Consider the following hash function. Messages are in the form of a sequence of

numbers in $Z_n,M=(a_1,a_2,$dots,$a_t).$ The hash value $h$ is calculated as $({\displaystyle \underset{i=1}{\overset{t}{}}}{a}_i^2)$

modn for some predefined value $n.$

$($a$)$ Does this hash function satisfy any of the requirements for a hash function listed

bellow? Explain your answer for each case.

It can be applied to a block of data of any size. $(5$ points$)$

It produces a fixed$-$length output. $(5$ points$)$

It is relatively easy to compute for any given input. $(5$ points$)$

Preimage resistance. $(10$ points$)$

Secondary preimage resistance. $(10$ points$)$

Collision resistance. $(10$ points$)$

$($b$)$ Compute the hash for $M=(120,145,224,657)$ for $n=981.(5$ points$)$