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

  • * Corresponding author: Sırma Zeynep Alparslan Gök

    * Corresponding author: Sırma Zeynep Alparslan Gök 
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  • 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.

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

    Citation:

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

    Figure 2.  The crypto-computing model of the study

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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] $
     | Show Table
    DownLoad: CSV

    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] $
     | Show Table
    DownLoad: CSV

    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) $
     | Show Table
    DownLoad: CSV

    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) $
     | Show Table
    DownLoad: CSV
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