Consider a variant of the substitution cipher E $=($E$,$ D$)$

defined in Example $2\mathrm{.}3$ where every symbol of the message is encrypted using an independent

permutation. That is$,$ let M $=$ C $=\backslash$Sigma $^$L for some a finite alphabet of symbols $\backslash$Sigma and some L$.$ Let he key space be K $=$ S$^$L where S is the set of all permutations on $\backslash$Sigma $.$ The encryption algorithm

E$($k$,$ m$)$ is defined as

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

Show that E is perfectly secure$.$