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 recent years, a great amount of secure communications systems based on chaotic synchronization have been published. Most of the proposed schemes fail to explain a number of features of fundamental importance to all cryptosystems, such as key definition, characterization, and generation. As a consequence, the proposed ciphers are difficult to realize in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a security analysis. Thus, it is hard for the reader to have a hint about their security. In this work we provide a set of guidelines that every new cryptosystems would benefit from adhering to. The proposed guidelines address these two main gaps, i.e., correct key management and security analysis, to help new cryptosystems be presented in a more rigorous cryptographic way. Also some recommendations are offered regarding some practical aspects of communications, such as channel noise, limited bandwith, and attenuation.

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Cryptographic requirements for chaotic secure communications

Impulsive control of a chaotic system is ideal for designing digital control schemes where the control laws are generated by digital devices which are discrete in time. In this paper, several theorems on the stability of impulsive control systems are presented. These theorems are then used to find the conditions under which the chaotic systems can be asymptotically controlled to the origin by using impulsive control. Given the parameters of the chaotic system and the impulsive control law, an estimation of the upper bound of the impulse interval is given. We also present a theory of impulsive synchronization of two chaotic systems. A promising application of impulsive synchronization of chaotic systems to a secure communication scheme is presented. In this secure communication scheme, the transmitted signals are divided into small time frames. In each time frame, the synchronization impulses and the scrambled message signal are embedded. Conventional cryptographic methods are used to scramble the message signal. Simulation results based on a typical chaotic system; namely, Chua's oscillator, are provided.

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Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication

A new adaptive control method is proposed for adaptive synchronization of two uncertain chaotic systems, using a specific uncertain unified chaotic model as an example for illustration.

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Synchronization of an uncertain unified chaotic system via adaptive control

In this paper, based on the invariant principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the synchronization of almost all kinds of coupled identical neural networks with time-varying delay, which can be chaotic, periodic, etc. We do not assume that the concrete values of the connection weight matrix and the delayed connection weight matrix are known. We show that two coupled identical neural networks with or without time-varying delay can achieve synchronization by enhancing the coupling strength dynamically. The update gain of coupling strength can be properly chosen to adjust the speed of achieving synchronization. Also, it is quite robust against the effect of noise and simple to implement in practice. In addition, numerical simulations are given to show the effectiveness of the proposed synchronization method.

Adaptive synchronization of neural networks with or without time-varying delay.

Impulsive control of Lorenz system

Cryptanalyzing chaotic secure communications using return maps

Impulsive synchronization of Lorenz systems

In a chaotic switching scheme, a binary message signal is scrambled by two chaotic attractors. In this paper we present examples to show how generalized chaotic synchronization (GS) can be used to break chaotic switching schemes. Since GS is a very robust phenomenon, we find that an intruder can recover the binary information signal from chaotic switching schemes without knowing both the structure and parameters of the chaotic transmitter. The breaking method presented in this paper is not sensitive to the order of the transmitter, which means that even in a chaotic switching scheme which uses two hyperchaotic systems, the degree of security may still be low. The simulation results for both low order and high order transmitters are presented.

Chun-Mei Yang

Papers

Impulsive control of Lorenz system

Cryptanalyzing chaotic secure communications using return maps

Impulsive synchronization of Lorenz systems

Breaking chaotic switching using generalized synchronization: examples

Breaking chaotic secure communication using a spectrogram