Relations between Evaluations of NIST Tests and Lyapunov Exponents of Sequences Generated by the Piecewise Logistic Map over Integers

Sota Eguchi, Takeru Miyazaki, Shunsuke Araki, Satoshi Uehara, Yasuyuki Nogami

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

Abstract

In this paper, we focus on binary sequences obtained from piecewise logistic map over integers, and show the relation between the Lyapunov exponents of the maps and results of the NIST tests for the sequences. When the Lyapunov exponent is a negative value, we confirm that the branch diagram is sparse and the bit occurrence rate is also greatly biased. We also give a sample of that the positive/negative signs of the Lyapunov exponents mostly coincide on the evaluations of the NIST tests. From the branching diagram of the piecewise logistic map, we can moreover find that there are many good pseudorandom sequences generated by the individual control parameters of the map.

Original languageEnglish
Title of host publication2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728116693
DOIs
Publication statusPublished - Oct 2019
Event9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019 - Dongguan, China
Duration: Oct 20 2019Oct 24 2019

Publication series

Name2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019

Conference

Conference9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019
CountryChina
CityDongguan
Period10/20/1910/24/19

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Keywords

  • control parameter
  • Lyapunov exponent
  • NIST tests
  • Piecewise logistic map over integers

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Signal Processing

Cite this

Eguchi, S., Miyazaki, T., Araki, S., Uehara, S., & Nogami, Y. (2019). Relations between Evaluations of NIST Tests and Lyapunov Exponents of Sequences Generated by the Piecewise Logistic Map over Integers. In 2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019 [8966109] (2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IWSDA46143.2019.8966109