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ACM Symposium on Theory of Computing (STOC)

Bounded-concurrent secure multi-party computation with a dishonest majority

Rafael Pass

Published Jun 13, 2004• 183 citations

Abstract

We show how to securely realize any multi-party functionality in a way that preserves security under an a-priori bounded number of concurrent executions, regardless of the number of corrupted parties. Previous protocols for the above task either rely on set-up assumptions such as a Common Reference String, or require an honest majority. Our constructions are in the plain model and rely on standard intractability assumptions (enhanced trapdoor permutations and collision resistant hash functions). Even though our main focus is on feasibility of concurrent multi-party computation we actually obtain a protocol using only a constant number of communication rounds. As a consequence our protocol yields the first construction of constant-round phstand-alone secure multi-party computation with a dishonest majority, proven secure under standard (polynomial-time) hardness assumptions; previous solutions to this task either require logarithmic round-complexity, or subexponential hardness assumptions. The core of our protocol is a novel construction of (concurrently) simulation-sound zero-knowledge protocols, which might be of independent interest. Finally, we extend the framework constructed to give a protocol for secure multi-party (and thus two-party) computation for any number of corrupted parties, which remains secure even when arbitrary subsets of parties concurrently execute the protocol, possibly with interchangeable roles. As far as we know, for the case of two-party or multi-party protocols with a dishonest majority, this is the first positive result for any non-trivial functionality which achieves this property in the plain model.

DOI: 10.1145/1007352.1007393

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We show how to securely realize any multi-party functionality in a way that preserves security under an a-priori bounded number of concurrent executions, regardless of the number of corrupted parties. Previous protocols for the above task either rely on set-up assumptions such as a Common Reference String, or require an honest majority. Our constructions are in the plain model and rely on standard intractability assumptions (enhanced trapdoor permutations and collision resistant hash functions). Even though our main focus is on feasibility of concurrent multi-party computation we actually obtain a protocol using only a constant number of communication rounds. As a consequence our protocol yields the first construction of constant-round phstand-alone secure multi-party computation with a dishonest majority, proven secure under standard (polynomial-time) hardness assumptions; previous solutions to this task either require logarithmic round-complexity, or subexponential hardness assumptions. The core of our protocol is a novel construction of (concurrently) simulation-sound zero-knowledge protocols, which might be of independent interest. Finally, we extend the framework constructed to give a protocol for secure multi-party (and thus two-party) computation for any number of corrupted parties, which remains secure even when arbitrary subsets of parties concurrently execute the protocol, possibly with interchangeable roles. As far as we know, for the case of two-party or multi-party protocols with a dishonest majority, this is the first positive result for any non-trivial functionality which achieves this property in the plain model.

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.

Until recently, most research on the topic of secure computation focused on the stand-alone model, where a single protocol execution takes place. In this paper, we construct protocols for the setting of bounded-concurrent self composition, where a (single) secure protocol is run many times concurrently, and there is a predetermined bound on the number of concurrent executions. In short, we show that any two-party functionality can be securely computed under boundedconcurrent self composition, in the plain model (where the only setup assumption made is that the parties communicate via authenticated channels). Our protocol provides the first feasibility result for general two-party computation in the plain model, for any model of concurrency. All previous protocols assumed a trusted setup phase in order to obtain a common reference string. On the downside, the number of rounds of communication in our protocol is super-linear in the bound on the number of concurrent executions. However, we believe that our constructions will lead to more efficient protocols for this task.

We show how to securely realize any multi-party functionality in a universally composable way, regardless of the number of corrupted participants. That is, we consider a multi-party network with open communication and an adversary that can adaptively corrupt as many parties as it wishes. In this setting, our protocols allow any subset of the parties (with pairs of parties being a special case) to securely realize any desired functionality of their local inputs, and be guaranteed that security is preserved regardless of the activity in the rest of the network. This implies that security is preserved under concurrent composition of an unbounded number of protocol executions, it implies non-malleability with respect to arbitrary protocols, and more. Our constructions are in the common reference string model and make general intractability assumptions.

We show how to securely realize any multi-party functionality in a universally composable way, regardless of the number of corrupted participants. That is, we consider a multi-party network with open communication and an adversary that can adaptively corrupt as many parties as it wishes. In this setting, our protocols allow any subset of the parties (with pairs of parties being a special case) to securely realize any desired functionality of their local inputs, and be guaranteed that security is preserved regardless of the activity in the rest of the network. This implies that security is preserved under concurrent composition of an unbounded number of protocol executions, it implies non-malleability with respect to arbitrary protocols, and more. Our constructions are in the common reference string model and make general intractability assumptions.

In this paper we study the feasibility of obtaining protocols for general two-party computation that remain secure under concurrent composition. (A general protocol can be used for obtaining secure computation of any functionality.) We consider a scenario where no trusted setup is assumed (and so, for example, there is no common reference string available to the parties); we call this the "plain model". We present both negative and positive results for this model. Specifically, we show that a general two-party protocol that remains secure for m concurrent executions and can be proven via black-box simulation, must have more than m rounds of communication. An important corollary of this result is that there do not exist protocols for black-box secure general two-party computation for the case of unbounded concurrency (where any polynomial number of concurrent executions may be run). On the positive side, we show that under general cryptographic assumptions, there exist secure protocols for general two-party computation in the model of bounded concurrent composition (in this model the number of concurrent executions is fixed and the protocol design may depend on this number). Our protocol has O(m) rounds of communication, where m is the bound on the number of concurrent executions, and uses both black-box and non black-box techniques. We note that this protocol constitutes the first feasibility result for general two-party computation without setup assumptions for any model of concurrency.

In this paper we study the feasibility of obtaining protocols for general two-party computation that remain secure under concurrent composition. (A general protocol can be used for obtaining secure computation of any functionality.) We consider a scenario where no trusted setup is assumed (and so, for example, there is no common reference string available to the parties); we call this the "plain model". We present both negative and positive results for this model. Specifically, we show that a general two-party protocol that remains secure for m concurrent executions and can be proven via black-box simulation, must have more than m rounds of communication. An important corollary of this result is that there do not exist protocols for black-box secure general two-party computation for the case of unbounded concurrency (where any polynomial number of concurrent executions may be run). On the positive side, we show that under general cryptographic assumptions, there exist secure protocols for general two-party computation in the model of bounded concurrent composition (in this model the number of concurrent executions is fixed and the protocol design may depend on this number). Our protocol has O(m) rounds of communication, where m is the bound on the number of concurrent executions, and uses both black-box and non black-box techniques. We note that this protocol constitutes the first feasibility result for general two-party computation without setup assumptions for any model of concurrency.