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arXiv 2501.15751cs.CRcs.LG
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对抗鲁棒的布隆过滤器:隐私、归约与开放问题

Adversarially Robust Bloom Filters: Privacy, Reductions, and Open Problems

City College of New York(纽约城市学院)

Hayder Tirmazi

AI总结:

本研究探讨布隆过滤器在对抗环境下的鲁棒性与隐私,建立了Filic与NOY模型间的联系,证明PRF过滤器不满足BP测试,并提出首批差分隐私布隆过滤器构造。

摘要:

布隆过滤器是一种空间高效的概率数据结构,用于表示来自更大全集 $U$ 的元素集合 $S$。这种高效性伴随着一种权衡,即它允许存在较小的假阳性概率。当您查询布隆过滤器关于某个元素 x 时,如果 $x \in S$,过滤器将回答“是”。如果 $x \notin S$,它仍可能以最多 $\varepsilon$ 的概率回答“是”。我们研究了布隆过滤器的对抗鲁棒性和隐私性,解决了三个重要框架中的开放问题:Naor-Oved-Yogev (NOY) 的基于博弈的模型、Filic 等人的基于模拟器的模型以及学习增强变体。我们证明了 Filic 模型与 NOY 模型之间的第一个正式联系,表明 Filic 正确性蕴含 AB 测试韧性。我们通过证明基于 PRF 的布隆过滤器无法通过 NOY 模型中更强的 BP 测试,解决了一个长期存在的开放问题。最后,我们引入了首批具有差分隐私保证的私有布隆过滤器,包括适用于学习型布隆过滤器的构造。我们的分类法组织了鲁棒性和隐私保证的空间,阐明了模型与构造之间的关系。

英文摘要:

A Bloom filter is a space-efficient probabilistic data structure that represents a set $S$ of elements from a larger universe $U$. This efficiency comes with a trade-off, namely, it allows for a small chance of false positives. When you query the Bloom filter about an element x, the filter will respond 'Yes' if $x \in S$. If $x \notin S$, it may still respond 'Yes' with probability at most $\varepsilon$. We investigate the adversarial robustness and privacy of Bloom filters, addressing open problems across three prominent frameworks: the game-based model of Naor-Oved-Yogev (NOY), the simulator-based model of Filic et. al., and learning-augmented variants. We prove the first formal connection between the Filic and NOY models, showing that Filic correctness implies AB-test resilience. We resolve a longstanding open question by proving that PRF-backed Bloom filters fail the NOY model's stronger BP-test. Finally, we introduce the first private Bloom filters with differential privacy guarantees, including constructions applicable to learned Bloom filters. Our taxonomy organizes the space of robustness and privacy guarantees, clarifying relationships between models and constructions.

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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