Let II $($Gen$,$ Enc, Dec$)$ be an encryption scheme with message space M $=\{0,1\}".$ Define II $\text{'}=($Gen$\text{'},$ Enc', Dec'$)$ to be an encryption scheme with message space M $=\{0,1\}2$n $($we

view m in $\{0,1\}2$n as two n$-$bit messages m$1,$ m$2)$ defined as follows:

$($Note m$=$ means that decryption fails. is just a special fail symbol.$)$

Gen' $(12)$

k $=$ II$.$Gen$(1")$

return k

Enc $($m$1,$ m$2)$

C$1=$ II$.$Enck $($m$1)$

C$2=$ I.Enck $($m$2)$

return $($C$1,$ C$2)$

Deck $($C$1,$ C$2)$

m$=$ II$.$Deck$($C$1)$

m$2=$ I.Deck$($C$2)$

If m$=$ or m$2=1,$ return Else return m$||$m$2$

$($a$)$ If II is CPA$-$secure$,$ is II$\text{'}$ CPA$-$secure$?$ Justify your answer.

$($b$)$ If II is CCA$-$secure$,$ is II$\text{'}$ also CCA$-$secure$?$ Justify your answer.