On selective-opening attacks against encryption schemes

Abstract

At FOCS’99, Dwork et al. put forth the notion of ‘selective- -opening attacks’ (SOAs, for short). In the literature, security against such attacks has been formalized via indistinguishability-based and simulation-based notions, respectively called IND-SO-CPA security and SIM-SO-CPA security. Furthermore, the IND-SO-CPA notion has been studied under two flavors – weak-IND-SO-CPA and full-IND-SO-CPA security. At Eurocrypt’09, Bellare et al. showed the first positive results on SOA security of encryption schemes: 1) any lossy encryption scheme is weak-IND-SO-CPA secure; 2) any lossy encryption scheme with efficient openability is SIM-SO--CPA secure. Despite rich further work on SOA security, the (un)feasibility of full--IND-SO-CPA remains a major open problem in the area of SOA security. The elusive nature of the full-IND-SO-CPA notion of security is attributed to a specific aspect of the security game, namely, the challenger requiring to perform a super-polynomial time task. Not only do we not know whether there exists a scheme that is full-IND-SO-CPA secure, but we also do not know concrete attacks against popular schemes such as the ElGamal and Cramer-Shoup schemes in the full-IND-SO-CPA model. The contribution of our work is three-fold. 1. Motivated by the difficulty in understanding (un)feasibility of the full-IND-SO-CPA notion, we study a variant of this notion that is closer in spirit to the IND-CPA notion but still embodies the security captured by the full-IND-SO-CPA notion. We observe that the weak form of our variation does not introduce any significant change to the weak-IND-SO-CPA notion; that is, the weak form of our notion is equivalent to the weak-IND-SO-CPA notion. 2. Interestingly, we can show that a large class of encryption schemes can be proven insecure for the full form of our notion. The large class includes most known constructions of weak-IND-SO-CPA secure schemes and SIM-SO-CPA secure schemes and also popular schemes like the ElGamal and Cramer-Shoup schemes. 3. Our third contribution studies the complexity of SIM-SO-CPA security. Complementing the result of Bellare et al., we show that lossiness is not necessary to achieve SIM-SO-CPA security. More specifically, we present a SIM-SO-CPA scheme that is not a lossy encryption scheme (regardless of efficient open ability). Since SIM-SO-CPA security implies weak-IND-SO-CPA security, it follows as a corollary that the converses of both the implications proved by Bellare et al. do not hold. Furthermore, as a corollary of our techniques, on a slightly unrelated but useful note, we obtain that lossiness is not required to obtain non-committing encryption. Previously, at Eurocrypt’09, Fehr et al. showed a construction of a non-committing encryption scheme from trapdoor permutations and this scheme was, as noted by the authors, possibly not lossy. Our scheme amounts to the first construction of a non-committing encryption scheme that is provably not lossy.