Consider the following simplified 2-rounds analogue E of DES. M=P=K=24 S-boxes: S1=[1,0] and S2=[1,1] The initial and the final permutation are the identity permutation. The expansion function is the identity function. The key schedule function is defined as follows: For a key K=(k1k2k3k4), the round 1 key is K1=(k4k1) and the round 2 key is K2=(k2k3). (a) Call a key K a weak key for the cipher E if for all xM it is the case that E(E(x,k1),k2)=x. Does E have weak keys? If yes, list the weak keys. (5 points) (d) For a key K there function E(K,) from M to M=E is one to one, so a permutation, called an encryption permutation. Are there any encryption permutations that have fixed points? If yes, provide a demonstration. If no, explair why. (5 points) (e) How many distinct permutations are represented by the cipher's encryption permutations? (5 points)