辅助公共信息及其在两方安全计算中的应用
Assisted Common Information with Applications to Secure Two-Party Computation
摘要：
安全多方计算是现代密码学的核心问题。其中一个重要的子类是以下形式的问题：Alice和Bob希望产生一对联合分布的随机变量的样本。每一方都必须了解对方的输出，而不是自己的输出所揭示的。为了帮助这一点，他们有一个可用的设置-相关的随机变量，其分布是不同于所需的分布-以及无限的无噪声通信。在本文中，我们提出了一个上限如何有效地一个给定的设置可以用来产生所需的分布样本。我们开发的关键工具是两个相依随机变量的公共信息概念的推广[Gacs-Korner，1973]。我们的推广-一个三维区域-补救的一些限制，原来的定义，只捕获了有限形式的依赖。它还包括作为特例的Wyner的共同信息[Wyner，1975]。为了推导出密码界，我们依赖于该区域的单调性：在任何协议中，Alice和Bob的“视图”区域只能单调扩展而不能收缩。因此，通过比较目标随机变量和给定随机变量的区域，我们得到了我们的上界。
英文摘要：
Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each party must learn nothing more about the other party's output than what its own output reveals. To aid in this, they have available a set up - correlated random variables whose distribution is different from the desired distribution - as well as unlimited noiseless communication. In this paper we present an upperbound on how efficiently a given set up can be used to produce samples from a desired distribution. The key tool we develop is a generalization of the concept of common information of two dependent random variables [Gacs-Korner, 1973]. Our generalization - a three-dimensional region - remedies some of the limitations of the original definition which captured only a limited form of dependence. It also includes as a special case Wyner's common information [Wyner, 1975]. To derive the cryptographic bounds, we rely on a monotonicity property of this region: the region of the "views" of Alice and Bob engaged in any protocol can only monotonically expand and not shrink. Thus, by comparing the regions for the target random variables and the given random variables, we obtain our upperbound.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
