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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)

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.

Cite as

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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  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}
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