$($A good substitution cipher$).$ Consider a variant of the substitution cipher E $=($E;D$)$ dened in Example $2\mathrm{.}3$ where every symbol of the message is encrypted using an independent permutation. That is$,$ let M $=$ C $=$ L for some a nite alphabet of symbols and some L$.$ Let the key space be K $=$ SL where S is the set of all permutations on $.$ The encryption algorithm E$($k;m$)$ is dened as

E$($k;m$)$ :$=$k$[0]($m$[0])$; k$[1]($m$[1])$; : : : ; k$[$L $1]($m$[$L $1])$

Show that E is perfectly secure$.$