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Paper 2024/1292

Bet-or-Pass: Adversarially Robust Bloom Filters

Moni Naor , Weizmann

Institute of Science

Noa Oved , Weizmann Institute of Science

Abstract

A Bloom filter

💳 is a data structure that maintains a succinct and probabilistic representation of a

setR$S\subseteq U$ of elements from a universeR$U$.💳 It supports approximate membership

queries. The price of the succinctness is allowing some error, namely false positives:

for anyR$x

otin S$,💳 it might answer `Yes' but with a small (non-negligible)

probability. When dealing with such data structures in adversarial settings, we💳 need to

define the correctness guarantee and formalize the requirement that bad events happen

infrequently and those false positives are💳 appropriately distributed. Recently, several

papers investigated this topic, suggesting different robustness definitions. In this

work we unify this line of💳 research and propose several robustness notions for Bloom

filters that allow the adaptivity of queries. The goal is that a💳 robust Bloom filter

should behave like a random biased coin even against an adaptive adversary. The

robustness definitions are expressed💳 by the type of test that the Bloom filter should

withstand. We explore the relationships between these notions and highlight💳 the notion

of Bet-or-Pass as capturing the desired properties of such a data structure.

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