4 Search Results for "Mazor, Noam"

Document
DOI: 10.4230/LIPIcs.ITC.2023.2
A Lower Bound on the Share Size in Evolving Secret Sharing

Authors: Noam Mazor

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
Secret sharing schemes allow sharing a secret between a set of parties in a way that ensures that only authorized subsets of the parties learn the secret. Evolving secret sharing schemes (Komargodski, Naor, and Yogev [TCC '16]) allow achieving this end in a scenario where the parties arrive in an online fashion, and there is no a-priory bound on the number of parties. An important complexity measure of a secret sharing scheme is the share size, which is the maximum number of bits that a party may receive as a share. While there has been a significant progress in recent years, the best constructions for both secret sharing and evolving secret sharing schemes have a share size that is exponential in the number of parties. On the other hand, the best lower bound, by Csirmaz [Eurocrypt '95], is sub-linear. In this work, we give a tight lower bound on the share size of evolving secret sharing schemes. Specifically, we show that the sub-linear lower bound of Csirmaz implies an exponential lower bound on evolving secret sharing.
Cite as

Noam Mazor. A Lower Bound on the Share Size in Evolving Secret Sharing. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 2:1-2:9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mazor:LIPIcs.ITC.2023.2,
  author =	{Mazor, Noam},
  title =	{{A Lower Bound on the Share Size in Evolving Secret Sharing}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{2:1--2:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.2},
  URN =		{urn:nbn:de:0030-drops-183300},
  doi =		{10.4230/LIPIcs.ITC.2023.2},
  annote =	{Keywords: Secret sharing, Evolving secret sharing}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.66
Incompressiblity and Next-Block Pseudoentropy

Authors: Iftach Haitner, Noam Mazor, and Jad Silbak

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
A distribution is k-incompressible, Yao [FOCS '82], if no efficient compression scheme compresses it to less than k bits. While being a natural measure, its relation to other computational analogs of entropy such as pseudoentropy, Hastad, Impagliazzo, Levin, and Luby [SICOMP '99], and to other cryptographic hardness assumptions, was unclear. We advance towards a better understating of this notion, showing that a k-incompressible distribution has (k-2) bits of next-block pseudoentropy, a refinement of pseudoentropy introduced by Haitner, Reingold, and Vadhan [SICOMP '13]. We deduce that a samplable distribution X that is (H(X)+2)-incompressible, implies the existence of one-way functions.
Cite as

Iftach Haitner, Noam Mazor, and Jad Silbak. Incompressiblity and Next-Block Pseudoentropy. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 66:1-66:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{haitner_et_al:LIPIcs.ITCS.2023.66,
  author =	{Haitner, Iftach and Mazor, Noam and Silbak, Jad},
  title =	{{Incompressiblity and Next-Block Pseudoentropy}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{66:1--66:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.66},
  URN =		{urn:nbn:de:0030-drops-175697},
  doi =		{10.4230/LIPIcs.ITCS.2023.66},
  annote =	{Keywords: incompressibility, next-block pseudoentropy, sparse languages}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.17
Comparison Graphs: A Unified Method for Uniformity Testing

Authors: Uri Meir

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Distribution testing can be described as follows: q samples are being drawn from some unknown distribution P over a known domain [n]. After the sampling process, a decision must be made about whether P holds some property, or is far from it. The most studied problem in the field is arguably uniformity testing, where one needs to distinguish the case that P is uniform over [n] from the case that P is ε-far from being uniform (in 𝓁₁). It is known that for this task Θ(√n/ε²) samples are necessary and sufficient. This problem was recently considered in various restricted models that pose, for example, communication or memory constraints. In more than one occasion, the known optimal solution boils down to counting collisions among the drawn samples (each two samples that have the same value add one to the count). This idea dates back to the first uniformity tester, and was coined the name "collision-based tester". In this paper, we introduce the notion of comparison graphs and use it to formally define a generalized collision-based tester. Roughly speaking, the edges of the graph indicate the tester which pairs of samples should be compared (that is, the original tester is induced by a clique, where all pairs are being compared). We prove a structural theorem that gives a sufficient condition for a comparison graph to induce a good uniformity tester. As an application, we develop a generic method to test uniformity, and devise nearly-optimal uniformity testers under various computational constraints. We improve and simplify a few known results, and introduce a new constrained model in which the method also produces an efficient tester. The idea behind our method is to translate computational constraints of a certain model to ones on the comparison graph, which paves the way to finding a good graph: a set of comparisons allowed by the model that suffice to test for uniformity. We believe that in future consideration of uniformity testing in new models, our method can be used to obtain efficient testers with minimal effort.
Cite as

Uri Meir. Comparison Graphs: A Unified Method for Uniformity Testing. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 17:1-17:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{meir:LIPIcs.ITCS.2021.17,
  author =	{Meir, Uri},
  title =	{{Comparison Graphs: A Unified Method for Uniformity Testing}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.17},
  URN =		{urn:nbn:de:0030-drops-135560},
  doi =		{10.4230/LIPIcs.ITCS.2021.17},
  annote =	{Keywords: Distribution Testing, Uniformity Testing, Distributed Algorithms, Streaming Algorithms, Comparison Graphs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.40
On the Communication Complexity of Key-Agreement Protocols

Authors: Iftach Haitner, Noam Mazor, Rotem Oshman, Omer Reingold, and Amir Yehudayoff

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
Key-agreement protocols whose security is proven in the random oracle model are an important alternative to protocols based on public-key cryptography. In the random oracle model, the parties and the eavesdropper have access to a shared random function (an "oracle"), but the parties are limited in the number of queries they can make to the oracle. The random oracle serves as an abstraction for black-box access to a symmetric cryptographic primitive, such as a collision resistant hash. Unfortunately, as shown by Impagliazzo and Rudich [STOC '89] and Barak and Mahmoody [Crypto '09], such protocols can only guarantee limited secrecy: the key of any l-query protocol can be revealed by an O(l^2)-query adversary. This quadratic gap between the query complexity of the honest parties and the eavesdropper matches the gap obtained by the Merkle's Puzzles protocol of Merkle [CACM '78]. In this work we tackle a new aspect of key-agreement protocols in the random oracle model: their communication complexity. In Merkle's Puzzles, to obtain secrecy against an eavesdropper that makes roughly l^2 queries, the honest parties need to exchange Omega(l) bits. We show that for protocols with certain natural properties, ones that Merkle's Puzzle has, such high communication is unavoidable. Specifically, this is the case if the honest parties' queries are uniformly random, or alternatively if the protocol uses non-adaptive queries and has only two rounds. Our proof for the first setting uses a novel reduction from the set-disjointness problem in two-party communication complexity. For the second setting we prove the lower bound directly, using information-theoretic arguments. Understanding the communication complexity of protocols whose security is proven (in the random-oracle model) is an important question in the study of practical protocols. Our results and proof techniques are a first step in this direction.
Cite as

Iftach Haitner, Noam Mazor, Rotem Oshman, Omer Reingold, and Amir Yehudayoff. On the Communication Complexity of Key-Agreement Protocols. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 40:1-40:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{haitner_et_al:LIPIcs.ITCS.2019.40,
  author =	{Haitner, Iftach and Mazor, Noam and Oshman, Rotem and Reingold, Omer and Yehudayoff, Amir},
  title =	{{On the Communication Complexity of Key-Agreement Protocols}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.40},
  URN =		{urn:nbn:de:0030-drops-101335},
  doi =		{10.4230/LIPIcs.ITCS.2019.40},
  annote =	{Keywords: key agreement, random oracle, communication complexity, Merkle's puzzles}
}
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