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 bounded-concurrent 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.
This is the full version of the upper bound from the paper Bounded-Concurrent Secure Two-Party Computation Without Setup Assumptions, STOC 2003.
Postscript, gzipped Postscript.