Question
In this difficulty you are asked to hand-turn the RSA protocol to encrypt and decrypt messages (using rather smaller numbers than are used in practice, so that calculations can be done by hand). Assume that Bob generates two primes, p = 11 and q = 23. (In reality these would be much larger numbers, with say 512 bits.) He computes the product N = pq = 253, and also selects 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 is Bob's private key?
(b) Assume that Alice wants to send the message 44 (an integer between 0 and 252) to Bob. What is encrypted message that Alice sends? Again, explain your calculation clearly.
(c) Assume that Bob receives from Alice the encrypted message 103. What was the original message that Alice sent?