Conditions for feedback shift registers to generate permutations

Vamshi Krishna Kammadanam, Virendra Sule, Yi Hong

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Abstract

The paper explores conditions to be satisfied by feedback shift registers (FSRs) to generate a permutation (alternatively a nonsingular map) of the state space over various fields. Such a condition is well known over the binary field F2. This is extended to small finite fields and a simple sufficient condition is stated for larger fields. Permutations with cycles or periodic sequences generated by their action of lengths which are of exponential order of the register length are attractive for construction of pseudorandom sequences which have many applications.

Original languageEnglish
Title of host publicationProceedings of the Fifth International Conference on Mathematics and Computing, ICMC 2019
EditorsDebasis Giri, Anthony T.S. Ho, S. Ponnusamy, Nai-Wei Lo
Place of PublicationSingapore Singapore
PublisherSpringer
Pages125-136
Number of pages12
ISBN (Print)9789811554100
DOIs
Publication statusPublished - 2021
Event5th International Conference on Mathematics and Computing, ICMC 2019 - Bhubaneswar, India
Duration: 6 Feb 20209 Feb 2020

Publication series

NameAdvances in Intelligent Systems and Computing
PublisherSpringer Nature Singapore Pte Ltd
Volume1170
ISSN (Print)2194-5357
ISSN (Electronic)2194-5365

Conference

Conference5th International Conference on Mathematics and Computing, ICMC 2019
Country/TerritoryIndia
CityBhubaneswar
Period6/02/209/02/20

Keywords

  • Boolean functions
  • Boole–Shannon expansion
  • Feedback shift registers
  • Permutations

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