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arXiv 2003.06826cs.CRcs.DB
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CoinMagic：一个差分隐私环签名方案框架

CoinMagic: A Differential Privacy Framework for Ring Signature Schemes

Wangze Ni, Han Wu, Peng Cheng, Lei Chen, Xuemin Lin, Lei Chen, Xin Lai, Xiao Zhang

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14 pages
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摘要：

通过允许用户通过包含“mixins”（谷壳币）来隐藏他们的交易，环签名方案已被广泛用于保护隐私保护区块链系统（如Monero和Bytecoin）中交易的发送者身份。然而，最近的工作指出，现有的环签名方案容易受到“链式反应”分析（即，可以通过消去法推导出给定环签名中的已用硬币）。特别是，当混入的多样性较低时，废硬币将具有较高的检测风险。为了克服这个弱点，环签名应该由一组具有高多样性的混合组成，并产生对任何两个硬币具有“相似”分布的观察结果。在本文中，我们提出了一个概念，即$ε$ -inputability（$ε$），形式化地定义了通过差分隐私方案保证的“相似”分布。然后，我们正式定义了CI感知的mixin选择问题与不相交超集约束（CIA-MS-DS），其目的是找到一个混合集，具有最大的多样性，并满足$ε$ -CI和预算的约束。在CIA-MS-DS中，每个环签名要么与其前面的环签名不相交，要么是其前面的环签名的超集。我们证明了CIA-MS-DS是NP难的，因此是棘手的。针对CIA-MS-DS问题，提出了两种近似算法，即渐进算法和博弈算法，并给出了理论保证。通过在真实数据集和合成数据集上的大量实验，我们证明了我们的方法的效率和有效性。

英文摘要：

By allowing users to obscure their transactions via including "mixins" (chaff coins), ring signature schemes have been widely used to protect a sender's identity of a transaction in privacy-preserving blockchain systems, like Monero and Bytecoin. However, recent works point out that the existing ring signature scheme is vulnerable to the "chain-reaction" analysis (i.e., the spent coin in a given ring signature can be deduced through elimination). Especially, when the diversity of mixins is low, the spent coin will have a high risk to be detected. To overcome the weakness, the ring signature should be consisted of a set of mixins with high diversity and produce observations having "similar" distributions for any two coins. In this paper, we propose a notion, namely $ε$-coin-indistinguishability ($ε$-CI), to formally define the "similar" distribution guaranteed through a differential privacy scheme. Then, we formally define the CI-aware mixins selection problem with disjoint-superset constraint (CIA-MS-DS), which aims to find a mixin set that has maximal diversity and satisfies the constraints of $ε$-CI and the budget. In CIA-MS-DS, each ring signature is either disjoint with or the superset of its preceding ring signatures. We prove that CIA-MS-DS is NP-hard and thus intractable. To solve the CIA-MS-DS problem, we propose two approximation algorithms, namely the Progressive Algorithm and the Game Theoretic Algorithm, with theoretic guarantees. Through extensive experiments on both real data sets and synthetic data sets, we demonstrate the efficiency and the effectiveness of our approaches.

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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