In this problem we will perform a security analysis of a simple mutual authentication protocol between

Alice and Bob. Assume Alice and Bob have a pre$-$shared secret key $k_{ab}.$ In this protocol $H$ represents the

hash operation, $||$ represents concatenation, and $\{m{\}}_k$ represents a message $m$ encrypted using key $k.$

a$)$ Discuss the security properties of the protocol shown in Figure $1$ in terms of mutual authentication in

the space below. Your discussion should include whether the protocol will be able to authenticate Alice

to Bob and Bob to Alice. Also describe why or why not.

b$)$How can you improve this protocol to ensure mutual authentication of Alice and Bob? Modify the

protocol diagram in Lucidchart by following this link: Protocol Diagram. Paste your protocol diagram

and discuss the improvements in the space provided below.