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DOI: 10.4230/LIPIcs.ITC.2023.12

Randomness Recoverable Secret Sharing Schemes

Authors: Mohammad Hajiabadi, Shahram Khazaei, and Behzad Vahdani

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

Abstract

It is well-known that randomness is essential for secure cryptography. The randomness used in cryptographic primitives is not necessarily recoverable even by the party who can, e.g., decrypt or recover the underlying secret/message. Several cryptographic primitives that support randomness recovery have turned out useful in various applications. In this paper, we study randomness recoverable secret sharing schemes (RR-SSS), in both information-theoretic and computational settings and provide two results. First, we show that while every access structure admits a perfect RR-SSS, there are very simple access structures (e.g., in monotone AC⁰) that do not admit efficient perfect (or even statistical) RR-SSS. Second, we show that the existence of efficient computational RR-SSS for certain access structures in monotone AC⁰ implies the existence of one-way functions. This stands in sharp contrast to (non-RR) SSS schemes for which no such results are known. RR-SSS plays a key role in making advanced attributed-based encryption schemes randomness recoverable, which in turn have applications in the context of designated-verifier non-interactive zero knowledge.

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Mohammad Hajiabadi, Shahram Khazaei, and Behzad Vahdani. Randomness Recoverable Secret Sharing Schemes. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 12:1-12:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hajiabadi_et_al:LIPIcs.ITC.2023.12,
  author =	{Hajiabadi, Mohammad and Khazaei, Shahram and Vahdani, Behzad},
  title =	{{Randomness Recoverable Secret Sharing Schemes}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{12:1--12:25},
  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.2023.12},
  URN =		{urn:nbn:de:0030-drops-183404},
  doi =		{10.4230/LIPIcs.ITC.2023.12},
  annote =	{Keywords: Secret sharing, Randomness recovery}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2022.2

Algebraic Restriction Codes and Their Applications

Authors: Divesh Aggarwal, Nico Döttling, Jesko Dujmovic, Mohammad Hajiabadi, Giulio Malavolta, and Maciej Obremski

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

Abstract

Consider the following problem: You have a device that is supposed to compute a linear combination of its inputs, which are taken from some finite field. However, the device may be faulty and compute arbitrary functions of its inputs. Is it possible to encode the inputs in such a way that only linear functions can be evaluated over the encodings? I.e., learning an arbitrary function of the encodings will not reveal more information about the inputs than a linear combination. In this work, we introduce the notion of algebraic restriction codes (AR codes), which constrain adversaries who might compute any function to computing a linear function. Our main result is an information-theoretic construction AR codes that restrict any class of function with a bounded number of output bits to linear functions. Our construction relies on a seed which is not provided to the adversary. While interesting and natural on its own, we show an application of this notion in cryptography. In particular, we show that AR codes lead to the first construction of rate-1 oblivious transfer with statistical sender security from the Decisional Diffie-Hellman assumption, and the first-ever construction that makes black-box use of cryptography. Previously, such protocols were known only from the LWE assumption, using non-black-box cryptographic techniques. We expect our new notion of AR codes to find further applications, e.g., in the context of non-malleability, in the future.

Cite as

Divesh Aggarwal, Nico Döttling, Jesko Dujmovic, Mohammad Hajiabadi, Giulio Malavolta, and Maciej Obremski. Algebraic Restriction Codes and Their Applications. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{aggarwal_et_al:LIPIcs.ITCS.2022.2,
  author =	{Aggarwal, Divesh and D\"{o}ttling, Nico and Dujmovic, Jesko and Hajiabadi, Mohammad and Malavolta, Giulio and Obremski, Maciej},
  title =	{{Algebraic Restriction Codes and Their Applications}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{2:1--2:15},
  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.2022.2},
  URN =		{urn:nbn:de:0030-drops-155987},
  doi =		{10.4230/LIPIcs.ITCS.2022.2},
  annote =	{Keywords: Algebraic Restriction Codes, Oblivious Transfer, Rate 1, Statistically Sender Private, OT, Diffie-Hellman, DDH}
}

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Randomness Recoverable Secret Sharing Schemes

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Algebraic Restriction Codes and Their Applications

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