A website authenticates its users by asking for a login$/$password$,$ and sends them a cookie C$,$ valid for one minute, to keep track of their authentication status. The cookie C is formed such as C $=$ Enc$("$user$=$username,tmstmp$=$timestamp"$),$ with username $=$ "anonymous" for unauthenticated users, or the name of the user when authenticated; and timestamp is a Unix$-$formated timestamp$1$ representing the time up to which the user is authenticated $($current time plus one minute$).$ Enc$()$ designates the AES$256$ encryption in OFB$-$mode using iv as a random IV and k as a random key; both k and iv are unknown to us$.$ The OFB mode of operation for encryption is described in Figure $1.$

In this exercise, we consider cookies delivered on February $1$st$,2024$ at $00$:$00$am UTC. At that time, an unauthenticated user coming to the website will receive a cookie: