How to prove the PRF, $F(k,x) = (k \wedge x ) \oplus k$ is PRP? I am trying to understand PRF's and PRP's. I have got a question where I have to decide whether $F(k,x) = (k \wedge x ) \oplus k$ (where $k$ and $x$ are simple $1$ bits (1 or 0)) is PRP or not. I am not sure if I understand PRP's correctly. As I have found:


  A Pseudo Random Permutation is a PRF that happens to have the property that every element in the input domain has a single associated member in the output co-domain and vice versa.


So what I have got in my example.

k x F(k,x)
0 0 0
0 1 0
1 0 1
1 1 0 


For each couple, I have an associated member in output co-domain, but for each output 0 and 1. I do not have a unique member in the input domain. So this function is not PRP. Am I right?
Your definition tries to say that a permutation must be invertible.

When the key is $0$, we can not determine the inverse of 0 and the inverse of 1 doesn't exist.