Applied Cryptography...

Suppose we want to encrypt using affine cipher with a = 5 and b = 8. a. What is the encryption function? b. What is the decryption function? c. Encrypt the plaintext: ITS COOL using this affine cipher. We consider the ring Z_4. Construct a table which describes the addition of all elements in the ring with each other: a. Construct the multiplication table for Z_4. b. Construct the addition and multiplication tables for Z_5. c. Construct the addition and multiplication tables for Z_6. d. There are elements In Z_4 and Z_6 without a multiplicative inverse. Which elements are these? Why does a multiplicative inverse exist for all nonzero elements in Z_5? Using the basic form of Euclid's algorithm, compute the greatest common divisor of a. 7469 and 2464 b. 2689 and 4001 For this problem use only a pocket calculator. Show every iteration step of Euclid's algorithm, i.e., don't write just the answer, which is only a number. Also, for every gcd, provide the chain of gcd computations, i.e., gcd(r_0/r_1) = gcd(r_1r_2) =