Two matrices for Blakley's secret sharing scheme
Two matrices for Blakley's secret sharing scheme
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DOI：
10.1109/icc.2012.6364198
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发表时间：
2012-06
期刊：
影响因子：
--
通讯作者：
X. Hei;Xiaojiang Du;Binheng Song
中科院分区：
文献类型：
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作者：
X. Hei;Xiaojiang Du;Binheng Song
这个秘密共享方案是由阿迪·沙米尔和乔治·布莱克利在1979年独立发明的。在（k, n）阈值线性秘密共享方案中，任何k (n)个参与者都可以恢复共享秘密，任何少于k个参与者都不能恢复共享秘密。Shamir的秘密共享方案比Blakley的更受欢迎，尽管前者比后者更复杂。原因是Blakley的方案缺乏确定的、一般的、合适的矩阵。本文给出了两个可用于Blakley秘密共享系统的矩阵。与Shamir方案使用的Vandermonde矩阵相比，这些矩阵中元素的增加速度较慢。进一步，我们提出了最优矩阵问题，并求出了k=2时矩阵的最小极大元素的下界和给定k时矩阵的最小极大元素的上界。
The secret sharing scheme was invented by Adi Shamir and George Blakley independently in 1979. In a (k, n)-threshold linear secret sharing scheme, any k-out-of-n participants could recover the shared secret, and any less than k participants could not recover the secret. Shamir's secret sharing scheme is more popular than Blakley's even though the former is more complex than the latter. The reason is that Blakley's scheme lacks determined, general and suitable matrices. In this paper, we present two matrices that can be used for Blakley's secret sharing system. Compared with the Vandermonde matrix used by Shamir's scheme, the elements in these matrices increase slowly. Furthermore, we formulate the optimal matrix problem and find the lower bound of the minimal maximized element for k=2 and upper bound of the minimal maximized element of matrix for given k.