Given the affine form of coordinates $(x,y)$ such as $(5,3)$, if I want to convert $(5,3)$ to projective coordinates $(x,y,z)$, should the form of point be $(5,3,1)$? It is triplet not a point, right?

So, is the true form from affine to projective $(x,y) \rightarrow (x/z),(y/z) \in Z_p$. For example: $(5,3) \rightarrow (5/1,3/1)$? But $1$ is BigInteger?

Then, I am coding in Java with BouncyCastle API:

public pointMultiplication (BigInteger x, BigInteger y, BigInteger z)
    this.X = x;
    this.Y = y;
    // Jika z = null atau z = 0 maka nilai Z menjadi 1 
    if (z == null) {
        this.Z = BigInteger.ONE;
    else {
        this.Z = z;
    this.zinv = null;

What the meaning of z = null?

  • $\begingroup$ Two options: $z=\text{null}\Leftrightarrow z=0$ or it could be that this has to be read like a pointer $z=\text{null} \Leftrightarrow z=\text{unassigned}$. I don't know which of the two it is. $\endgroup$ – SEJPM Jan 19 '16 at 10:12
  • 1
    $\begingroup$ +1 for the AI translation of the comment: "If z = null or z = 0, then the value Z becomes 1", which is better than the code is. $\endgroup$ – fgrieu Jan 19 '16 at 12:50

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