Paper 2023/959

Randomness Recoverable Secret Sharing Schemes

Mohammad Hajiabadi, University of Waterloo
Shahram Khazaei, Sharif University of Technology
Behzad Vahdani, Sharif University of Technology

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 $\mathsf{AC}^0$) 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 $\mathsf{AC}^0$ 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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Published elsewhere. Leibniz International Proceedings in Informatics (LIPIcs)
Secret sharingRandomness recovery
Contact author(s)
mdhajiabadi @ uwaterloo ca
shahram khazaei @ sharif ir
vahdani behzad @ proton me
2023-06-20: approved
2023-06-19: received
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      author = {Mohammad Hajiabadi and Shahram Khazaei and Behzad Vahdani},
      title = {Randomness Recoverable Secret Sharing Schemes},
      howpublished = {Cryptology ePrint Archive, Paper 2023/959},
      year = {2023},
      note = {\url{}},
      url = {}
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