doi: 10.3934/dcdss.2020255

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:
[1]

E. BeckE. Batista and S. Rui, Norm-constrained adaptive algorithms for sparse system identification based on projections onto intersections of hyperplanes, Signal Processing, 118 (2016), 259-271.  doi: 10.1016/j.sigpro.2015.06.019.  Google Scholar

[2]

F. CaoJ. Chen and H. Ye, Recovering low-rank and sparse matrix based on the truncated nuclear norm, Neural Networks, 85 (2017), 10-20.  doi: 10.1016/j.neunet.2016.09.005.  Google Scholar

[3]

J. ChenY. ZhouJ. Li and Y. Zhu, The method of mimo radar target parameter estimation based on sl0 algorithm and truncated singular value decomposition, Journal of China Academy of Electronics and Information Technology, 12 (2017), 295-301.   Google Scholar

[4]

X. Chen, Simulation of visual apparent evaluation method for multimedia human-computer interaction, Computer Simulation, 35 (2018), 178-181,185.   Google Scholar

[5]

S. Cho, S. Kang and S. Lee, On data space selection and data processing for parameter identification in a reaction-diffusion model based on frap experiments, Abstract and Applied Analysis, 1–17. Google Scholar

[6]

Z. HarchaouiA. Juditsky and A. Nemirovski, Conditional gradient algorithms for norm-regularized smooth convex optimization, Mathematical Programming, 152 (2015), 75-112.  doi: 10.1007/s10107-014-0778-9.  Google Scholar

[7]

B. Hong-XiaX. Bai and J. Zhao, Joint matrix form sar imaging and autofocus based on compressed sensing, Acta Electronica Sinica, 45 (2017), 874-881.   Google Scholar

[8]

W. JeongB. Yeo and K. Kim, Performance analysis of the encryption algorithms in a satellite communication network based on h-arq, Math Pract Theory, 15 (2015), 45-52.   Google Scholar

[9]

Q. Li, Q. Si and Q. Hai, Delay dependent robust control for optimal h infinite generalized nonlinear systems with uncertain state delay, Automation and Instrumentation, 89–91. Google Scholar

[10]

M. Mishra and V. Mankar, Text encryption algorithms based on pseudo random number generator, International Journal of Computer Applications, 111 (2015), 1-6.  doi: 10.5120/19507-0756.  Google Scholar

[11]

S. NagarajG. Raju and K. Rao, Image encryption using elliptic curve cryptograhy and matrix, Procedia Computer Science, 48 (2015), 276-281.  doi: 10.1016/j.procs.2015.04.182.  Google Scholar

[12]

F. NieZ. Hu and X. Li, Matrix completion based on non-convex low rank approximation, Transactions on Image Processing, 28 (2019), 2378-2388.  doi: 10.1109/TIP.2018.2886712.  Google Scholar

[13]

C. Popescu, A secure and efficient payment protocol based on elgamal cryptographic algorithms, Electronic Commerce Research, 18 (2018), 339-358.  doi: 10.1007/s10660-016-9236-5.  Google Scholar

[14]

X. Rong, Design and safety analysis of power monitoring system based on wsn, Chinese Journal of Power Sources, 39 (2015), 2761-2762.   Google Scholar

[15]

V. SchulzM. Siebenborn and K. Welker, Efficient pde constrained shape optimization based on steklov-poincaré type metrics, Mathematics, 26 (2016), 2800-2819.  doi: 10.1137/15M1029369.  Google Scholar

[16]

F. ShangJ. ChengY. Liu and e. al., Bilinear factor matrix norm minimization for robust PCA: Algorithms and applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20 (2018), 2066-2080.  doi: 10.1109/TPAMI.2017.2748590.  Google Scholar

[17]

C. SoussenJ. Idier and J. Duan, Homotopy based algorithms for l0-regularized least-squares, Transactions on Signal Processing, 63 (2015), 3301-3316.  doi: 10.1109/TSP.2015.2421476.  Google Scholar

[18]

F. Wang, New upper bounds for the infinity norm of inverse matrix of strictly diagonally dominant m-matrix, Journal of Jilin University (Science Edition), 54 (2016), 61-65.   Google Scholar

[19]

H. ZhangX. LiS. ZhangF. WuY. Huang and D. Gao, Design of remote debugging software system for himm digital power supplies, Journal of Power Supply, 14 (2016), 38-42.   Google Scholar

[20]

Y. ZhangL. Yi and X. Li, Salt and pepper noise removal in surveillance video based on low-rank matrix recovery, Computational Visual Media, 1 (2015), 59-68.  doi: 10.1007/s41095-015-0005-5.  Google Scholar

show all references

References:
[1]

E. BeckE. Batista and S. Rui, Norm-constrained adaptive algorithms for sparse system identification based on projections onto intersections of hyperplanes, Signal Processing, 118 (2016), 259-271.  doi: 10.1016/j.sigpro.2015.06.019.  Google Scholar

[2]

F. CaoJ. Chen and H. Ye, Recovering low-rank and sparse matrix based on the truncated nuclear norm, Neural Networks, 85 (2017), 10-20.  doi: 10.1016/j.neunet.2016.09.005.  Google Scholar

[3]

J. ChenY. ZhouJ. Li and Y. Zhu, The method of mimo radar target parameter estimation based on sl0 algorithm and truncated singular value decomposition, Journal of China Academy of Electronics and Information Technology, 12 (2017), 295-301.   Google Scholar

[4]

X. Chen, Simulation of visual apparent evaluation method for multimedia human-computer interaction, Computer Simulation, 35 (2018), 178-181,185.   Google Scholar

[5]

S. Cho, S. Kang and S. Lee, On data space selection and data processing for parameter identification in a reaction-diffusion model based on frap experiments, Abstract and Applied Analysis, 1–17. Google Scholar

[6]

Z. HarchaouiA. Juditsky and A. Nemirovski, Conditional gradient algorithms for norm-regularized smooth convex optimization, Mathematical Programming, 152 (2015), 75-112.  doi: 10.1007/s10107-014-0778-9.  Google Scholar

[7]

B. Hong-XiaX. Bai and J. Zhao, Joint matrix form sar imaging and autofocus based on compressed sensing, Acta Electronica Sinica, 45 (2017), 874-881.   Google Scholar

[8]

W. JeongB. Yeo and K. Kim, Performance analysis of the encryption algorithms in a satellite communication network based on h-arq, Math Pract Theory, 15 (2015), 45-52.   Google Scholar

[9]

Q. Li, Q. Si and Q. Hai, Delay dependent robust control for optimal h infinite generalized nonlinear systems with uncertain state delay, Automation and Instrumentation, 89–91. Google Scholar

[10]

M. Mishra and V. Mankar, Text encryption algorithms based on pseudo random number generator, International Journal of Computer Applications, 111 (2015), 1-6.  doi: 10.5120/19507-0756.  Google Scholar

[11]

S. NagarajG. Raju and K. Rao, Image encryption using elliptic curve cryptograhy and matrix, Procedia Computer Science, 48 (2015), 276-281.  doi: 10.1016/j.procs.2015.04.182.  Google Scholar

[12]

F. NieZ. Hu and X. Li, Matrix completion based on non-convex low rank approximation, Transactions on Image Processing, 28 (2019), 2378-2388.  doi: 10.1109/TIP.2018.2886712.  Google Scholar

[13]

C. Popescu, A secure and efficient payment protocol based on elgamal cryptographic algorithms, Electronic Commerce Research, 18 (2018), 339-358.  doi: 10.1007/s10660-016-9236-5.  Google Scholar

[14]

X. Rong, Design and safety analysis of power monitoring system based on wsn, Chinese Journal of Power Sources, 39 (2015), 2761-2762.   Google Scholar

[15]

V. SchulzM. Siebenborn and K. Welker, Efficient pde constrained shape optimization based on steklov-poincaré type metrics, Mathematics, 26 (2016), 2800-2819.  doi: 10.1137/15M1029369.  Google Scholar

[16]

F. ShangJ. ChengY. Liu and e. al., Bilinear factor matrix norm minimization for robust PCA: Algorithms and applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20 (2018), 2066-2080.  doi: 10.1109/TPAMI.2017.2748590.  Google Scholar

[17]

C. SoussenJ. Idier and J. Duan, Homotopy based algorithms for l0-regularized least-squares, Transactions on Signal Processing, 63 (2015), 3301-3316.  doi: 10.1109/TSP.2015.2421476.  Google Scholar

[18]

F. Wang, New upper bounds for the infinity norm of inverse matrix of strictly diagonally dominant m-matrix, Journal of Jilin University (Science Edition), 54 (2016), 61-65.   Google Scholar

[19]

H. ZhangX. LiS. ZhangF. WuY. Huang and D. Gao, Design of remote debugging software system for himm digital power supplies, Journal of Power Supply, 14 (2016), 38-42.   Google Scholar

[20]

Y. ZhangL. Yi and X. Li, Salt and pepper noise removal in surveillance video based on low-rank matrix recovery, Computational Visual Media, 1 (2015), 59-68.  doi: 10.1007/s41095-015-0005-5.  Google Scholar

Figure 1.  Comparisons of attacks of different encryption service protocols at different time nodes
Table 1.  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
Table 2.  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
Table 3.  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
Table 4.  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
[1]

Yifu Feng, Min Zhang. A $p$-spherical section property for matrix Schatten-$p$ quasi-norm minimization. Journal of Industrial & Management Optimization, 2020, 16 (1) : 397-407. doi: 10.3934/jimo.2018159

[2]

Lingling Lv, Zhe Zhang, Lei Zhang, Weishu Wang. An iterative algorithm for periodic sylvester matrix equations. Journal of Industrial & Management Optimization, 2018, 14 (1) : 413-425. doi: 10.3934/jimo.2017053

[3]

Vassilios A. Tsachouridis, Georgios Giantamidis, Stylianos Basagiannis, Kostas Kouramas. Formal analysis of the Schulz matrix inversion algorithm: A paradigm towards computer aided verification of general matrix flow solvers. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2019047

[4]

Wei-guo Wang, Wei-chao Wang, Ren-cang Li. Deflating irreducible singular M-matrix algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 491-518. doi: 10.3934/naco.2013.3.491

[5]

Paul Skerritt, Cornelia Vizman. Dual pairs for matrix groups. Journal of Geometric Mechanics, 2019, 11 (2) : 255-275. doi: 10.3934/jgm.2019014

[6]

Meijuan Shang, Yanan Liu, Lingchen Kong, Xianchao Xiu, Ying Yang. Nonconvex mixed matrix minimization. Mathematical Foundations of Computing, 2019, 2 (2) : 107-126. doi: 10.3934/mfc.2019009

[7]

Adel Alahmadi, Hamed Alsulami, S.K. Jain, Efim Zelmanov. On matrix wreath products of algebras. Electronic Research Announcements, 2017, 24: 78-86. doi: 10.3934/era.2017.24.009

[8]

Zhengshan Dong, Jianli Chen, Wenxing Zhu. Homotopy method for matrix rank minimization based on the matrix hard thresholding method. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 211-224. doi: 10.3934/naco.2019015

[9]

K. T. Arasu, Manil T. Mohan. Optimization problems with orthogonal matrix constraints. Numerical Algebra, Control & Optimization, 2018, 8 (4) : 413-440. doi: 10.3934/naco.2018026

[10]

Peizhao Yu, Guoshan Zhang, Yi Zhang. Decoupling of cubic polynomial matrix systems. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2020012

[11]

Lei Zhang, Anfu Zhu, Aiguo Wu, Lingling Lv. Parametric solutions to the regulator-conjugate matrix equations. Journal of Industrial & Management Optimization, 2017, 13 (2) : 623-631. doi: 10.3934/jimo.2016036

[12]

Heide Gluesing-Luerssen, Fai-Lung Tsang. A matrix ring description for cyclic convolutional codes. Advances in Mathematics of Communications, 2008, 2 (1) : 55-81. doi: 10.3934/amc.2008.2.55

[13]

Houduo Qi, ZHonghang Xia, Guangming Xing. An application of the nearest correlation matrix on web document classification. Journal of Industrial & Management Optimization, 2007, 3 (4) : 701-713. doi: 10.3934/jimo.2007.3.701

[14]

Angelo B. Mingarelli. Nonlinear functionals in oscillation theory of matrix differential systems. Communications on Pure & Applied Analysis, 2004, 3 (1) : 75-84. doi: 10.3934/cpaa.2004.3.75

[15]

A. Cibotarica, Jiu Ding, J. Kolibal, Noah H. Rhee. Solutions of the Yang-Baxter matrix equation for an idempotent. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 347-352. doi: 10.3934/naco.2013.3.347

[16]

Haixia Liu, Jian-Feng Cai, Yang Wang. Subspace clustering by (k,k)-sparse matrix factorization. Inverse Problems & Imaging, 2017, 11 (3) : 539-551. doi: 10.3934/ipi.2017025

[17]

Leda Bucciantini, Angiolo Farina, Antonio Fasano. Flows in porous media with erosion of the solid matrix. Networks & Heterogeneous Media, 2010, 5 (1) : 63-95. doi: 10.3934/nhm.2010.5.63

[18]

Debasisha Mishra. Matrix group monotonicity using a dominance notion. Numerical Algebra, Control & Optimization, 2015, 5 (3) : 267-274. doi: 10.3934/naco.2015.5.267

[19]

Joshua Du, Jun Ji. An integral representation of the determinant of a matrix and its applications. Conference Publications, 2005, 2005 (Special) : 225-232. doi: 10.3934/proc.2005.2005.225

[20]

Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami Radunskaya, Ian Tucker. Predicting the drug release kinetics of matrix tablets. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 261-277. doi: 10.3934/dcdsb.2009.12.261

2018 Impact Factor: 0.545

Metrics

  • PDF downloads (26)
  • HTML views (101)
  • Cited by (0)

Other articles
by authors

[Back to Top]