Protocols for Bounded-Concurrent Secure Two-Party Computation in the Plain Model.

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. Subsequent to this work, constant-round protocols and protocols for the multiparty case were presented by Pass and Rosen (FOCS 2003) and by Pass (STOC 2004). We remark that this paper contains the full version of the upperbound portion of the extended abstract presented by the author at STOC 2003 [29] (the lower bound from [29] appears in [33] together with other lower bounds from [32])