Chaos communications is an application of

chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...

which is aimed to provide security in the transmission of information performed through telecommunications technologies. By secure communications, one has to understand that the contents of the message transmitted are inaccessible to possible eavesdroppers. In chaos communications security (i.e., privacy) is based on the complex dynamic behaviors provided by chaotic systems. Some properties of

chaotic dynamics Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids, ...

, such as complex behaviour, noise-like dynamics ( pseudorandom noise) and spread spectrum, are used to encode data. On the other hand, chaos being a

deterministic Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and consi ...

phenomenon, it is possible to decode data using this determinism. In practice, implementations of chaos communications devices resort to one of two chaotic phenomena:

synchronization of chaos Synchronization of chaos is a phenomenon that may occur when two or more dissipative chaotic systems are coupled. Because of the exponential divergence of the nearby trajectories of chaotic systems, having two chaotic systems evolving in synchrony ...

, or

control of chaos In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. Any chaotic attractor contains an infinite number of unstable, periodic orbits. Chaotic dynamics, then, consists of ...

. To implement chaos communications using such properties of chaos, two chaotic oscillators are required as a transmitter (or master) and receiver (or slave). At the transmitter, a message is added onto a chaotic signal and then, the message is masked in the chaotic signal. As it carries the information, the chaotic signal is also called chaotic carrier. Synchronizing of these oscillators is similar to synchronizing random neural nets in

neural cryptography Neural cryptography is a branch of cryptography dedicated to analyzing the application of stochastic algorithms, especially artificial neural network algorithms, for use in encryption and cryptanalysis. Definition Artificial neural networks are ...

. When chaos synchronization is used, a basic scheme of a communications device (Cuomo and Oppenheim 1993) is made by two identical chaotic oscillators. One of them is used as the transmitter, and the other as the receiver. They are connected in a configuration where the transmitter drives the receiver in such a way that identical synchronization of chaos between the two oscillators is achieved. For the purpose of transmission of information, at the transmitter, a message is added as a small perturbation to the chaotic signal that drives the receiver. In this way, the message transmitted is masked by the chaotic signal. When the receiver synchronizes to the transmitter, the message is decoded by a subtraction between the signal sent by transmitter and its copy generated at the receiver by means of the

mechanism. This works because, whilst the transmitter output contains the chaotic carrier plus the message, the receiver output is made only by a copy of the chaotic carrier without the message.

Optical chaos communications

Chaos communications has been a success in optical communications.

Articles

* Nonlinear systems Chaos theory Theory of cryptography {{cryptography-stub