# American Institute of Mathematical Sciences

July  2020, 16(4): 1927-1941. doi: 10.3934/jimo.2019036

## An application of crypto cloud computing in social networks by cooperative game theory

 1 Department of Electrical and Electronic Engineering, Isparta University of Applied Sciences, Isparta, Turkey 2 Department of Mathematics, Süleyman Demirel University, Isparta, Turkey, Institute of Applied Mathematics, METU, Ankara, Turkey 3 Faculty of Engineering Management, Chair of Marketing and Economic Engineering, Poznan University of Technology, Poznan, Poland, Institute of Applied Mathematics, METU, Ankara, Turkey

* Corresponding author: Sırma Zeynep Alparslan Gök

Received  June 2018 Revised  December 2018 Published  May 2019

In this paper, we mathematically associate Crypto Cloud Computing, that has become an emerging research area, with Cooperative Game Theory in the presence of uncertainty. In the sequel, we retrieve data from the database of Amazon Web Service. The joint view upon Crypto Cloud Computing, Cooperative Game Theory and Uncertainty management is a novel approach. For this purpose, we construct a cooperative interval game model and apply this model to Social Networks. Then, we suggest some interval solutions related with the model by proposing a novel elliptic curve public key encryption scheme over finite fields having the property of semantic security. The paper ends with concluding words and an outlook to future studies.

Citation: Serap Ergün, Bariş Bülent Kırlar, Sırma Zeynep Alparslan Gök, Gerhard-Wilhelm Weber. An application of crypto cloud computing in social networks by cooperative game theory. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1927-1941. doi: 10.3934/jimo.2019036
##### References:

show all references

##### References:
The Amazon Cloud Service properties of one social network company
The crypto-computing model of the study
Cost of arithmetic on alternate forms of elliptic curves
 Form of elliptic curves Coordinates Unified addition Weierstrass Projective 11M+5S+1D Edwards [23] Projective 10M+1S+1D Projective 10M+1S+2D Twisted Edwards [9,31] Inverted 9M+1S+2D Extended 9M+2D Jacobi Intersections [14] Projective 13M+2S+1D Twisted Jacobi Intersections [27] Projective 13M+2S+5D Extended Jacobi Quartics [32] Jacobian 10M+3S+1D Extended Projective 8M+3S+2D Hessian Curves [34] Projective 12M Generalized Hessian Curves [26] Projective 12M+1D Twisted Hessian Curves [10] Projective 11M Huff Curves [35] Projective 11M Generalized Huff Curves [55] Projective 11M+3D New Generalized Huff Curves [20] Projective 12M+4D Extended Huff Curves [48] Projective 10M
 Form of elliptic curves Coordinates Unified addition Weierstrass Projective 11M+5S+1D Edwards [23] Projective 10M+1S+1D Projective 10M+1S+2D Twisted Edwards [9,31] Inverted 9M+1S+2D Extended 9M+2D Jacobi Intersections [14] Projective 13M+2S+1D Twisted Jacobi Intersections [27] Projective 13M+2S+5D Extended Jacobi Quartics [32] Jacobian 10M+3S+1D Extended Projective 8M+3S+2D Hessian Curves [34] Projective 12M Generalized Hessian Curves [26] Projective 12M+1D Twisted Hessian Curves [10] Projective 11M Huff Curves [35] Projective 11M Generalized Huff Curves [55] Projective 11M+3D New Generalized Huff Curves [20] Projective 12M+4D Extended Huff Curves [48] Projective 10M
The parameters of companies
 PARAMETERS SNC1 SNC2 SNC3 SNC1-SNC2 SNC1-SNC3 SNC2-SNC3 SNC1-SNC2-SNC3 Load Balancer 500 500 3000 1000 3500 3500 4000 (GB/Month) for EC2 Web Server 1/2 1/2 1/2 1/4 1/4 1/4 1/6 (Year/Piece) for EC2 App Server 1/2 1/2 1/2 1/4 1/4 1/4 1/6 (Year/Piece) for EC2 Storage: EBS Volume 6/2500 6/3000 6/8000 12/5500 12/10500 12/11000 18/13500 (Volume/GB) for EC2 Storage 10 100 200 110 210 300 310 (TB) for S3 Data Transfer Out 200 900 6400 1100 6600 7300 7700 (GB/Month) for EC2 Data Transfer In (GB/Month) 1000 500 10000 1500 11000 10500 11500 for EC2 Data Transfer Out 1000 3000 10000 4000 11000 13000 11000 (GB/Month) for CloudFront Data Storage 30 200 350 230 380 550 380 (TB) for Dynoma Data Transfer Out 200 250 1500 450 17000 1750 1700 (GB/Month) for Dynoma
 PARAMETERS SNC1 SNC2 SNC3 SNC1-SNC2 SNC1-SNC3 SNC2-SNC3 SNC1-SNC2-SNC3 Load Balancer 500 500 3000 1000 3500 3500 4000 (GB/Month) for EC2 Web Server 1/2 1/2 1/2 1/4 1/4 1/4 1/6 (Year/Piece) for EC2 App Server 1/2 1/2 1/2 1/4 1/4 1/4 1/6 (Year/Piece) for EC2 Storage: EBS Volume 6/2500 6/3000 6/8000 12/5500 12/10500 12/11000 18/13500 (Volume/GB) for EC2 Storage 10 100 200 110 210 300 310 (TB) for S3 Data Transfer Out 200 900 6400 1100 6600 7300 7700 (GB/Month) for EC2 Data Transfer In (GB/Month) 1000 500 10000 1500 11000 10500 11500 for EC2 Data Transfer Out 1000 3000 10000 4000 11000 13000 11000 (GB/Month) for CloudFront Data Storage 30 200 350 230 380 550 380 (TB) for Dynoma Data Transfer Out 200 250 1500 450 17000 1750 1700 (GB/Month) for Dynoma
The total costs
 Amazon Web Services Total Cost of Company (＄) $\left( \left[ 0\%,100\%\right] \right)$ SNC1 $\left[ 13063.02,35506.80\right]$ SNC2 $\left[ 64401.07,91333.57\right]$ SNC3 $\left[ 116776.67,188596.67\right]$ SNC1-SNC2 $\left[ 41587.70,81986.54\right]$ SNC1-SNC3 $\left[ 141710.26,330237.82\right]$ SNC2-SNC3 $\left[ 193574.13,391079.13\right]$ SNC1-SNC2-SNC3 $\left[ 168389.68,531978.52\right]$
 Amazon Web Services Total Cost of Company (＄) $\left( \left[ 0\%,100\%\right] \right)$ SNC1 $\left[ 13063.02,35506.80\right]$ SNC2 $\left[ 64401.07,91333.57\right]$ SNC3 $\left[ 116776.67,188596.67\right]$ SNC1-SNC2 $\left[ 41587.70,81986.54\right]$ SNC1-SNC3 $\left[ 141710.26,330237.82\right]$ SNC2-SNC3 $\left[ 193574.13,391079.13\right]$ SNC1-SNC2-SNC3 $\left[ 168389.68,531978.52\right]$
The interval costs of the coalitions
 $c\left( \left\{ \emptyset \right\} \right) =\left[ 0,0\right]$ $c\left( \left\{ 1\right\} \right) =\left[ 13063.02+\underline{\psi },35506.80+\underline{\psi }\right]$ $c\left( \left\{ 2\right\} \right) =\left[ 64401.07+\underline{\psi },91333.57+\underline{\psi }\right]$ $c\left( \left\{ 3\right\} \right) =\left[ 116776.67+\underline{\psi },188596.67+\underline{\psi }\right]$ $c\left( \left\{ 1,2\right\} \right) =\left[ 54650.72+\underline{\psi },117493.34+\underline{\psi }\right]$ $c\left( \left\{ 1,3\right\} \right) =\left[ 154773.28+\underline{\psi },365744.62+\underline{\psi }\right]$ $c\left( \left\{ 2,3\right\} \right) =\left[ 257975.2+\underline{\psi },482412.7+\underline{\psi }\right]$ $c\left( \left\{ 1,2,3\right\} \right) =\left[ 196360.98+\underline{\psi },447731.16+\underline{\psi }\right]$
 $c\left( \left\{ \emptyset \right\} \right) =\left[ 0,0\right]$ $c\left( \left\{ 1\right\} \right) =\left[ 13063.02+\underline{\psi },35506.80+\underline{\psi }\right]$ $c\left( \left\{ 2\right\} \right) =\left[ 64401.07+\underline{\psi },91333.57+\underline{\psi }\right]$ $c\left( \left\{ 3\right\} \right) =\left[ 116776.67+\underline{\psi },188596.67+\underline{\psi }\right]$ $c\left( \left\{ 1,2\right\} \right) =\left[ 54650.72+\underline{\psi },117493.34+\underline{\psi }\right]$ $c\left( \left\{ 1,3\right\} \right) =\left[ 154773.28+\underline{\psi },365744.62+\underline{\psi }\right]$ $c\left( \left\{ 2,3\right\} \right) =\left[ 257975.2+\underline{\psi },482412.7+\underline{\psi }\right]$ $c\left( \left\{ 1,2,3\right\} \right) =\left[ 196360.98+\underline{\psi },447731.16+\underline{\psi }\right]$
The one-point solutions by using PROP for the interval Bird rule
 $\ \ \ \ \ \ \ \ \ f$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d$ $PROP(E_{1},d)$ $\left( 324.91,584.83,2729.26\right)$ $PROP(E_{2},d)$ $\left( 4789.20,8620.57,40229.25\right)$ $PROP(E_{3},d)$ $\left( 22646.36,40763.47,190229.19\right)$
 $\ \ \ \ \ \ \ \ \ f$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d$ $PROP(E_{1},d)$ $\left( 324.91,584.83,2729.26\right)$ $PROP(E_{2},d)$ $\left( 4789.20,8620.57,40229.25\right)$ $PROP(E_{3},d)$ $\left( 22646.36,40763.47,190229.19\right)$
The one-point solutions by using PROP for the interval Shapley rule
 $\ \ \ \ \ \ \ f$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d$ $PROP(E_{1},d)$ $\left( 660.66,790.62,2187.74\right)$ $PROP(E_{2},d)$ $\left( 9738.05,11653.72,32247.25\right)$ $PROP(E_{3},d)$ $\left( 46047.64,55106.10,152485.28\right)$
 $\ \ \ \ \ \ \ f$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d$ $PROP(E_{1},d)$ $\left( 660.66,790.62,2187.74\right)$ $PROP(E_{2},d)$ $\left( 9738.05,11653.72,32247.25\right)$ $PROP(E_{3},d)$ $\left( 46047.64,55106.10,152485.28\right)$
 [1] Lars Grüne. Computing Lyapunov functions using deep neural networks. Journal of Computational Dynamics, 2020  doi: 10.3934/jcd.2021006 [2] Jann-Long Chern, Sze-Guang Yang, Zhi-You Chen, Chih-Her Chen. On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3291-3304. doi: 10.3934/dcds.2020127 [3] Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, 2021, 14 (1) : 115-148. doi: 10.3934/krm.2020051 [4] Tuoc Phan, Grozdena Todorova, Borislav Yordanov. Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1071-1099. doi: 10.3934/dcds.2020310 [5] Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020272 [6] Lucio Damascelli, Filomena Pacella. Sectional symmetry of solutions of elliptic systems in cylindrical domains. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3305-3325. doi: 10.3934/dcds.2020045 [7] Pierre Baras. A generalization of a criterion for the existence of solutions to semilinear elliptic equations. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 465-504. doi: 10.3934/dcdss.2020439 [8] Pierre-Etienne Druet. A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020458 [9] Sergio Zamora. Tori can't collapse to an interval. Electronic Research Archive, , () : -. doi: 10.3934/era.2021005 [10] Nguyen Thi Kim Son, Nguyen Phuong Dong, Le Hoang Son, Alireza Khastan, Hoang Viet Long. Complete controllability for a class of fractional evolution equations with uncertainty. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020104 [11] Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276 [12] Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020436 [13] Yongxiu Shi, Haitao Wan. Refined asymptotic behavior and uniqueness of large solutions to a quasilinear elliptic equation in a borderline case. Electronic Research Archive, , () : -. doi: 10.3934/era.2020119 [14] Hoang The Tuan. On the asymptotic behavior of solutions to time-fractional elliptic equations driven by a multiplicative white noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1749-1762. doi: 10.3934/dcdsb.2020318 [15] Gongbao Li, Tao Yang. Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020469 [16] Xiaoxian Tang, Jie Wang. Bistability of sequestration networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1337-1357. doi: 10.3934/dcdsb.2020165 [17] Yining Cao, Chuck Jia, Roger Temam, Joseph Tribbia. Mathematical analysis of a cloud resolving model including the ice microphysics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 131-167. doi: 10.3934/dcds.2020219 [18] Balázs Kósa, Karol Mikula, Markjoe Olunna Uba, Antonia Weberling, Neophytos Christodoulou, Magdalena Zernicka-Goetz. 3D image segmentation supported by a point cloud. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 971-985. doi: 10.3934/dcdss.2020351 [19] Knut Hüper, Irina Markina, Fátima Silva Leite. A Lagrangian approach to extremal curves on Stiefel manifolds. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020031 [20] Vieri Benci, Marco Cococcioni. The algorithmic numbers in non-archimedean numerical computing environments. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020449

2019 Impact Factor: 1.366