Chaotic cryptography is the application of the mathematical chaos theory to the practice of the cryptography, the study or techniques used to privately and securely transmit information with the presence of a third-party or adversary. The use of chaos or randomness in cryptography has long been sought after by entities wanting a new way to encrypt messages. However, because of the lack of thorough, provable security properties and low acceptable performance, chaotic cryptography has encountered setbacks.
In order to use chaos theory acceptably in cryptography, they must first be mapped to each other. Properties in chaotic systems and cryptographic primitives share unique characteristics that allow for the chaotic systems to be applied to cryptography. If chaotic parameters as well as cryptographic keys can be mapped symmetrically or mapped to produce acceptable and functional outputs, it will make it next to impossible for an adversary to find the outputs without any knowledge of the initial values. Since chaotic maps in a real life scenario require a set of numbers that are limited, they may in fact have no real purpose in a cryptosystem if the chaotic behavior can be predicted. To counter this possibility, there exists simple to advanced ciphers. Chaos theory used in cryptosystems for commercial implementation has proven to be unsuccessful mainly because a chaos theories’ requirement to use intervals of real numbers. Given enough resources and time, an adversary could be able to predict functional outcomes. Since chaotic cryptosystems have no root in number theory this would make it difficult or impossible to implement therefore impractical.