Question $(100$ points$)$

Consider the following mutual authentication protocol, where $K_{AB}$ is a symmetric key only known to Alice

and Bob, $R$ is a number chosen by Alice, and $E$ is the encryption function of a secure symmetric cipher.

$"$I$\text{'}$m Alice", $R$

Alice, $K_{AB}$

a$)$ Assume Trudy has observed and recorded the three messages exchanged between Alice and Bob.

Design and explain a replay attack that Trudy can use to convince Bob that she is Alice.

b$)$ Assume Trudy knows this protocol but is not able to record and observe the three messages exchanged between Alice and Bob. Design and explain a reflection attack that Trudy can use to convince Bob that she is Alice.

$($Hint: One step is: Trudy suspends the initial connection, and opens a new connection and send some number related to R to Bob, Bob replies with some information. Such information will be useful for Trudy$).$