Let $=($Gen$,$ Enc, Dec$)$ be a private$-$key encryption scheme that has indistinguishable encryptions in the presence of an eavesdropper. Which of the following encryption schemes are also necessarily secure against an eavesdropper? If you think a scheme is secure$,$ sketch a proof, if not, provide a counterexample.

Here, for a bit string $s,$ parity$($s$)$ is $1$ if the number of $1\text{'}$s in $s$ is odd, and $0$ otherwise.

The $||$ symbol stands for concatenation. So$,$ for strings if $x=00$ and $y=11,x||y=0011.$

$($a$)En{c}_k^1(m)=0||En{c}_k(m)$

$($b$)En{c}_k^2(m)=En{c}_k(m)||$ parity $(m)$

$($c$)En{c}_k^3(m)=En{c}_k(m)||En{c}_k(m)$

$($d$)En{c}_k^4(m)=En{c}_k(m)||En{c}_k(m+1).$ Here think of $m$ as an integer.