Feasibility and Infeasibility of Adaptively Secure Fully Homomorphic Encryption
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.
Unable to display preview. Download preview PDF.
- 1.Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press (2009)Google Scholar
- 5.Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: ACM Conference on Computer and Communications Security, pp. 784–796 (2012)Google Scholar
- 6.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)Google Scholar
- 8.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)Google Scholar
- 11.Gentry, C.: Fully homomorphic encryption using ideal lattices. In: 41st Annual ACM Symp. on Theory of Computing (STOC), pp. 169–178. ACM Press (2009)Google Scholar
- 12.Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009), http://crypto.stanford.edu/craig
- 18.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
- 19.Yao, A.C.: How to generate and exchange secrets. In: 27th Annual Symposium on Foundations of Computer Science (FOCS), pp. 162–167. IEEE (1986)Google Scholar