# Hardness of elliptic curve discrete logarithm problem?

I have just started to study Elliptic curve cryptography. I have a question: In elliptic curves in Fp (such as prime256v1 curve) I just learned that the discrete logarithm problem is, "finding k, where Q=kG and G and Q are known, is hard" (k is big integer and G is generator)

I'm curious if the below sentence is still correct?

"finding x or y or z is hard, where P0=xG, P1=xyG and P2=xyzG and P0, P1, P2 and G (also generator) are known"

I think there is too much information. Is this still hard?

• Your problem is an easy exercise in a security proof by reduction to a standard DL problem. It is also not primarily related to elliptic curves but can be proved for arbitrary groups where the DL problem is difficult. – user27950 Oct 26 '16 at 15:49

## 1 Answer

This depends a bit on your group structure because P0, P1, P2 could lie in small subgroups but if you avoid that you are still trying to solve a hard discrete logarithm problem.