Chosen-Ciphertext Security via Correlated Products

We initiate the study of one-wayness under correlated products. We are interested in identifying necessary and sufficient conditions for a function f and a distribution on inputs (x1, . . . , xk), so that the function (f(x1), . . . , f(xk)) is one-way. The main motivation of this study is the construction of public-key encryption schemes that are secure against chosen-ciphertext attacks (CCA). We show that any collection of injective trapdoor functions that is secure under a very natural correlated product can be used to construct a CCA-secure public-key encryption scheme. The construction is simple, black-box, and admits a direct proof of security. It can be viewed as a simplification of the seminal work of Dolev, Dwork and Naor (SICOMP ’00), while relying on a seemingly incomparable assumption. We provide evidence that security under correlated products is achievable by demonstrating that lossy trapdoor functions (Peikert and Waters, STOC ’08) yield injective trapdoor functions that are secure under the above mentioned correlated product. Although we currently base security under correlated products on existing constructions of lossy trapdoor functions, we argue that the former notion is potentially weaker as a general assumption. Specifically, there is no fully-black-box construction of lossy trapdoor functions from trapdoor functions that are secure under correlated products. ∗A preliminary version of this work appeared in Proceedings of the 6th Theory of Cryptography Conference (TCC), pages 419–436, 2009. †Efi Arazi School of Computer Science, Herzliya Interdisciplinary Center (IDC), Herzliya 46150, Israel. Email: [email protected]. Research supported in part by BSF grant 2006317. ‡Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel. Email: [email protected]. Research supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.