Robust Chaos of Cubic Polynomial Discrete Maps with Application to Pseudorandom Number Generators. (7th April 2019)

• Record Type: Journal Article
• Authors: Han, Dandan; Min, Lequan; Zang, Hongyan; Yang, Xiuping
• Other Names: Benito Rosa M. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2019(2019)
• Publication Date: 2019-04-07
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2019/8250903
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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 of1000 chaotic sequences with length3 × 1 0 7 generated by different initial value conditions exponentially increase with the resolutions. When the resolutions reach1 0 - 7 ~ 1 0 - 13, the maximum cycle lengths of the cubic polynomial chaotic sequences are significantly greater than these of the Logistic map. When the resolution reaches1 0 - 14, there is the situation without cycle for1000 cubic polynomial chaotic sequences with length3 × 1 0 7 . By using the CPDM and Logistic map, we design four chaos-based pseudorandom number generators (CPRNGs): CPRNGI, CPRNGII, CPRNGIII, and CPRNGIV. The randomness of two1000 key streams consisting of20000 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.