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.
This work is supported by ARC Future Fellowship FT0991397.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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/
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)
Gentry, C.: A Fully Homomorphic Encyrption Scheme. PhD thesis, Stanford University (2009)
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) STOC, pp. 169–178. ACM (2009)
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)
Myers, S., Shelat, A.: Bit encryption is complete. In: FOCS, pp. 607–616. IEEE Computer Society (2009)
Rivest, R., Adleman, L., Dertouzos, M.: On data banks and privacy homomorphisms. In: Foundations of Secure Computation, pp. 169–177. Academic Press (1978)
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)
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)
Stehlé, D., Steinfeld, R.: Faster Fully Homomorphic Encryption. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 377–394. Springer, Heidelberg (2010)
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)
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)
Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)
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)
Georgii, H.O.: Stochastics: Introduction to Probability and Statistics (de Gruyter Textbook), 1st edn. Walter de Gruyter (2008)
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)
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)
Brakerski, Z., Gentry, C., Vaikuntanathan, V.: Fully homomorphic encryption without bootstrapping. Electronic Colloquium on Computational Complexity (ECCC) 18, 111 (2011)
Gentry, C.: Computing arbitrary functions of encrypted data. Commun. ACM 53(3), 97–105 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, Z., Plantard, T., Susilo, W. (2012). Reaction Attack on Outsourced Computing with Fully Homomorphic Encryption Schemes. In: Kim, H. (eds) Information Security and Cryptology - ICISC 2011. ICISC 2011. Lecture Notes in Computer Science, vol 7259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31912-9_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-31912-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31911-2
Online ISBN: 978-3-642-31912-9
eBook Packages: Computer ScienceComputer Science (R0)