0];
SecP192K1FieldElement Z2 = (SecP192K1FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat192.CreateExt();
uint[] t2 = Nat192.Create();
uint[] t3 = Nat192.Create();
uint[] t4 = Nat192.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
SecP192K1Field.Square(Z1.x, S2);
U2 = t2;
SecP192K1Field.Multiply(S2, X2.x, U2);
SecP192K1Field.Multiply(S2, Z1.x, S2);
SecP192K1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP192K1Field.Square(Z2.x, S1);
U1 = tt1;
SecP192K1Field.Multiply(S1, X1.x, U1);
SecP192K1Field.Multiply(S1, Z2.x, S1);
SecP192K1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat192.Create();
SecP192K1Field.Subtract(U1, U2, H);
uint[] R = t2;
SecP192K1Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat192.IsZero(H))
{
if (Nat192.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;
SecP192K1Field.Square(H, HSquared);
uint[] G = Nat192.Create();
SecP192K1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP192K1Field.Multiply(HSquared, U1, V);
SecP192K1Field.Negate(G, G);
Nat192.Mul(S1, G, tt1);
c = Nat192.AddBothTo(V, V, G);
SecP192K1Field.Reduce32(c, G);
SecP192K1FieldElement X3 = new SecP192K1FieldElement(t4);
SecP192K1Field.Square(R, X3.x);
SecP192K1Field.Subtract(X3.x, G, X3.x);
SecP192K1FieldElement Y3 = new SecP192K1FieldElement(G);
SecP192K1Field.Subtract(V, X3.x, Y3.x);
SecP192K1Field.MultiplyAddToExt(Y3.x, R, tt1);
SecP192K1Field.Reduce(tt1, Y3.x);
SecP192K1FieldElement Z3 = new SecP192K1FieldElement(H);
if (!Z1IsOne)
{
SecP192K1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP192K1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return(new SecP192K1Point(curve, X3, Y3, zs, IsCompressed));
}
/**
* 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 2^190 - 2^30 - 2^10 - 2^6 - 2^5 - 2^4 - 2^1
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 159 1s } { 1 0s } { 19 1s } { 1 0s } { 3 1s } { 3 0s} { 3 1s } { 1 0s }
*
* Therefore we need an addition chain containing 3, 19, 159 (the lengths of the repunits)
* We use: 1, 2, [3], 6, 8, 16, [19], 35, 70, 140, [159]
*/
uint[] x1 = this.x;
if (Nat192.IsZero(x1) || Nat192.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat192.Create();
SecP192K1Field.Square(x1, x2);
SecP192K1Field.Multiply(x2, x1, x2);
uint[] x3 = Nat192.Create();
SecP192K1Field.Square(x2, x3);
SecP192K1Field.Multiply(x3, x1, x3);
uint[] x6 = Nat192.Create();
SecP192K1Field.SquareN(x3, 3, x6);
SecP192K1Field.Multiply(x6, x3, x6);
uint[] x8 = x6;
SecP192K1Field.SquareN(x6, 2, x8);
SecP192K1Field.Multiply(x8, x2, x8);
uint[] x16 = x2;
SecP192K1Field.SquareN(x8, 8, x16);
SecP192K1Field.Multiply(x16, x8, x16);
uint[] x19 = x8;
SecP192K1Field.SquareN(x16, 3, x19);
SecP192K1Field.Multiply(x19, x3, x19);
uint[] x35 = Nat192.Create();
SecP192K1Field.SquareN(x19, 16, x35);
SecP192K1Field.Multiply(x35, x16, x35);
uint[] x70 = x16;
SecP192K1Field.SquareN(x35, 35, x70);
SecP192K1Field.Multiply(x70, x35, x70);
uint[] x140 = x35;
SecP192K1Field.SquareN(x70, 70, x140);
SecP192K1Field.Multiply(x140, x70, x140);
uint[] x159 = x70;
SecP192K1Field.SquareN(x140, 19, x159);
SecP192K1Field.Multiply(x159, x19, x159);
uint[] t1 = x159;
SecP192K1Field.SquareN(t1, 20, t1);
SecP192K1Field.Multiply(t1, x19, t1);
SecP192K1Field.SquareN(t1, 4, t1);
SecP192K1Field.Multiply(t1, x3, t1);
SecP192K1Field.SquareN(t1, 6, t1);
SecP192K1Field.Multiply(t1, x3, t1);
SecP192K1Field.Square(t1, t1);
uint[] t2 = x3;
SecP192K1Field.Square(t1, t2);
return(Nat192.Eq(x1, t2) ? new SecP192K1FieldElement(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;
SecP192R1FieldElement secP192R1FieldElement = (SecP192R1FieldElement)base.RawXCoord;
SecP192R1FieldElement secP192R1FieldElement2 = (SecP192R1FieldElement)base.RawYCoord;
SecP192R1FieldElement secP192R1FieldElement3 = (SecP192R1FieldElement)b.RawXCoord;
SecP192R1FieldElement secP192R1FieldElement4 = (SecP192R1FieldElement)b.RawYCoord;
SecP192R1FieldElement secP192R1FieldElement5 = (SecP192R1FieldElement)base.RawZCoords[0];
SecP192R1FieldElement secP192R1FieldElement6 = (SecP192R1FieldElement)b.RawZCoords[0];
uint[] array = Nat192.CreateExt();
uint[] array2 = Nat192.Create();
uint[] array3 = Nat192.Create();
uint[] array4 = Nat192.Create();
bool isOne = secP192R1FieldElement5.IsOne;
uint[] array5;
uint[] array6;
if (isOne)
{
array5 = secP192R1FieldElement3.x;
array6 = secP192R1FieldElement4.x;
}
else
{
array6 = array3;
SecP192R1Field.Square(secP192R1FieldElement5.x, array6);
array5 = array2;
SecP192R1Field.Multiply(array6, secP192R1FieldElement3.x, array5);
SecP192R1Field.Multiply(array6, secP192R1FieldElement5.x, array6);
SecP192R1Field.Multiply(array6, secP192R1FieldElement4.x, array6);
}
bool isOne2 = secP192R1FieldElement6.IsOne;
uint[] array7;
uint[] array8;
if (isOne2)
{
array7 = secP192R1FieldElement.x;
array8 = secP192R1FieldElement2.x;
}
else
{
array8 = array4;
SecP192R1Field.Square(secP192R1FieldElement6.x, array8);
array7 = array;
SecP192R1Field.Multiply(array8, secP192R1FieldElement.x, array7);
SecP192R1Field.Multiply(array8, secP192R1FieldElement6.x, array8);
SecP192R1Field.Multiply(array8, secP192R1FieldElement2.x, array8);
}
uint[] array9 = Nat192.Create();
SecP192R1Field.Subtract(array7, array5, array9);
uint[] array10 = array2;
SecP192R1Field.Subtract(array8, array6, array10);
if (Nat192.IsZero(array9))
{
if (Nat192.IsZero(array10))
{
return(Twice());
}
return(curve.Infinity);
}
uint[] array11 = array3;
SecP192R1Field.Square(array9, array11);
uint[] array12 = Nat192.Create();
SecP192R1Field.Multiply(array11, array9, array12);
uint[] array13 = array3;
SecP192R1Field.Multiply(array11, array7, array13);
SecP192R1Field.Negate(array12, array12);
Nat192.Mul(array8, array12, array);
uint x = Nat192.AddBothTo(array13, array13, array12);
SecP192R1Field.Reduce32(x, array12);
SecP192R1FieldElement secP192R1FieldElement7 = new SecP192R1FieldElement(array4);
SecP192R1Field.Square(array10, secP192R1FieldElement7.x);
SecP192R1Field.Subtract(secP192R1FieldElement7.x, array12, secP192R1FieldElement7.x);
SecP192R1FieldElement secP192R1FieldElement8 = new SecP192R1FieldElement(array12);
SecP192R1Field.Subtract(array13, secP192R1FieldElement7.x, secP192R1FieldElement8.x);
SecP192R1Field.MultiplyAddToExt(secP192R1FieldElement8.x, array10, array);
SecP192R1Field.Reduce(array, secP192R1FieldElement8.x);
SecP192R1FieldElement secP192R1FieldElement9 = new SecP192R1FieldElement(array9);
if (!isOne)
{
SecP192R1Field.Multiply(secP192R1FieldElement9.x, secP192R1FieldElement5.x, secP192R1FieldElement9.x);
}
if (!isOne2)
{
SecP192R1Field.Multiply(secP192R1FieldElement9.x, secP192R1FieldElement6.x, secP192R1FieldElement9.x);
}
ECFieldElement[] zs = new ECFieldElement[1] {
secP192R1FieldElement9
};
return(new SecP192R1Point(curve, secP192R1FieldElement7, secP192R1FieldElement8, zs, base.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;
SecP192K1FieldElement rawXCoord = (SecP192K1FieldElement)base.RawXCoord;
SecP192K1FieldElement rawYCoord = (SecP192K1FieldElement)base.RawYCoord;
SecP192K1FieldElement element3 = (SecP192K1FieldElement)b.RawXCoord;
SecP192K1FieldElement element4 = (SecP192K1FieldElement)b.RawYCoord;
SecP192K1FieldElement element5 = (SecP192K1FieldElement)base.RawZCoords[0];
SecP192K1FieldElement element6 = (SecP192K1FieldElement)b.RawZCoords[0];
uint[] zz = Nat192.CreateExt();
uint[] numArray2 = Nat192.Create();
uint[] numArray3 = Nat192.Create();
uint[] x = Nat192.Create();
bool isOne = element5.IsOne;
if (isOne)
{
numArray5 = element3.x;
numArray6 = element4.x;
}
else
{
numArray6 = numArray3;
SecP192K1Field.Square(element5.x, numArray6);
numArray5 = numArray2;
SecP192K1Field.Multiply(numArray6, element3.x, numArray5);
SecP192K1Field.Multiply(numArray6, element5.x, numArray6);
SecP192K1Field.Multiply(numArray6, element4.x, numArray6);
}
bool flag2 = element6.IsOne;
if (flag2)
{
numArray7 = rawXCoord.x;
numArray8 = rawYCoord.x;
}
else
{
numArray8 = x;
SecP192K1Field.Square(element6.x, numArray8);
numArray7 = zz;
SecP192K1Field.Multiply(numArray8, rawXCoord.x, numArray7);
SecP192K1Field.Multiply(numArray8, element6.x, numArray8);
SecP192K1Field.Multiply(numArray8, rawYCoord.x, numArray8);
}
uint[] z = Nat192.Create();
SecP192K1Field.Subtract(numArray7, numArray5, z);
uint[] numArray10 = numArray2;
SecP192K1Field.Subtract(numArray8, numArray6, numArray10);
if (Nat192.IsZero(z))
{
if (Nat192.IsZero(numArray10))
{
return(this.Twice());
}
return(curve.Infinity);
}
uint[] numArray11 = numArray3;
SecP192K1Field.Square(z, numArray11);
uint[] numArray12 = Nat192.Create();
SecP192K1Field.Multiply(numArray11, z, numArray12);
uint[] numArray13 = numArray3;
SecP192K1Field.Multiply(numArray11, numArray7, numArray13);
SecP192K1Field.Negate(numArray12, numArray12);
Nat192.Mul(numArray8, numArray12, zz);
SecP192K1Field.Reduce32(Nat192.AddBothTo(numArray13, numArray13, numArray12), numArray12);
SecP192K1FieldElement element7 = new SecP192K1FieldElement(x);
SecP192K1Field.Square(numArray10, element7.x);
SecP192K1Field.Subtract(element7.x, numArray12, element7.x);
SecP192K1FieldElement y = new SecP192K1FieldElement(numArray12);
SecP192K1Field.Subtract(numArray13, element7.x, y.x);
SecP192K1Field.MultiplyAddToExt(y.x, numArray10, zz);
SecP192K1Field.Reduce(zz, y.x);
SecP192K1FieldElement element9 = new SecP192K1FieldElement(z);
if (!isOne)
{
SecP192K1Field.Multiply(element9.x, element5.x, element9.x);
}
if (!flag2)
{
SecP192K1Field.Multiply(element9.x, element6.x, element9.x);
}
ECFieldElement[] zs = new ECFieldElement[] { element9 };
return(new SecP192K1Point(curve, element7, y, zs, base.IsCompressed));
}