Hello everyone

I have a pool of binary data with n elements. k of those elements (the private keys) have been xored with each other, generating another element (a public key), which is also in the pool. All the other elements are irrelevant.

So when xoring the private keys and the public key, the result should be 0.

I don't know the position of the k private keys and the position of the public key. I have to figure those out.

What would be an approach I could try, a phrase I could search for or an existing algorithm?

What I've tried (and failed because of runtime)

Of course I tried the brute force approach.

1. My first attempt was the worst. I made an iterator, and checked every option until I got there.
2. I did the same thing like in the first attempt but with an imaginary tree.

Those worked, but the runtime was to bad, with n = 115; k = 11.

I've tried something like this but I couldn't get something in this direction work for my needs.

Please help I put way to much time in this, Hellow2