1. Alice is using one-time pad and notices that when her key is the all-zeroes string k = 0 , then Enc(k,m) = m and her message is sent in the clear (without encryption) ! To avoid this problem, she decides to modify Gen to exclude the all-zeroes key. She modifies Gen algorithm to choose a key uniformly from {0, 1} \ {0 }, the set of all -bit strings except 0 . In this way, she guarantees that her plaintext is never sent in the clear. Is it still true that the eavesdroppers ciphertext distribution is uniformly distributed on {0, 1} ? Justify your answer.