More efficient construction of bounded kdm secure encryption

Abstract

Let ski be the secret-key of user i for i = 1, …,l, and pkj be the public-key of user j ∈ {1,…, l}. A bounded Key Dependent Message (KDM) secure encryption scheme εb−KDM provides security even when one encrypts f(sk1,…, skl) under pkj for any function f which has arbitrarily fixed circuit size. An Eb−KDM is known to be constructed from projection KDM seucrity. In this paper, we first show that it can be obtained from much weaker KDM security than the projection KDM security. We next present more efficient εb−KDM than before under various assumptions.