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Randomness Recoverable Secret Sharing Schemes

Authors Mohammad Hajiabadi, Shahram Khazaei , Behzad Vahdani

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Mohammad Hajiabadi
  • Cheriton School of Computer Science, University of Waterloo, Canada
Shahram Khazaei
  • Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran
Behzad Vahdani
  • Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

Acknowledgements

We would like to thank Sorush Bahariyan for bringing Fact 1 to our attention and Motahareh Gharahi for fruitful discussions on the proof of Theorem 20.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.ITC.2023.12

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.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
  • Security and privacy → Mathematical foundations of cryptography
Keywords
  • Secret sharing
  • Randomness recovery

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