Secure communication with chaotic systems of difference equations

1997 ◽  
Vol 46 (1) ◽  
pp. 27-38 ◽  
Author(s):  
S. Papadimitriou ◽  
A. Bezerianos ◽  
T. Bountis
Keyword(s):  
Difference Equations ◽  
Secure Communication ◽  
Chaotic Systems

A PROBABILISTIC SYMMETRIC ENCRYPTION SCHEME FOR VERY FAST SECURE COMMUNICATION BASED ON CHAOTIC SYSTEMS OF DIFFERENCE EQUATIONS

2001 ◽  
Vol 11 (12) ◽  
pp. 3107-3115 ◽  
Author(s):  
S. PAPADIMITRIOU ◽  
T. BOUNTIS ◽  
S. MAVROUDI ◽  
A. BEZERIANOS
Keyword(s):  
State Space ◽  
Difference Equations ◽  
Secure Communication ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Virtual State ◽  
Encryption Scheme ◽  
System Of Difference Equations ◽  
Symmetric Key ◽  
Transmitted Symbol

We present a new probabilistic symmetric key encryption scheme based on the chaotic dynamics of properly designed chaotic systems. This technique exploits the concept of virtual attractors, which are not real attractors of the underlying chaotic dynamics but are created and maintained artificially. Each virtual attractor represents a symbol of the alphabet used to encode messages. The state space is partitioned over the virtual attractors creating clusters of states. The enciphering process randomizes over the set of states mapped to a virtual attractor in order to construct the ciphertext for the transmited symbol. The receiver can reconstruct perfectly this virtual state space, given the possession of the same chaotic system of difference equations with parameters tuned perfectly to those of the transmitter. Therefore, from the ciphertext chunk corresponding to a state, the virtual attractor can be derived from the details of the virtual state space. The knowledge of the virtual attractor leads to the recovery of the transmitted symbol. We demonstrate that the new algorithm is secure, reliable and very fast. It uses discrete time chaotic recurrent systems and is simple, flexible and modular. These systems can be constructed easily dynamically from an alphanumeric encryption key. The cryptographic security of the algorithm is evaluated with combinatorial arguments.

Design and implementation of digital secure communication based on synchronized chaotic systems

2010 ◽  
Vol 20 (1) ◽  
pp. 229-237 ◽  
Author(s):  
Jui-Sheng Lin ◽  
Cheng-Fang Huang ◽  
Teh-Lu Liao ◽  
Jun-Juh Yan
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Design And Implementation

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

2022 ◽  
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Dynamic Characteristics ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Two Dimensional ◽  
Initial State ◽  
One Dimensional ◽  
Backward Euler ◽  
Short Period

Abstract The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

scholarly journals Study on Chaotic Fault Tolerant Synchronization Control Based on Adaptive Observer

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dongming Chen ◽  
Xinyu Huang ◽  
Tao Ren
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Adaptive Observer ◽  
Synchronization Control ◽  
Slave System ◽  
Chen System ◽  
Master System ◽  
Abrupt Faults

Aiming at the abrupt faults of the chaotic system, an adaptive observer is proposed to trace the states of the master system. The sufficient conditions for synchronization of such chaotic systems are also derived. Then the feasibility and effectiveness of the proposed method are illustrated via numerical simulations of chaotic Chen system. Finally, the proposed synchronization schemes are applied to secure communication system successfully. The experimental results demonstrate that the employed observer can manage real-time fault diagnosis and parameter identification as well as states tracing of the master system, and so the synchronization of master system and slave system is achieved.

scholarly journals Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jiaxun Liu ◽  
Zuoxun Wang ◽  
Minglei Shu ◽  
Fangfang Zhang ◽  
Sen Leng ◽  
...  
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Digital Signal ◽  
Fractional Difference ◽  
Voice Signal ◽  
Difference Function ◽  
Image Cryptosystem ◽  
Definition Of ◽  
Complex Chaotic Systems ◽  
Function Synchronization

Fractional complex chaotic systems have attracted great interest recently. However, most of scholars adopted integer real chaotic system and fractional real and integer complex chaotic systems to improve the security of communication. In this paper, the advantages of fractional complex chaotic synchronization (FCCS) in secure communication are firstly demonstrated. To begin with, we propose the definition of fractional difference function synchronization (FDFS) according to difference function synchronization (DFS) of integer complex chaotic systems. FDFS makes communication secure based on FCCS possible. Then we design corresponding controller and present a general communication scheme based on FDFS. Finally, we respectively accomplish simulations which transmit analog signal, digital signal, voice signal, and image signal. Especially for image signal, we give a novel image cryptosystem based on FDFS. The results demonstrate the superiority and good performances of FDFS in secure communication.

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