Bounded KDM security from iO and OWF

Abstract

To date, all constructions in the standard model (i.e., without random oracles) of Bounded Key-Dependent Message (KDM) secure (or even just circularly-secure) encryption schemes rely on specific assumptions (LWE, DDH, QR or DCR); all of these assumptions are known to imply the existence of collision-resistant hash functions. In this work, we demonstrate the existence of bounded KDM secure encryption assuming indistinguishability obfuscation for P/poly and just one-way functions. Relying on the recent result of Asharov and Segev (STOC’15), this yields the first construction of a Bounded KDM secure (or even circularly secure) encryption scheme from an assumption that provably does not imply collision-resistant hash functions w.r.t. black-box constructions. Combining this with prior constructions, we show how to augment this Bounded KDM scheme into a Bounded CCA2-KDM scheme.