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));
}
// 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);
}
