Paper 2012/166 Original: eprint.iacr.org/2012/166 ↗
A List of Maximum Period NLFSRs
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
- Preprint.
- History
- 2012-03-30: last updated
- 2012-03-30: published
- Short URL
- https://ia.cr/2012/166
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2012/166,
author = {Elena Dubrova},
title = {A List of Maximum Period NLFSRs},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/166},
year = {2012},
url = {https://eprint.iacr.org/2012/166}
}