In the zero$-$knowledge proof of logarithm possession:

$($a$)$ Justify why the information seen by the verifier or by a third$-$party

observer does not leak anything on the secret x $($zero$-$knowledge

property$).(1\mathrm{.}5$ points$)$

$($b$)$ Would the protocol work well if the challenge c was always c $=1?$

Why? $(1\mathrm{.}5$ points$)$