7 Search Results for "Yankovitz, Tal"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.17
Spectral Refutations of Semirandom k-LIN over Larger Fields

Authors: Nicholas Kocurek and Peter Manohar

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the problem of strongly refuting semirandom k-LIN(𝔽) instances: systems of k-sparse inhomogeneous linear equations over a finite field 𝔽. For the case of 𝔽 = 𝔽₂, this is the well-studied problem of refuting semirandom instances of k-XOR, where the works of [Venkatesan Guruswami et al., 2022; Jun-Ting Hsieh et al., 2023] establish a tight trade-off between runtime and clause density for refutation: for any choice of a parameter 𝓁, they give an n^{O(𝓁)}-time algorithm to certify that there is no assignment that can satisfy more than 1/2 + ε-fraction of constraints in a semirandom k-XOR instance, provided that the instance has O(n)⋅(n/𝓁)^{k/2 - 1} log n/ε⁴ constraints, and the work of [Pravesh K. Kothari et al., 2017] provides good evidence that this tight up to a polylog(n) factor via lower bounds for the Sum-of-Squares hierarchy. However, for larger fields, the only known results for this problem are established via black-box reductions to the case of 𝔽₂, resulting in a |𝔽|^{3k} gap between the current best upper and lower bounds. In this paper, we give an algorithm for refuting semirandom k-LIN(𝔽) instances with the "correct" dependence on the field size |𝔽|. For any choice of a parameter 𝓁, our algorithm runs in (|𝔽|)^O(𝓁)-time and strongly refutes semirandom k-LIN(𝔽) instances with at least O(n) ⋅ (|𝔽^*| n/𝓁) ^{k/2 - 1} log(n|𝔽^*|)/ε⁴ constraints. We give good evidence that this dependence on the field size |𝔽| is optimal by proving a lower bound for the Sum-of-Squares hierarchy that matches this threshold up to a polylog(n |𝔽^*|) factor. Our results also extend beyond finite fields to the more general case of ℤ_m and arbitrary finite Abelian groups. Our key technical innovation is a generalization of the "𝔽₂ Kikuchi matrices" of [Alexander S. Wein et al., 2019; Venkatesan Guruswami et al., 2022] to larger fields, and finite Abelian groups more generally.
Cite as

Nicholas Kocurek and Peter Manohar. Spectral Refutations of Semirandom k-LIN over Larger Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kocurek_et_al:LIPIcs.APPROX/RANDOM.2025.17,
  author =	{Kocurek, Nicholas and Manohar, Peter},
  title =	{{Spectral Refutations of Semirandom k-LIN over Larger Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.17},
  URN =		{urn:nbn:de:0030-drops-243834},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.17},
  annote =	{Keywords: Spectral Algorithms, CSP Refutation, Kikuchi Matrices}
}
Document
DOI: 10.4230/LIPIcs.ITC.2025.12
Key-Agreement with Perfect Completeness from Random Oracles

Authors: Noam Mazor

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract
In the Random Oracle Model (ROM) all parties have oracle access to a common random function, and the parties are limited in the number of queries they can make to the oracle. The Merkle’s Puzzles protocol, introduced by Merkle [CACM '78], is a key-agreement protocol in the ROM with a quadratic gap between the query complexity of the honest parties and the eavesdropper. This quadratic gap is known to be optimal, by the works of Impagliazzo and Rudich [STOC ’89] and Barak and Mahmoody [Crypto ’09]. When the oracle function is injective or a permutation, Merkle’s Puzzles has perfect completeness. That is, it is certain that the protocol results in agreement between the parties. However, without such an assumption on the random function, there is a small error probability, and the parties may end up holding different keys. This fact raises the question: Is there a key-agreement protocol with perfect completeness and super-linear security in the ROM? In this paper we give a positive answer to the above question, showing that changes to the query distribution of the parties in Merkle’s Puzzles, yield a protocol with perfect completeness and roughly the same security.
Cite as

Noam Mazor. Key-Agreement with Perfect Completeness from Random Oracles. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mazor:LIPIcs.ITC.2025.12,
  author =	{Mazor, Noam},
  title =	{{Key-Agreement with Perfect Completeness from Random Oracles}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{12:1--12:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.12},
  URN =		{urn:nbn:de:0030-drops-243628},
  doi =		{10.4230/LIPIcs.ITC.2025.12},
  annote =	{Keywords: Key-Agreement, Random Oracle, Merkle’s Puzzles, Perfect Completeness}
}
Document
DOI: 10.4230/LIPIcs.ITC.2025.1
Amortized Locally Decodable Codes for Insertions and Deletions

Authors: Jeremiah Blocki and Justin Zhang

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract
Locally Decodable Codes (LDCs) are error correcting codes which permit the recovery of any single message symbol with a low number of queries to the codeword (the locality). Traditional LDC tradeoffs between the rate, locality, and error tolerance are undesirable even in relaxed settings where the encoder/decoder share randomness or where the channel is resource-bounded. Recent work by Blocki and Zhang initiated the study of Hamming amortized Locally Decodable Codes (aLDCs), which allow the local decoder to amortize their number of queries over the recovery of a small subset of message symbols. Surprisingly, Blocki and Zhang construct asymptotically ideal (constant rate, constant amortized locality, and constant error tolerance) Hamming aLDCs in private-key and resource-bounded settings. While this result overcame previous barriers and impossibility results for Hamming LDCs, it is not clear whether the techniques extend to Insdel LDCs. Constructing Insdel LDCs which are resilient to insertion and/or deletion errors is known to be even more challenging. For example, Gupta (STOC'24) proved that no Insdel LDC with constant rate and error tolerance exists even in relaxed settings. Our first contribution is to provide a Hamming-to-Insdel compiler which transforms any amortized Hamming LDC that satisfies a particular property (consecutive interval querying) to amortized Insdel LDC while asymptotically preserving the rate, error tolerance and amortized locality. Prior Hamming-to-Insdel compilers of Ostrovsky and Paskin-Cherniavsky (ICITS'15) and Block et al. (FSTTCS'20) worked for arbitrary Hamming LDCs, but incurred an undesirable polylogarithmic blow-up in the locality. Our second contribution is a construction of an ideal amortized Hamming LDC which satisfies our special property (consecutive interval querying) in the relaxed settings where the sender/receiver share randomness or where the channel is resource bounded. Taken together, we obtain ideal Insdel aLDCs in private-key and resource-bounded settings with constant amortized locality, constant rate and constant error tolerance. This result is surprising in light of Gupta’s (STOC'24) impossibility result which demonstrates a strong separation between locality and amortized locality for Insdel LDCs.
Cite as

Jeremiah Blocki and Justin Zhang. Amortized Locally Decodable Codes for Insertions and Deletions. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blocki_et_al:LIPIcs.ITC.2025.1,
  author =	{Blocki, Jeremiah and Zhang, Justin},
  title =	{{Amortized Locally Decodable Codes for Insertions and Deletions}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{1:1--1:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.1},
  URN =		{urn:nbn:de:0030-drops-243518},
  doi =		{10.4230/LIPIcs.ITC.2025.1},
  annote =	{Keywords: Amortized Locally Decodable Codes, Insertion and Deletion Errors}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.88
Detecting and Correcting Computationally Bounded Errors: A Simple Construction Under Minimal Assumptions

Authors: Jad Silbak and Daniel Wichs

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We study error detection and error correction in a computationally bounded world, where errors are introduced by an arbitrary polynomial time adversarial channel. We consider codes where the encoding procedure uses random coins and define two distinct variants: (1) in randomized codes, fresh randomness is chosen during each encoding operation and is unknown a priori, while (2) in self-seeded codes, the randomness of the encoding procedure is fixed once upfront and is known to the adversary. In both cases, the randomness need not be known to the decoding procedure, and there is no trusted common setup between the encoder and decoder. The encoding and decoding algorithms are efficient and run in some fixed polynomial time, independent of the run time of the adversary. The parameters of standard codes for worst-case (inefficient) errors are limited by the Singleton bound: for rate R it is not possible to detect more than a 1-R fraction of errors, or uniquely correct more than a (1-R)/2 fraction of errors, and efficient codes matching this bound exist for sufficiently large alphabets. In the computationally bounded setting, we show that going beyond the Singleton bound implies one-way functions in the case of randomized codes and collision-resistant hash functions in the case of self-seeded codes. We construct randomized and self-seeded codes under these respective minimal assumptions with essentially optimal parameters over a constant-sized alphabet: - Detection: the codes have a rate R ≈ 1 while detecting a ρ ≈ 1 fraction of errors. - Correction: for any ρ < 1/2, the codes uniquely correct a ρ fraction of errors with rate R ≈ 1-ρ. Codes for computationally bounded errors were studied in several prior works starting with Lipton (STACS '94), but all such works either: (a) need some trusted common setup (e.g., public-key infrastructure, common reference string) between the encoder and decoder, or (b) only handle channels whose complexity is a prior bounded below that of the code.
Cite as

Jad Silbak and Daniel Wichs. Detecting and Correcting Computationally Bounded Errors: A Simple Construction Under Minimal Assumptions. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 88:1-88:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{silbak_et_al:LIPIcs.ITCS.2025.88,
  author =	{Silbak, Jad and Wichs, Daniel},
  title =	{{Detecting and Correcting Computationally Bounded Errors: A Simple Construction Under Minimal Assumptions}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{88:1--88:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.88},
  URN =		{urn:nbn:de:0030-drops-227167},
  doi =		{10.4230/LIPIcs.ITCS.2025.88},
  annote =	{Keywords: Error Correction, One-Way Functions, Collision Resistant Hashing}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.8
Asymptotically-Good RLCCs with (log n)^(2+o(1)) Queries

Authors: Gil Cohen and Tal Yankovitz

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
Recently, Kumar and Mon reached a significant milestone by constructing asymptotically good relaxed locally correctable codes (RLCCs) with poly-logarithmic query complexity. Specifically, they constructed n-bit RLCCs with O(log^{69} n) queries. Their construction relies on a clever reduction to locally testable codes (LTCs), capitalizing on recent breakthrough works in LTCs. As for lower bounds, Gur and Lachish (SICOMP 2021) proved that any asymptotically-good RLCC must make Ω̃(√{log n}) queries. Hence emerges the intriguing question regarding the identity of the least value 1/2 ≤ e ≤ 69 for which asymptotically-good RLCCs with query complexity (log n)^{e+o(1)} exist. In this work, we make substantial progress in narrowing the gap by devising asymptotically-good RLCCs with a query complexity of (log n)^{2+o(1)}. The key insight driving our work lies in recognizing that the strong guarantee of local testability overshoots the requirements for the Kumar-Mon reduction. In particular, we prove that we can replace the LTCs by "vanilla" expander codes which indeed have the necessary property: local testability in the code’s vicinity.
Cite as

Gil Cohen and Tal Yankovitz. Asymptotically-Good RLCCs with (log n)^(2+o(1)) Queries. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cohen_et_al:LIPIcs.CCC.2024.8,
  author =	{Cohen, Gil and Yankovitz, Tal},
  title =	{{Asymptotically-Good RLCCs with (log n)^(2+o(1)) Queries}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.8},
  URN =		{urn:nbn:de:0030-drops-204045},
  doi =		{10.4230/LIPIcs.CCC.2024.8},
  annote =	{Keywords: Relaxed locally decodable codes, Relxaed locally correctable codes, RLCC, RLDC}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.44
LCC and LDC: Tailor-Made Distance Amplification and a Refined Separation

Authors: Gil Cohen and Tal Yankovitz

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
The Alon-Edmonds-Luby distance amplification procedure (FOCS 1995) is an algorithm that transforms a code with vanishing distance to a code with constant distance. AEL was invoked by Kopparty, Meir, Ron-Zewi, and Saraf (J. ACM 2017) for obtaining their state-of-the-art LDC, LCC and LTC. Cohen and Yankovitz (CCC 2021) devised a procedure that can amplify inverse-polynomial distances, exponentially extending the regime of distances that can be amplified by AEL. However, the improved procedure only works for LDC and assuming rate 1-1/(poly log n). In this work we devise a distance amplification procedure for LCC with inverse-polynomial distances even for vanishing rate 1/(poly log log n). For LDC, we obtain a more modest improvement and require rate 1-1/(poly log log n). Thus, the tables have turned and it is now LCC that can be better amplified. Our key idea for accomplishing this, deviating from prior work, is to tailor the distance amplification procedure to the code at hand. Our second result concerns the relation between linear LDC and LCC. We prove the existence of linear LDC that are not LCC, qualitatively extending a separation by Kaufman and Viderman (RANDOM 2010).
Cite as

Gil Cohen and Tal Yankovitz. LCC and LDC: Tailor-Made Distance Amplification and a Refined Separation. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 44:1-44:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cohen_et_al:LIPIcs.ICALP.2022.44,
  author =	{Cohen, Gil and Yankovitz, Tal},
  title =	{{LCC and LDC: Tailor-Made Distance Amplification and a Refined Separation}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{44:1--44:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.44},
  URN =		{urn:nbn:de:0030-drops-163858},
  doi =		{10.4230/LIPIcs.ICALP.2022.44},
  annote =	{Keywords: Locally Correctable Codes, Locally Decodable Codes, Distance Amplifications}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.1
Rate Amplification and Query-Efficient Distance Amplification for Linear LCC and LDC

Authors: Gil Cohen and Tal Yankovitz

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
The main contribution of this work is a rate amplification procedure for LCC. Our procedure converts any q-query linear LCC, having rate ρ and, say, constant distance to an asymptotically good LCC with q^poly(1/ρ) queries. Our second contribution is a distance amplification procedure for LDC that converts any linear LDC with distance δ and, say, constant rate to an asymptotically good LDC. The query complexity only suffers a multiplicative overhead that is roughly equal to the query complexity of a length 1/δ asymptotically good LDC. This improves upon the poly(1/δ) overhead obtained by the AEL distance amplification procedure [Alon and Luby, 1996; Alon et al., 1995]. Our work establishes that the construction of asymptotically good LDC and LCC is reduced, with a minor overhead in query complexity, to the problem of constructing a vanishing rate linear LCC and a (rapidly) vanishing distance linear LDC, respectively.
Cite as

Gil Cohen and Tal Yankovitz. Rate Amplification and Query-Efficient Distance Amplification for Linear LCC and LDC. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 1:1-1:57, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cohen_et_al:LIPIcs.CCC.2021.1,
  author =	{Cohen, Gil and Yankovitz, Tal},
  title =	{{Rate Amplification and Query-Efficient Distance Amplification for Linear LCC and LDC}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{1:1--1:57},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.1},
  URN =		{urn:nbn:de:0030-drops-142750},
  doi =		{10.4230/LIPIcs.CCC.2021.1},
  annote =	{Keywords: Locally decodable codes, Locally correctable codes}
}
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