5.1 (Double encryption). Let E = (E,D) be a cipher. Consider the cipher E2 = (E2, D2), where E2(k,m) = E(k, E(k,m)). One would expect that if encrypting a message once with E is secure then encrypting it twice as in E2 should be no less secure. However, that is not always true. (a) Show that there is a semantically secure cipher E such that E2 is not semantically secure. (b) Prove that for every CPA secure ciphers E, the cipher E2 is also CPA secure. That is, show that for every CPA adversary A attacking E2 there is a CPA adversary B attacking E with about the same advantage and running time.