(Secure PRF). Let = {0,1}. Consider the following Pseudo Random Permutation (PRP): . Let Key space: = {0,1} and Input Space = {0,1}. The PRP is defined as: (,) = , Prove that it is not a secure Pseudo-Random Function (PRF). Proof: Let [,] be the set of all the mapping functions from set X to set X. Construct two experiments EXP(0) and EXP(1) as follows.

a) Compute Pr[(0) = 1] [5 pts] and Pr[(1) = 1] [5 pts] b) Compute the advantage [,] to see whether it is negligible or non-negligible. [5 pts]