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

Serap Ergün; Bariş Bülent Kırlar; Sırma Zeynep Alparslan Gök; Gerhard-Wilhelm Weber

doi:10.3934/jimo.2019036

Article Contents

2020, Volume 16, Issue 4: 1927-1941. Doi: 10.3934/jimo.2019036

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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
^* Corresponding author: Sırma Zeynep Alparslan Gök

Received: June 2018

Revised: December 2018

Early access: May 2019

Published: May 2020

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 91A12, 94A60; Secondary: 68P25.

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Figure 1. The Amazon Cloud Service properties of one social network company

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Figure 2. The crypto-computing model of the study

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Table 1. 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

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Table 2. 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

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Table 3. 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] $

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Table 4. 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] $

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Table 5. 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) $

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Table 6. 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) $

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