$3.$ In this problem we will compare the security services that are provided by digital signatures $($DS$)$ and message authentication codes $($MAC$).$ We assume that Oscar is able to observe all messages sent from Alice to Bob and vice versa. Oscar has no knowledge of any keys but the public one in case of DS$.$ State whether and how $($i$)$ DS and $($ii$)$ MAC protect against each attack. The value auth$($x$)$ is computed with a DS or a MAC algorithm, respectively.