How to Play ANY Mental Game Over the Net Concurrently composable secure computation without setup assumptions

We construct a protocol for general multi-party computation that remains secure even if executed concurrently with multiple copies of itself and of arbitrary other protocols. This is the first such construction that is based on standard cryptographic assumptions and does not require setup conditions such as the existence of a common reference string. Furthermore, our protocol utilizes only a constant number of communication rounds and remains secure also with respect to adaptive adversaries (without using memory erasures). The security of our protocol is demonstrated by a simulator with a quasi-polynomial simu- lation overhead, as opposed to the standard notion of polynomial simulation. However, quasi- polynomial simulation still provides sufficient security for almost all appl ications. Furthermore, it was previously shown that there does not exist such a protocol with polynomial simulation (Lindell, FOCS '03).