Alice picks the two prime numbers p = 31, q = 47 as her secret numbers for an RSA cipher, and publishes the public key N, e with e = 11. a. What is N? b. Bob wishes to send an enciphered kiss to Alice, so decides to transmit the ASCII code for X (88 in decimal notation) using Alice's public key cipher. Let C denote the enciphered message. Using the fact that 8811 = 888 882 x 88 compute C. c. On receiving Bob's message Alice computes the private key d in order to decipher it. The number f is defined by the linear congruence 11f = 1 mod (p-1) (q-1). Compute p - 1, q - 1 and solve the congruence to find f.