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 generators where the choice of the primitive polynomial corresponding to the specific m-sequence is considered to be a design parameter. Using this approach, we obtain computational results on certain randomness properties of the generalized 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.