Problem 1 (40 points) Diffie-Hellman Key Exchange Assume that Alice and Bob agree on p = 47 and g = 157. Show all the calculations to determine a shared secret key by Alice and Bob. You should show your calculations using python programming. Problem 2 (50 points) Using the RSA programming, demonstrate encryption and decryption process for the given plaintext information. Plaintext: This is week 4 and we have learnt RSA and DHKE. Provide your output screenshots and your program. Problem 3 (10 points) What are the pros and cons of identity-based cryptography system