A Class Of Measurable Dynamical Systems For Chaotic Cryptography
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Date
2008-04
Authors
Akhshani, Afshin
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
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 kind 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.
Description
Keywords
A Class Of Measurable Dynamical Systems , Chaotic Cryptography