You cannot get private keys from public keys, that's exactly why they exist. If this was possible, you would have broken Bitcoin.
The solution for your CTF must lie somewhere else, not in breaking cryptography.

This is a clear example of the XY Problem, in my opinion.

What is Local, what is Server?

In general, you ask for a very difficult subject. Knowing public key you may find corresponding private key only with huge cost of time and computational power. In other words - it is doable in reasonable time only for a limited number of private keys, in the range which is just a fraction of the full range used by Bitcoin secp256k1 etc.
We may say that there are some methods to solve the problem you ask for (like https://arxiv.org/pdf/1501.07019.pdf) and even there exists programs for that, but all that works only in some cases. Imagine that you look for someone, and to find him you must check manually every apartment, every house on the planet. Clearly you will not be able to find that person in reasonable time - but if it is just a test for your method and given person will be in the same building you start your search, or even on the same street, it confirms the method is mathematically correct.
In other words - yes, it is possible that you find private key if you know public key only (it is not impossible), but the chance is so low that we say it is improbable.

This is imho the spot-on question.



@mluired you may have misunderstood something. Bitcoin is not the usual client-server application. Creating a private key doesn't need a server. Signing the private key doesn't need a server.
Getting a private key from a public key is not possible under normal circumstances. (It can be possible only if crucial mistakes are done.)