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IEEE Computer Security Foundations Workshop (CSFW)

Polynomial Runtime in Simulatability Definitions

Dennis Hofheinz, Jörn Müller‐Quade, Dominique Unruh

Published Jul 6, 2005• 23 citations
Publisher

Abstract

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.

DOI
10.1109/csfw.2005.22

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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.
We elaborate on the problem of polynomial runtime in simulatability definitions for multi-party 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 multi-party computation. In particular, a composition theorem is shown for this notion.
Abstract. To prove security of a multi-party cryptographic protocol, one often reduces attacks on the protocol to attacks on a suitable computational problem. Thus, if the computational problem is hard, then the protocol is secure. But to allow for a security reduction, the protocol itself and the attack on the protocol must be efficient, i.e., polynomialtime. Of course, the obvious way to enforce an overall polynomial runtime of the protocol is to require each individual protocol machine and adversarial entity to be polynomialtime. However, as the specific case of zero-knowledge protocols demonstrates, an a priori polynomial-time bound on all entities may not be an optimal choice because the running time of some machines needs to depend on that of others. As we want to be able to model arbitrary protocol tasks, we work in the Universal Composability framework (UC). This framework additionally provides strong composability guarantees. We will point out that in the UC setting, finding a useful notion of polynomial-time for the analysis of general protocols is a highly non-trivial task. Our goal in this work is to find a good and useful definition of polynomial-time for multiparty protocols in the UC setting that matches the intuition of what is feasible. A good
Simulatable security is a security notion for multi-party protocols that implies strong composability features. The main definitional flavours of simulatable security are standard simulatability, universal simulatability, and black-box simulatability. All three come in "computational," "statistical" and "perfect" subflavours indicating the considered adversarial power. Universal and black-box simulatability, in all of their subflavours, are already known to guarantee that the concurrent composition even of a polynomial number of secure protocols stays secure. We show that computational standard simulatability does not allow for secure concurrent composition of polynomially many protocols, but we also show that statistical standard simulatability does. The first result assumes the existence of an interesting cryptographic tool (namely time-lock puzzles), and its proof employs a cryptographic multi-party computation in an interesting and unconventional way
Simulatability constitutes the cryptographic notion of a secure refinement and has asserted its position as one of the fundamental concepts of modern cryptography. Although simulatability carefully captures that a distributed protocol does not behave any worse than an ideal specification, it however does not capture any form of liveness guarantees, i.e., that something good eventually happens in the protocol.We show how one can extend the notion of simulatability to comprise liveness guarantees by imposing specific fairness constraints on the adversary. As the common notion of fairness based on infinite runs and eventual message delivery is not suited for reasoning about polynomial-time, cryptographic systems, we propose a new definition of fairness that enforces the delivery of messages after a polynomial number of steps. We provide strengthened variants of this definition by granting the protocol parties explicit guarantees on the maximum delay of messages. The variants thus capture fairness with explicit timeout signals, and we further distinguish between fairness with local timeouts and fairness with global timeouts.We compare the resulting notions of fair simulatability, and provide separating examples that help to classify the strengths of the definitions and that show that the different definitions of fairness imply different variants of simulatability.
We propose a modification to the framework of Universally Composable (UC) security [3]. Our new notion involves comparing the real protocol execution with an ideal execution involving ideal functionalities (just as in UC-security), but allowing the environment and adversary access to some super-polynomial computational power. We argue the meaningfulness of the new notion, which in particular subsumes many of the traditional notions of security. We generalize the Universal Composition theorem of [3] to the new setting. Then under new computational assumptions, we realize secure multi-party computation (for static adversaries) without a common reference string or any other set-up assumptions, in the new framework. This is known to be impossible under the UC framework.
The notion of simulatable security (reactive simulatability, universal composability) is a powerful tool for allowing the modular design of cryptographic protocols (composition of protocols) and showing the security of a given protocol embedded in a larger one. Recently, these methods have received much attention in the quantum cryptographic community. We give a short introduction to simulatable security in general and proceed by sketching the many different definitional choices together with their advantages and disadvantages. Based on the reactive simulatability modelling of Backes, Pfitzmann and Waidner we then develop a quantum security model. By following the BPW modelling as closely as possible, we show that composable quantum security definitions for quantum protocols can strongly profit from their classical counterparts, since most of the definitional choices in the modelling are independent of the underlying machine model. In particular, we give a proof for the simple composition theorem in our framework.