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Documents authored by Wichs, Daniel

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.ITC.2022.10
Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC

Authors: Saikrishna Badrinarayanan, Yuval Ishai, Dakshita Khurana, Amit Sahai, and Daniel Wichs

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

Abstract
We provide counterexamples to the "dream" version of Yao’s XOR Lemma. In particular, we put forward explicit candidates for hard predicates, such that the advantage of predicting the XOR of many independent copies does not decrease beyond some fixed negligible function, even as the number of copies gets arbitrarily large. We provide two such constructions: - Our first construction is in the ideal obfuscation model (alternatively, assuming virtual black-box obfuscation for a concrete class of circuits). It develops a general framework that may be of broader interest, and allows us to embed an instance of a resettably-secure multiparty computation protocol into a one-way function. Along the way, we design the first resettably-secure multiparty computation protocol for general functionalities in the plain model with super-polynomial simulation, under standard assumptions. - The second construction relies on public-coin differing-inputs obfuscation (PCdiO) along with a certain form of hash-function security called extended second-preimage resistance (ESPR). It starts with a previously known counterexample to the dream direct-product hardness amplification based on ESPR, and uses PCdiO to upgrade it into a counterexample for the XOR lemma. Prior to our work, even completely heuristic counterexamples of this type were not known.
Cite as

Saikrishna Badrinarayanan, Yuval Ishai, Dakshita Khurana, Amit Sahai, and Daniel Wichs. Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{badrinarayanan_et_al:LIPIcs.ITC.2022.10,
  author =	{Badrinarayanan, Saikrishna and Ishai, Yuval and Khurana, Dakshita and Sahai, Amit and Wichs, Daniel},
  title =	{{Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{10:1--10:21},
  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.2022.10},
  URN =		{urn:nbn:de:0030-drops-164885},
  doi =		{10.4230/LIPIcs.ITC.2022.10},
  annote =	{Keywords: XOR Lemma, Resettable MPC, Obfuscation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.56
Small-Box Cryptography

Authors: Yevgeniy Dodis, Harish Karthikeyan, and Daniel Wichs

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

Abstract
One of the ultimate goals of symmetric-key cryptography is to find a rigorous theoretical framework for building block ciphers from small components, such as cryptographic S-boxes, and then argue why iterating such small components for sufficiently many rounds would yield a secure construction. Unfortunately, a fundamental obstacle towards reaching this goal comes from the fact that traditional security proofs cannot get security beyond 2^{-n}, where n is the size of the corresponding component. As a result, prior provably secure approaches - which we call "big-box cryptography" - always made n larger than the security parameter, which led to several problems: (a) the design was too coarse to really explain practical constructions, as (arguably) the most interesting design choices happening when instantiating such "big-boxes" were completely abstracted out; (b) the theoretically predicted number of rounds for the security of this approach was always dramatically smaller than in reality, where the "big-box" building block could not be made as ideal as required by the proof. For example, Even-Mansour (and, more generally, key-alternating) ciphers completely ignored the substitution-permutation network (SPN) paradigm which is at the heart of most real-world implementations of such ciphers. In this work, we introduce a novel paradigm for justifying the security of existing block ciphers, which we call small-box cryptography. Unlike the "big-box" paradigm, it allows one to go much deeper inside the existing block cipher constructions, by only idealizing a small (and, hence, realistic!) building block of very small size n, such as an 8-to-32-bit S-box. It then introduces a clean and rigorous mixture of proofs and hardness conjectures which allow one to lift traditional, and seemingly meaningless, "at most 2^{-n}" security proofs for reduced-round idealized variants of the existing block ciphers, into meaningful, full-round security justifications of the actual ciphers used in the real world. We then apply our framework to the analysis of SPN ciphers (e.g, generalizations of AES), getting quite reasonable and plausible concrete hardness estimates for the resulting ciphers. We also apply our framework to the design of stream ciphers. Here, however, we focus on the simplicity of the resulting construction, for which we managed to find a direct "big-box"-style security justification, under a well studied and widely believed eXact Linear Parity with Noise (XLPN) assumption. Overall, we hope that our work will initiate many follow-up results in the area of small-box cryptography.
Cite as

Yevgeniy Dodis, Harish Karthikeyan, and Daniel Wichs. Small-Box Cryptography. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 56:1-56:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dodis_et_al:LIPIcs.ITCS.2022.56,
  author =	{Dodis, Yevgeniy and Karthikeyan, Harish and Wichs, Daniel},
  title =	{{Small-Box Cryptography}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{56:1--56:25},
  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.2022.56},
  URN =		{urn:nbn:de:0030-drops-156527},
  doi =		{10.4230/LIPIcs.ITCS.2022.56},
  annote =	{Keywords: Block Ciphers, S-Box, Cryptography}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ITC.2020
LIPIcs, Volume 163, ITC 2020, Complete Volume

Authors: Yael Tauman Kalai, Adam D. Smith, and Daniel Wichs

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract
LIPIcs, Volume 163, ITC 2020, Complete Volume
Cite as

1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 1-352, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{taumankalai_et_al:LIPIcs.ITC.2020,
  title =	{{LIPIcs, Volume 163, ITC 2020, Complete Volume}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{1--352},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020},
  URN =		{urn:nbn:de:0030-drops-121048},
  doi =		{10.4230/LIPIcs.ITC.2020},
  annote =	{Keywords: LIPIcs, Volume 163, ITC 2020, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ITC.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Yael Tauman Kalai, Adam D. Smith, and Daniel Wichs

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{taumankalai_et_al:LIPIcs.ITC.2020.0,
  author =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{0:i--0:xiv},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.0},
  URN =		{urn:nbn:de:0030-drops-121057},
  doi =		{10.4230/LIPIcs.ITC.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
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