4. (10 points) A New Mode of Operation. You are given the following new mode of operation called Double Forward Mode (DFM). The encryption function of this new mode is described below

1: procedure DFM-Enc(k, M1, M2, ..., Mn)

2: Choose random IV

3: for i = 1 to n do

Ci = Ek(Ek(Mi)) IV

5: end for

6: return (IV, C1, C2, ..., Cn)

7: end procedure

a) (5 points) Write down the decryption algorithm

(b) (5 points) State two properties that the IV must have in order to avoid ciphertext-only attackers? Justify your answer.

c) (5 points) Show that DFM is not IND-CPA secure. In other words, show a CPA attacker that chooses two different messages to encrypt to get back C0 and C1 and is able to tell apart which ciphertext encrypts which message.