The BBS Generator is a pseudo-random bit generator$($PRBG$)$ which generates random bits from a quadratic residues of modulo $n$, where $n = pq$ and $p$, $q$ are primes such that $p\equiv q\equiv 3 \pmod 4$.

In this paper we investigate the group structure of $QR(n)$, the set of quadratic residues of modulo $n$, and study certain periodicities of the random bits due to this group structure.

key words: PRBG, BBS Generator, cyclic group, GAP