  In 2004, Y. Hu and G. Xiao introduced the generalized self-shrinking
generator, a simple bit-stream generator considered as a specialization of the
shrinking generator as well as a generalization of the self-shrinking
generator. The authors conjectured that the family of generalized
self-shrinking sequences took their least periods in the set {1, 2, 2**(L-1)},
where L is the length of the Linear Feedback Shift Register included in the
generator. In this correspondence, it is proved that the least periods of such
generated sequences take values exclusively in such a set. As a straight
consequence of this result, other characteristics of such sequences (linear
complexity or pseudorandomness) and their potential use in cryptography are
also analyzed.
