Abstract
In a basic (t,n)-threshold secret sharing scheme the adversary is passive and the security goal is to ensure that unauthorized subsets do not learn any information about the secret. In this paper we consider the case that the corrupted parties submit incorrect shares and there are extra security goals with respect to incorrect shares. We consider two such security requirements: in a (t,n)-threshold robust secret sharing (RSS) scheme we require that the shared secret can be recovered from the set of all n shares even if up to t of them are incorrect; and in a (t,n)-threshold secret sharing scheme with cheating detection (SSCD) property we require to prevent cheaters who try to make another player reconstruct an invalid secret.
We make the following contributions. Firstly, we construct a robust (t,n)-threshold secret sharing (RSS) scheme with the lowest known share size for n = 2t + 1. In our RSS scheme the share size is \(\log_{2}s+\log_{2}\frac{1}{\delta} + n\) bits which is less than the share size of the best known scheme by \(\log_{2}\frac{1}{\delta} + n\) bits. Here log2 s bits denotes secret size and δ denotes error probability in reconstructing the correct secret. We then consider the problem of reducing the size of public information in RSS. We will motivate this problem and propose a scheme that nearly halves the amount of public information. For this we first construct a new variant of Shamir secret sharing scheme and then modify it to provide robustness. The construction achieves the least total share storage/communication among all known threshold robust secret sharing schemes.
The final contribution of this paper is the constriction of an optimal threshold secret sharing with cheating detection property. We propose a scheme that achieves the lower bound on the share size of cheating detection schemes, and hence is optimal. The scheme is the first to achieve the bound without having special requirements.
Financial support for this research was provided in part by Alberta Innovates - Technology Futures, in the Province of Alberta in Canada.
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Jhanwar, M.P., Safavi-Naini, R. (2013). On the Share Efficiency of Robust Secret Sharing and Secret Sharing with Cheating Detection. In: Paul, G., Vaudenay, S. (eds) Progress in Cryptology – INDOCRYPT 2013. INDOCRYPT 2013. Lecture Notes in Computer Science, vol 8250. Springer, Cham. https://doi.org/10.1007/978-3-319-03515-4_12
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