Abstract
We propose a computationally secure and non-interactive verifiable secret sharing scheme that can be efficiently constructed from any monotone Boolean circuit. By non-interactive we mean that the dealer needs to be active only once, where he posts a public message as well as a private message to each shareholder. In the random oracle model, we can even avoid interaction between shareholders. By efficient, we mean that we avoid generic zero-knowledge techniques. Such efficient constructions were previously only known from linear secret sharing schemes (LSSS). It is believed that the class of access structures that can be handled with polynomial size LSSS is incomparable to the class that can be recognized by polynomial size monotone circuits, so in this sense we extend the class of access structures with efficient and non-interactive VSS.
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Notes
- 1.
However, since there are doubly exponentially many (families of) access structures, an easy counting argument shows that we cannot hope to handle all access structures with polynomial time sharing algorithms.
- 2.
On the way to our result, as a secondary contribution, we also prove that the construction of [VNS+03] satisfies a strong, simulation based notion of privacy, while the original paper only argues for a weaker, “one-way” definition of privacy.
- 3.
In case where no trusted party exists to run this setup, a secure computation protocol can be used instead. We note that our setup algorithm will output an RSA modulus, and that several efficient protocols for this task exist, depending on the desired security guarantees and threshold.
- 4.
(Note that the scheme would not be secure if the adversary could make 2 CPA queries, since in that case it could recover k in the same way as the reduction does.).
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Bai, G., Damgård, I., Orlandi, C., Xia, Y. (2016). Non-Interactive Verifiable Secret Sharing for Monotone Circuits. In: Pointcheval, D., Nitaj, A., Rachidi, T. (eds) Progress in Cryptology – AFRICACRYPT 2016. AFRICACRYPT 2016. Lecture Notes in Computer Science(), vol 9646. Springer, Cham. https://doi.org/10.1007/978-3-319-31517-1_12
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