59 research outputs found
Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems
Traditionally, chaotic systems are built on the domain of infinite precision
in mathematics. However, the quantization is inevitable for any digital
devices, which causes dynamical degradation. To cope with this problem, many
methods were proposed, such as perturbing chaotic states and cascading multiple
chaotic systems. This paper aims at developing a novel methodology to design
the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite
precision. The proposed system is based on the chaos generation strategy
controlled by random sequences. It is proven to satisfy the Devaney's
definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The
application of HDDCS in image encryption is demonstrated via FPGA platform. As
each operation of HDDCS is executed in the same fixed precision, no
quantization loss occurs. Therefore, it provides a perfect solution to the
dynamical degradation of digital chaos.Comment: 12 page
Discrete-time and digital chaotic systems synthesis
This paper describes new method of high order discrete-time chaotic systems synthesis. Proposed method is based on
a special system structure called dissipation normal form and leads to chaos in conservative systems. A study of quantization effects
indicates that presented method is suitable for digital chaotic systems design
Cryptographic requirements for chaotic secure communications
In recent years, a great amount of secure communications systems based on
chaotic synchronization have been published. Most of the proposed schemes fail
to explain a number of features of fundamental importance to all cryptosystems,
such as key definition, characterization, and generation. As a consequence, the
proposed ciphers are difficult to realize in practice with a reasonable degree
of security. Likewise, they are seldom accompanied by a security analysis.
Thus, it is hard for the reader to have a hint about their security. In this
work we provide a set of guidelines that every new cryptosystems would benefit
from adhering to. The proposed guidelines address these two main gaps, i.e.,
correct key management and security analysis, to help new cryptosystems be
presented in a more rigorous cryptographic way. Also some recommendations are
offered regarding some practical aspects of communications, such as channel
noise, limited bandwith, and attenuation.Comment: 13 pages, 3 figure
Network analysis of chaotic dynamics in fixed-precision digital domain
When implemented in the digital domain with time, space and value discretized
in the binary form, many good dynamical properties of chaotic systems in
continuous domain may be degraded or even diminish. To measure the dynamic
complexity of a digital chaotic system, the dynamics can be transformed to the
form of a state-mapping network. Then, the parameters of the network are
verified by some typical dynamical metrics of the original chaotic system in
infinite precision, such as Lyapunov exponent and entropy. This article reviews
some representative works on the network-based analysis of digital chaotic
dynamics and presents a general framework for such analysis, unveiling some
intrinsic relationships between digital chaos and complex networks. As an
example for discussion, the dynamics of a state-mapping network of the Logistic
map in a fixed-precision computer is analyzed and discussed.Comment: 5 pages, 9 figure
Transmission of digital chaotic and information-bearing signals in optical communication systems
A new proposal to have secure communications in a system is reported. The basis is the use of a synchronized digital chaotic systems, sending the information signal added to an initial chaos. The received signal is analyzed by another chaos generator located at the receiver and, by a logic boolean function of the chaotic and the received signals, the original information is recovered. One of the most important facts of this system is that the bandwidth needed by the system remain the same with and without chaos
A reliable chaos-based cryptography using Galois field
Chaos-based image encryption schemes have been extensively employed over the past few years. Many issues such as the dynamical degradation of digital chaotic systems and information security have been explored, and plenty of successful solutions have also been proposed.
However, the impact of finite precision in different hardware and software setups has received little attention. In this work, we have shown
that the finite precision error may produce distinct cipher-images on different devices. In order to overcome this problem, we introduce an
efficient cryptosystem, in which the chaotic logistic map and the Galois field theory are applied. Our approach passes in the ENT test suite
and in several cyberattacks. It also presents an astonishing key space of up to 24096. Benchmark images have been effectively encrypted and
decrypted using dissimilar digital devices
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