chebyshev polynomial
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2022 ◽  
Vol 155 ◽  
pp. 111712
Author(s):  
Donglin Yan ◽  
Yang Zheng ◽  
Wanying Liu ◽  
Tianya Chen ◽  
Qijuan Chen

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 100
Author(s):  
Robert Reynolds ◽  
Allan Stauffer

The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) and derive in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. The zero distribution of almost all Hurwitz-Lerch zeta functions is asymmetrical. All the results in this work are new.


Author(s):  
Костянтин Станіславович Васюта ◽  
Уляна Романівна Збежховська ◽  
Валерій Валерійович Слободянюк ◽  
Ірина Вікторівна Захарченко ◽  
Олександр Леонтійович Кащишин ◽  
...  

The subject of the research is the processes of formation and processing of signals with orthogonal frequency divisionand multiplexing (OFDM) of chaotic sequences to ensure the stealthiness of data transmission. The research synthesizes the method for increasing the stealthiness of information transmission systems based on signals with OFDM-modulation on the basis of forming an analytical signal and chaotic mapping of Chebyshev polynomial. It would enable ensuring reliable information protection in radio transmission systems that use signals with OFDM-modulation, at the cost of the high level of structural and independent and Identically distributed (IID) (the degree of signal masking under noise) stealthiness of the signals. The tasks are to investigate the effectiveness of the developed method for increasing the stealthiness of information transmission systems by numerical assessment of the level of structural and IID-stealthiness and the quality of recovery of the masked information on the receiving side. The methods used are for the formation and processing of chaotic subcarriers in the signal with OFDM-modulation – methods of nonlinear dynamics, approaches to the formation of analytical chaotic signal and methods of the statistical theory of observation processing; to assess the level of structural and IID-stealthiness – steganography theory, a method of nonlinear time series analysis based on the use of BDS-statistics. The following results are obtained: the method for increasing the stealthiness of information transmission systems based on the use of signals with OFDM-modulation and chaotic subcarriers has been synthesized, has also evaluated the level of structural and IID-stealthiness of signals, that generated using the proposed method. It is established that compared with systems that use harmonic signals with OFDM-modulation, chaotic signals with OFDM-modulation can provide a higher level of IID-stealthiness. It was confirmed by the obtained results of visual, frequency, statistical and dynamic analysis. To assess the level of structural stealthiness, the expenditure of detecting the generated signals with a given probability has been estimated. The obtained results showed that the level of structural stealthiness increased by 2…2.5 times. It has shown that to ensure the required level of recovery of the generated signal, the signal-to-noise ratio at the input of the receiver must be greater than 4 dB. Conclusions. The scientific novelty of the obtained results lies in the following: for the first time, the method of subcarrier formation for signals with OFDM-modulation based on the use of analytical signal and Chebyshev polynomial of the first kind of tertiary is obtained. The proposed method provides the required level of structural and IID-stealthiness of information transmission systems, compared with conventional methods of signal generation with OFDM-modulation, due to the similarity of the generated signals with “white” noise. 


Author(s):  
Majid Khan ◽  
Ammar S. Alanazi ◽  
Lal Said Khan ◽  
Iqtadar Hussain

AbstractThe security of digital content during transmission and storage through insecure communication links and databases is a challenging issue in today's world. In this article, an encryption scheme based on fractal Tromino and Chebyshev polynomial-based generated chaotic matrix is presented. The scheme fulfills the most fundamental aspect of encryption that is diffusion and confusion. For confusion highly non-linear, pre-defined S-boxes are used. The proposed scheme has been tested using state-of-the-art key performance indicators including differential analysis, statistical analysis. Information entropy analysis, mean square error, and NIST-based randomness analysis. The encrypted images have the highest practically achievable entropy of 7.999 and the time analysis shows that the proposed system is suitable for real-time implementation. The rest of the results indicates that the proposed cryptosystem possesses high immunity toward various attacks. The security analysis compared with the existing scheme shows the strength of the suggested scheme.


2021 ◽  
Author(s):  
Jiyun Yang ◽  
Jiamin Deng ◽  
Tao Xiang ◽  
Bo Tang

Abstract Vehicle ad hoc network (VANET) is an open communication environment. Any user can broadcast messages, which means that it can be easily attacked by malicious users. Therefore, the authentication of vehicles is needed. In this paper, we propose a Chebyshev polynomial-based conditional privacy-preserving authentication and group-key agreement scheme for VANET. Specifically, we solve three problems in VANET: (1) we improve the effectiveness of TA by using Chebyshev polynomial to authenticate vehicles; (2) we reduce the computational burden of TA by using Chinese remainder theorem to manage group members; (3) we provide conditional privacy for users by using traceable pseudonym scheme. Theoretical and experimental results show that the proposed scheme is more efficient than existing related work.


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