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Documents authored by Kolobov, Victor I.

Document
DOI: 10.4230/LIPIcs.ITC.2022.17
Information-Theoretic Distributed Point Functions

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

Published in: LIPIcs, Volume 230, 3rd Conference on Information-Theoretic Cryptography (ITC 2022)

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.
Cite as

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)

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@InProceedings{boyle_et_al:LIPIcs.ITC.2022.17,
  author =	{Boyle, Elette and Gilboa, Niv and Ishai, Yuval and Kolobov, Victor I.},
  title =	{{Information-Theoretic Distributed Point Functions}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-238-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{230},
  editor =	{Dachman-Soled, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2022.17},
  URN =		{urn:nbn:de:0030-drops-164957},
  doi =		{10.4230/LIPIcs.ITC.2022.17},
  annote =	{Keywords: Information-theoretic cryptography, homomorphic secret sharing, private information retrieval, secure multiparty computation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.71
On the Download Rate of Homomorphic Secret Sharing

Authors: Ingerid Fosli, Yuval Ishai, Victor I. Kolobov, and Mary Wootters

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
A homomorphic secret sharing (HSS) scheme is a secret sharing scheme that supports evaluating functions on shared secrets by means of a local mapping from input shares to output shares. We initiate the study of the download rate of HSS, namely, the achievable ratio between the length of the output shares and the output length when amortized over 𝓁 function evaluations. We obtain the following results. - In the case of linear information-theoretic HSS schemes for degree-d multivariate polynomials, we characterize the optimal download rate in terms of the optimal minimal distance of a linear code with related parameters. We further show that for sufficiently large 𝓁 (polynomial in all problem parameters), the optimal rate can be realized using Shamir’s scheme, even with secrets over 𝔽₂. - We present a general rate-amplification technique for HSS that improves the download rate at the cost of requiring more shares. As a corollary, we get high-rate variants of computationally secure HSS schemes and efficient private information retrieval protocols from the literature. - We show that, in some cases, one can beat the best download rate of linear HSS by allowing nonlinear output reconstruction and 2^{-Ω(𝓁)} error probability.
Cite as

Ingerid Fosli, Yuval Ishai, Victor I. Kolobov, and Mary Wootters. On the Download Rate of Homomorphic Secret Sharing. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 71:1-71:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fosli_et_al:LIPIcs.ITCS.2022.71,
  author =	{Fosli, Ingerid and Ishai, Yuval and Kolobov, Victor I. and Wootters, Mary},
  title =	{{On the Download Rate of Homomorphic Secret Sharing}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{71:1--71:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.71},
  URN =		{urn:nbn:de:0030-drops-156675},
  doi =		{10.4230/LIPIcs.ITCS.2022.71},
  annote =	{Keywords: Information-theoretic cryptography, homomorphic secret sharing, private information retrieval, secure multiparty computation, regenerating codes}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2020.28
Fast Deterministic Algorithms for Highly-Dynamic Networks

Authors: Keren Censor-Hillel, Neta Dafni, Victor I. Kolobov, Ami Paz, and Gregory Schwartzman

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Abstract
This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which arbitrarily many edge changes may occur in each round. Our algorithm significantly improves upon prior work in its combination of (1) having an O(1) amortized time complexity, (2) using only O(log{n})-bit messages, (3) not posing any restrictions on the dynamic behavior of the environment, (4) being deterministic, (5) having strong guarantees for intermediate solutions, and (6) being applicable for a wide family of tasks. The tasks for which we deduce such an algorithm are maximal matching, (degree+1)-coloring, 2-approximation for minimum weight vertex cover, and maximal independent set (which is the most subtle case). For some of these tasks, node insertions can also be among the allowed topology changes, and for some of them also abrupt node deletions.
Cite as

Keren Censor-Hillel, Neta Dafni, Victor I. Kolobov, Ami Paz, and Gregory Schwartzman. Fast Deterministic Algorithms for Highly-Dynamic Networks. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{censorhillel_et_al:LIPIcs.OPODIS.2020.28,
  author =	{Censor-Hillel, Keren and Dafni, Neta and Kolobov, Victor I. and Paz, Ami and Schwartzman, Gregory},
  title =	{{Fast Deterministic Algorithms for Highly-Dynamic Networks}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.28},
  URN =		{urn:nbn:de:0030-drops-135138},
  doi =		{10.4230/LIPIcs.OPODIS.2020.28},
  annote =	{Keywords: dynamic distributed algorithms}
}
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