Secret sharing schemes based on min-entropies
Secret sharing schemes based on min-entropies
复制标题
DOI：
10.1109/isit.2014.6874863
复制
发表时间：
2014-01
期刊：
影响因子：
--
通讯作者：
Mitsugu Iwamoto;Junji Shikata
中科院分区：
文献类型：
--
作者：
Mitsugu Iwamoto;Junji Shikata
在安全性和共享大小由（条件）最小熵度量的情况下，讨论了秘密共享方案（SSSs）的基本结果。本文首先形式化了一个基于（条件）Rε <$nyi熵的SSSS的统一框架，其中包括基于Shannon熵和最小熵等的SSSS作为特例。通过基于岩本-志方介绍的技术推导出以Rέnyi熵表示的股票规模下限，我们以统一的方式获得了以最小熵和香农熵衡量的股票规模下限。作为本文的主要贡献，我们在几个重要的条件下，给出了基于极小熵的非完美SSS的存在性结果。我们首先证明了对于任意二进制秘密信息和任意单调访问结构，存在一个非完美的SSS。此外，对任意整数k和n（k ≤ n），证明了即使秘密的分布不是均匀分布，也存在理想的非完美（k，n）门限方案。
Fundamental results on secret sharing schemes (SSSs) are discussed in the setting where security and share size are measured by (conditional) min-entropies. We first formalize a unified framework of SSSs based on (conditional) Rέnyi entropies, which includes SSSs based on Shannon and min entropies etc. as special cases. By deriving the lower bound of share sizes in terms of Rέnyi entropies based on the technique introduced by Iwamoto-Shikata, we obtain the lower bounds of share sizes measured by min entropies as well as by Shannon entropies in a unified manner. As the main contributions of this paper, we show two existential results of non-perfect SSSs based on min-entropies under several important settings. We first show that there exists a nonperfect SSS for arbitrary binary secret information and arbitrary monotone access structure. In addition, for every integers k and n (k ≤ n), we prove that the ideal non-perfect (k, n)-threshold scheme exists even if the distribution of the secret is not uniformly distributed.