In network and information security, RSA algorithm and Diffie-Hellman key-exchange algorithm are two important cryptosystems which both involve the use of large prime numbers and modular math, though RSA is a public-key cryptosystem, and Diffie-Heilman is a protocol for the exchange and establishment of a shared key between two parties. Assume Alice and Bob each has worked out a pair of Apub = [Ear Na] and Apriv = [Da, Nal and a pair of Bpub = [Eb, N] and Bpriv = [Db, N] respectively using the RSA algorithm, and has made the public keys known to each other; they also have further established a shared secret key KAB by using Diffie-Hellman key- exchange protocol. For this problem, you are required to answer the following question with justification: a. Suppose Alice wants to encrypt a confidential number S such as a biding price for a potential contract with Bob, and she also wants to prove to Bob that it is her who has made the offer. what is the mathematical formula to encrypt S so that only Bob can reveal the encrypted and verify it is Alice who made the offer? b. Further assume Bob has chosen Alice to sign a final contract which is more than 1MB long, design a mathematical operation for Alice and Bob to encrypt the entire contract using the already established shared key KAB so that only the Alice and Bob can decryp and read the contract.