Q$2.($a$)$ Formally define what is meant by a $($symmetric$)$ cryptosystem. $[5$ marks$]$

$($b$)$ Briefly describe what a perfectly secure $($symmetric$)$ cryptosystem is$.$ Do

perfectly secure cryptosystems exist?

$[5$ marks$]$

$($c$)$ State and prove Shannon's Theorem.

$[15$ marks$]$