Point division Elliptic Curve in Java

Question

Suppose I have G(x,y) = k.P(x,y). I know G(x,y) and P(x,y).
How do I calculate k?

Answer 1

If G(x,y) and P(x,y)are on a secure elliptic curve for ECC, the problem of solving k is called "elliptic curve discrete logarithm problem", or ECDLP. It is infeasible to find k on a secure elliptic curve.

If you're not on such curve, enumerating all possible k and see if G=kP is a reasonable approach.