# American Institute of Mathematical Sciences

February  2018, 1(1): 77-100. doi: 10.3934/mfc.2018005

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

 1 Key Laboratory of Dependable Service Computing in Cyber Physical Society, Ministry of Education, Chongqing University, China 2 School of Software Engineering, Chongqing University, China 3 School of Information Science and Engineering, Qufu Normal University, China 4 Department of Computer Science, The George Washington University, USA 5 Electrical & Computer Engineering Department, George Mason University, USA 6 Electrical & Computer Engineering Department, Florida International University, USA 7 Beijing Key Laboratory of IOT Information Security Technology, Institute of Information Engineering, Chinese Academy of Sciences (CAS), China

*Corresponding author: Chunqiang Hu

The preliminary version of this paper appears in [16]

Received  September 2017 Revised  November 2017 Published  February 2018

Fund Project: 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.

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.

Citation: Chunqiang Hu, Jiguo Yu, Xiuzhen Cheng, Zhi Tian, Kemal Akkaya, and Limin Sun. CP_ABSC: An attribute-based signcryption scheme to secure multicast communications in smart grids. Mathematical Foundations of Computing, 2018, 1 (1) : 77-100. doi: 10.3934/mfc.2018005
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##### References:
A communication architecture in smart grid systems
An access control tree structure
An example access control structure in Smart Grid
Key generation time
Encryption time
Decryption time
ABS signature running-time
ABS verification running-time
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.
 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.
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.
 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.
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.
 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.
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)
 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)
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
 SS512 MNT159 MNT159.S BN.S 3.67 ms 9.72 ms 1.13 ms 2.30 ms
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