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LPM2DA: a lattice-based privacy-preserving multi-functional and multi-dimensional data aggregation scheme for smart grid

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Abstract

The smart grid provides efficient transmission of energy and data. However, the frequent gathering of users’ consumption data discloses users’ privacy. Plenty of data aggregation schemes have been introduced to preserve the privacy of users’ private information. Unfortunately, with the advent of quantum machines, most of these schemes will be rendered vulnerable and insecure. Hence, to preserve privacy and provide other security services like integrity and authentication in smart grid, we attempt to introduce a secure scheme based on lattice-based cryptography named LPM2DA: a lattice-based privacy-preserving multi-functional and multi-dimensional data aggregation scheme. The proposed scheme enables the control center to acquire temporal and spatial aggregation of multi-dimensional data in a privacy-preserving manner. Also, it empowers the control center to calculate different statistical functions such as mean, variance, and skewness on users’ multi-dimensional data. Eventually, through analytical evaluation, we illustrate the efficiency of the proposed scheme.

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Notes

  1. The circuit depth of a function is the number of multiplication levels required for the implementation of that function.

References

  1. Li, H., Lai, L., Caiming Qiu, R.: Scheduling of wireless metering for power market pricing in smart grid. IEEE Trans. Smart Grid 3(4), 1611–1620 (2012)

    Article  Google Scholar 

  2. Desai, S., Alhadad, R., Chilamkurti, N., et al.: A survey of privacy preserving schemes in IoE enabled Smart Grid Advanced Metering Infrastructure. Clust. Comput. 22, 43–69 (2019)

    Article  Google Scholar 

  3. Jokar, P., Arianpoo, N., Leung, V.C.M.: A survey on security issues in smart grid. Secur. Commun. Netw. 9, 262–273 (2012)

    Article  Google Scholar 

  4. Vahedi, E., Bayat, M., Pakravan, M.R., Aref, M.R.: A secure ECC-based privacy preserving data aggregation scheme for smart grids. Comput. Netw. 129(P1), 28–36 (2017)

    Article  Google Scholar 

  5. Kanwal, T., Anjum, A., Khan, A.: Privacy preservation in e-health cloud: taxonomy, privacy requirements, feasibility analysis, and opportunities. Clust. Comput. 24, 293–317 (2021)

    Article  Google Scholar 

  6. Abdallah, A., Shen, X.: Security and privacy of customer-side networks. In: Abdallah, S., Shen, X. (eds.) Security and Privacy in Smart Grid, pp. 27–64. Springer, Berlin (2018)

    Chapter  Google Scholar 

  7. Aghili, S.F., Mala, H., Shojafar, M., Peris-Lopez, P.: LACO: lightweight three-factor authentication, access control and ownership transfer scheme for E-health systems in IoT. Future Gener. Comput. Syst. 96, 410–424 (2019)

    Article  Google Scholar 

  8. Singh, S., Chaurasiya, V.K.: Mutual authentication scheme of IoT devices in fog computing environment. Clust. Comput. (2020). https://doi.org/10.1007/s10586-020-03211-1

    Article  Google Scholar 

  9. Lu, R., Liang, X., Li, X., Lin, X., Shen, X.: EPPA: an efficient and privacy-preserving aggregation scheme for secure smart grid communications. IEEE Trans. Parallel Distrib. Syst. 23(9), 1621–1631 (2012)

    Article  Google Scholar 

  10. Zhang, L., Zhang, J., Hen Hu, Y.: A privacy-preserving distributed smart metering temporal and spatial aggregation scheme. IEEE Access 7, 28372–28382 (2019)

    Article  Google Scholar 

  11. Chen, L., Lu, R., Cao, Zh., Alharbi, Kh., Lin, X.: MuDA: maultifunctional data aggregation in privacy-preserving smart grid communications. Peer-to-Peer Netw. Appl. 8, 777–792 (2015)

    Article  Google Scholar 

  12. Ge, Sh., Zeng, P., Lu, R., Choo, K.-K.R.: FGDA: fine-grained data analysis in privacy-preserving smart grid communications. Peer-to-Peer Netw. Appl. 11(5), 966–978 (2018)

    Article  Google Scholar 

  13. Ni, J., Zhang, K., Alharbi, Kh., Lin, X., Zhang, N., Shen, XSh.: Differentially private smart metering with fault tolerance and ranged-based filtering. IEEE Trans. Smart Grid 8(5), 2483–2493 (2017)

    Article  Google Scholar 

  14. Ming, Y., Zhang, X., Shen, X.: Efficient privacy-preserving multi-dimensional data aggregation scheme in smart grid. IEEE Access 7, 32907–32921 (2019)

    Article  Google Scholar 

  15. Huang, C., Wang, X., Gan, Q., et al.: A lightweight and fault-tolerable data aggregation scheme for privacy-friendly smart grids environment. Clust. Comput. (2021). https://doi.org/10.1007/s10586-021-03345-w

    Article  Google Scholar 

  16. Shor, P.W.: Algorithm for quantum computations: discrete logarithm and factoring. In: Proceedings of 35th annual symposium on foundations of computer science, pp. 124–134 (1994)

  17. Agarkar, A.A., Agrawal, H.: LRSPPP: lightweight R-LWE-based secure and privacy-preserving scheme for prosumer side network in smart grid. Heliyon 5(3), e01321 (2019)

    Article  Google Scholar 

  18. Abdallah, A., Shen, X.: Lightweight security and privacy preserving scheme for smart grid customer-side networks. IEEE Trans. Smart Grid 8(3), 1064–1074 (2017)

    Article  Google Scholar 

  19. Abdallah, A., Shen, X.S.H.: A lightweight lattice-based homomorphic privacy-preserving data aggregation scheme for smart grid. IEEE Trans. Smart Grid 9(1), 396–405 (2018)

    Article  Google Scholar 

  20. Li, Ch., Lu, R., Li, H., Chen, L., Chen, J.: PDA: a privacy-preserving dual-functional aggregation scheme for smart grid. Secur. Commun. Netw. 8(15), 2494–2506 (2015)

    Article  Google Scholar 

  21. Arun Jees, S., Gomathi, V.: Load forecasting for smart grid using non-linear model in Hadoop distributed file system. Clust. Comput. 22, 13533–13545 (2019)

    Article  Google Scholar 

  22. Rabie, A.H., Ali, S.H., Ali, H.A., et al.: A fog based load forecasting strategy for smart grids using big electrical data. Clust. Comput. 22, 241–270 (2019)

    Article  Google Scholar 

  23. Rabie, A.H., Ali, S.H., Saleh, A.I., Ali, H.A.: A new outlier rejection methodology for supporting load forecasting in smart grids based on big data. Clust. Comput. 23, 509–535 (2020)

    Article  Google Scholar 

  24. Wu, Y., Huang, Z., Zhang, J., Wen, Q.: A lattice-based digital signature from the ring-LWE. In: Proceedings of 3rd IEEE International conference on network infrastructure and digital content, Beijing, China (2012)

  25. Khedr, A., Gulak, G., Vaikuntanathan, V.: SHIELD: scalable homomorphic implementation of encrypted data-classifiers. IEEE Trans. Comput. 65, 2848–2858 (2016)

    Article  MathSciNet  Google Scholar 

  26. Ajtai, M.: Generating hard instances of lattice problems. Electron. Colloq. Comput. Complex. (ECCC) 3, 1 (1996)

    MathSciNet  MATH  Google Scholar 

  27. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (JACM) 56, 84–93 (2005)

    MathSciNet  MATH  Google Scholar 

  28. Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Proceedings of 29th International conference on the theory and applications of cryptographic techniques (EUROCRYPT), Berlin, Heidelberg (2010)

  29. Ding, C., Pei, D., Salomaa, A.: Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography, pp. 1–213. World Scientific Publishing, Singapore (1996)

    Book  Google Scholar 

  30. Shen, H., Zhang, M., Shen, J.: Efficient privacy-preserving cube-data aggregation scheme for smart grids. IEEE Trans. Inf. Forensics Secur. 12(6), 1369–1381 (2017)

    Article  Google Scholar 

  31. Lynn, B.: PBC Library. http://crypto.stanford.edu/pbc/ (2012)

  32. http://www.shamus.ie/, Multiprecision Integer and Rational Arithmetic c/c++ Library (2012)

  33. Longa, P., Naehrig, M.: Speeding up the number theoretic transform for faster ideal lattice-based cryptography. In: Proceedings of International conference on cryptology and network security (CANS) (2016)

  34. Can Mert, A., Öztürk, E., Savas, E.: Design and implementation of a fast and scalable NTT-based polynomial multiplier architecture. In: Proceedings of 22nd Euromicro conference on digital system design (DSD) (2019)

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Acknowledgements

The authors are grateful to the editor and the referees for their very meticulous reading of this manuscript. Their suggestions were very helpful in creating the improved final version. This work was supported in part by the Niroo Research Institute (NRI) under Grant No. 95/10615/51. The research of the third author was supported by a Grant from IPM (No. 1400050115).

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Authors and Affiliations

  1. Faculty of Electrical Engineering, K. N. Toosi University of Technology, P. O. Box: 16315-1355, Tehran, Iran

    Saleh Darzi & Bahareh Akhbari

  2. Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: 16765-3381, Tehran, Iran

    Hassan Khodaiemehr

  3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box: 19395-5746, Tehran, Iran

    Hassan Khodaiemehr

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  1. Saleh Darzi
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  2. Bahareh Akhbari
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  3. Hassan Khodaiemehr
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Correspondence to Bahareh Akhbari.

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Darzi, S., Akhbari, B. & Khodaiemehr, H. LPM2DA: a lattice-based privacy-preserving multi-functional and multi-dimensional data aggregation scheme for smart grid. Cluster Comput 25, 263–278 (2022). https://doi.org/10.1007/s10586-021-03387-0

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