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

numbers in Z$\_$n$,\backslash$ M$\backslash =\backslash ($a$\_1,\backslash$ a$\_2,\backslash ...,$a$\_$t$).$ The hash value h is calculated as $(\backslash$sum$\_\{$i$=1\}^\{$t$\}\{$a$\_$i$^2)\}$mod$\backslash$ n for some predefined value n$.$

Does this hash function satisfy any of the requirements for a hash function listed below? Explain your answer for each case.

It can be applied to a block of data of any size.

It produces a fixed$-$length output.

It is relatively easy to compute for any given input.

Preimage resistance.

Secondary preimage resistance.

Collision resistance.