Hash Functions Using Chaotic Iterations

International audienceIn this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proven that, under some conditions, these iterations have a chaotic behavior as defined by Devaney. This chaotic behavior allows us to propose a way to generate new hash functions. An illustrative example is detailed in order to show how to use our theoretical study in practice

Chaotic iterations versus Spread-spectrum: chaos and stego security

A new framework for information hiding security, called chaos-security, has been proposed in a previous study. It is based on the evaluation of unpredictability of the scheme, whereas existing notions of security, as stego-security, are more linked to information leaks. It has been proven that spread-spectrum techniques, a well-known stego-secure scheme, are chaos-secure too. In this paper, the links between the two notions of security is deepened and the usability of chaos-security is clarified, by presenting a novel data hiding scheme that is twice stego and chaos-secure. This last scheme has better scores than spread-spectrum when evaluating qualitative and quantitative chaos-security properties. Incidentally, this result shows that the new framework for security tends to improve the ability to compare data hiding scheme

Quantitative Evaluation of Chaotic CBC Mode of Operation

The cipher block chaining (CBC) block cipher mode of operation presents a very popular way of encrypting which is used in various applications. In previous research work, we have mathematically proven that, under some conditions, this mode of operation can admit a chaotic behavior according to Devaney. Proving that CBC mode is chaotic is only the beginning of the study of its security. The next step, which is the purpose of this paper, is to develop the quantitative study of the chaotic CBC mode of operation by evaluating the level of sensibility and expansivity for this mode.Comment: in International Conference on Advanced Technologies for Signal & Images Processing ATSIP'2016 , Mar 2016, Monastir, Tunisi

The dynamics of the CBC Mode of Operation

In cryptography, the Cipher Block Chaining (CBC), one of the most commonly used mode in recent years, is a mode of operation that uses a block cipher to provide confidentiality or authenticity. In our previous research work, we have shown that this mode of operation exhibits, under some conditions, a chaotic behaviour. We have studied this behaviour by evaluating both its level of sensibility and expansivity. In this paper, we intend to deepen the topological study of the CBC mode of operation and evaluate its property of topological mixing. Additionally, other quantitative evaluations are performed, and the level of topological entropy has been evaluated too.Comment: Nonlinearity, IOP Publishing, 2016. arXiv admin note: text overlap with arXiv:1601.0813

On the design of a family of CI pseudo-random number generators

Chaos and its applications in the field of secure communications have attracted a lot of attention. Chaos-based pseudo-random number generators are critical to guarantee security over open networks as the Internet. We have previously demonstrated that it is possible to define such generators with good statistical properties by using a tool called "chaotic iterations", which depends on an iteration function. An approach to find update functions such that the associated generator presents a random-like and chaotic behavior is proposed in this research work. To do so, we use the vectorial Boolean negation as a prototype and explain how to modify this iteration function without deflating the good properties of the associated generator. Simulation results and basic security analysis are then presented to evaluate the randomness of this new family of generators.Comment: 4 pages, In WICOM'11, 7th Int. IEEE Conf. on Wireless Communications, Networking and Mobile Computing, Wuhan, China, pages 1--4, September 201

Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems

Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaney's definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.Comment: 12 page

Building a Chaotic Proven Neural Network

International audienceChaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global recurrent multi-layer perceptrons. We show formally that it is possible to make these iterations behave chaotically, as defined by Devaney, and thus we obtain the first neural networks proven chaotic. Several neural networks with different architectures are trained to exhibit a chaotical behavior