public override ECFieldElement Sqrt()
{
uint[] y = this.x;
if (Nat160.IsZero(y) || Nat160.IsOne(y))
{
return(this);
}
uint[] array = Nat160.Create();
SecP160R2Field.Square(y, array);
SecP160R2Field.Multiply(array, y, array);
uint[] array2 = Nat160.Create();
SecP160R2Field.Square(array, array2);
SecP160R2Field.Multiply(array2, y, array2);
uint[] array3 = Nat160.Create();
SecP160R2Field.Square(array2, array3);
SecP160R2Field.Multiply(array3, y, array3);
uint[] array4 = Nat160.Create();
SecP160R2Field.SquareN(array3, 3, array4);
SecP160R2Field.Multiply(array4, array2, array4);
uint[] array5 = array3;
SecP160R2Field.SquareN(array4, 7, array5);
SecP160R2Field.Multiply(array5, array4, array5);
uint[] array6 = array4;
SecP160R2Field.SquareN(array5, 3, array6);
SecP160R2Field.Multiply(array6, array2, array6);
uint[] array7 = Nat160.Create();
SecP160R2Field.SquareN(array6, 14, array7);
SecP160R2Field.Multiply(array7, array5, array7);
uint[] array8 = array5;
SecP160R2Field.SquareN(array7, 31, array8);
SecP160R2Field.Multiply(array8, array7, array8);
uint[] z = array7;
SecP160R2Field.SquareN(array8, 62, z);
SecP160R2Field.Multiply(z, array8, z);
uint[] array9 = array8;
SecP160R2Field.SquareN(z, 3, array9);
SecP160R2Field.Multiply(array9, array2, array9);
uint[] z2 = array9;
SecP160R2Field.SquareN(z2, 18, z2);
SecP160R2Field.Multiply(z2, array6, z2);
SecP160R2Field.SquareN(z2, 2, z2);
SecP160R2Field.Multiply(z2, y, z2);
SecP160R2Field.SquareN(z2, 3, z2);
SecP160R2Field.Multiply(z2, array, z2);
SecP160R2Field.SquareN(z2, 6, z2);
SecP160R2Field.Multiply(z2, array2, z2);
SecP160R2Field.SquareN(z2, 2, z2);
SecP160R2Field.Multiply(z2, y, z2);
uint[] array10 = array;
SecP160R2Field.Square(z2, array10);
if (!Nat160.Eq(y, array10))
{
return(null);
}
return(new SecP160R2FieldElement(z2));
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat160.IsZero(x) || Nat160.IsOne(x))
{
return(this);
}
uint[] z = Nat160.Create();
SecP160R2Field.Square(x, z);
SecP160R2Field.Multiply(z, x, z);
uint[] numArray3 = Nat160.Create();
SecP160R2Field.Square(z, numArray3);
SecP160R2Field.Multiply(numArray3, x, numArray3);
uint[] numArray4 = Nat160.Create();
SecP160R2Field.Square(numArray3, numArray4);
SecP160R2Field.Multiply(numArray4, x, numArray4);
uint[] numArray5 = Nat160.Create();
SecP160R2Field.SquareN(numArray4, 3, numArray5);
SecP160R2Field.Multiply(numArray5, numArray3, numArray5);
uint[] numArray6 = numArray4;
SecP160R2Field.SquareN(numArray5, 7, numArray6);
SecP160R2Field.Multiply(numArray6, numArray5, numArray6);
uint[] numArray7 = numArray5;
SecP160R2Field.SquareN(numArray6, 3, numArray7);
SecP160R2Field.Multiply(numArray7, numArray3, numArray7);
uint[] numArray8 = Nat160.Create();
SecP160R2Field.SquareN(numArray7, 14, numArray8);
SecP160R2Field.Multiply(numArray8, numArray6, numArray8);
uint[] numArray9 = numArray6;
SecP160R2Field.SquareN(numArray8, 0x1f, numArray9);
SecP160R2Field.Multiply(numArray9, numArray8, numArray9);
uint[] numArray10 = numArray8;
SecP160R2Field.SquareN(numArray9, 0x3e, numArray10);
SecP160R2Field.Multiply(numArray10, numArray9, numArray10);
uint[] numArray11 = numArray9;
SecP160R2Field.SquareN(numArray10, 3, numArray11);
SecP160R2Field.Multiply(numArray11, numArray3, numArray11);
uint[] numArray12 = numArray11;
SecP160R2Field.SquareN(numArray12, 0x12, numArray12);
SecP160R2Field.Multiply(numArray12, numArray7, numArray12);
SecP160R2Field.SquareN(numArray12, 2, numArray12);
SecP160R2Field.Multiply(numArray12, x, numArray12);
SecP160R2Field.SquareN(numArray12, 3, numArray12);
SecP160R2Field.Multiply(numArray12, z, numArray12);
SecP160R2Field.SquareN(numArray12, 6, numArray12);
SecP160R2Field.Multiply(numArray12, numArray3, numArray12);
SecP160R2Field.SquareN(numArray12, 2, numArray12);
SecP160R2Field.Multiply(numArray12, x, numArray12);
uint[] numArray13 = z;
SecP160R2Field.Square(numArray12, numArray13);
return(!Nat160.Eq(x, numArray13) ? null : new SecP160R2FieldElement(numArray12));
}
// 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 - 2^30 - 2^12 - 2^10 - 2^7 - 2^6 - 2^5 - 2^1 - 2^0
*
* Breaking up the exponent's binary representation into "repunits", we get: { 127 1s } { 1
* 0s } { 17 1s } { 1 0s } { 1 1s } { 1 0s } { 2 1s } { 3 0s } { 3 1s } { 1 0s } { 1 1s }
*
* Therefore we need an Addition chain containing 1, 2, 3, 17, 127 (the lengths of the repunits)
* We use: [1], [2], [3], 4, 7, 14, [17], 31, 62, 124, [127]
*/
uint[] x1 = this.x;
if (Nat160.IsZero(x1) || Nat160.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat160.Create();
SecP160R2Field.Square(x1, x2);
SecP160R2Field.Multiply(x2, x1, x2);
uint[] x3 = Nat160.Create();
SecP160R2Field.Square(x2, x3);
SecP160R2Field.Multiply(x3, x1, x3);
uint[] x4 = Nat160.Create();
SecP160R2Field.Square(x3, x4);
SecP160R2Field.Multiply(x4, x1, x4);
uint[] x7 = Nat160.Create();
SecP160R2Field.SquareN(x4, 3, x7);
SecP160R2Field.Multiply(x7, x3, x7);
uint[] x14 = x4;
SecP160R2Field.SquareN(x7, 7, x14);
SecP160R2Field.Multiply(x14, x7, x14);
uint[] x17 = x7;
SecP160R2Field.SquareN(x14, 3, x17);
SecP160R2Field.Multiply(x17, x3, x17);
uint[] x31 = Nat160.Create();
SecP160R2Field.SquareN(x17, 14, x31);
SecP160R2Field.Multiply(x31, x14, x31);
uint[] x62 = x14;
SecP160R2Field.SquareN(x31, 31, x62);
SecP160R2Field.Multiply(x62, x31, x62);
uint[] x124 = x31;
SecP160R2Field.SquareN(x62, 62, x124);
SecP160R2Field.Multiply(x124, x62, x124);
uint[] x127 = x62;
SecP160R2Field.SquareN(x124, 3, x127);
SecP160R2Field.Multiply(x127, x3, x127);
uint[] t1 = x127;
SecP160R2Field.SquareN(t1, 18, t1);
SecP160R2Field.Multiply(t1, x17, t1);
SecP160R2Field.SquareN(t1, 2, t1);
SecP160R2Field.Multiply(t1, x1, t1);
SecP160R2Field.SquareN(t1, 3, t1);
SecP160R2Field.Multiply(t1, x2, t1);
SecP160R2Field.SquareN(t1, 6, t1);
SecP160R2Field.Multiply(t1, x3, t1);
SecP160R2Field.SquareN(t1, 2, t1);
SecP160R2Field.Multiply(t1, x1, t1);
uint[] t2 = x2;
SecP160R2Field.Square(t1, t2);
return(Nat160.Eq(x1, t2) ? new SecP160R2FieldElement(t1) : null);
}
