Polynomial runtime in simulatability definitions

We elaborate on the problem of polynomial runtime in simulatability definitions for multiparty computation. First, the need for a new definition is demonstrated by showing which problems occur with common definitions of polynomial runtime. Then, we give a definition which captures in an intuitive manner what it means for a protocol or an adversary to have polynomial runtime. We show that this notion is suitable for simulatability definitions for multiparty computation. In particular, a composition theorem is shown for this notion.