Robust Chaos of Cubic Polynomial Discrete Maps with Application to Pseudorandom Number Generators
Joint Authors
Han, Dandan
Min, Lequan
Zang, Hongyan
Yang, Xiuping
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-04-07
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
Based on the robust chaos theorem of S-unimodal maps, this paper studies a kind of cubic polynomial discrete maps (CPDMs) and sets up a novel theorem.
This theorem gives general conditions for the occurrence of robust chaos in the CPDMs.
By using the theorem, we construct a CPDM.
The parameter regions of chaotic robustness of the CPDM are larger than these of Logistic map.
By using a fixed point arithmetic, we investigate the cycle lengths of the CPDM and a Logistic map.
The results show that the maximum cycle lengths of 1000 chaotic sequences with length 3×107 generated by different initial value conditions exponentially increase with the resolutions.
When the resolutions reach 10-7~10-13, the maximum cycle lengths of the cubic polynomial chaotic sequences are significantly greater than these of the Logistic map.
When the resolution reaches 10-14, there is the situation without cycle for 1000 cubic polynomial chaotic sequences with length 3×107.
By using the CPDM and Logistic map, we design four chaos-based pseudorandom number generators (CPRNGs): CPRNGI, CPRNGII, CPRNGIII, and CPRNGIV.
The randomness of two 1000 key streams consisting of 20000 bits is tested, respectively, generated by the four CPRNGs.
The result suggests that CPRNGIII based on the cubic polynomial chaotic generalized synchronic system has better performance.
American Psychological Association (APA)
Han, Dandan& Min, Lequan& Zang, Hongyan& Yang, Xiuping. 2019. Robust Chaos of Cubic Polynomial Discrete Maps with Application to Pseudorandom Number Generators. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-17.
https://search.emarefa.net/detail/BIM-1197475
Modern Language Association (MLA)
Han, Dandan…[et al.]. Robust Chaos of Cubic Polynomial Discrete Maps with Application to Pseudorandom Number Generators. Mathematical Problems in Engineering No. 2019 (2019), pp.1-17.
https://search.emarefa.net/detail/BIM-1197475
American Medical Association (AMA)
Han, Dandan& Min, Lequan& Zang, Hongyan& Yang, Xiuping. Robust Chaos of Cubic Polynomial Discrete Maps with Application to Pseudorandom Number Generators. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-17.
https://search.emarefa.net/detail/BIM-1197475
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197475