Question

o-8. (15 points) Bob's simple toy RSA eryptosystem has public key kyub(n, e) (65,5), where n =p,-5x13-65 and e-5. I. Describe the key pair generation procedure for Bob to generate his private key kor- d. With the above given parameters, use EEA to calculate d 2. Describe RSA encryption procedure that Alice uses to encrypt her plaintext message x to its above given parameters, what will be y? ciphertext y before sending the message to Bob. Suppose Alice's message x- 10, together with the 3. Describe RSA decryption procedure that Bob uses to decrypt Alice's ciphertext y to its plaintext x Continuing with previous question, compute the plaintext message x (-10) from the ciphertext y. Hint: To calculate large integer power modular exponentiation like x" mod n (suppose a is a large integer you can use two basic exponentiation facts: (i) (x" x" and (2) x x" x And then repeatedly square the base number x until the power reaches to a using the basic fact (1) decompose a into the sum of smaller powers that adds up to a. Then use the basic fact (2) to compute the final result.

Answer 1

RSA em-re 恨止pt LU y and G Giken nmadn given Ma c mad ん︶

d 5 mod 48-1 1- (A 14) 2, 0 48 0154 -93 I 102 231 3 1102

0 2巩 2. 0 5 3 (55)