Research on 4-dimensional Systems without Equilibria with Application

Ruibin Hao, Lequan Min, Hongyan Zang


Recently chaos-based encryption has been obtained more and more attention. Chaotic systems without equilibria may be suitable to be used to design pseudorandom number generators (PRNGs) because there does not exist corresponding chaos criterion theorem on such systems. This paper proposes two propositions on 4-dimensional systems without equilibria. Using one of the propositions introduces a chaotic system without equilibria. Using this system and the generalized chaos synchronization (GCS) theorem constructs an 8-dimensional discrete generalized chaos synchronization (8DBDGCS) system. Using the 8DBDGCS system designs a 216-word chaotic PRNG. Simulation results show that there are no significant correlations between the key stream and the perturbed key streams generated via the 216-word chaotic PRNG. The key space of the chaotic PRNG is larger than 21275. As an application, the chaotic PRNG is used with an avalanche-encryption scheme to encrypt an RGB image. The results demonstrate that the chaotic PRNG is able to generate the avalanche effects which are similar to those generated via ideal chaotic PRNGs.


chaotic map; pseudorandom number generator; randomness test; avalanche encryption scheme;

Full Text:



Article Metrics

Abstract view : 106 times
PDF - 226 times


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

TELKOMNIKA Telecommunication, Computing, Electronics and Control
ISSN: 1693-6930, e-ISSN: 2302-9293
Universitas Ahmad Dahlan, 4th Campus, 9th Floor, LPPI Room
Jl. Ringroad Selatan, Kragilan, Tamanan, Banguntapan, Bantul, Yogyakarta, Indonesia 55191
Phone: +62 (274) 563515, 511830, 379418, 371120 ext. 4902, Fax: +62 274 564604