Lingfeng Liu

Pseudorandom sequence generator based on the Chen chaotic system

Abstract In this paper, the Chen chaotic system is proposed as a pseudorandom sequence generator. A new algorithm is created to solve the problem of non-uniform distribution of the sequence generated by the Chen chaotic system. Statistical tests and security analysis show that it has good pseudorandom characteristics and is highly capable of withstanding attacks.

A general hybrid model for chaos robust synchronization and degradation reduction

This paper focuses on the problem of robust synchronization of uncertain continuous chaos and dynamical degradation of digital chaos. A hybrid model is established based on the complementarities between continuous chaos and digital chaos. An impulse-like controller along with a state feedback controller is designed to guarantee the robust synchronization of uncertain continuous chaotic systems and reduce the dynamical degradation of digital chaotic systems respectively. Simulation studies are conducted to illustrate the effectiveness of the hybrid model. Compared with the existing synchronization schemes, this model can realize the synchronization of two uncertain continuous chaotic systems without transmission of synchronization control signals and has better robustness. Meanwhile, it can make the properties of given digital chaotic systems achieve desirable levels, while the existing remedies for digital chaotic systems fail to. Thus, the hybrid model is very applicable to cryptography, secure communication and other potential applications.

Analysis and Design of Digital Chaotic Systems With Desirable Performance via Feedback Control

The dynamical degradation of digital chaotic systems (DCSs) often has serious negative influences on some digital chaos-based systems and then becomes one of the bottleneck problems stopping chaos from some applications. In this paper, we first restrict the Devaneys chaos definition to finite state sets to describe the chaotic motion of digital systems. Then, we propose a novel control method for DCSs based on the differential mean value theorem and state feedback technology. Simulation results show the effectiveness, robustness, and superiority of the proposed method. Finally, we construct a new pseudorandom number generator (PRNG) and evaluate its randomness via NIST SP800-22 and TestU01 test suites. Statistical test results show that the proposed PRNG has high reliability of randomness, thus it can be used for cryptography and other potential applications.

On the eigenvalue and Shannon's entropy of finite length random sequences

Pseudorandom binary sequences play a significant role in many fields, such as spread spectrum communications, stochastic computation, and cryptography. The complexity measures of sequences and their relationship still remain an interesting open problem. In this article, we study on the eigenvalue of random sequences, deduce its theoretical expectation and variance of random sequences with length N, and establish the relationship between eigenvalue and Shannons entropy. The results show that these two measures are consistent. Furthermore, the eigenvalue of random n-block sequences and its relation to Shannons entropy are also been studied.

Delay-introducing method to improve the dynamical degradation of a digital chaotic map

In this paper, a new delay-introducing method is proposed to improve the dynamical degradation of a digital chaotic map. The delayed state is introduced to construct a function that is used to replace the control parameter of an original chaotic map. The numerical experimental results indicate that the delayed digital chaotic maps are more complex, have larger periods, and do not completely disrupt the phase space of an original chaotic map, indicating that our method is effective and can be competitive with other proposed methods. The most significant advantage of this method is that external systems are no longer required, making it easier to implement than the other popular methods. We also propose a type of pseudorandom bit generator (PRBG) based on the delay-introducing method as a simple application.

On Nonlinear Complexity and Shannon’s Entropy of Finite Length Random Sequences

Pseudorandom binary sequences have important uses in many fields, such as spread spectrum communications, statistical sampling and cryptography. There are two kinds of method in evaluating the properties of sequences, one is based on the probability measure, and the other is based on the deterministic complexity measures. However, the relationship between these two methods still remains an interesting open problem. In this paper, we mainly focus on the widely used nonlinear complexity of random sequences, study on its distribution, expectation and variance of memoryless sources. Furthermore, the relationship between nonlinear complexity and Shannon’s entropy is also established here. The results show that the Shannon’s entropy is strictly monotonically decreased with nonlinear complexity.

A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) ...

Feedback control of digital chaotic systems with application to pseudorandom number generator

The dynamical properties will degrade when chaotic systems are implemented in digital computers with finite precisions, and such degradation often has serious negative influence on some digital chaos-based systems. Degradation reduction for a class of digital chaotic systems is investigated in this paper. A varying parameter control method is proposed based on the state feedback control technology at first. Then two chaotic maps are applied to verify its validity. Finally, a novel pseudorandom number generator is constructed, which can pass all the tests of NIST SP800-22 at both level-one and level-two approaches and also most of the tests of TestU01. Moreover, it performs better than some existing pseudorandom number generators. Thus, it has acceptable quality of randomness and can be used for cryptography and other applications.