Alawida, Moatsum Khalif Oduh
(2022)
Chaotification Methods For
Enhancing One-Dimension Digital
Chaotic Maps For Applications In
Cryptography.
PhD thesis, Universiti Sains Malaysia.
Abstract
Digital one-dimensional chaotic maps are becoming increasingly popular in the
area of cryptography due to their commonalities and their simple structures. However,
these maps have well-known drawbacks which contribute negatively towards
the security of the cryptographic algorithms that utilize them. Thus, enhancing digital
one-dimensional chaotic maps in terms of their chaoticity and statistical properties
will contribute towards the improvement of chaos-based cryptography. Many
chaotification methods have been recently proposed to address these issues. However,
most of these methods are dependent on an external entropy source to enhance
the characteristics of one-dimensional chaotic maps. In this study, four novel chaotification
methods are proposed to address these issues without the need of external
entropy sources. The first method hybridizes deterministic finite state automata with
one-dimensional chaotic maps under control the existing chaotification methods. The
aim of this method is to weaken dynamical degradation issue through prolonging cycle
length. To increase chaotic complexity and enlarge chaotic parameter range, the
second method is proposed based on modifying chaotic state values by reversing the
order of their fractional bits. To take advantage of the first two proposed methods, the
third method is proposed based on a one-dimensional chaotic map and deterministic
finite state machine under the control of bitwise permutations. The fourth method is
introduced based on cascade and combination methods as a simple framework to enlarge
the chaotic parameter range and to enhance chaotic performance.
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