Problem $3$: AE Practice $[20$ points$].$ For this problem, assume that the cipher $($Enc$,$Dec$)$ provides authenticated encryption, that $($EncCPA$,$DecCPA$)$ provides CPA security, and that H is a collision resistant hash function. For each proposed cipher, state whether it provides AE$,$ provides CPA security only, or provides neither AE nor CPA security. In each case, provide an attack on AE$/$CPA security and$/$or a proof sketch $($in at most a few sentences each$).$ Note that if you say a cipher provides CPA security, you will need to both showanattackonAE$($ciphertext integrity$)$ and a proof sketch for CPA security. $($a$)$ Enc$($k$,$m$)$:$=($Enc$($k$,$m$),$Enc$($k$,$m$))$ Dec$($k$,($c$1,$c$2))$ :$=$ Dec$($k$,$c$1)$ if Dec$($k$,$c$1)=$Dec$($k$,$c$2)$; $$ otherwise$($b$)$ Enc$($k$,$m$)$:$=$c $$Enc$($k$,$m$)$;Output$($c$,$c$)$ Dec$($k$,($c$1,$c$2))$ :$=$ Dec$($k$,$c$1)$ if c$1=$c$2$; $$ otherwise $($c$)$ Enc$($k$,$m$)$:$=($EncCPA$($k$,$m$),$H$($m$))$ Dec$($k$,($c$1,$c$2))$ :$=$ DecCPA$($k$,$c$1)$ if H$($DecCPA$($k$,$c$1))=$c$2$; $$ otherwise $($d$)$ Enc$($k$,$m$)$:$=$c $$EncCPA$($k$,$m$)$;Output$($c$,$H$($c$))$ Dec$($k$,($c$1,$c$2))$ :$=$ DecCPA$($k$,$c$1)$ if H$($c$1)=$c$2$; $$ otherwise