SOLUTION: Public-Key Encryption | My Assignment Tutor

3809ICT/7809ICT – 2021 T1Workshop 4: Public-Key Encryption and RSALecturer: Qinyi Li Scribe: Qinyi LiQuestion 11. What are the principal elements of a public-key encryption system?2. What are the roles of the public and private key in a public-key encryption system?3. What are three broad categories of applications of public-key cryptosystems?4. Why in public-key encryption systems, it should be infeasible to obtain private keys fromthe public keys.5. Explain the encryption process and the decryption process of hybrid encryption?Question 2A median-size company with 400 employees’ security policy requires ensuring secret communication for every possible pair of employees. How many secret keys are needed if a symmetric-keycipher, e.g., AES, is used? How about if an asymmetric-key cipher, e.g., RSA, is used?Question 3Bob created his RSA encryption system with a public modulus n = p × q and a public key e.After some time, Bob decides that it is the time to refresh the keys. He generates a new modulusn0 = p × q0 with only one new prime q0 generated at random from an appropriate range. To savetime and effort, he reuses the prime p. Are there any security implications of the shortcut taken byBob? Justify your answer.Question 4Let p = 3, q = 11, e = 5. Encrypt plaintext M = 10 to get the ciphertext. You need to do thecalculation by hand. (Hint: You need to first figure out the modulo number n and then apply theencryption algorithm of RSA.)1Question 5We learned the working of the RSA encryption system and have seen two examples from thelecture slides. However, no proof is given showing the decryption process is correct in general.Such a proof uses the Euler’s phi function and its property given in the slides. Suppose the publickey is (n; e) and the private decryption key is d. To encrypt plaintext M, we doC = Me mod nTo decrypt, we doCd mod nAssume gcd(M; n) = 1 and M