对抗性列删除下的数据库匹配
Database Matching Under Adversarial Column Deletions
AI总结：
本文研究对抗性列删除下的数据库匹配问题，提出基于列直方图检测删除模式并精确匹配用户的两阶段方案，推导出成功匹配的充分与必要条件，证明对抗性匹配容量远低于随机情形，凸显对抗机制在隐私保护上的优势。
摘要：
通过将匿名微数据与公开可用的相关数据库进行匹配或对齐来实现用户去匿名化，近年来引起了科学界的关注。虽然大多数严格的数据库匹配分析都集中在随机失真模型上，但对抗性失真模型在相关文献中一直缺乏。在这项工作中，受时间索引微数据采样中同步误差的启发，研究了对抗性列删除下随机数据库的匹配（对齐）问题。假设一个受限的对抗者，能够观察到匿名数据库，可以删除最多δ比例的列（属性）以阻碍匹配并保护隐私。利用两个数据库的列直方图作为排列不变特征来检测对抗者选择的列删除模式。列删除模式的检测之后是精确的行（用户）匹配方案。该两阶段方案的最坏情况分析，在近乎完美恢复条件下，为两个数据库的成功匹配提供了充分条件。对错误概率的更详细研究得出了数据库增长率的紧致必要条件，进而得到了对抗性匹配容量的单字母表征。该对抗性匹配容量被证明显著低于随机匹配容量，后者中列删除是随机发生的。总体而言，我们的结果分析性地证明了在匿名时间索引数据发布过程中，对抗性机制相对于随机机制在隐私方面的优势。
英文摘要：
The de-anonymization of users from anonymized microdata through matching or aligning with publicly-available correlated databases has been of scientific interest recently. While most of the rigorous analyses of database matching have focused on random-distortion models, the adversarial-distortion models have been wanting in the relevant literature. In this work, motivated by synchronization errors in the sampling of time-indexed microdata, matching (alignment) of random databases under adversarial column deletions is investigated. It is assumed that a constrained adversary, which observes the anonymized database, can delete up to a $δ$ fraction of the columns (attributes) to hinder matching and preserve privacy. Column histograms of the two databases are utilized as permutation-invariant features to detect the column deletion pattern chosen by the adversary. The detection of the column deletion pattern is then followed by an exact row (user) matching scheme. The worst-case analysis of this two-phase scheme yields a sufficient condition for the successful matching of the two databases, under the near-perfect recovery condition. A more detailed investigation of the error probability leads to a tight necessary condition on the database growth rate, and in turn, to a single-letter characterization of the adversarial matching capacity. This adversarial matching capacity is shown to be significantly lower than the random matching capacity, where the column deletions occur randomly. Overall, our results analytically demonstrate the privacy-wise advantages of adversarial mechanisms over random ones during the publication of anonymized time-indexed data.
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