I've read the original paper and some related ones. But the best I can find about the period of BBS is that the period is a factor of $((M))$, where $$ is Carmichael function and $M$ is the product of two large primes that are congruent to 3 (mod 4).Is there any way to determine the exact period of BBS?
How to find the exact period of Blum-Blum-Shub random number generator?
cr.crypto security;nt.number theory;pseudorandom generators