10. (RSA Cryptography) Let p = 47, q = 59, N = pq = 2773, and e = 157.
(a) Compute a multiplicative inverse of e modulo Φ(N).
(b) Every two-letter string (including A-Z and spaces) can be digitized into a number between 0 and 2626 by letting space=00, A=01, B=02, etc. For example, the two-letter word "Me" becomes 1305. Encrypt the two-letter message "Hi" by computing it's digitization m, and the ciphertext m^e (mod N).
(c) Decrypt the sequence of ciphertexts 0802, 2179, 2657, 1024 to find a message.