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2020 | OriginalPaper | Buchkapitel

PSI from PaXoS: Fast, Malicious Private Set Intersection

verfasst von : Benny Pinkas, Mike Rosulek, Ni Trieu, Avishay Yanai

Erschienen in: Advances in Cryptology – EUROCRYPT 2020

Verlag: Springer International Publishing

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Abstract

We present a 2-party private set intersection (PSI) protocol which provides security against malicious participants, yet is almost as fast as the fastest known semi-honest PSI protocol of Kolesnikov et al. (CCS 2016).

Our protocol is based on a new approach for two-party PSI, which can be instantiated to provide security against either malicious or semi-honest adversaries. The protocol is unique in that the only difference between the semi-honest and malicious versions is an instantiation with different parameters for a linear error-correction code. It is also the first PSI protocol which is concretely efficient while having linear communication and security against malicious adversaries, while running in the OT-hybrid model (assuming a non-programmable random oracle).

State of the art semi-honest PSI protocols take advantage of cuckoo hashing, but it has proven a challenge to use cuckoo hashing for malicious security. Our protocol is the first to use cuckoo hashing for malicious-secure PSI. We do so via a new data structure, called a probe-and-XOR of strings (\(\mathsf{PaXoS}\)), which may be of independent interest. This abstraction captures important properties of previous data structures, most notably garbled Bloom filters. While an encoding by a garbled Bloom filter is larger by a factor of \(\varOmega (\lambda )\) than the original data, we describe a significantly improved \(\mathsf{PaXoS}\) based on cuckoo hashing that achieves constant rate while being no worse in other relevant efficiency measures.

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Vorheriges Kapitel Lightweight Authenticated Encryption Mode Suitable for Threshold Implementation

Nächstes Kapitel Two-Round Oblivious Transfer from CDH or LPN

A hash table is a simple key-value mapping, but it encounters issues such as collisions. More importantly for our application, a hash table explicitly reveals whether an item is encoded in it and therefore has a privacy leakage.

When defining the cost of encoding and decoding we ignore the length (m) of the y-values.

I.e., \(\varvec{v}^H(x) = H(x)\) where H is a random oracle with m output bits.

For example, considering an adversary who makes \(q=2^{80}\) queries to \(H_1\) leads to \(\ell _1\) in the range of 70 to 90, and codeword length t in the range of 460 to 510.

For now, we ignore the case where \(h_1(x) = h_2(x)\).

Such an upper bound for the case of Cuckoo hashing can be derived from [24, Lemma 3.4], but that analysis assumes that the graph has 8n edges, and shows that an upper bound of size d fails with probability \(n/2^{-\varOmega (d)}\). Therefore we must set \(d=(\log n)^{1+\epsilon }\) to get a negligible failure probability.

The parameter \(\varepsilon \) used here is independent of the parameter \(\epsilon \) used in Cuckoo hashing.

https://github.com/osu-crypto.

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Titel: PSI from PaXoS: Fast, Malicious Private Set Intersection
verfasst von: Benny Pinkas
Mike Rosulek
Ni Trieu
Avishay Yanai
Verlag: Springer International Publishing
Buch: Advances in Cryptology – EUROCRYPT 2020
Print ISBN: 978-3-030-45723-5

Electronic ISBN: 978-3-030-45724-2

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-45724-2_25

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