a$.$ Suppose $P=61$ and $Q=67,$ encrypt $C$ and decrypt $D$ the message $($M$)"$HI$",$ if $k=4$ and

$(12$ marks$)$

b$.$ Alice and Bob get public numbers $P=23,G=9,$ they then select private keys a and $b$ respectively. Compute their public values $x$ and $Y$ and also determine the shared secret $($s$).$