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

doi:10.1109/IWSDA46143.2019.8966109

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 proceeding › Conference 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 language	English
Title of host publication	2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781728116693
DOIs	https://doi.org/10.1109/IWSDA46143.2019.8966109
Publication status	Published - Oct 2019
Event	9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019 - Dongguan, China Duration: Oct 20 2019 → Oct 24 2019

Publication series

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

Conference

Conference	9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019
Country	China
City	Dongguan
Period	10/20/19 → 10/24/19

Keywords

Lyapunov exponent
NIST tests
Piecewise logistic map over integers
control parameter

ASJC Scopus subject areas

Computer Networks and Communications
Signal Processing

Access to Document

10.1109/IWSDA46143.2019.8966109

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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

Relations between Evaluations of NIST Tests and Lyapunov Exponents of Sequences Generated by the Piecewise Logistic Map over Integers. / Eguchi, Sota; Miyazaki, Takeru; Araki, Shunsuke; Uehara, Satoshi; Nogami, Yasuyuki.

2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8966109 (2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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., 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019, Dongguan, China, 10/20/19. https://doi.org/10.1109/IWSDA46143.2019.8966109

Eguchi S, Miyazaki T, Araki S, Uehara S, Nogami Y. 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. Institute of Electrical and Electronics Engineers Inc. 2019. 8966109. (2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019). https://doi.org/10.1109/IWSDA46143.2019.8966109

Eguchi, Sota ; Miyazaki, Takeru ; Araki, Shunsuke ; Uehara, Satoshi ; Nogami, Yasuyuki. / Relations between Evaluations of NIST Tests and Lyapunov Exponents of Sequences Generated by the Piecewise Logistic Map over Integers. 2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019. Institute of Electrical and Electronics Engineers Inc., 2019. (2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019).

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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.",

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