Universal Composability Notion for Functional Encryption Schemes

Abstract

We have developed an ideal functionality for security requirement of functional encryption schemes. The functionality is needed when we want to show the security of a functional encryption scheme in universal composable (UC) framework. A functionality F fe was developed to represent ideal respond of a functional encryption scheme against any polynomial time active attacker. We show that UC security notion of functional encryption scheme F fe is as strong as fully secure functional encryption in an indistinguishable game with chosen cipher text attack. The proof used a method that showing for any environment algorithm, it can not distinguish ideal world where the attacker play with ideal functionality F fe and real world where the attacker play a fully secure functional encryption scheme.