TLS $(1)(5-5$ points$)$: Given a simplified SSL protocol as below, where $K=h(S,R_A,R_B),$

msgs are all previous messages, $S_B$ is $S$ encrypted with publick key of Bob, $E$ is a symmetric

encryption scheme and $h$ is a hash function.

$Al*$

$n,$

$($a$)$ Does the protocol support perfect forward secrecy $($PFS$)?$ PFS is if someone would get

Bob's private key in future, could this attacker learn any of the previous session keys

between Alice and Bob. Explain your answer.

$($b$)$ Revise the simplified TLS protocol above so that it achieves PFS$,$ i$.$e$.$ integrate a session

key establishment algorithm ensuring the original security framework of TLS remains

the same $($Bob authenticated to Alice, public key crypto$).$