Lindell（2003 STOC）已经表明，任何安全性通过黑箱模拟而建立的有界并发安全两方计算的协议，必须具有严格大于回合并行会话数的回合复杂性。在本文中，我们构造了用于在回合常数中实现有界并发安全两方计算的（非黑箱）协议。 能实现上述任务的先前已知的协议需要比预先指定边界更多有关会话数量的回合（尽管使用了非黑箱模拟技术）。
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 apriori bound on the number of concurrent sessions is specified before the protocol is constructed (a.k.a. bounded concurrency). We make no set-up assumptions.
Lindell (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. The only previously known protocol for realizing the above task required more rounds than the pre-specified bound on the number of sessions (despite usage of non black-box simulation techniques).
Our constructions rely on the existence of enhanced trap- door permutations, as well as on the existence of hash functions that are collision-resistant against subexponential sized circuits.