A new and efficient scheme for improving the digitized chaotic systems from dynamical degradation.

The performance of digital chaotic systems in secure communications and cryptographic applications is significantly degraded due to the limited precision of digital computational devices that are used to implement digital chaotic systems. However, regardless of the initial value, the digital chaotic map employed in these applications converges to several periodic orbits. Thus, a periodic orbit search algorithm (POSA) can be designed to accurately locate fixed points and limit cycles. In addition, an effective method based on stochastic jumps of chaotic orbits is proposed to counteract the performance degradation of digital chaos. Numerical simulations were performed to assess the effectiveness and feasibility of the proposed method in terms of autocorrelation, phase space inspection, approximate entropy and periodicity analysis. Furthermore, comparison with other existing methods is presented to show the competitiveness of the proposed scheme. Finally, a pseudorandom bit generator (PRBG), with desirable statistical properties, is constructed for chaos cryptography and other applications.

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Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

Entropy ◽

10.3390/e23050578 ◽

2021 ◽

Vol 23 (5) ◽

pp. 578

Author(s):

Yuhui Shi ◽

Yashuang Deng

Keyword(s):

Chaotic Systems ◽

Control Method ◽

Hybrid Control ◽

Chaotic Map ◽

Random Number Generator ◽

Pseudorandom Number Generator ◽

Number Generator ◽

Digital Devices ◽

Dynamical Degradation ◽

Dynamical Properties

Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In this paper, a unidirectional hybrid control method is proposed to improve the dynamical properties and to eliminate the biases of digital chaotic maps. A continuous chaotic system is introduced to provide external feedback control of the given digital chaotic map. Three different control modes are investigated, and the influence of control parameter on the properties of the controlled system is discussed. The experimental results show that the proposed method can not only improve the dynamical degradation of the digital chaotic map but also make the controlled digital system produce outputs with desirable performances. Finally, a pseudorandom number generator (PRNG) is proposed. Statistical analysis shows that the PRNG has good randomness and almost ideal entropy values.

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PROBLEMS WITH A PROBABILISTIC ENCRYPTION SCHEME BASED ON CHAOTIC SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127403008442 ◽

2003 ◽

Vol 13 (10) ◽

pp. 3063-3077 ◽

Cited By ~ 33

Author(s):

SHUJUN LI ◽

XUANQIN MOU ◽

BOLIYA L. YANG ◽

ZHEN JI ◽

JIHONG ZHANG

Keyword(s):

State Space ◽

Chaotic Systems ◽

Virtual State ◽

Permutation Matrix ◽

Practical Implementation ◽

Encryption Scheme ◽

High Security ◽

Dynamical Degradation ◽

Probabilistic Encryption ◽

Practical Security

Recently S. Papadimitriou et al. have proposed a new probabilistic encryption scheme based on chaotic systems. In this letter, we point out some problems with Papadimitriou et al.'s chaotic cryptosystem: (1) the size of the ciphertext and the plaintext cannot simultaneously ensure practical implementation and high security; (2) the estimated number of all possible virtual states is wrong; (3) the practical security to exhaustive attack is overestimated; (4) the fast encryption speed is dependent on the first defect; (5) problems about the dynamical degradation of digital chaotic systems; (6) no explicit indications are given to explain how to construct the virtual state space with the 2d virtual attractors, the 2e virtual states and the permutation matrix P. The detailed analyses and discussions on the above problems show that the proposed chaotic cipher is insecure and unpractical. Also, we give our suggestions on the design of general digital chaotic ciphers, and give some open topics in this area.

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ON THE DYNAMICAL DEGRADATION OF DIGITAL PIECEWISE LINEAR CHAOTIC MAPS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405014052 ◽

2005 ◽

Vol 15 (10) ◽

pp. 3119-3151 ◽

Cited By ~ 223

Author(s):

SHUJUN LI ◽

GUANRONG CHEN ◽

XUANQIN MOU

Keyword(s):

Chaotic Systems ◽

Chaotic Maps ◽

Piecewise Linear ◽

Negative Influence ◽

Performance Comparison ◽

Point Of View ◽

Random Number Generators ◽

Finite Precision ◽

Dynamical Degradation ◽

Digital Chaos

When chaotic systems are realized with finite precisions in digital computers, their dynamical properties are often found to be entirely different from the original versions in the continuous setting. In the literature, there does not seem to be much work on quantitative analysis of such degradation of digitized chaos and how to reduce its negative influence on chaos-based digital systems. Focusing on 1D piecewise linear chaotic maps (PWLCM), this paper reports some findings on a new series of dynamical indicators, which can quantitatively reflect the degradation effects on a digital PWLCM realized with a fixed-point finite precision. On top of that, the paper introduces a new method for studying digital chaos from an algorithmic point of view. In addition, the theoretical results obtained in this paper should be very helpful for the consideration of reducing negative influence of dynamical degradation in real design of various digital chaotic systems. As typical examples, the proposed dynamical indicators are applied to the performance comparison of different remedies for improving dynamical degradation, cryptanalysis of digital chaotic ciphers based on 1D PWLCM, and design of chaotic pseudo-random number generators with desired characteristics.

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Counteracting Dynamical Degradation of a Class of Digital Chaotic Systems via Unscented Kalman Filter and Perturbation

Information Sciences ◽

10.1016/j.ins.2020.12.065 ◽

2020 ◽

Author(s):

Yuling Luo ◽

Yunqi Liu ◽

Junxiu Liu ◽

Shunbin Tang ◽

Jim Harkin ◽

...

Keyword(s):

Kalman Filter ◽

Chaotic Systems ◽

Unscented Kalman Filter ◽

Dynamical Degradation

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A Novel Method to Improve the Dynamical Degradation of Digital Chaotic Systems

2018 3rd International Conference on Mechanical, Control and Computer Engineering (ICMCCE) ◽

10.1109/icmcce.2018.00084 ◽

2018 ◽

Author(s):

Xiang Xia ◽

Jun Zheng

Keyword(s):

Chaotic Systems ◽

Dynamical Degradation ◽

Novel Method

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An analogue–digital mixed method for solving the dynamical degradation of digital chaotic systems

IMA Journal of Mathematical Control and Information ◽

10.1093/imamci/dnu015 ◽

2014 ◽

pp. dnu015 ◽

Cited By ~ 1

Author(s):

LingFeng Liu ◽

HanPing Hu ◽

YaShuang Deng

Keyword(s):

Mixed Method ◽

Chaotic Systems ◽

Dynamical Degradation

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Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case

Fractal and Fractional ◽

10.3390/fractalfract5040214 ◽

2021 ◽

Vol 5 (4) ◽

pp. 214

Author(s):

Aleksandra Tutueva ◽

Denis Butusov

Keyword(s):

Computer Simulation ◽

Data Storage ◽

Secure Communication ◽

Chaotic Systems ◽

Numerical Solutions ◽

Traditional Approach ◽

Rounding Errors ◽

Explicit Integration ◽

Nonlinear Properties ◽

Dynamical Degradation

Dynamical degradation is a known problem in the computer simulation of chaotic systems. Data type limitations, sampling, and rounding errors give rise to the periodic behavior. In applications of chaotic systems in secure communication and cryptography systems, such effects can reduce data storage security and operation. In this study, we considered a possible solution to this problem by using semi-explicit integration. The key idea is to perturb the chaotic trajectory by switching between two integrators, which possess close but still different numerical solutions. Compared with the traditional approach based on the perturbation of the bifurcation parameter, this technique does not significantly change the nonlinear properties of the system. We verify the efficiency of the proposed perturbation method through several numerical experiments using the well-known Rössler oscillator.

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