Chaotification Methods For Enhancing One-Dimension Digital Chaotic Maps For Applications In Cryptography
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Date
2020-03
Authors
Alawida, Moatsum Khalif Oduh
Journal Title
Journal ISSN
Volume Title
Publisher
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. Theoretical
analysis and chaotic performance evaluation indicate that the proposed methods have long cycle lengths (cycle length > 105 at bit precision 108 ), higher nonlinearity (average
symplectic entropy of approximately 0:824), better complexities (average fuzzy
entropy of approximately 1:87 ), and larger chaotic parameter ranges (control parameter
r 2 (0;¥) ) as compared to other recently proposed chaotification methods. The
new chaotic maps are then used in the design of new cryptographic algorithms (image
encryption, hash function, pseudo random number/bit generator). Security and performance
analysis indicate that the proposed chaotic image encryption algorithms are
highly secure as indicated by average number of pixels change rate (NPCR) scores of
up to 99:65% and unified average changing intensity (UACI) values of up to 33:45%.
The proposed algorithms also surpass existing chaotic image encryption algorithms in
terms of security and performance. A number of analysis performed on the new chaotic
hash function indicates that the proposed function has a good statistical properties with
average bit changes and probabilities of ¯B = 64:127 and P = 50:09 respectively, collision
resistance with zero collisions ofWN(0) = 9403, and generally has better statistical
performance when compared to the other existing chaotic hash functions. Chaotic
random number generators are proposed and the statistical results shows that the proposed
generator has better security than existing chaotic generators, as indicated by the
passing of all the 15 sub-tests of NIST SP 800-22.
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Keywords
Computer science