Abstract
Fully homomorphic encryption (FHE) is a form of public-key encryption that enables arbitrary computation over encrypted data. The past few years have seen several realizations of FHE under different assumptions, and FHE has been used as a building block in many cryptographic applications.
Adaptive security for public-key encryption schemes is an important security notion proposed by Canetti et al. It is intended to ensure security when encryption is used within an interactive protocol and parties may be adaptively corrupted by an adversary during the course of the protocol execution. Due to the extensive applications of FHE to protocol design, it is natural to understand whether adaptively secure FHE is achievable.
In this paper we show two contrasting results in this direction. First, we show that adaptive security is impossible for FHE satisfying the (standard) compactness requirement. On the other hand, we show a construction of adaptively secure FHE that is not compact, but that does achieve circuit privacy.
Chapter PDF
References
Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press (2009)
Barak, B., Haitner, I., Hofheinz, D., Ishai, Y.: Bounded Key-Dependent Message Security. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 423–444. Springer, Heidelberg (2010)
Beaver, D.: Plug and Play Encryption. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 75–89. Springer, Heidelberg (1997)
Beaver, D., Haber, S.: Cryptographic Protocols Provably Secure against Dynamic Adversaries. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 307–323. Springer, Heidelberg (1993)
Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: ACM Conference on Computer and Communications Security, pp. 784–796 (2012)
Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: 28th Annual ACM Symposium on Theory of Computing (STOC), pp. 639–648. ACM Press (1996)
Canetti, R., Halevi, S., Katz, J.: Adaptively-Secure, Non-interactive Public-Key Encryption. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 150–168. Springer, Heidelberg (2005)
Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: 34th ACM STOC Annual ACM Symposium on Theory of Computing (STOC), pp. 494–503. ACM Press (2002)
Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Improved Non-committing Encryption with Applications to Adaptively Secure Protocols. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 287–302. Springer, Heidelberg (2009)
Damgård, I., Nielsen, J.B.: Improved Non-committing Encryption Schemes Based on a General Complexity Assumption. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 432–450. Springer, Heidelberg (2000)
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: 41st Annual ACM Symp. on Theory of Computing (STOC), pp. 169–178. ACM Press (2009)
Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009), http://crypto.stanford.edu/craig
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)
Jarecki, S., Lysyanskaya, A.: Adaptively Secure Threshold Cryptography: Introducing Concurrency, Removing Erasures (Extended Abstract). In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 221–242. Springer, Heidelberg (2000)
Katz, J., Ostrovsky, R.: Round-Optimal Secure Two-Party Computation. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 335–354. Springer, Heidelberg (2004)
Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. Journal of Cryptology 22(2), 161–188 (2009)
Nielsen, J.B.: Separating Random Oracle Proofs from Complexity Theoretic Proofs: The Non-committing Encryption Case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002)
Rivest, R., Adleman, L., Dertouzos, M.: On data banks and privacy homomorphisms. In: Foundations of Secure Computation, pp. 169–177. Academic Press (1978)
Yao, A.C.: How to generate and exchange secrets. In: 27th Annual Symposium on Foundations of Computer Science (FOCS), pp. 162–167. IEEE (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 International Association for Cryptologic Research
About this paper
Cite this paper
Katz, J., Thiruvengadam, A., Zhou, HS. (2013). Feasibility and Infeasibility of Adaptively Secure Fully Homomorphic Encryption. In: Kurosawa, K., Hanaoka, G. (eds) Public-Key Cryptography – PKC 2013. PKC 2013. Lecture Notes in Computer Science, vol 7778. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36362-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-36362-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36361-0
Online ISBN: 978-3-642-36362-7
eBook Packages: Computer ScienceComputer Science (R0)