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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?

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

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