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CP_ABSC: An attribute-based signcryption scheme to secure multicast communications in smart grids

  • *Corresponding author: Chunqiang Hu

    *Corresponding author: Chunqiang Hu 

This research was partially supported by the National Natural Science Foundation of China under grants 61702062,61373027 and 61472418, and the National Science Foundation of the US under grants CCF-1442642, IIS-1343976, CNS-1318872, and CNS-1550313

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  • In this paper, we present a signcryption scheme called CP_ABSC based on Ciphertext-Policy Attribute Based Encryption (CP_ABE)[7] to secure the multicast communications in smart grids that require access control, data encryption, and authentication to ensure message integrity and confidentiality. CP_ABSC provides algorithms for key management, signcryption, and designcryption. It can be used to signcrypt a message based on the access rights specified by the message itself. A user can designcrypt a ciphertext if and only if it possesses the attributes required by the access structure of the data. Thus CP_ABSC effectively defines a multicast group based on the access rights of the data specified by the data itself, which differs significantly from the traditional Internet based multicast where the destination group is predetermined and must be known by the data source. CP_ABSC provides collusion attack resistance, message authentication, forgery prevention, and confidentiality. It can be easily applied in smart grids to secure the instructions/commands broadcast from a utility company to multiple smart meters (push-based multicast) and the data retrieved from a smart meter to multiple destinations (pull-based multicast). Compared to CP_ABE, CP_ABSC combines encryption with signature at a lower computational cost for signcryption and a slightly higher cost in designcryption for signature verification. We also consider the adoption of attribute-based signature (ABS), and conclude that CP_ABSC has a much lower computational cost than ABS.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  A communication architecture in smart grid systems

    Figure 2.  An access control tree structure

    Figure 3.  An example access control structure in Smart Grid

    Figure 4.  Key generation time

    Figure 5.  Encryption time

    Figure 6.  Decryption time

    Figure 7.  ABS signature running-time

    Figure 8.  ABS verification running-time

    Table 1.  The Computational Cost of Different Functions and Operations between CP_ABE and our scheme

    CP_ABE [7] CP_ABSC
    Key Generation $n{{\mathbb{G}}_{1}} + (n+2){{\mathbb{G}}_{2}} + nH_{{{\mathbb{G}}_{2}}}$ $(2n+5){{\mathbb{G}}_{2}}$
    Encryption $(k+1){{\mathbb{G}}_{1}} + k{{\mathbb{G}}_{2}} + 1{{\mathbb{G}}_{3}} + kH_{{{\mathbb{G}}_{2}}}$ $2((k+1){{\mathbb{G}}_{1}} +{{\mathbb{G}}_{2}}+{{\mathbb{G}}_{3}})+2$ (pairings)
    Decryption $(2k^\prime + 1)$ (pairings) $1{{\mathbb{G}}_{3}} + (2k^\prime+3)$ (pairings)
    Notes: ${{\mathbb{G}}_{1}}$ in the table means an exponentiation operation in ${{\mathbb{G}}_{1}}$ group; ${{\mathbb{G}}_{2}}$ and ${{\mathbb{G}}_{3}}$ are defined similarly. $H_{{{\mathbb{G}}_{1}}}$ means hashing an attribute string or a message into an element in ${{\mathbb{G}}_{1}}$; $H_{{{\mathbb{G}}_{2}}}$ is defined similarly.
     | Show Table
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    Table 2.  The Computational Cost of Different Operations in Charm Library

    Group ${{\mathbb{G}}_{1}}$ ${{\mathbb{G}}_{2}}$ ${{\mathbb{G}}_{3}}$ (pairings) $H_{{{\mathbb{G}}_{1}}}$ $H_{{{\mathbb{G}}_{2}}}$
    SS512 3.73 3.70 0.48 3.92 8.34 8.39
    MNT159 1.12 9.84 2.62 8.42 0.10 34.82
    Notes: Time is in ms. The result in this table is the average of 1000 runs.
     | Show Table
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    Table 3.  Comparison between CP_ABE and CP_ABSC

    The scheme System Initial. KeyGeneration Encryption Decryption
    CP_ABE[7] symmetric groups private key encryption decryption
    CP_ABSC asymmetric groups (sign+verify) key signcrypt. decrypt.&verify.
     | Show Table
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    Table 4.  Number of operations in the Maji's ABS scheme

    TSetup() 1${{\mathbb{G}}_{1}}$ /user
    AttrGen() 1${{\mathbb{G}}_{1}}$ / attribute
    Sign() 2${{\mathbb{G}}_{1}}$+3($\ell_r$)${{\mathbb{G}}_{1}}$+2($\ell - \ell_r$)${{\mathbb{G}}_{1}}$ + 2($\ell \cdot t$)${{\mathbb{G}}_{2}}$
    Verify() 1${{\mathbb{G}}_{1}}$+2($\ell \cdot t + t$)${{\mathbb{G}}_{2}}$+($\ell+4$)(pairings)
     | Show Table
    DownLoad: CSV

    Table 5.  Key generation per attribute of the Maji's ABS scheme

    SS512 MNT159 MNT159.S BN.S
    3.67 ms 9.72 ms 1.13 ms 2.30 ms
     | Show Table
    DownLoad: CSV
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