Chaotic cryptology

Chaotic cryptology includes two integral opposite parts: Chaotic cryptography and Chaotic cryptanalysis. 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. Since first being investigated by Robert Matthews in 1989, the use of chaos in cryptography has attracted much interest; however, long-standing concerns about its security and implementation speed continue to limit its implementation.

In order to use chaos theory efficiently in cryptography, the chaotic maps should be implemented such that the entropy generated by the map can produce required Confusion and diffusion. 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. One of the most important issues for any cryptographic primitive is the security of the system. However, in numerous cases, chaos-based cryptography algorithms are proved unsecure. The main issue in many of the cryptanalyzed algorithms is the inadequacy of the chaotic maps implemented in the system.

Types of Chaos Cryptography 
The concept of chaos cryptography or in the other words chaos-based cryptography can be divided into two major groups: the asymmetric and symmetric chaos-based cryptography. The majority of the symmetric chaos-based algorithms are based on the application of discrete chaotic maps in their process.

Chaos-based Image Encryption 
Bourbakis and Alexopoulos in 1991 proposed supposedly the earliest fully intended digital image encryption scheme which was based on SCAN language. Later on, with the emergence of chaos-based cryptography hundreds of new image encryption algorithms, all with the aim of improving the security of digital images were proposed. However, there were three main aspects of the design of an image encryption that was usually modified in different algorithms (chaotic map, application of the map and structure of algorithm). The initial and perhaps most crucial point was the chaotic map applied in the design of the algorithms. The speed of the cryptosystem is always an important parameter in the evaluation of the efficiency of a cryptography algorithm, therefore, the designers were initially interested in using simple chaotic maps such as tent map, and the logistic map. However, in 2006 and 2007, the new image encryption algorithms based on more sophisticated chaotic maps proved that application of chaotic map with higher dimension could improve the quality and security of the cryptosystems.

== Chaos-based Hash Function 
This is very simple function 
That is,  (a+b)^2

Chaos-based Random Number Generation 
The unpredictable behavior of the chaotic maps can be used in the generation of random numbers. Some of the earliest chaos-based random number generators tried to directly generate random numbers from the logistic map.

References 

Category:Chaos theory
Category:Cryptography