Hand writen

7. The Hill cipher uses matrices and congruence arithmetic. First, the alphabetic message is converted to a string of numbers, use 0 for a, 1 for b and so on until we reach 25 for z. The message is then broken up into segments of equal length, and each of these segments treated as a column matrix and mutiplied by an enciphering matrix, C, and the result modulo 26 is used to give the ciphertext. The deciphering process uses the with same procedure, but with a deciphering matrix, D. We will work with the Hill cipher (a) Encipher the message 'um (b) Show that the deciphering matrix (4 marks) 4 17 D=123 7 (2 marks) recovers the original message (c) Calculate the matrix CD. (Remember to give your answer modulo 26.) (2 marks)