Graph-Based Modelling of Maximum Period Property for Nonlinear Feedback Shift Registers

Eric Filiol, Eric Filiol, Pierre Filiol

2024

Abstract

NonLinear Feedback Shift Registers (NLFSRs) are key primitives to design pseudorandom generators in modern stream ciphers, especially when the feedback function is of low degree. Contrary to their linear counterparts (LFSRs) for which a general and comprehensive theory has been established, many fundamental problems related to NLFSRs remain open. In particular finding a systematic procedure of acceptable complexity for constructing NLFSRs with a guaranteed long period is still a general open problem and only a few results have been obtained so far. In this paper, we present the results of a exhaustive exploratory search and analysis of NLFSRs of low degree. We first model NLFSRs as graphs using their incidence matrix and express the maximum period property as graph properties. This enables to reduce the number of possible candidates greatly that can be tested finally for the maximum period property by HPC on GPGPUs and Massively Parallel Processor Array (MPPA).

Paper Citation

in Harvard Style

Filiol E. and Filiol P. (2024). Graph-Based Modelling of Maximum Period Property for Nonlinear Feedback Shift Registers. In Proceedings of the 21st International Conference on Security and Cryptography - Volume 1: SECRYPT; ISBN 978-989-758-709-2, SciTePress, pages 832-837. DOI: 10.5220/0012839300003767

in Bibtex Style

@conference{secrypt24,
author={Eric Filiol and Pierre Filiol},
title={Graph-Based Modelling of Maximum Period Property for Nonlinear Feedback Shift Registers},
booktitle={Proceedings of the 21st International Conference on Security and Cryptography - Volume 1: SECRYPT},
year={2024},
pages={832-837},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012839300003767},
isbn={978-989-758-709-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 21st International Conference on Security and Cryptography - Volume 1: SECRYPT
TI - Graph-Based Modelling of Maximum Period Property for Nonlinear Feedback Shift Registers
SN - 978-989-758-709-2
AU - Filiol E.
AU - Filiol P.
PY - 2024
SP - 832
EP - 837
DO - 10.5220/0012839300003767
PB - SciTePress