Simulation-based security with inexhaustible interactive Turing machines

Abstract

Recently, there has been much interest in extending models for simulation-based security in such a way that the runtime of protocols may depend on the length of their input. Finding such extensions has turned out to be a non-trivial task. In this work, we propose a simple, yet expressive general computational model for systems of interactive Turing machines (ITMs) where the runtime of the ITMs may be polynomial per activation and may depend on the length of the input received. One distinguishing feature of our model is that the systems of ITMs that we consider involve a generic mechanism for addressing dynamically generated copies of ITMs. We study properties of such systems and, in particular, show that systems satisfying a certain acyclicity condition run in polynomial time. Based on our general computational model, we state different notions of simulation-based security in a uniform and concise way, study their relationships, and prove a general composition theorem for composing a polynomial number of copies of protocols, where the polynomial is determined by the environment. The simplicity of our model is demonstrated by the fact that many of our results can be proved by mere equational reasoning based on a few equational principles on systems