Let $=(,,)$ be a private$-$key encryption scheme that is EAV$-$

secure$.$ The message space is $\{00000,01010,00100,11111\},$ where the corresponding

probabilities of selecting each message are $[0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}1,0\mathrm{.}4].$ Suppose a new scheme is

defined: $=(,,)$ where$-$

$$ is the same as $,$

$!$

$"()=$# $||!()$ where $$# is the first bit of m$,$ and

$!$

$"()=!($$ $\%...).$

Is the encryption scheme $$ an EAV$-$Secure encryption scheme or not? Show your derivation