Let p$=337$ be a prime number of length k bits. Let H$($x$)=$ x

$2$

$($mod p$)$ be a hash function which maps any

message to a k$-$bit hash value.

$($a$)$ Is this function pre$-$image resistant? Why?

$($b$)$ Is this function second pre$-$image resistant? Why?

$($c$)$ Is this function collision resistant? Why?