Advertisement

Linearly Homomorphic Authenticated Encryption with Provable Correctness and Public Verifiability

  • Patrick Struck
  • Lucas SchabhüserEmail author
  • Denise Demirel
  • Johannes Buchmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10194)

Abstract

In this work the first linearly homomorphic authenticated encryption scheme with public verifiability and provable correctness, called \(\mathsf {LEPCoV}\), is presented. It improves the initial proposal by avoiding false negatives during the verification algorithm. This work provides a detailed description of \(\mathsf {LEPCoV}\), a comparison with the original scheme, a security and correctness proof, and a performance analysis showing that all algorithms run in reasonable time for parameters that are currently considered secure. The scheme presented here allows a user to outsource computations on encrypted data to the cloud, such that any third party can verify the correctness of the computations without having access to the original data. This makes this work an important contribution to cloud computing and applications where operations on sensitive data have to be performed, such as statistics on medical records and tallying of electronically cast votes.

Keywords

Authenticated encryption Public verifiability Cloud computing 

Notes

Acknowledgments

This work has been co-funded by the DFG as part of project “Long-Term Secure Archiving” within the CRC 1119 CROSSING. In addition, it has received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 644962.

References

  1. 1.
    An, J.H., Bellare, M.: Does encryption with redundancy provide authenticity? In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 512–528. Springer, Heidelberg (2001). doi: 10.1007/3-540-44987-6_31 CrossRefGoogle Scholar
  2. 2.
    Attrapadung, N., Libert, B.: Homomorphic network coding signatures in the standard model. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 17–34. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-19379-8_2 CrossRefGoogle Scholar
  3. 3.
    Attrapadung, N., Libert, B., Peters, T.: Computing on authenticated data: new privacy definitions and constructions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 367–385. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-34961-4_23 CrossRefGoogle Scholar
  4. 4.
    Attrapadung, N., Libert, B., Peters, T.: Efficient completely context-hiding quotable and linearly homomorphic signatures. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 386–404. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-36362-7_24 CrossRefGoogle Scholar
  5. 5.
    Bellare, M., Namprempre, C.: Authenticated encryption: relations among notions and analysis of the generic composition paradigm. J. Crypt. 21(4), 469–491 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Benaloh, J.: Dense probabilistic encryption. In: Proceedings of the Workshop on Selected Areas of Cryptography, pp. 120–128 (1994)Google Scholar
  7. 7.
    Boneh, D., Freeman, D., Katz, J., Waters, B.: Signing a linear subspace: signature schemes for network coding. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 68–87. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-00468-1_5 CrossRefGoogle Scholar
  8. 8.
    Boneh, D., Freeman, D.M.: Homomorphic signatures for polynomial functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 149–168. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-20465-4_10 CrossRefGoogle Scholar
  9. 9.
    Boneh, D., Freeman, D.M.: Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 1–16. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-19379-8_1 CrossRefGoogle Scholar
  10. 10.
    Catalano, D., Fiore, D., Gennaro, R., Vamvourellis, K.: Algebraic (trapdoor) one-way functions and their applications. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 680–699. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-36594-2_38 CrossRefGoogle Scholar
  11. 11.
    Catalano, D., Fiore, D., Warinschi, B.: Efficient network coding signatures in the standard model. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 680–696. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-30057-8_40 CrossRefGoogle Scholar
  12. 12.
    Catalano, D., Marcedone, A., Puglisi, O.: Authenticating computation on groups: new homomorphic primitives and applications. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 193–212. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-45608-8_11 Google Scholar
  13. 13.
    Desmedt, Y.: Computer security by redefining what a computer is. In: Proceedings on the 1992–1993 Workshop on New security paradigms, pp. 160–166. ACM (1993)Google Scholar
  14. 14.
    ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985). doi: 10.1007/3-540-39568-7_2 CrossRefGoogle Scholar
  15. 15.
    Freeman, D.M.: Improved security for linearly homomorphic signatures: a generic framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 697–714. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-30057-8_41 CrossRefGoogle Scholar
  16. 16.
    Gennaro, R., Katz, J., Krawczyk, H., Rabin, T.: Secure network coding over the integers. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 142–160. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-13013-7_9 CrossRefGoogle Scholar
  17. 17.
    Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002). doi: 10.1007/3-540-45760-7_17 CrossRefGoogle Scholar
  18. 18.
    Joo, C., Yun, A.: Homomorphic authenticated encryption secure against chosen-ciphertext attack. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 173–192. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-45608-8_10 Google Scholar
  19. 19.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). doi: 10.1007/3-540-48910-X_16 Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Patrick Struck
    • 1
  • Lucas Schabhüser
    • 1
    Email author
  • Denise Demirel
    • 1
  • Johannes Buchmann
    • 1
  1. 1.Technische Universität DarmstadtDarmstadtGermany

Personalised recommendations