Secret Sharing Schemes Based on Linear Codes Can Be Precisely Characterized by the Relative Generalized Hamming Weight
Secret Sharing Schemes Based on Linear Codes Can Be Precisely Characterized by the Relative Generalized Hamming Weight
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DOI：
10.1587/transfun.e95.a.2067
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发表时间：
2012-11-01
影响因子：
0.5
通讯作者：
Matsumoto, Ryutaroh
中科院分区：
文献类型：
--
作者：
Kurihara, Jun;Uyematsu, Tomohiko;Matsumoto, Ryutaroh
本文利用相对尺寸/长度轮廓（RDLP）和相对广义汉明权（RGHW）精确表征了基于任意线性码的秘密共享方案。我们首先描述秘密向量(s)在右箭头= [s(1)，…]上的模糊Delta(m)。， s(l)]给出m股的线性码的RDLP。我们还用线性码的RGHW刻画了秘密共享方案中的两个阈值t(1)和t(2)。一个显示了任何最多t(1)个共享的集合都不会泄露关于(s)的信息，另一个显示了任何至少t(2)个共享的集合唯一地确定了(s)。结果表明，t(1)和t(2)的两种表征都优于Chen等人用规则最小汉明权导出的表征。此外，本文通过推广强安全门限斜坡方案的定义，刻画了基于线性码的秘密共享方案的强安全性。我们定义了一种具有强安全性的秘密共享方案，即（s(1)）中任意r个元素之间的互信息，…s(l))和任何- r + 1份额总是零。然后，阐明了基于线性码的秘密共享方案总是能够实现α强安全性，其中α值被RGHW精确表征。
This paper precisely characterizes secret sharing schemes based on arbitrary linear codes by using the relative dimension/length profile (RDLP) and the relative generalized Hamming weight (RGHW). We first describe the equivocation Delta(m) of the secret vector (s) over right arrow = [s(1), . . . , s(l)] given m shares in terms of the RDLP of linear codes. We also characterize two thresholds t(1) and t(2) in the secret sharing schemes by the RGHW of linear codes. One shows that any set of at most t(1) shares leaks no information about (s) over right arrow, and the other shows that any set of at least t(2) shares uniquely determines (s) over right arrow. It is clarified that both characterizations for t(1) and t(2) are better than Chen et al.'s ones derived by the regular minimum Hamming weight. Moreover, this paper characterizes the strong security in secret sharing schemes based on linear codes, by generalizing the definition of strongly-secure threshold ramp schemes. We define a secret sharing scheme achieving the alpha-strong security as the one such that the mutual information between any r elements of (s(1), . . . , s(l)) and any alpha - r + 1 shares is always zero. Then, it is clarified that secret sharing schemes based on linear codes can always achieve the alpha-strong security where the value alpha is precisely characterized by the RGHW.