Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 619257, 12 pages
Research Article

Theorem to Generate Independently and Uniformly Distributed Chaotic Key Stream via Topologically Conjugated Maps of Tent Map

1Department of Control Science and Engineering, School of Automation, University of Science and Technology Beijing, Beijing 100083, China
2Department of Control Science and Engineering, School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Received 26 July 2012; Revised 4 October 2012; Accepted 16 October 2012

Academic Editor: Kwok-Wo Wong

Copyright © 2012 Zheng guang Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a theorem to generate chaotic key stream from topologically conjugated maps of Tent Map. In this theorem, the condition for topological conjugation between Tent Map and a class of chaotic maps is first determined. Then, the chaotic attractor of the maps is divided into unequal subintervals, the chaotic orbit is sampled once in time iteration, and, finally, the independently and uniformly distributed phase key stream is obtained. The theoretical and numerical analyses show that the chaotic key stream generated by the proposed theorem successfully is independent and uniform, has a certain complex degree close to the maximum approximate entropy for 2n phase key stream, and satisfies the randomness requirement defined in NIST SP800-22. This theorem can be used in fields such as cryptography and numerical simulation.