2013/09/05 by Amparo Fúster-Sabater, Fúster-Sabater, Amparo
Computer Science · Engineering · Mathematics · #11T71 #11T99 #14G50 #94A60 #B.6.1 #Cellular Automata and Applications #Coding theory and cryptography #E.3 #F.1.1 #FOS: Computer and information sciences #G.2.1 #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #acm:11T71 #acm:11T99 #acm:14G50 #acm:94A60 #cs.IT #graph theory and CDMA systems #math.IT #msc:11T71 #msc:11T99 #msc:14G50 #msc:94A60
paper · pdf · doi:10.48550/arxiv.1309.1319
Submitted at IEEE Transactions on Information Theory
arxiv created 2013/09/05 · openalex publication_date 2013/09/05 · arxiv updated 2013/09/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
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.