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During the last two decades, chaos theory in the field of secure communication has attracted a lot of attention in various branches of Science and Engineering. Also, an application of chaos synchronization, opened a whole new dimension in cryptography.

Chaotic regimes can be observed in nature, in weather and climate, biology and ecological processes ,economy and societies etc. The most important characteristic of chaos is to produce various complex patterns. The corresponding mathematical models can generate a large number of data, which are applicable as secret keys in the field of cryptography. Chaos theory has also the inherent property to connect it directly with cryptographic fundamental characteristics of "confusion" and "diffusion". Additionally, chaotic systems have a deterministic yet unpredictable dynamics, which can be used as an effective tool in terms of a better cryptosystem.

In the beginning of secure communication using chaos theory, the approach was to use the pseudorandom properties of the trajectories. Mainly basic models of discrete Chaotic maps were used for crypto schemes. Chaos synchronization has changed the approach of communication, it works as a whole cryptosystem. The driving system can be the transmitter and the response is the receiver. The simple idea was to mask a message with a chaotic signal and at the receiver end to decrypt it with the same synchronized signals.

The dynamics of nonlinearity and chaos theory can be well applied to the modern communications such as internet, satellite, wireless, optical fiber, semiconductor devices etc.

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©2015. Laboratory of Cryptography, Analysis and Structure. Institute for Mathematical Research. UPM.