A Generalized Stability Theorem for Discrete Chaos Systems with Application in Avalanche Image Encryption

DOI

10.2991/icitmi-15.2015.172How to use a DOI?

Keywords

Generalized stability; constructive theorem; 4D chaotic map; pseudorandom number generator; FIPS 140-2 test; avalanche encryption scheme

Abstract

This study first proposes a concept of generalized stability (GST) for discrete chaos system, which is the generalization of chaos generalized synchronization (CGS). Then this study sets up a constructive theorem of GST for discrete chaos system, which provides a general representation of GST in discrete chaos system. Using the theorem designs an 8-dimensional GST system consisting of a driving chaotic system and a driven chaotic system. Numerical simulation verifies the chaotic dynamic behaviors of such GST system, which is used to design a chaotic pseudorandom number generator (CPRNG). Using FIPS 140-2 test suite and G FIPS 140-2 test suite test the randomness of four 1,000-key streams consisting of 20,000 bits generated respectively by the CPRNG, the RC4 algorithm and the ZUC algorithm. The results show that the randomness performances of the CPRNG is promising, and suggest that the statistical properties of the randomness of the sequences generated via the CPRNG and the two algorithms do not have significant differences. As an application, using the sequences generated via the CPRNG and a stream encryption scheme with avalanche effect (SESAE) encrypts an RGB image. The results show that the encrypted RGB image have significant avalanche effects, and suggest the CPRNG is a qualified candidate for the stream encryption scheme with avalanche effect.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Xue Wang
AU  - Lequan Min
AU  - E Chen
PY  - 2015/10
DA  - 2015/10
TI  - A Generalized Stability Theorem for Discrete Chaos Systems with Application in Avalanche Image Encryption
BT  - Proceedings of the 4th International Conference on Information Technology and Management Innovation
PB  - Atlantis Press
SP  - 1021
EP  - 1034
SN  - 2352-538X
UR  - https://doi.org/10.2991/icitmi-15.2015.172
DO  - 10.2991/icitmi-15.2015.172
ID  - Wang2015/10
ER  -