Can we define universal hash function from $U \rightarrow T$ when $T=\{0,1,2,..,m-1\}$ and $m=p^a$? (where $p$ is a prime and a is an integer)
I know that we can define universal hash funciton when $m=p$ and p is a prime in this way:
$h_{\alpha}(x)=\alpha \cdot x \space mod \space m$ but what about $m=p^a$?
a hash function is universal if $Prob(h(x)=i)=1/m \space$ for $i=0,1,...m-1$.