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Lecture notes in computer science

Concurrently Secure Computation in Constant Rounds

Sanjam Garg, Vipul Goyal, Abhishek Jain, Amit Sahai

Published Jan 1, 2012• 50 citations
Publisher
DOI
10.1007/978-3-642-29011-4_8

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We consider the problem of constructing a general protocol for secure two-party computation in a way that preserves security under concurrent composition. In our treatment, we focus on the case where an a-priori bound on the number of concurrent sessions is specified before the protocol is constructed. (a.k.a. bounded concurrency). We make no setup assumptions. Lindel (STOC 2003) has shown that any protocol for bounded-concurrent secure two-party computation, whose security is established via black-box simulation, must have round complexity that is strictly larger than the bound on the number of concurrent sessions. In this paper, we construct a (non black-box) protocol for realizing bounded-concurrent secure two-party computation in a constant number of rounds. Our constructions rely on the existence of enhanced trapdoor permutations, as well as on the existence of hash functions that are collision-resistant against subexponential sized circuits.

Annual Symposium on Foundations of Computer Science•Mar 1, 2004•87 citations
We study the problem of constructing concurrently secure computation protocols in the plain model, where no trust is required in any party or setup. While the well established UC framework for concurrent security is impossible to achieve in this setting, a meaningful notion of concurrent security based on super-polynomial simulation (SPS) is achievable and has been extensively studied [Pas03, PS04, BS05, LPV09, CLP10]. The recent work of [CLP10] obtains a concurrently secure computation protocol in the plain model with SPS security under standard assumptions, but requires a number of rounds of interaction that is polynomial in the security parameter. In this work, we obtain the first concurrently secure computation protocol in the plain model with SPS security that uses only a constant number of rounds and requires only standard assumptions. To accomplish our result, we introduce a new proof technique that significantly reduces the demands placed on “rewinding techniques ” employed in previous work. We believe that our techniques are of independent interest and likely to be applicable in other settings related to secure
We consider the problem of constructing a general protocol for secure two-party computation in a way that preserves security under concurrent composition. In our treatment, we focus on the case where an a-priori bound on the number of concurrent sessions is specified before the protocol is constructed. (a.k.a. bounded concurrency). We make no setup assumptions. Lindel (STOC 2003) has shown that any protocol for bounded-concurrent secure two-party computation, whose security is established via black-box simulation, must have round complexity that is strictly larger than the bound on the number of concurrent sessions. In this paper, we construct a (non black-box) protocol for realizing bounded-concurrent secure two-party computation in a constant number of rounds. Our constructions rely on the existence of enhanced trapdoor permutations, as well as on the existence of hash functions that are collision-resistant against subexponential sized circuits.