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.