A large number of analog chaos-based secure communication systems have been proposed since the early 1990s exploiting the technique of chaos synchronization. A brief survey of these chaos-based cryptosystems and of related cryptanalytic results is given. Some recently proposed countermeasures against known attacks are also introduced.
Since the late 1980s, chaos-based cryptography has attracted more and more attention from researchers in many different areas. It has been found that chaotic systems and cryptosystems share many similar properties. For instance, chaotic systems are sensitive to the initial conditions, which corresponds to the diffusion property of good cryptosystems (for a comparison of chaos and cryptography, see Table 1 in [1]). Basically, there are two major types of chaos-based cryptosystems: analog chaos-based secure communication systems and digital chaos-based ciphers, which are designed employing completely different principles.
Almost all analog chaos-based secure communication systems are designed based on the technique for chaos synchronization, which was first discovered in the 1980s and then well developed in the 1990s [2]. The establishment of chaos synchronization between two remote chaotic systems actually means that some information has successfully been transmitted from one end to the other. This fact naturally leads to the foundation of a chaos-based communication system. Then, by keeping some part of the involved chaotic systems secret, a third party not knowing the secret key will not be able to reconstruct the information transmitted. Thus, a chaos-based secure communication system is created. Following this basic idea, a large number of analog chaosbased secure communication systems have been proposed since the 1990s. Meanwhile, related cryptanalytic work has also been developed to evaluate performance (mainly the security) of various analog chaos-based secure communication systems. Though a number of surveys have been published to introduce progress in this area, they become relatively obsolete due to the rapid growth of new research work in recent years. The purpose of this paper is to give a brief survey of analog chaos-based secure communications and related cryptanalytic work, especially focusing on latest work reported since the year 2000. This paper is organized as follows. In the next section we first introduce some preliminary knowledge about the underlying chaos synchronization technique. Then, we classify most early chaos-based secure communication systems into three basic types. Next, different kinds of cryptanalysis are discussed with some concrete examples. Finally, we enumerate some new countermeasures that have been proposed to resist known attacks. A few concluding remarks are given at the end of the paper to express our opinion on future trends in this area.
Just as its name implies, synchronization of chaos denotes a process in which two (or many) chaotic systems achieve a common dynamical behavior after a period of transient period. Here, the common behavior may be a complete coincidence of the chaotic trajectories, or just a phase locking.
To achieve synchronization, one or more driving signals have to be sent from a source to the chaotic systems to be synchronized. According to the source of the driving signal and the mode of coupling, there are mainly four types of driving modes:
• directional (internal) driving: one chaotic system serves as the source of driving and one or more driving signals are sent from this systems to the others; • bidirectional (internal) driving: two chaotic systems are coupled with each other and are driven by each other in a mutual way; • network-like coupling: many (more than two) chaotic systems are coupled with others in some way to form a complex dynamic network; • external driving: one or more external signals drive all the chaotic systems involved towards a synchronized behavior. Owing to the nature of secure communications (which means secret information transmitted from one end to the other), directional driving between two chaotic systems is employed for almost all chaos-based secure communication systems. Therefore, in this section we focus only on this kind of chaos synchronization.
For chaos synchronization of two chaotic systems with directional driving, one of the chaotic systems serves as the master (or drive) system, and the other is the slave (or response) system. From the communication point of view, the master and slave system may also be called sender and receiver system, respectively. For purpose of chaos synchronization, one or more driving signals have to be transmitted from the master system to the slave system as external force to influence the the slave system’s dynamics. As a result of the driving force, the slave system may be able to follow the the master system’s dynamics exactly or in some other forms, thus leading to different kinds of chaos synchronization like the following ones that are widely used in chaos-based secure communications:
• complete synchronization (CS, also called identical synchronization): the simplest form of chaos synchronization, corresponding to a complete agreement of the trajectories of the master and slave systems; • generalized synchronization (GS): a generalized form of complete synchro
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