Lattice-Based IBE with Equality Test in Standard Model

  • Dung Hoang DuongEmail author
  • Huy Quoc Le
  • Partha Sarathi Roy
  • Willy Susilo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11821)


Public key encryption with equality test (PKEET) allows the testing of equality of underlying messages of two ciphertexts. PKEET is a potential candidate for many practical applications like efficient data management on encrypted databases. Identity-based encryption scheme with equality test (IBEET), which was introduced by Ma (Information Science 2016), can simplify the certificate management of PKEET. Potential applicability of IBEET leads to intensive research from its first instantiation. Ma’s IBEET and most of the constructions are proven secure in the random oracle model based on number-theoretic hardness assumptions which are vulnerable in the post-quantum era. Recently, Lee et al. (ePrint 2016) proposed a generic construction of IBEET schemes in the standard model and hence it is possible to yield the first instantiation of IBEET schemes based on lattices. Their method is to use a 3-level hierarchical identity-based encryption (HIBE) scheme together with a one-time signature scheme. In this paper, we propose, for the first time, a concrete construction of an IBEET scheme based on the hardness assumption of lattices in the standard model and compare the data sizes with the instantiation from Lee et al. (ePrint 2016). Further, we have modified our proposed IBEET to make it secure against insider attack.



This work is supported by the Australian Research Council Discovery Project DP180100665. We would like to thank Tsz Hon Yuen and anonymous reviewers for many helpful comments and fruitful discussions.


  1. 1.
    Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010). Scholar
  2. 2.
    Ajtai, M.: Generating hard instances of the short basis problem. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 1–9. Springer, Heidelberg (1999). Scholar
  3. 3.
    Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. In: Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009, Freiburg, Germany, 26–28 February 2009, pp. 75–86 (2009)Google Scholar
  4. 4.
    Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2007)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010). Scholar
  6. 6.
    Duong, D.H., Fukushima, K., Kiyomoto, S., Roy, P.S., Susilo, W.: A lattice-based public key encryption with equality test in standard model. In: Jang-Jaccard, J., Guo, F. (eds.) ACISP 2019. LNCS, vol. 11547, pp. 138–155. Springer, Cham (2019). Scholar
  7. 7.
    Lee, H.T., Ling, S., Seo, J.H., Wang, H., Youn, T.-Y.: Public key encryption with equality test in the standard model. Cryptology ePrint Archive, Report 2016/1182 (2016)Google Scholar
  8. 8.
    Lee, H.T., Ling, S., Seo, J.H., Wang, H.: Semi-generic construction of public key encryption and identity-based encryption with equality test. Inf. Sci. 373, 419–440 (2016)CrossRefGoogle Scholar
  9. 9.
    Lee, H.T., Wang, H., Zhang, K.: Security analysis and modification of ID-based encryption with equality test from ACISP 2017. In: Susilo, W., Yang, G. (eds.) ACISP 2018. LNCS, vol. 10946, pp. 780–786. Springer, Cham (2018). Scholar
  10. 10.
    Ma, S.: Identity-based encryption with outsourced equality test in cloud computing. Inf. Sci. 328, 389–402 (2016)CrossRefGoogle Scholar
  11. 11.
    Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. In: Proceedings of the 45th Symposium on Foundations of Computer Science (FOCS 2004), Rome, Italy, 17–19 October 2004, pp. 372–381 (2004)Google Scholar
  12. 12.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, 22–24 May 2005, pp. 84–93 (2005)Google Scholar
  13. 13.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Shoup, V.: A Computational Introduction to Number Theory and Algebra, 2nd edn. Cambridge University Press, Cambridge (2008)CrossRefGoogle Scholar
  15. 15.
    Wu, T., Ma, S., Mu, Y., Zeng, S.: ID-based encryption with equality test against insider attack. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017, Part I. LNCS, vol. 10342, pp. 168–183. Springer, Cham (2017). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Dung Hoang Duong
    • 1
    Email author
  • Huy Quoc Le
    • 1
  • Partha Sarathi Roy
    • 1
  • Willy Susilo
    • 1
  1. 1.Institute of Cybersecurity and Cryptology, School of Computing and Information TechnologyUniversity of WollongongWollongongAustralia

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