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Information-Theoretic Distributed Point Functions

Authors Elette Boyle, Niv Gilboa, Yuval Ishai, Victor I. Kolobov

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Author Details

Elette Boyle
  • IDC Herzliya, Israel
Niv Gilboa
  • Ben-Gurion University of the Negev, Beer-Sheva, Israel
Yuval Ishai
  • Technion, Haifa, Israel
Victor I. Kolobov
  • Technion, Haifa, Israel

Funding

  • Boyle, Elette: Supported by AFOSR Award FA9550-21-1-0046, ERC Project HSS (852952), ERC Project NTSC (742754), and a Google Research Scholar Award.
  • Gilboa, Niv: Supported by ISF grant 2951/20, ERC grant 876110, and a grant by the BGU Cyber Center.
  • Ishai, Yuval: Supported by ERC Project NTSC (742754), BSF grant 2018393, and ISF grant 2774/20.
  • Kolobov, Victor I.: Supported by ERC Project NTSC (742754) and ISF grant 2774/20.

Cite AsGet BibTex

Elette Boyle, Niv Gilboa, Yuval Ishai, and Victor I. Kolobov. Information-Theoretic Distributed Point Functions. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ITC.2022.17

Abstract

A distributed point function (DPF) (Gilboa-Ishai, Eurocrypt 2014) is a cryptographic primitive that enables compressed additive secret-sharing of a secret weight-1 vector across two or more servers. DPFs support a wide range of cryptographic applications, including efficient private information retrieval, secure aggregation, and more. Up to now, the study of DPFs was restricted to the computational security setting, relying on one-way functions. This assumption is necessary in the case of a dishonest majority. We present the first statistically private 3-server DPF for domain size N with subpolynomial key size N^{o(1)}. We also present a similar perfectly private 4-server DPF. Our constructions offer benefits over their computationally secure counterparts, beyond the superior security guarantee, including better computational complexity and better protocols for distributed key generation, all while having comparable communication complexity for moderate-sized parameters.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic primitives
Keywords
  • Information-theoretic cryptography
  • homomorphic secret sharing
  • private information retrieval
  • secure multiparty computation

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