Paper 2012/166

A List of Maximum Period NLFSRs

Elena Dubrova

Abstract

Non-Linear Feedback Shift Registers (NLFSRs) are a generalization of Linear Feedback Shift Registers (LFSRs) in which a current state is a non-linear function of the previous state. While the theory behind LFSRs is well-understood, many fundamental problems related to NLFSRs remain open. Probably the most important one is finding a systematic procedure for constructing NLFSRs with a guaranteed long period. Available algorithms either consider some special cases, or are applicable to small NLFSRs only. In this paper, we present a complete list of $n$-bit NLFSRs with the period $2^n-1$, $n < 25$, for three different types of feedback functions with algebraic degree two. We hope that the presented experimental data might help analysing feedback functions of maximum-period NLFSRs and finding a supporting theory characterizing them.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
NLFSRmaximum length sequence
Contact author(s)
dubrova @ kth se
History
2012-03-30: received
Short URL
https://ia.cr/2012/166
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2012/166,
      author = {Elena Dubrova},
      title = {A List of Maximum Period NLFSRs},
      howpublished = {Cryptology ePrint Archive, Paper 2012/166},
      year = {2012},
      note = {\url{https://eprint.iacr.org/2012/166}},
      url = {https://eprint.iacr.org/2012/166}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.