A New Metric and Its Scheme Construction for Evolving 2-Threshold Secret Sharing Schemes

05/21/2022

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by   Wei Yan, et al.

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Evolving secret sharing schemes do not require prior knowledge of the number of parties n and n may be infinitely countable. It is known that the evolving 2-threshold secret sharing scheme and prefix coding of integers have a one-to-one correspondence. However, it is not known what prefix coding of integers to use to construct the scheme better. In this paper, we propose a new metric K_Σ for evolving 2-threshold secret sharing schemes Σ. We prove that the metric K_Σ≥ 1.5 and construct a new prefix coding of integers, termed λ code, to achieve the metric K_Λ=1.59375. Thus, it is proved that the range of the metric K_Σ for the optimal (2,∞)-threshold secret sharing scheme is 1.5≤ K_Σ≤1.59375. In addition, the reachable lower bound of the sum of share sizes for (2,n)-threshold secret sharing schemes is proved.