Quantum Chaotic Cryptography : A New Approach
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Date
2015-07
Authors
Akhshani, Afshin
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Since 1990s chaotic dynamical systems have been widely used to design new
strategies to encrypt information in analog and digital areas. Recently, many digital
chaos-based cryptosystems are proposed and a number of them have been cryptanalyzed.
The fact that an optimum designs in the context of chaotic cryptography not
only demands a solid background in cryptography, but also a thorough knowledge of
nonlinear dynamics and chaos. However, in the design of digital chaotic cryptosystems,
there are two important issues that have not been seriously considered by most
designers of digital chaotic ciphers. First, avoiding the reconstruction of the dynamics
of the underlying chaotic systems and the second, non-periodicity of chaotic orbits.
The two main contributions of this work are its responses to these two theoretical and
methodological problems. In this way, one possible solution for avoiding the reconstruction
of chaotic orbits is increasing the complexity of orbits. In this work, two new
dynamical systems, quantum and synchronized coupled chaotic maps are proposed and
applied in two main application fields, which are pseudo random number generator and
image encryption fields. Both theoretical and experimental analysis of proposed cryptosystems
are reported and discussed. In addition, in this work in order to quantify the degree of non-periodicity of chaotic orbits, the scale index approach as a mathematical tool is proposed. This method allows the selection of the adequate configurations (optimal parameter selection) of a dynamical system to implement strategies of confusion and diffusion of information. The security analysis of the chaos-based cryptosystems
is one of the most important aspects in chaotic cryptography. In this sense, measuring
the randomness and spatial complexity of cipher images are two important tasks that
should be considered. To this end, first the accuracy of different entropy (as a measure
of randomness) measures such as Shannon entropy, Min-entropy and Renyi entropy
is examined. However, the results obtained are not reliable. In this work, new alternative
approaches, the Mean-block entropy and entropy growth curve, are proposed
for quantifying the presence randomness in the cipher images. Moreover, in this work
two fractal measures, lacunarity and succolarity, are proposed to quantify spatial complexity
in the chaos-based cipher images since the fractal dimension alone could not
sufficiently explain the complex patterns of the encrypted images. The results obtained
indicate that the mean-block entropy is more accurate than Shannon, Min and Renyi
entropies. Also, the asymptotic behavior of entropy growth curve can be considered as
a signature of randomness. Moreover, the results of lacunarity and succolarity analyses
clearly show that the encryption process could lead to the destruction of self-similarity
and connectivity among the pixels, respectively. As a conclusion, it can be strongly
recommended to use the proposed mathematical tool and scale-dependent complexity
measures including mean-block entropy, entropy growth curve and fractal measures,
to guide researchers through designing and implementing of new cryptosystems.
Description
Keywords
Chaotic cryptography