I am studying cryptography and having some trouble with the PRFsHow do I show that  $f_{k}(x) =x+k^2$ mod $2^n$ is not a Psuedo Random function?  I know that I need to show that the distignuisher can tell this is not random with a better then $\frac{1}{2}$ probability but how would it do that? (I don't just want an algorithm but a means to find such an algorithm for a query attack) Thanks
Show that a function is not a PRFs
proof techniques;cryptography;randomness
Any known plaintext attack instantly reveals the key:$$f_k(x) - x + 2^n \equiv k^2\mod 2^n$$On top of that, even without knowing the key or the plaintext, here's a property that no random function should have:$$f_k(x + 1) \equiv f_k(x) + 1 \mod 2^n$$