Periods of sequences generated by the logistic map over finite fields with control parameter four

Kazuyoshi Tsuchiya, Yasuyuki Nogami

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Recently, binary sequences generated by chaotic maps have been widely studied. In particular, the logistic map is used as one of the chaotic map. However, if the logistic map is implemented by using unite precision computer arithmetic, rounding is required. In order to avoid rounding, Miyazaki, Araki, Uehara and Nogami proposed the logistic map over finite fields, and show some properties of sequences generated by the logistic map over finite fields. In this paper, we show some properties of periods of sequences generated by the logistic map over finite fields with control parameter four. In particular, we show conditions for parameters and initial values to have a long period, and asymptotic properties for periods by numerical experiments.

Original languageEnglish
Title of host publication7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages155-159
Number of pages5
ISBN (Electronic)9781467383080
DOIs
Publication statusPublished - Apr 22 2016
Event7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015 - Bengaluru, India
Duration: Sep 13 2015Sep 18 2015

Other

Other7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015
CountryIndia
CityBengaluru
Period9/13/159/18/15

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Keywords

  • Hyperbola
  • Legendre symbol
  • logistic map over finite fields
  • long period sequences
  • square map

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Signal Processing

Cite this

Tsuchiya, K., & Nogami, Y. (2016). Periods of sequences generated by the logistic map over finite fields with control parameter four. In 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015 (pp. 155-159). [7458394] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IWSDA.2015.7458394