Cryptosystems Based on Chaos Theory

Abstract

This paper reviews some developments in cryptographic primitives based on chaotic systems; such as Mandelbrot set, Julia set, and logistic map. However we classified the reviewed chaotic cryptosystems into two categorizes; public-key and nonpublic key cryptosystems. Chaos system has attracted much attention in the field of cryptography due to its properties such as being deterministic and sensitive to the initial values. As it will be indicated in the following sections, researchers are urgently looking for new public-key primitives (encryption, key sharing and digital signature) and nonpublic key system (Hash function) which might be able to replace standard cryptographic algorithms. In the surveyed nonpublic key system, we are showing the latest hash function (chaos Hash Algorithm 1 (CHA-1)) which is based on chaos theory. CHA-1 accepts messages with length less than 280 bits and produces a unique message digest of length 160-bit. As well as in the public-key systems, the creation of the Fractal based public-key primitives is possible because of the intrinsic connection between the Mandelbrot and Julia Fractal sets. The surveyed chaotic cryptosystems are attractive alternative to the traditional number theory based cryptosystems.