Consider a cryptosystem that encrypts a message m in M$,$ M $=\{0,1,2\},$ using a shared key k that is uniformly chosen from the key space k in $,=\{0,1,2,3\}.$

c $=$ Enc$($k$,$ m$)=$ m $+$ k $($mod $3),$ and

m $=$ Dec$($k$,$ c$)=$ c $-$ k $($mod $3)$

Is this encryption scheme perfectly secret? Explain your answer.