// 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 2^158 - 2^29
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 129 1s } { 29 0s }
*
* Therefore we need an addition chain containing 129 (the length of the repunit) We use:
* 1, 2, 4, 8, 16, 32, 64, 128, [129]
*/
uint[] x1 = this.x;
if (Nat160.IsZero(x1) || Nat160.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat160.Create();
SecP160R1Field.Square(x1, x2);
SecP160R1Field.Multiply(x2, x1, x2);
uint[] x4 = Nat160.Create();
SecP160R1Field.SquareN(x2, 2, x4);
SecP160R1Field.Multiply(x4, x2, x4);
uint[] x8 = x2;
SecP160R1Field.SquareN(x4, 4, x8);
SecP160R1Field.Multiply(x8, x4, x8);
uint[] x16 = x4;
SecP160R1Field.SquareN(x8, 8, x16);
SecP160R1Field.Multiply(x16, x8, x16);
uint[] x32 = x8;
SecP160R1Field.SquareN(x16, 16, x32);
SecP160R1Field.Multiply(x32, x16, x32);
uint[] x64 = x16;
SecP160R1Field.SquareN(x32, 32, x64);
SecP160R1Field.Multiply(x64, x32, x64);
uint[] x128 = x32;
SecP160R1Field.SquareN(x64, 64, x128);
SecP160R1Field.Multiply(x128, x64, x128);
uint[] x129 = x64;
SecP160R1Field.Square(x128, x129);
SecP160R1Field.Multiply(x129, x1, x129);
uint[] t1 = x129;
SecP160R1Field.SquareN(t1, 29, t1);
uint[] t2 = x128;
SecP160R1Field.Square(t1, t2);
return(Nat160.Eq(x1, t2) ? new SecP160R1FieldElement(t1) : null);
}
public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat160.IsZero(y) || Nat160.IsOne(y))
{
return(this);
}
uint[] array = Nat160.Create();
SecP160R1Field.Square(y, array);
SecP160R1Field.Multiply(array, y, array);
uint[] array2 = Nat160.Create();
SecP160R1Field.SquareN(array, 2, array2);
SecP160R1Field.Multiply(array2, array, array2);
uint[] array3 = array;
SecP160R1Field.SquareN(array2, 4, array3);
SecP160R1Field.Multiply(array3, array2, array3);
uint[] array4 = array2;
SecP160R1Field.SquareN(array3, 8, array4);
SecP160R1Field.Multiply(array4, array3, array4);
uint[] array5 = array3;
SecP160R1Field.SquareN(array4, 16, array5);
SecP160R1Field.Multiply(array5, array4, array5);
uint[] array6 = array4;
SecP160R1Field.SquareN(array5, 32, array6);
SecP160R1Field.Multiply(array6, array5, array6);
uint[] array7 = array5;
SecP160R1Field.SquareN(array6, 64, array7);
SecP160R1Field.Multiply(array7, array6, array7);
uint[] array8 = array6;
SecP160R1Field.Square(array7, array8);
SecP160R1Field.Multiply(array8, y, array8);
uint[] z = array8;
SecP160R1Field.SquareN(z, 29, z);
uint[] array9 = array7;
SecP160R1Field.Square(z, array9);
if (!Nat160.Eq(y, array9))
{
return(null);
}
return(new SecP160R1FieldElement(z));
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat160.IsZero(x) || Nat160.IsOne(x))
{
return(this);
}
uint[] z = Nat160.Create();
SecP160R1Field.Square(x, z);
SecP160R1Field.Multiply(z, x, z);
uint[] numArray3 = Nat160.Create();
SecP160R1Field.SquareN(z, 2, numArray3);
SecP160R1Field.Multiply(numArray3, z, numArray3);
uint[] numArray4 = z;
SecP160R1Field.SquareN(numArray3, 4, numArray4);
SecP160R1Field.Multiply(numArray4, numArray3, numArray4);
uint[] numArray5 = numArray3;
SecP160R1Field.SquareN(numArray4, 8, numArray5);
SecP160R1Field.Multiply(numArray5, numArray4, numArray5);
uint[] numArray6 = numArray4;
SecP160R1Field.SquareN(numArray5, 0x10, numArray6);
SecP160R1Field.Multiply(numArray6, numArray5, numArray6);
uint[] numArray7 = numArray5;
SecP160R1Field.SquareN(numArray6, 0x20, numArray7);
SecP160R1Field.Multiply(numArray7, numArray6, numArray7);
uint[] numArray8 = numArray6;
SecP160R1Field.SquareN(numArray7, 0x40, numArray8);
SecP160R1Field.Multiply(numArray8, numArray7, numArray8);
uint[] numArray9 = numArray7;
SecP160R1Field.Square(numArray8, numArray9);
SecP160R1Field.Multiply(numArray9, x, numArray9);
uint[] numArray10 = numArray9;
SecP160R1Field.SquareN(numArray10, 0x1d, numArray10);
uint[] numArray11 = numArray8;
SecP160R1Field.Square(numArray10, numArray11);
return(!Nat160.Eq(x, numArray11) ? null : new SecP160R1FieldElement(numArray10));
}
