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# 4. [RSA] In this problem you are asked to hand-turn the RSA protocol to encrypt and decrypt messages (using rather smaller numbers than are used in

4. [RSA]In this problem you are asked to hand-turn the RSA protocol to encrypt and decrypt messages (using rathersmaller numbers than are used in practice, so that calculations can be done by hand). Suppose that Bobgenerates two primes, p = 11 and q = 23. (In reality these would be much larger numbers, with say 512bits.) He computes the product N = pq = 253, and also selects the number e = 7, which is relatively primeto (p − 1)(q − 1) = 220. Bob then publishes the pair (N, e) as his public key.(a) What is Bob’s private key, d? [HINT: Part (c) of Problem 1 may be useful here!](b) Suppose that Alice wants to send the message 44 (an integer between 0 and 252) to Bob. What is theencrypted message that Alice sends? Again, show your calculation clearly.(c) Suppose that Bob receives from Alice the encrypted message 103. What was the original message thatAlice sent?[NOTE: In this and similar problems, little or no credit will be given for numerical answers (even if theyare correct) without a clear explanation of how they were derived, showing all the steps. Also, you areexpected to perform your calculations in an intelligent manner, using techniques such as repeated squaringand reducing intermediate answers mod N.]