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Problem 2.3 In this exercise, we look at different conditions under which the shift, mono- alphabetic substitution, and Vigenere ciphers are perfectly secret: (a) Show that if only a single character is encrypted, then the shift cipher is perfectly secret. (b) What is the largest message space M for which the mono-alphabetic substitution cipher provides perfect secrecy? (c) Show that the Vigenere cipher using (fixed) period t is perfectly secret when used to encrypt messages of length t