Bloom filters in adversarial environments

Moni Naor, Eylon Yogev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

24 Scopus citations

Abstract

Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and/or correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are independent of the internal randomness of the data structure. In this work, we consider data structures in a more robust model, which we call the adversarial model. Roughly speaking, this model allows an adversary to choose inputs and queries adaptively according to previous responses. Specifically, we consider a data structure known as “Bloom filter” and prove a tight connection between Bloom filters in this model and cryptography. A Bloom filter represents a set S of elements approximately, by using fewer bits than a precise representation. The price for succinctness is allowing some errors: for any x ∈ S it should always answer ‘Yes’, and for any x ∉ S it should answer ‘Yes’ only with small probability. In the adversarial model, we consider both efficient adversaries (that run in polynomial time) and computationally unbounded adversaries that are only bounded in the amount of queries they can make. For computationally bounded adversaries, we show that non-trivial (memory-wise) Bloom filters exist if and only if one-way functions exist. For unbounded adversaries we show that there exists a Bloom filter for sets of size n and error ε, that is secure against t queries and uses only O(n log 1/ε +t) bits of memory. In comparison, n log 1/ε is the best possible under a non-adaptive adversary.

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Proceedings
EditorsRosario Gennaro, Matthew Robshaw
PublisherSpringer Verlag
Pages565-584
Number of pages20
ISBN (Print)9783662479995
DOIs
StatePublished - 2015
Externally publishedYes
Event35th Annual Cryptology Conference, CRYPTO 2015 - Santa Barbara, United States
Duration: 16 Aug 201520 Aug 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9216
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference35th Annual Cryptology Conference, CRYPTO 2015
Country/TerritoryUnited States
CitySanta Barbara
Period16/08/1520/08/15

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2015.

Fingerprint

Dive into the research topics of 'Bloom filters in adversarial environments'. Together they form a unique fingerprint.

Cite this