Security Protocols

Consider the following authentication protocol

$AB$:$A$

$BA$:$B,N_B$

$AB$:$E(K,|A,B,N_B|)$

where $K$ is a key shared between A and $B,N_B$ is a nonce generated by $B$ and $E(K,M)=$

$Ko+M.($We thus assume that the length of the key $K$ is equal to length of the bitstring

obtained by concatenating the bitstrings representing $A,B,$ and $N_B.)$

$($a$)$ The protocol is used by $B$ to authenticate $A.$ Does the protocol achieve this goal?

Please justify your answer.

$($b$)$ Now consider the protocol consisting of the following single step:

$1.AB$:$E(K,|A,B,TA|)$

where $K$ is a key shared between A und $B,T_A$ is a timestamp generated by $A,$ and

$E(K,M)=Ko+M.($As above, we thus assume that the length of the hey $K$ is cqual

to length of the bitstring obtained by concatenating the bilstrings representing $A,B,$ and

$T_A.)$ Upon reception of the message $I1$ must clieck that $T_A-T_h>$ whem $T_1$ is the

current value of its own clock and o is a threshold that depends on the latenoy of the

communication link, Similarly to the protocol in the prevlous question, this protowt is

ured by $B$ to authenticats $A,$ Does the protocol achleve thits goal?

Please justify your answer.