Reproducible Circularly Secure Bit Encryption: Applications and Realizations

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 reproducibility property (Bellare et al. in Public key cryptography—PKC 2003, vol. 2567, pp. 85–99, Springer, 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 in SIAM J Comput 39(7):3058–3088, 2010), chosen-ciphertext-attack-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 decisional Diffie–Hellman-based circularly secure scheme of Boneh et al. (Advances in cryptology—CRYPTO 2008, vol. 5157, Springer, 2008) and the subgroup indistinguishability-based scheme of Brakerski and Goldwasser (Advances in cryptology—CRYPTO 2010, vol. 6223, pp. 1–20, Springer, 2010) are both reproducible.