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 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.