Is there any time efficient way of achieving the result of FKS hashing lemma?
DGS prove a hashing lemma that bijectively hashes a sparse set to a set from a smaller universe (without involving a primality test). In particular see Lemma 3 in the paper that maps a set of size at most $(\log n)^{1/3}$ from the universe $[n]$ to a set  of size at most $v &lt; \log{n}$ by using the hash function $((x \bmod{u})\bmod{v})$ where $u &lt; n$.

I guess in your setting the set consists of elements from $n$-bit numbers and you can therefore plug in $2^n$ instead of $n$ in the DGS-lemma.