In recent years, a large amount of work on chaos-based cryptosystems have been published. However, many of the proposed schemes fail to explain or do not possess a number of features that are fundamentally important to all kind of cryptosystems. As a result, many proposed systems are difficult to implement in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a thorough security analysis. Consequently, it is difficult for other researchers and end users to evaluate their security and performance. This work is intended to provide a common framework of basic guidelines that, if followed, could benefit every new cryptosystem. The suggested guidelines address three main issues: implementation, key management and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements. Meanwhile, several recommendations are made regarding some practical aspects of analog chaos-based secure communications, such as channel noise, limited bandwith and attenuation.

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Some basic cryptographic requirements for chaos-based cryptosystems

In this paper, a fast chaos-based image encryption system with stream cipher structure is proposed. In order to achieve a fast throughput and facilitate hardware realization, 32-bit precision representation with fixed point arithmetic is assumed. The major core of the encryption system is a pseudo-random keystream generator based on a cascade of chaotic maps, serving the purpose of sequence generation and random mixing. Unlike the other existing chaos-based pseudo-random number generators, the proposed keystream generator not only achieves a very fast throughput, but also passes the statistical tests of up-to-date test suite even under quantization. The overall design of the image encryption system is to be explained while detail cryptanalysis is given and compared with some existing schemes.

A fast image encryption system based on chaotic maps with finite precision representation

When chaotic systems are realized with finite precisions in digital computers, their dynamical properties are often found to be entirely different from the original versions in the continuous setting. In the literature, there does not seem to be much work on quantitative analysis of such degradation of digitized chaos and how to reduce its negative influence on chaos-based digital systems. Focusing on 1D piecewise linear chaotic maps (PWLCM), this paper reports some findings on a new series of dynamical indicators, which can quantitatively reflect the degradation effects on a digital PWLCM realized with a fixed-point finite precision. On top of that, the paper introduces a new method for studying digital chaos from an algorithmic point of view. In addition, the theoretical results obtained in this paper should be very helpful for the consideration of reducing negative influence of dynamical degradation in real design of various digital chaotic systems. As typical examples, the proposed dynamical indicators are applied to the performance comparison of different remedies for improving dynamical degradation, cryptanalysis of digital chaotic ciphers based on 1D PWLCM, and design of chaotic pseudo-random number generators with desired characteristics.

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On the dynamical degradation of digital piecewise linear chaotic maps

The security of digital images attracts much attention recently, and many image encryption methods have been proposed. In IS-CAS2000, a new chaotic key-based algorithm (CKBA) for image encryption was proposed. This paper points out CKBA is very weak to the chosen/known-plaintext attack with only one plain-image, and its security to brute-force ciphertext-only attack is overestimated by the authors. That is to say, CKBA is not secure at all from cryptographic viewpoint. Some experiments are made to show the feasibility of the chosen/known-plaintext attack. We also discuss some remedies to the original scheme and their performance, and we find none of them can essentially improve the security of CKBA.

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Cryptanalysis of a chaotic image encryption method

Chaotic cryptology is widely investigated recently. This paper reviews the progress in this area and points out some existent problems in digital chaotic ciphers. As a comprehensive solution to these problems, a novel pseudo-random bit generator based on a couple of chaotic systems called CCS-PRBG is presented. Detailed theoretical analyses show that it has perfect cryptographic properties, and can be used to construct stream ciphers with higher security than other chaotic ciphers. Some experiments are made for confirmation. Finally, several examples of stream ciphers based on digital CCS-PRBG are given, and their security is discussed.

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Pseudo-random Bit Generator Based on Couple Chaotic Systems and Its Applications in Stream-Cipher Cryptography

The applications of digital chaotic maps in discrete-time chaotic cryptography and pseudo-random coding are widely studied recently. However, the statistical properties of digital chaotic maps are rather different from the continuous ones, which impedes the theoretical analyses of the digital chaotic ciphers and pseudo-random coding. This paper detailedly investigates the statistical properties of a class of digital piecewise linear chaotic map (PLCM), and rigorously proves some useful results. Based on the proved results, we further discuss some notable problems in chaotic cryptography and pseudo-random coding employing digital PLCM-s. Since the analytic methods proposed in this paper can essentially extended to a large number of PLCM-s, they will be valuable for the research on the performance of such maps in chaotic cryptography and pseudo-random coding.

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Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding

Pseudo-random bit generator based on couple chaotic systems and its applications in stream-cipher cryptography

This paper introduces a new method of research on evolvement of non-linear dynamic system employing color space, such as fractal sets and chaos systems. In contrast to traditional methods, it has more intuitionistic display and can express more information of systems, and we can observe more hidden features of dynamic systems by employing it. One can also obtain the bifurcation figures, final iterative figures. This method is mainly used for researches on those iterative systems whose dimension is lower than 3. It also can be used for research of low dimensions mapping characteristics of those high-dimension dynamic systems. This paper gives three samples on Mandelbrot/Julia set, logistic mapping and Henon trajectory.

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Research on non-linear dynamic systems employing color space

Chaotic cryptology is widely investigated recently This pa- per reviews the progress in this area and points out some existent prob- lems in digital chaotic ciphers As a comprehensive solution to these prob- lems, a novel pseudo-random bit generator based on a couple of chaotic systems called CCS-PRBG is presented Detailed theoretical analyses show that it has perfect cryptographic properties, and can be used to construct stream ciphers with higher security than other chaotic ciphers Some experiments are made for confirmation Finally, several examples of stream ciphers based on digital CCS-PRBG are given, and their security is discussed

Li Shujun

Papers

Pseudo-random Bit Generator Based on Couple Chaotic Systems and Its Applications in Stream-Cipher Cryptography

Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding

Pseudo-random bit generator based on couple chaotic systems and its applications in stream-cipher cryptography

Research on non-linear dynamic systems employing color space

Pseudo-Random Bit Generator Based on Couple Chaotic Systems and its Applications in