Security Protocols Consider the following authentication protocol

$1.AB$:$E(K,[A,B,T])$

where $K$ is a key shared between A and $B$ and $T$ is a time$-$stamp generated by $A.$

$($a$)$ Indicate which of the following security properties are met by the protocol. For the properties that are

met by the protocol describe the assumptions that must hold for the property to hold. For the properties

that are not met by the protocol write an execution trace witnessing the violation of the property.

A$.$ A authenticates $B$

B$.B$ authenticates $A$

C$.$ Secrecy of $N$

D$.$ Secrecy of $K$

$($b$)$ Describe the actions carried out by $B$ upon receipt of the message for a proper functioning of the

protocol.

$($c$)$ What are the consequences of using an implementation of the protocol where the timestamp $T$ is very

coarse, e$.$g$.$ successive time instants correspond to large intervals $($say several seconds$).$

$($d$)$ Assume that successive time instants correspond to $1$ second and that timestamps are represented by

$16$ bits. How long must an attacker wait to mount a replay attack?