Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a cryptographic system. In the end, the question is, can chaotic systems provide alternative techniques able to enhance cryptographic algorithms?. This chapter can be a worthy material to guide the reader in order to answer himself this question. Thus, the objective of this chapter is to give a general vision of what chaotic cryptography is and a comprehensive example that illustrates the main techniques used in this field.
http://arxiv.org/abs/1203.4134
A remarkable characteristic of chaotic systems is their capability of producing quite complex patterns of behavior from simple real systems or in simulations from low dimensional systems given by a small set of evolution equations. This quality has made them particularly useful for application in a wide variety of disciplines, such as biology, economics, engineering and others (Cambel, 1993; Kocarev et al., 2009). In these applications, chaotic systems are used to produce, simulate, assist or control different processes improving their performance or providing a more suitable output. The use of chaos in cryptography seems quite natural, as its inherent properties connect it directly with cryptographic characteristics of confusion and diffusion. This idea is present in Shannon’s works (Shannon, 1949), even earlier than the term “chaos” appeared in the scientific literature.
Additionally, chaotic dynamical systems have the advantage of providing qualitatively simple mechanisms to generate deterministic pseudo randomness. For cryptography, this could be the promise of producing simpler or better randomness in terms of performance (Tenny et al., 2006). By now, the history of chaos-based cryptography is more than two decades long. First, some works appear in the 80’s (Wolfram, 1985; Guan, 1987), but it is in the 90’s, when chaotic cryptography really takes off. Two papers mark this beginning (Matews, 1989) and (Pecora, 1989). The first one proposes a digital stream cipher where a signal generated from a chaotic system is used to mask the clear message. The second proposes chaos synchronization to mask the clear message with a chaotic signal at the physical level of the communication channel and to use synchronization techniques at the receiver to filter the chaotic signal. These two papers also open two different views of the application of chaos to cryptography that will be later referred as digital or analog techniques (Alvarez & Li, 2006). Since then, the number of chaotic cryptosystems that have been proposed is too large to be covered in this chapter. The interested reader can find a complete and updated view of this field in (Kocarev, 2011). In addition, for more recent developments, some work is also needed to assess their security.
Nevertheless these works have been published in journals of physics or engineering; they have revealed the potential of this field, but also a series of errors and weak points that need to be overcome. As a consequence, chaotic cryptography has been an active research field but with marginal impact in classical cryptography (Dachselt & Schwarz, 2001; Amigó, 2009). In the end, the question is, can chaotic systems provide alternative techniques able to enhance cryptographic algorithms?. This chapter can be a worthy material so that the reader can find some guides in order to answer himself this question. Thus, the objective of this chapter is to give a general vision of what chaotic cryptography is and a comprehensive example that illustrates the main techniques used in this field. In it, the authors are intended to present a series of selected topics of special interest in this field. In successive sections of this chapter the reader will be introduced to the following topics: fundamentals of chaos, relation between chaos and cryptography, different kinds of chaotic cryptosystems and their main characteristics, Pseudo-Random Number Generation (PRNG) based on digitized chaos, cipher design based on two dimensional chaotic maps, and the corresponding best practices and guidelines required for designing good cryptographic algorithms.
