A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications
Firstly, this study introduces a definition of generalized stability (GST) in discrete-time nonautonomous chaos system (DNCS), which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2015-01-01
|
Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2015/121359 |
id |
doaj-6983fb7271d44ad2b20c41e5e0530298 |
---|---|
record_format |
Article |
spelling |
doaj-6983fb7271d44ad2b20c41e5e05302982020-11-24T21:09:01ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/121359121359A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with ApplicationsMei Zhang0Danling Wang1Lequan Min2Xue Wang3School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaFirstly, this study introduces a definition of generalized stability (GST) in discrete-time nonautonomous chaos system (DNCS), which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG) based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 21116. As another application, this study designs a stream avalanche encryption scheme (SAES) in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.http://dx.doi.org/10.1155/2015/121359 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mei Zhang Danling Wang Lequan Min Xue Wang |
spellingShingle |
Mei Zhang Danling Wang Lequan Min Xue Wang A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications Mathematical Problems in Engineering |
author_facet |
Mei Zhang Danling Wang Lequan Min Xue Wang |
author_sort |
Mei Zhang |
title |
A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications |
title_short |
A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications |
title_full |
A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications |
title_fullStr |
A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications |
title_full_unstemmed |
A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications |
title_sort |
generalized stability theorem for discrete-time nonautonomous chaos system with applications |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2015-01-01 |
description |
Firstly, this study introduces a definition of generalized stability (GST) in discrete-time nonautonomous chaos system (DNCS), which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG) based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 21116. As another application, this study designs a stream avalanche encryption scheme (SAES) in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs. |
url |
http://dx.doi.org/10.1155/2015/121359 |
work_keys_str_mv |
AT meizhang ageneralizedstabilitytheoremfordiscretetimenonautonomouschaossystemwithapplications AT danlingwang ageneralizedstabilitytheoremfordiscretetimenonautonomouschaossystemwithapplications AT lequanmin ageneralizedstabilitytheoremfordiscretetimenonautonomouschaossystemwithapplications AT xuewang ageneralizedstabilitytheoremfordiscretetimenonautonomouschaossystemwithapplications AT meizhang generalizedstabilitytheoremfordiscretetimenonautonomouschaossystemwithapplications AT danlingwang generalizedstabilitytheoremfordiscretetimenonautonomouschaossystemwithapplications AT lequanmin generalizedstabilitytheoremfordiscretetimenonautonomouschaossystemwithapplications AT xuewang generalizedstabilitytheoremfordiscretetimenonautonomouschaossystemwithapplications |
_version_ |
1716758853372084224 |