I stuck on the same problem in a cryptography, as stated in this question
I found following statement in famous textbook by J. Katz (main wiki PRP article refers to this textbook)
PROPOSITION 3.27 If F is a pseudorandom permutation and additionally L-input(n) >= n, then F is also a pseudorandom function.
So the question is extremely simple, but I spent hours trying to find an answer. If Fk(x) - is a PRP which takes n-length input, uniform n-length key k, and x - as an input n-bit string. How it can be a pseudorandom function?!
Permutation means F(00000) = 00000 ? So the function just reorder given input bits in pseudorandom manner determined by key K? If not, can someone explain what actually does a PRP? And what is the difference with PRF? Except invertibility.