Alice wants to encrypt some sequence of independent decimal digits and send to Bob. Let EK denote…

Alice wants to encrypt some sequence of independent decimal digits and send to Bob. Let EK denote the encryption function operating on decimal digits. A sequence of decimal digits M1, M2, . . . , Mn ? Z10 is encrypted to a sequence of ciphertext symbols C1, C2, . . . , Cn, Ci ? Z10 by Ci = EK(Mi), ?i, 1 = i = n. a) Determine which of the following mappings that are possible encryption functions: EK(M) = M, EK(M) = K, EK(M) = M + K, EK(M) = M · K, EK(M) = MK+1 , if M, K ? Z10, and all operations above are performed (mod 10). 4 b) Determine the unicity distance if the cipher is a simple substitution cipher and P(M = 0) = P(M = 1) = 4 · P(M = 2), together with P(M = 2) = P(M = 3) = · · · = P(M = 8) = P(M = 9). Hint: The entropy of language, denoted by HL in the textbook, is here the entropy per definition of plaintext (message) digits.