In this exercise, we look at different conditions under which the shift, mono-alphabetic substitution, and Vigenre ciphers are perfectly secret:
(a) Prove 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) Prove that the Vigenre cipher using (fixed) period t is perfectly secret when used to encrypt messages of length t.
Reconcile this with the attacks shown in the previous chapter.