research-article

Private Set Intersection Using Multi-Message Symmetric Private Information Retrieval

Authors:
Zhusheng Wang

University of Maryland,Department of Electrical and Computer Engineering,College Park,MD,USA

University of Maryland,Department of Electrical and Computer Engineering,College Park,MD,USA
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,
Karim Banawan

Alexandria University,Electrical Engineering Department,Alexandria,Egypt

Alexandria University,Electrical Engineering Department,Alexandria,Egypt
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,
Sennur Ulukus

University of Maryland,Department of Electrical and Computer Engineering,College Park,MD,USA

University of Maryland,Department of Electrical and Computer Engineering,College Park,MD,USA
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2020 IEEE International Symposium on Information Theory (ISIT)Jun 2020Pages 1035–1040https://doi.org/10.1109/ISIT44484.2020.9174221

Published:21 June 2020Publication History

2020 IEEE International Symposium on Information Theory (ISIT)

Pages 1035–1040

ABSTRACT

We study the problem of private set intersection (PSI). In PSI, there are two entities, each storing a set ${\mathcal{P}_i}$, whose elements are picked from a finite set ${\mathbb{S}_K}$, on N<inf>i</inf> replicated and non-colluding databases. It is required to determine the set intersection ${\mathcal{P}_1} \cap {\mathcal{P}_2}$ without leaking any information about the remaining elements to the other entity. We first show that the PSI problem can be recast as a multi-message symmetric private information retrieval (MM-SPIR) problem. Next, as a stand-alone result, we show that the exact capacity of MM-SPIR is ${C_{MM - SPIR}} = 1 - \frac{1}{N}$ when P ≤ K − 1, if the common randomness S satisfies $H(S) \geq \frac{P}{{N - 1}}$ per desired symbol. This result implies that there is no gain for MM-SPIR over successive single-message SPIR. We present a novel capacity-achieving scheme which builds seamlessly over the multi-message PIR (MM-PIR) scheme. Based on this capacity result for the MM-SPIR problem, we show that the optimal download cost for the PSI problem is given by $\min \left\{ {\left[ {\begin{array}{c} {\frac{{{P_1}{N_2}}}{{{N_2} - 1}}} \end{array}} \right],\left[ {\begin{array}{c} {\frac{{{P_2}{N_1}}}{{{N_1} - 1}}} \end{array}} \right]} \right\}$, where P<inf>i</inf> is the cardinality of the set ${\mathcal{P}_i}$.

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2020 IEEE International Symposium on Information Theory (ISIT)
Jun 2020
3072 pages

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Private Set Intersection Using Multi-Message Symmetric Private Information Retrieval

2020 IEEE International Symposium on Information Theory (ISIT)

ABSTRACT

References

Cited By

Index Terms

Recommendations

Private Information Delivery

Constructing Set-Systems with Prescribed Intersection Size

Differentially private generalized linear models revisited

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Private Set Intersection Using Multi-Message Symmetric Private Information Retrieval

2020 IEEE International Symposium on Information Theory (ISIT)

ABSTRACT

References

Cited By

Index Terms

Recommendations

Private Information Delivery

Constructing Set-Systems with Prescribed Intersection Size

Differentially private generalized linear models revisited

Comments

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