Statistical dependencies in the self-shrinking generator

Using the so-called m-sequences as input, the Self-Shrinking Generator (SSG) was introduced in 1996 and has largely withstood cryptanalytic attacks. It is natural to view the SSG as an ensemble of gen- erators where the choice of the primitive polynomial corre- sponding to the specific m-sequence is considered to be a design parameter. Using this approach, we obtain computa- tional results on certain randomness properties of the gener- alized SSG and their dependence on the specific polynomial. Our results suggest that the choice of the polynomial for the SSG is a delicate question that requires sufficient care.