You are asked to hand-turn the RSA protocol in order to encrypt and decrypt the messages (utilizing smaller numbers than are used in the practice, so that calculations may be done through the hand). Assume that Bob produces two primes, p = 11 and q = 23. (In reality these could be much larger numbers, with say 512 bits.) He determines the product N = pq = 253, and also choose the number e = 7 that is relatively prime to (p − 1)(q − 1) = 220. Bob then publishes the pair (N, e) as his public key.

a) What do you meant by Bob’s private key, d?

b) Assume that the Alice wishes to transmit the message 44 (an integer between 0 and 252) to the Bob. What is the encrypted message which Alice sends? Explain with your calculations.

c) Assume that the Bob receives the encrypted message 103from Alice. Compute the original message that Alice had sent?