Running cipher:-

One method for increasing the security of Vigenère-type encryption is to use a running text as key. For example, the key might be the letters, in order, from an obscure novel that is possessed by both the sender and intended receiver of the message. The message itself is encoded by the Vigenère system-encoding the i-th letter of the message by shifting the alphabet by an amount determined by the i-th letter of the key.

Both the message and the key are in the same language, which has L letters in its alphabet, and which has a redundancy of rL. As an approximation, assume that the resulting ciphertext is essentially completely random, with all letters having the same probability and each letter being independent of the others.

(a) What is H(Cⁿ)?

(b) What are H(Mⁿ) and H(Kⁿ)?

(c) What degree of redundancy rL (a percentage) of the language is necessary in order that this code system be breakable?

(d) Is the system breakable if the language is standard English?