Consider the following protocol that allows entities A and B to mutually authenticate each other and to establish a shared session key. $1.$ A $$ B : A$,$ NA $2.$ B $$ S : B$,$ NB$,\{$A$,$ NA$\}$KhB$,$Si $3.$ S $$ A : NB$,\{$B$,$ NA$,$ KhA,Bi$\}$KhA$,$Si $,\{$A$,$ B$,$ NB$,$ KhA,Bi$\}$KhB$,$Si $4.$ A $$ B : $\{$A$,$ B$,$ NB$,$ KhA,Bi$\}$KhB$,$Si $,\{$NB$\}$KhA$,$Bi $5($a$)[6$ Marks$]$ Explain the role played by S and the use of the keys KhA,Si $,$ KhB$,$Si and KhA,Bi in this protocol. $5($b$)[8$ Marks$]$ Explain how the nonces NA and NB ensure the freshness of the session key, and their role in the mutual authentication of A and B$.5($c$)[6$ Marks$]$ Consider the protocol obtained by replacing step $4$ with the following step: $40.$ A $$ B : $\{$A$,$ B$,$ NB$,$ KhA,Bi$\}$KhB$,$Si Does this new protocol still achieve mutual authentication? Explain your answer