Universally Composable Non-Interactive Key Exchange

We consider the notion of a non-interactive key exchange (NIKE). A NIKE scheme allows a party A to compute a common shared key with another party B from B’s public key and A’s secret key alone. This computation requires no interaction between A and B, a feature which distinguishes NIKE from regular (i.e., interactive) key exchange not only quantitatively, but also qualitatively. Our first contribution is a formalization of NIKE protocols as ideal functionalities in the Universal Composability (UC) framework. As we will argue, existing NIKE definitions (all of which are game-based) do not support a modular analysis either of NIKE schemes themselves, or of the use of NIKE schemes. We provide a simple and natural UC-based NIKE definition that allows for a modular analysis both of NIKE schemes and their use in larger protocols. We proceed to investigate the properties of our new definition, and in particular its relation to existing game-based NIKE definitions. We find that (a) game-based NIKE security is equivalent to UC-based NIKE security against static corruptions, and (b) UC-NIKE security against adaptive corruptions cannot be achieved without additional assumptions (but can be achieved in the random oracle model). Our results suggest that our UC-based NIKE definition is a useful and simple abstraction of non-interactive key exchange.