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Fully Homomorphic Encryption Scheme Based on Public Key Compression and Batch Processing

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10726))

Abstract

Fully homomorphic encryption is a type of encryption technique that allows arbitrary complex operations to be performed on the ciphertext, thus generating an encrypted result that, when decrypted, matches the results of those operations performed on the plaintext. The DGHV scheme over the integers is one of the key schemes in fully homomorphic encryption research field, but the incredible size of the public key and the low computational efficiency are the main challenges. Based on the original DGHV encryption structure and parameters’ design, the idea of batch processing was introduced in this paper. With the combination of the quadratic parameter-based public key compression mechanism, a complete public key compression and batch processing fully homomorphic encryption (PKCB-FHE) scheme was presented. Like those in the original DGHV scheme, the parameter restriction of the proposed scheme was presented. Further analysis and simulation of the proposed scheme indicate that the required storage space of the public key is immensely reduced and that the overall length of the public key is compressed. Furthermore, the total processing time of the proposed scheme is reduced, which makes it much more efficient than those existing schemes.

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References

  1. Kaosar, M.G., Paulet, R., Yi, X.: Fully homomorphic encryption based two-party association rule mining. Data Knowl. Eng. 76, 1–15 (2012)

    Article  Google Scholar 

  2. Yan, H., Li, J., Han, J.: A novel efficient remote data possession checking protocol in cloud storage. IEEE Trans. Inf. Forensics Secur. 12(1), 78–88 (2017)

    Article  Google Scholar 

  3. Wang, W., Hu, Y., Chen, L., Huang, X.: Exploring the feasibility of fully homomorphic encryption. IEEE Trans. Comput. 64(3), 698–706 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cheon, J.H., Kim, J.: A hybrid scheme of public-key encryption and somewhat homomorphic encryption. IEEE Trans. Inf. Forensics Secur. 10(5), 1208–1212 (2015)

    Google Scholar 

  5. Rivest, R., Adleman, L., Dertouzos, M.: On data banks and privacy homomorphisms. Found. Secur. Comput. 4(11), 169–180 (1978)

    MathSciNet  Google Scholar 

  6. Gentry, C.: A Fully Homomorphic Encryption Scheme. Stanford University, Stanford (2009)

    MATH  Google Scholar 

  7. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, New York, vol. 9, pp. 169–178 (2009)

    Google Scholar 

  8. van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_2

    Chapter  Google Scholar 

  9. Stehlé, D., Steinfeld, R.: Faster fully homomorphic encryption. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 377–394. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_22

    Chapter  Google Scholar 

  10. Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_50

    Chapter  Google Scholar 

  11. Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (Standard) LWE. In: Proceedings of IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 97–106 (2011)

    Google Scholar 

  12. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: Fully homomorphic encryption without bootstrapping. In: Proceedings of the 3rd Innovations in Theoretical Computer Science Conference (ITCS), pp. 309–325 (2012)

    Google Scholar 

  13. Zhang, X., Xu, C., Jin, C.: Efficient fully homomorphic encryption from RLWE with an extension to a threshold encryption scheme. Future Gener. Comput. Syst. 36, 180–186 (2014)

    Article  Google Scholar 

  14. Plantard, T., Susilo, W., Zhang, Z.: Fully homomorphic encryption using hidden ideal lattice. IEEE Trans. Inf. Forensics Secur. 8(12), 2127–2137 (2013)

    Article  Google Scholar 

  15. Coron, J.S., Naccached, D., Tibouchi, M.: Optimization of fully homomorphic encryption. IACR Cryptology ePrint Archive, pp. 440–458 (2011)

    Google Scholar 

  16. Coron, J.-S., Mandal, A., Naccache, D., Tibouchi, M.: Fully homomorphic encryption over the integers with shorter public keys. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 487–504. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_28

    Chapter  Google Scholar 

  17. Coron, J.-S., Naccache, D., Tibouchi, M.: Public key compression and modulus switching for fully homomorphic encryption over the integers. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 446–464. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_27

    Chapter  Google Scholar 

  18. Chen, Z., Wang, J., Zhang, Z., Song, X.: A fully homomorphic encryption scheme with better key size. China Commun. 28(4), 82–92 (2014)

    Article  Google Scholar 

  19. Smart, N.P., Vercauteren, F.: Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 420–443. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_25

    Chapter  Google Scholar 

  20. Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations. Des. Codes Crypt. 71(1), 57–81 (2014)

    Article  MATH  Google Scholar 

  21. Cheon, J.H., Coron, J.-S., Kim, J., Lee, M.S., Lepoint, T., Tibouchi, M., Yun, A.: Batch fully homomorphic encryption over the integers. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 315–335. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_20

    Chapter  Google Scholar 

  22. Beneš, V.E.: Optimal rearrangeable multistage connecting networks. Bell Syst. Tech. J. 43(4), 1641–1656 (2013)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported in part by the European Commission Marie Curie IRSES project “AdvIOT” and the national Natural Science Foundation of China (NSFC) under grant No.61372103.

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Correspondence to Liquan Chen .

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Chen, L., Lim, M., Wang, M. (2018). Fully Homomorphic Encryption Scheme Based on Public Key Compression and Batch Processing. In: Chen, X., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2017. Lecture Notes in Computer Science(), vol 10726. Springer, Cham. https://doi.org/10.1007/978-3-319-75160-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-75160-3_16

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-75160-3

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