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arXiv 1102.1443cs.CRcs.GT
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关于几乎秘密计算的通信协议

On Communication Protocols that Compute Almost Privately

Marco Comi, Bhaskar DasGupta, Michael Schapira, Venkatakumar Srinivasan

摘要:

在设计拍卖机制时,传统上期望的目标是激励相容性,即,确保投标人通过如实报告他们的偏好获得最佳结果。一个补充目标是保护隐私,即,以确保投标人不会透露不必要的信息。我们进一步研究和推广的近似隐私模型的两方通信最近推出的Feigenbaum等人。[8]的一项建议。我们探讨的隐私属性的一个自然类的通信协议,我们称之为“解剖协议”。解剖协议包括[9,10]中的二分拍卖和[8]中的百万富翁问题的二分协议。非正式地,在解剖协议中,通信方被限制为回答以下形式的简单问题:“您的输入是否在值α和β之间(在可能输入的预定义顺序下)?".我们证明,对于一个大类的功能,称为平铺功能,其中包括第二价格Vickrey拍卖,总是存在一个解剖协议,提供了一个恒定的平均情况下的隐私近似比均匀或“几乎均匀”的概率分布的输入。为了建立这一结果,我们提出了一个有趣的近似隐私框架和计算几何的基本概念之间的联系。我们表明,这样一个很好的隐私近似比平铺功能不存在,在一般情况下,在最坏的情况下。我们还讨论了扩展的基本设置到两个以上的缔约方和非平铺功能,并提供计算的隐私近似比为两个功能的利益。

英文摘要:

A traditionally desired goal when designing auction mechanisms is incentive compatibility, i.e., ensuring that bidders fare best by truthfully reporting their preferences. A complementary goal, which has, thus far, received significantly less attention, is to preserve privacy, i.e., to ensure that bidders reveal no more information than necessary. We further investigate and generalize the approximate privacy model for two-party communication recently introduced by Feigenbaum et al.[8]. We explore the privacy properties of a natural class of communication protocols that we refer to as "dissection protocols". Dissection protocols include, among others, the bisection auction in [9,10] and the bisection protocol for the millionaires problem in [8]. Informally, in a dissection protocol the communicating parties are restricted to answering simple questions of the form "Is your input between the values αand β(under a predefined order over the possible inputs)?". We prove that for a large class of functions, called tiling functions, which include the 2nd-price Vickrey auction, there always exists a dissection protocol that provides a constant average-case privacy approximation ratio for uniform or "almost uniform" probability distributions over inputs. To establish this result we present an interesting connection between the approximate privacy framework and basic concepts in computational geometry. We show that such a good privacy approximation ratio for tiling functions does not, in general, exist in the worst case. We also discuss extensions of the basic setup to more than two parties and to non-tiling functions, and provide calculations of privacy approximation ratios for two functions of interest.

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。

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