Predefined-time vector-polynomial-based synchronization among a group of chaotic systems and its application in secure information transmission

Qiaoping Li; Sanyang Liu; Qiaoping Li; Sanyang Liu

doi:10.3934/math.2021639

AIMS Mathematics

2021, Volume 6, Issue 10: 11005-11028. doi: 10.3934/math.2021639

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Research article

Predefined-time vector-polynomial-based synchronization among a group of chaotic systems and its application in secure information transmission

Qiaoping Li ^{1,2
,
,},
Sanyang Liu ²

1.
Zhengzhou University of Aeronautics, Zhengzhou 450015, China
2.
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China

Received: 10 May 2021 Accepted: 18 July 2021 Published: 30 July 2021
MSC : 93C10

This article aims to improve the security and timeliness of chaotic synchronization scheme in chaotic secure information transmission. Firstly, a novel nonlinear synchronization scheme among multiple chaotic systems is defined based on vector polynomial to improve the complexity of the carrier signal, and then to enhance the attack resistance of the communication scheme. Secondly, a more flexible and accurate synchronization control technology is proposed so that the above vector-polynomial-based chaotic synchronization can be realized within a time that is predefined as a tunable control parameter. Subsequently, the theoretical derivation is carried out to prove the synchronization time in the above-mentioned synchronization control scheme can be set independently without being affected by the initial conditions or other control parameters. Finally, several simulation experiments on secure information transmission are presented to verify the efficiency and superiority of the designed chaotic synchronization scheme and synchronization control technology.
- vector-polynomial-based synchronization,
- predefined-time control technique,
- fixed-time control technique,
- secure information transmission,
- image encryption
Citation: Qiaoping Li, Sanyang Liu. Predefined-time vector-polynomial-based synchronization among a group of chaotic systems and its application in secure information transmission[J]. AIMS Mathematics, 2021, 6(10): 11005-11028. doi: 10.3934/math.2021639

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Abstract

This article aims to improve the security and timeliness of chaotic synchronization scheme in chaotic secure information transmission. Firstly, a novel nonlinear synchronization scheme among multiple chaotic systems is defined based on vector polynomial to improve the complexity of the carrier signal, and then to enhance the attack resistance of the communication scheme. Secondly, a more flexible and accurate synchronization control technology is proposed so that the above vector-polynomial-based chaotic synchronization can be realized within a time that is predefined as a tunable control parameter. Subsequently, the theoretical derivation is carried out to prove the synchronization time in the above-mentioned synchronization control scheme can be set independently without being affected by the initial conditions or other control parameters. Finally, several simulation experiments on secure information transmission are presented to verify the efficiency and superiority of the designed chaotic synchronization scheme and synchronization control technology.

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