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 - 2^30 - 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);
}
