A Linear Construction of Perfect Secret Sharing Schemes
A Linear Construction of Perfect Secret Sharing Schemes
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完美秘密共享方案的线性构造
DOI：
10.1007/bfb0053421
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Marten van Dijk
中科院分区：
文献类型：
--
作者：
Marten van Dijk
本文推广了Brickell [5]的向量空间构造。由Bertilsson [1]引入的这种推广导致了具有合理信息率的完美秘密共享方案，其中每个合格组可以有效地计算秘密。指出了广义构造与线性分组码之间的一一对应关系。事实证明，Massey [15]的最小码字方法是这种构造的特殊情况。对于一般的访问结构，我们提出了一个轮廓的算法，用于确定是否有理数可以实现为信息率通过广义向量空间的建设。如果是，该算法产生一个完美的秘密共享方案与此信息率。作为一个副结果，我们显示了访问结构的对偶性和代码的对偶性之间的对应关系。
In this paper, we generalize the vector space construction due to Brickell [5]. This generalization, introduced by Bertilsson [1], leads to perfect secret sharing schemes with rational information rates in which the secret can be computed efficiently by each qualified group. A one to one correspondence between the generalized construction and linear block codes is stated. It turns out that the approach of minimal codewords by Massey [15] is a special case of this construction. For general access structures we present an outline of an algorithm for determining whether a rational number can be realized as information rate by means of the generalized vector space construction. If so, the algorithm produces a perfect secret sharing scheme with this information rate. As a side-result we show a correspondence between the duality of access structures and the duality of codes.