# Is this a PRP? How can I create a distinguisher to show it isn't?

Consider the keyed permutation $$F_k : \{0,1\}^2 \to \{0,1\}^2$$ with two-bit keys defined as $$F_k(x) = k\oplus x$$.

Is this F a PRP? How can I create a distinguisher D and calculate the difference when using this D?

I know that $$F_k(x_1) \oplus x_1$$ will give me the key and that all $$x$$ and $$F_k(x)$$ in the same permutation use the same key. Can I use this to create a distinguisher?

• Yes. You already got the key to solve the problem. Try to understand the PRP definition again :) – Shan Chen Nov 7 '18 at 20:16