A CLASS OF MEASURABLE DYNAMICAL SYSTEMS FOR CHAOTIC CRYPTOGRAPHY

Presenter	:	AFSHIN AKHSHANI
E-mail	:	-
Date	:	16 / 9 / 2009
Time	:	3.00 PM
Venue	:	BILIK MESYUARAT SISWAZAH, ARAS 2, PUSAT PENGAJIAN SAINS FIZIK
Sypnosis	:	Chaos theory is a blanketing theory that covers all aspects of science, hence, it shows up everywhere in the world today: mathematics, physics, biology, finance, computer and even music. As an application of chaos theory, secure communications have been studied since the early 1990s. The attractiveness of using chaos as the basis for developing cryptosystem is mainly due to the intrinsic nature of chaos such as the sensitivity to the initial condition and control parameter, random-like behaviors, ergodicity and mixing property, which have tight relationships with the requirements of cryptography. The most important features of chaos are ergodicity and mixing, which can be connected with two basic cryptographic properties; confusion and diffusion. To prove ergodicity and strength of the mixing, it’s enough to show that the system possess an invariant measure and Kolmogorov-Sinai (K-S) entropy from dynamical systems point of view. In this thesis, a new hierarchy of two-dimensional piecewise nonlinear chaotic maps with an invariant measure is introduced. Also the K-S entropy of these chaotic maps is calculated analytically by using their invariant measure. Furthermore, some numerical simulations for demonstrating chaotic behavior of these kinds of chaotic maps are presented. As regards to piecewise chaotic maps having perfect dynamical properties which can be realized simply in both hardware and software, they are widely used in digital chaotic cryptography. Therefore, their potential for exploitation as a cryptosystem is investigated. In this thesis, two new chaos based cryptosystem schemes for hash function and image encryption, based on two-dimensional nonlinear piecewise chaotic maps are also presented. The proposed schemes are described in detail, along with its security analysis and implementation.

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