Reaction Attack on Outsourced Computing with Fully Homomorphic Encryption Schemes

  • Zhenfei Zhang
  • Thomas Plantard
  • Willy Susilo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7259)

Abstract

Outsourced computations enable more efficient solutions towards practical problems that require major computations. Nevertheless, users’ privacy remains as a major challenge, as the service provider can access users’ data freely. It has been shown that fully homomorphic encryption schemes might be the perfect solution, as it allows one party to process users’ data homomorphically, without the necessity of knowing the corresponding secret keys. In this paper, we show a reaction attack against full homomorphic schemes, when they are used for securing outsourced computation. Essentially, our attack is based on the users’ reaction towards the output generated by the cloud. Our attack enables us to retrieve the associated secret key of the system. This secret key attack takes O(λlogλ) time for both Gentry’s original scheme and the fully homomorphic encryption scheme over integers, and O(λ) for the implementation of Gentry’s fully homomorphic encryption scheme.

Keywords

Cloud Computing Fully Homomorphic Encryption Reaction Attack CCA security Secured Outsource Computation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    van Dijk, M., Juels, A.: On the impossibility of cryptography alone for privacy-preserving cloud computing. Cryptology ePrint Archive, Report 2010/305 (2010), http://eprint.iacr.org/
  2. 2.
    Gennaro, R., Gentry, C., Parno, B.: Non-interactive Verifiable Computing: Outsourcing Computation to Untrusted Workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010)Google Scholar
  3. 3.
    Gentry, C.: A Fully Homomorphic Encyrption Scheme. PhD thesis, Stanford University (2009)Google Scholar
  4. 4.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) STOC, pp. 169–178. ACM (2009)Google Scholar
  5. 5.
    Hall, C., Goldberg, I., Schneier, B.: Reaction Attacks against Several Public-Key Cryptosystem. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 2–12. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Myers, S., Shelat, A.: Bit encryption is complete. In: FOCS, pp. 607–616. IEEE Computer Society (2009)Google Scholar
  7. 7.
    Rivest, R., Adleman, L., Dertouzos, M.: On data banks and privacy homomorphisms. In: Foundations of Secure Computation, pp. 169–177. Academic Press (1978)Google Scholar
  8. 8.
    Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    Stehlé, D., Steinfeld, R.: Faster Fully Homomorphic Encryption. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 377–394. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Gentry, C., Halevi, S.: Implementing Gentry’s Fully-Homomorphic Encryption Scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129–148. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Bellare, M., Desai, A., Pointcheval, D., Rogaway, P.: Relations among Notions of Security for Public-Key Encryption Schemes. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 26–45. Springer, Heidelberg (1998)Google Scholar
  15. 15.
    Georgii, H.O.: Stochastics: Introduction to Probability and Statistics (de Gruyter Textbook), 1st edn. Walter de Gruyter (2008)Google Scholar
  16. 16.
    Loftus, J., May, A., Smart, N.P., Vercauteren, F.: On CCA-Secure Somewhat Homomorphic Encryption. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 55–72. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Gentry, C., Halevi, S., Vaikuntanathan, V.: i-Hop Homomorphic Encryption and Rerandomizable Yao Circuits. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 155–172. Springer, Heidelberg (2010)Google Scholar
  18. 18.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: Fully homomorphic encryption without bootstrapping. Electronic Colloquium on Computational Complexity (ECCC) 18, 111 (2011)Google Scholar
  19. 19.
    Gentry, C.: Computing arbitrary functions of encrypted data. Commun. ACM 53(3), 97–105 (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zhenfei Zhang
    • 1
  • Thomas Plantard
    • 1
  • Willy Susilo
    • 1
  1. 1.Centre for Computer and Information Security Research, School of Computer Science & Software Engineering (SCSSE)University of WollongongAustralia

Personalised recommendations