When using the one-time pad (Vernam's cipher) with key k = 0, it follows that Enck...

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When using the one-time pad (Vernam's cipher) with key k = 0, it follows that Enck (m) = = m and the message is released in the clear! Your TA therefore suggests that we improve the one-time pad by only encrypting with a key k 0 (i.e., to have Gen choose k uniformly at random from the set of non-zero keys of length e). (i) (10 pts) Is this an improvement? In particular, is it still perfectly secret? Prove your assertion. (ii) (5 pts) If your answer is positive, explain why the one-time pad is not described in this way. If it is negative, reconcile this with the fact that encrypting with 0 doesn't change the plaintext. When using the one-time pad (Vernam's cipher) with key k = 0, it follows that Enck (m) = = m and the message is released in the clear! Your TA therefore suggests that we improve the one-time pad by only encrypting with a key k 0 (i.e., to have Gen choose k uniformly at random from the set of non-zero keys of length e). (i) (10 pts) Is this an improvement? In particular, is it still perfectly secret? Prove your assertion. (ii) (5 pts) If your answer is positive, explain why the one-time pad is not described in this way. If it is negative, reconcile this with the fact that encrypting with 0 doesn't change the plaintext.