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On the Notion of Statistical Security in Simulatability Definitions.

Dennis Hofheinz, Dominique Unruh

Published Jan 1, 2005• 1 citation
OpenAlex

Abstract

Abstract. We investigate the definition of statistical security (i.e., security against unbounded adversaries) in the framework of reactive simulatability. This framework allows to formulate and analyze multi-party protocols modularly by providing a composition theorem for protocols. However, we show that the notion of statistical security, as defined by Backes, Pfitzmann and Waidner for the reactive simulatability framework, does not allow for secure composition of protocols. This in particular invalidates the proof of the composition theorem. We give evidence that the reason for the non-composability of statistical security is no artifact of the framework itself, but of the particular formulation of statistical security. Therefore, we give a modified notion of statistical security in the reactive simulatability framework. We prove that this notion allows for secure composition of protocols. As to the best of our knowledge, no formal definition of statistical security has been fixed for Canetti’s universal composability framework, we believe that our observations and results can also help to avoid potential pitfalls there.

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Abstract. We investigate the definition of statistical security (i.e., security against unbounded adversaries) in the framework of reactive simulatability. This framework allows to formulate and analyze multi-party protocols modularly by providing a composition theorem for protocols. However, we show that the notion of statistical security, as defined by Backes, Pfitzmann and Waidner for the reactive simulatability framework, does not allow for secure composition of protocols. This in particular invalidates the proof of the composition theorem. We give evidence that the reason for the non-composability of statistical security is no artifact of the framework itself, but of the particular formulation of statistical security. Therefore, we give a modified notion of statistical security in the reactive simulatability framework. We prove that this notion allows for secure composition of protocols. As to the best of our knowledge, no formal definition of statistical security has been fixed for Canetti’s universal composability framework, we believe that our observations and results can also help to avoid potential pitfalls there.
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
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.
Abstract. Simulatability has established itself as a salient notion for defining and proving the security of cryptographic protocols since it entails strong security and compositionality guarantees, which are achieved by universally quantifying over all environmental behaviors of the analyzed protocol. As a consequence, however, protocols that are secure except for certain environmental behaviors are not simulatable, even if these behaviors are efficiently identifiable and thus can be prevented by the surrounding protocol. We propose a relaxation of simulatability by conditioning the permitted environmental behaviors, i.e., simulation is only required for environmental behaviors that fulfill explicitly stated constraints. This yields a more fine-grained security definition that is achievable for several protocols for which unconditional simulatability is too strict a notion, or at lower cost for the underlying cryptographic primitives. Although imposing restrictions on the environment destroys unconditional composability in general, we show that the composition of a large class of conditionally simulatable protocols yields protocols that are again simulatable under suitable conditions. This even holds for the case of cyclic assume-guarantee conditions where protocols only guarantee suitable behavior if they themselves are offered certain guarantees. Furthermore, composing several commonly investigated protocol classes with conditionally simulatable subprotocols yields protocols that are again simulatable in the standard, unconditional sense. 1
Abstract. We investigate the security of protocols with logarithmic communication complexity. We show that for the security definitions with environment, i.e., Reactive Simulatability and Universal Composability, computational security of logarithmic protocols implies statistical security. The same holds for advantage-based security definitions as commonly used for individual primitives. While this matches the folklore that logarithmic protocols cannot be computationally secure unless they are already statistically secure, we show that under realistic complexity assumptions, this folklore does surprisingly not hold for the stand-alone model without auxiliary input, i.e., there are logarithmic protocols that are statistically insecure but computationally secure in this model. The proof is conducted by showing how to transform an instance of an NP-complete problem into a protocol with two properties: There exists an adversary such that the protocol is statistically insecure in the stand-alone model, and given such an adversary we can find a witness for the problem instance, hence yielding a computationally secure protocol assuming the hardness of finding a witness. The proof relies on a novel technique that establishes a link between cryptographic definitions and foundations of computational
We investigate the question of whether security of protocols in the information-theoretic setting (where the adversary is computationally unbounded) implies the security of these protocols under concurrent composition. This question is motivated by the folklore that all known protocols that are secure in the information-theoretic setting are indeed secure under concurrent composition. We provide answers to this question for a number of different settings (i.e., considering perfect versus statistical security, and concurrent composition with adaptive versus fixed inputs). Our results enhance the understanding of what is necessary for obtaining security under composition, as well as providing tools (i.e., composition theorems) that can be used for proving the security of protocols under composition while considering only the standard stand-alone definitions of security.
We investigate the question of whether security of protocols in the information-theoretic setting (where the adversary is computationally unbounded) implies security under concurrent composition. This question is motivated by the folklore that all known protocols that are secure in the information-theoretic setting are indeed secure under concurrent composition. We provide answers to this question for a number of different settings (i.e., considering perfect versus statistical security, and concurrent composition with adaptive versus fixed inputs). Our results enhance the understanding of what is necessary for obtaining security under composition, as well as providing tools (i.e., composition theorems) that can be used for proving the security of protocols under composition while considering only the standard stand-alone definitions of security.