iv List of figures v List of tables v

The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.

This paper introduces a simple and effective chaotic system using a combination of two existing one-dimension (1D) chaotic maps (seed maps). Simulations and performance evaluations show that the proposed system is able to produce many 1D chaotic maps with larger chaotic ranges and better chaotic behaviors compared with their seed maps. To investigate its applications in multimedia security, a n...

In any communication system, including the satellite and the Internet, it is almost impossible to prevent unauthorized people from eavesdropping. When information is broadcast from a satellite or transmitted through the Internet, there is a risk of information interception. Security of image and video data has become increasingly important for many applications, including video conferencing, se...

The current paper presents a method for image watermarking based on chaotic sequences produced by different functions. The effect of embedding a chaotic watermark on an image is examined. Extensive experimental results for JPEG and filtering attacks on images watermarked by the different functions are presented together with a comparative study of them. The results show that efficient watermark...

We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws with given statistical properties, i.e. invariant density and autocorrelation function. A variety of different examples are presented to demonstrate the power o...

Recently, a parallel hash function based on chaotic maps with changeable parameters was proposed by Li et al (2011, pp.1305-1312). In this paper, the security of it is analyzed and the weakness of the architecture is pointed out. It is found that the main limitations are the error using of floor, round and exclusive OR operations in the algorithm. In order to counterstrike these, some improveme...

In this paper, the authors propose a new chaotic block cryptosystem based on multiple one-dimensional chaotic maps. In the proposed cryptosystem, the authors establish map-to-task relations between the multiple chaotic maps and the tasks, which must be performed in the encryption rounds. The encryption process is based on these map-to-task relations. The authors enhance the security of the cryp...

The aim of this paper is to prove the following results: a continuous map f : [0, 1]→ [0, 1] is chaotic iff the shift map σf : lim ← ([0, 1], f)→ lim ← ([0, 1], f) is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. σf : lim ← ([0, 1], f) → lim ← ([0, 1], f) is chaotic iff there exists an increasing sequence of positive integers A such that the topological s...