Cryptographic primitives based on piecewise nonlinear chaotic maps
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Date
2008-12
Authors
Masoumi, Amir Akhavan
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Abstract
During the last decades, -information security has become a major issue. Subsequently
chaotic cryptology has recently been widely investigated and developed. Since the 80s, the idea
of using nonlinear dynamics and chaos to design new chaotic ciphers bas attracted more and
more attention and many new algorithms based on modified chaotic maps were suggested for
protecting different types of multimedia data, especially digital images and videos. But most
of the proposed ciphers encountered some problems such as lack of robustness and security.
The main goal of this thesis is to come up with a new chaos based cryptographic primitives
with high security which is capable of resisting against different types of attacks. There are
two paradigms in applying chaos for secure applications: analog chaotic secure communications
(mainly based on chaos synchronization technique) and digital chaotic ciphers realized
in computers. This thesis only focuses on digital chaotic ciphers, i.e., the area lying between
chaos theory and pure cryptography in finite-state (digital) world. The use of nonlinear dynamics
and chaotic systems in cryptography depends on the natural relation between the two
research areas: Strong dynamical properties of chaotic systems, which implies strong cryptographic
properties of the proposed cryptosystems and the basic design of the cryptosystem that
make maximum use of the strong chaotic systems properties.
A new combination of Piecewise Nonlinear Chaotic Maps (PWNLCM) are introduced and
used to design new chaos based cryptographic primitives. In this thesis a new image encryption
algorithm and a new hash function based on the proposed PWNLCM is presented. Several
tests are performed to investigate the security of the presented algorithms. The experimental
results prove the effectiveness of the proposed map, methods and the implementation of the
algorithms. The application of these chaotic maps shows the advantages of large key space and
high-level security.
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Keywords
Primitives based , Piecewise nonlinear chaotic maps