When using the l-bit one-time pad with the key k = 0' (here, o denotes the l-bit string where every bit is 0, i.e., O' = 00...0), it follows that Enc (m) = kom= m and the message is l times effectively sent in the clear! It has therefore been suggested to improve the one-time pad by only encrypting with a key k 0'; that is, Gen: choose k uniformly at random from the set of non-zero keys of length 6. Is this an improvement? In particular, is it still perfectly indistinguishable? Justify your answer. If your answer is positive, you need to show the modified scheme satisfies the definition of perfect indistinguishability. You can use either of the formulations (game-based or probability-based) that we have seen.. If your answer is negative, you need to give a counter-example in the form of an adversary that can win the distinguishing game with non-zero advantage. Also, describe the information (informally) that the adversary gains by observing the ciphertext