# American Institute of Mathematical Sciences

## Encryption service protocol based on matrix norm algorithm

 1 Quality Management Office, Yantai Vocational College, Yantai 264670, China 2 Open Education College, Yantai Vocational College, Yantai 264670, China 3 Department of Computer Science and Technology, Tongji University, Shanghai 201804, China 4 School of Computer and Control Engineering, Yantai University, Yantai 264670, China

* Corresponding author: Lejun Shi

Received  April 2019 Revised  May 2019 Published  January 2020

With the development of computer and communication technology, users have more and more urgent security requirements for information storage, processing and transmission. One of the effective means to ensure information security is to adopt encryption service protocol. Traditional cryptographic protocols have the problems of high communication cost and high computational difficulty. To solve this problem, a geographic service protocol based on matrix norm algorithm is proposed. After the related mathematical foundations such as confidentiality, matrix singular value decomposition, matrix norm, etc. are studied, the matrix is transformed to solve the matrix eigenvalues, and the matrix singular values and norms are solved confidentially. The security of the protocol is verified by the difference constant relationship between the reader random number and the guard agent random number in the protocol. The simulation results show that the number and probability of successful attack of the designed protocol and the communication cost under different noise conditions are lower than the comparison encryption service protocol, and the computational complexity is reduced. The communication complexity is 1, which indicates that the designed protocol performs better.

Citation: Lejun Shi, Shaocui Guo, Xu Yang. Encryption service protocol based on matrix norm algorithm. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020255
##### References:

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##### References:
Comparisons of attacks of different encryption service protocols at different time nodes
Simulated experimental environment
 The server Client Attack procedure Operating system Windows 7 Windows 7 Windows 7 Software IDE MS VS2010 VC+2011 VC+2011 Data base SQLserver 2012 MySQL 6.0 MySQL 6.0
 The server Client Attack procedure Operating system Windows 7 Windows 7 Windows 7 Software IDE MS VS2010 VC+2011 VC+2011 Data base SQLserver 2012 MySQL 6.0 MySQL 6.0
Attack experimental data
 Attack time /s Total attack number /Times Number of successful attacks /Times Successful Attack Ratio /% Total cost Encryption Service Protocol Based on Sequential Logic 10000 15016 3357 22.36 Lower Encryption Service Protocol Based on Web Service Authentication 10000 16332 2723 16.67 Moderate Encryption Service Protocol Based on Hash Protocol Chain 10000 22069 777 3.52 Moderate Encryption Service Protocol Based on O-FRAP Protocol 10000 26208 787 3.00 Aigher The Encryption Service Protocol in this paper 10000 19002 96 0.51 Lower
 Attack time /s Total attack number /Times Number of successful attacks /Times Successful Attack Ratio /% Total cost Encryption Service Protocol Based on Sequential Logic 10000 15016 3357 22.36 Lower Encryption Service Protocol Based on Web Service Authentication 10000 16332 2723 16.67 Moderate Encryption Service Protocol Based on Hash Protocol Chain 10000 22069 777 3.52 Moderate Encryption Service Protocol Based on O-FRAP Protocol 10000 26208 787 3.00 Aigher The Encryption Service Protocol in this paper 10000 19002 96 0.51 Lower
Comparisons of Computing Complexity and Communication Complexity (Number of Communication Rounds)
 Complexity Computational complexity Communication complexity Singular Value of Matrix Encryption Service Protocol Using Matrix Norm Traditional Mathematical Algorithms O($n^{3}$) The Encryption Service Protocol in this paper O(n) 1 Matrix norm Encryption Service Protocol Using Matrix Norm Traditional Mathematical Algorithms O($n^{3}$) The Encryption Service Protocol in this paper 1 1
 Complexity Computational complexity Communication complexity Singular Value of Matrix Encryption Service Protocol Using Matrix Norm Traditional Mathematical Algorithms O($n^{3}$) The Encryption Service Protocol in this paper O(n) 1 Matrix norm Encryption Service Protocol Using Matrix Norm Traditional Mathematical Algorithms O($n^{3}$) The Encryption Service Protocol in this paper 1 1
Comparisons of Communication Costs of Encryption Service Protocols under Different Noise Conditions
 Noise-free conditions /bit Outlier Noise Conditions /bit Gaussian noise /bit Mixed noise conditions with Gaussian outliers /bit Encryption Service Protocol Based on Sequential Logic 3.16107 8.62107 6.35107 12.25107 Encryption Service Protocol Based on Web Service Authentication 3.35107 8.94107 6.06107 11.95107 Encryption Service Protocol Based on Hash Protocol Chain 3.08107 6.65 107 9.31107 12.86107 Encryption Service Protocol Based on O-FRAP Protocol 3.46107 9.33107 7.82107 16.50107 The Encryption Service Protocol in this paper 2.83107 4.22107 5.10107 7.07107
 Noise-free conditions /bit Outlier Noise Conditions /bit Gaussian noise /bit Mixed noise conditions with Gaussian outliers /bit Encryption Service Protocol Based on Sequential Logic 3.16107 8.62107 6.35107 12.25107 Encryption Service Protocol Based on Web Service Authentication 3.35107 8.94107 6.06107 11.95107 Encryption Service Protocol Based on Hash Protocol Chain 3.08107 6.65 107 9.31107 12.86107 Encryption Service Protocol Based on O-FRAP Protocol 3.46107 9.33107 7.82107 16.50107 The Encryption Service Protocol in this paper 2.83107 4.22107 5.10107 7.07107
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