Answer ALL Questions Question 1: (33 marks) Applying the RSA algorithm, calculate the public key pair and private key pair, and encryption and decryption when the given values of parameters are

as follows: • two large prime numbers p=113 and q=73, • a. b. random integer e=13 (encryption key or public exponent). Demonstrate all steps and formulae of the RSA algorithm Calculate multiplicative inverse using the extended Euclidean algorithm Perform the encryption and decryption process when the plaintext is P = 113 Requirement: You may need a calculator that can handle large numbers, you can use any online calculator such as https://www.calculator.net/big-number-calculator.html Note: You need to demonstrate step-by-step calculations/operations in each answer. No marks will be awarded for only writing the final answers. Question 2: Question 2a: Applying the Diffie-Hellman key exchange algorithm, calculate the public key and shared secret when the given values of parameters are as follows: • public prime number p=761, • generator/base number g= 56, • sender's secret number s=13, (9 marks) (12 marks) (12 marks) receiver's secret number r-15. (33 marks) Question 2b: If 208 = 33 mod 25, then prove the following properties of Modular Congruence: (i) Show all steps and calculations. (10 marks) Requirement: You may need a calculator that can handle large numbers, you can use any online calculator such as https://www.calculator.net/big-number-calculator.html Note: You need to demonstrate step-by-step calculations/operations in the answer. No marks will be awarded for only writing the final answers. Addition Property of Modular Congruence: If a = b mod n, and a+b=c, then [(a mod n) + (b mod n) ] mod n = c mod n (3 marks) (ii) Multiplication Property of Modular Congruence: If a = b mod n, and axb=c, then [(a mod n) x (b mod n) ] mod n = c mod n (3 marks) Note: You need to demonstrate step-by-step calculations/operations in the answer. No marks will be awarded for only writing the final answer.