# 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:

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##### 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
 $\ \ \ \ \ \ \ f$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d$ $PROP(E_{1},d)$ $\left( 660.66,790.62,2187.74\right)$ $PROP(E_{2},d)$ $\left( 9738.05,11653.72,32247.25\right)$ $PROP(E_{3},d)$ $\left( 46047.64,55106.10,152485.28\right)$
 $\ \ \ \ \ \ \ f$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d$ $PROP(E_{1},d)$ $\left( 660.66,790.62,2187.74\right)$ $PROP(E_{2},d)$ $\left( 9738.05,11653.72,32247.25\right)$ $PROP(E_{3},d)$ $\left( 46047.64,55106.10,152485.28\right)$
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