Question: Consider the following encryption scheme. The message space is M 10,13. Thein . Gen, the key generation algorithm, produces a uniformly random key in the

Consider the following encryption scheme. The message space is M 10,13.

Consider the following encryption scheme. The message space is M 10,13. Thein . Gen, the key generation algorithm, produces a uniformly random key in the set f0,1,...,9) . The encryption algorithm is given by Enck (m) - 9-k ifm=1. . The decryption algorithm is 0 ifk c, Deck(c) ifkt c. . Part 1: Explain why this scheme is correct (that is, explain why for all k and m we have Deck(Enck(m) m) Part 2: Is this scheme perfectly secure (yes or no)? Part 3: Prove your answer for part 2. Hint: This should be done in two steps- first step: if you answered "no" to Part 2, then change your answer to "yes." Second step: prove it is perfectly secure

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