Reproducible Circularly-Secure Bit Encryption: Applications and Realizations.

Abstract. We give generic constructions of several fundamental cryptographic primitives based on a new encryption primitive that combines circular security for bit encryption with the so-called repro-ducibility property (Bellare et al. PKC 2003). At the heart of our constructions is a novel technique which gives a way of de-randomizing reproducible public-key bit-encryption schemes and also a way of reducing one-wayness conditions of a constructed trapdoor-function family (TDF) to circular security of the base scheme. The main primitives that we build from our encryption primitive include k-wise one-way TDFs (Rosen and Segev TCC 2009), CCA2-secure encryption and deterministic encryption. Our results demonstrate a new set of applications of circularly-secure encryption beyond fully-homomorphic encryption and symbolic soundness. Finally, we show the plausibility of our assumptions by showing that the DDH-based circularly-secure scheme of Boneh et al. (Crypto 2008) and the subgroup indistin-guishability based scheme of Brakerski and Goldwasser (Crypto 2010) are both reproducible.