# Brute forcing an elliptic curve encrypted key

I've been reading about ECC, and what I've established so far (correct me if I'm wrong) is that:

pubKey = privKey * G

where G is some special point on the secp256k1 curve.

Doesn't this mean we could attempt to brute force a private key by using:

privKey = pubKey/G

for all potential values of G.

I know it would require some unfeasible amount of attempts, but what if by chance that one of the first few attempts happened to have the correct value?

$$\mathit{privKey} = \mathit{pubKey}/G$$ for all potential values of $G$?
There seems to be a misunderstanding here: $\mathit{pubKey}$ and $G$ are fixed and publicly known, so there's nothing left to brute-force. The operation of "dividing" $\mathit{pubKey}$ by $G$ is (to the best of current public knowledge) computationally infeasible; this is the elliptic-curve discrete logarithm problem (ECDLP). However, of course, one can brute-force by trying all possible values of $\mathit{privKey}$ and checking whether $\mathit{privKey}\cdot G=\mathit{pubKey}$ holds.