We study the round and communication complexities of various cryptographic protocols. We give tight lower bounds on the round and communication complexities of any fully black-box reduction of a statistically hiding commitment scheme from one-way permutations, and from trapdoor permutations. As a corollary, we derive similar tight lower bounds for several other cryptographic protocols, such as single-server private information retrieval, interactive hashing, and oblivious transfer that guarantees statistical security for one of the parties. Our techniques extend the collision-finding oracle due to Simon (EUROCRYPT '98) to the setting of interactive protocols and the reconstruction paradigm of Gennaro and Trevisan (FOCS '00).

中文翻译：

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在交互协议中查找冲突-关于统计隐藏承诺的回合和通信复杂性的较低界限

我们研究了各种密码协议的回合和通信复杂性。对于单向置换和活板门置换中的统计隐藏承诺方案的任何完全黑盒缩减，我们给出了严格的下界和通信复杂度。因此，我们推导出了其他几种加密协议的相似下限，例如单服务器私有信息检索，交互式哈希和遗忘传输，从而保证了其中一方的统计安全性。我们的技术将Simon（EUROCRYPT '98）的碰撞发现预言扩展到了交互协议的设置以及Gennaro和Trevisan（FOC​​S '00）的重构范例。