Consider the following keyexchange protocol: $($a$)$ Alice chooses uniform k$,$r in $\{0,1\}$n$,$ and sends s :$=$ k $$r to Bob. $($b$)$ Bob chooses uniform t in $\{0,1\}$n$,$ and sends u :$=$ s$$t to Alice. $($c$)$ Alice computes w :$=$ u$$r and sends w to Bob.$($d$)$ Alice outputs k and Bob outputs w $$t$.$ Show that Alice and Bob output the same key. Analyze the security of this protocol $($i$.$e$.,$ either prove its security or show a concrete attack$).$