Secure Construction for Nonlinear Function Threshold Ramp Secret Sharing
Secure Construction for Nonlinear Function Threshold Ramp Secret Sharing
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DOI：
10.1109/isit.2007.4557361
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
Maki Yoshida;T. Fujiwara
中科院分区：
文献类型：
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作者：
Maki Yoshida;T. Fujiwara
阈值斜坡秘密共享（TRSS）方案有两种类型：线性函数斜坡和非线性函数斜坡。线性（相应地，非线性）函数TRSS方案线性地（相应地，非线性地）揭示秘密信息。关于线性方案已有很多研究，并且已经提出了各种安全且高效的构造。相比之下，非线性函数方案的概念是最近才引入的，并且之前的任何构造要么不安全，要么效率低下。本文首先指出了之前不安全构造的缺陷，然后提出了第一个安全且高效的构造。所提出的构造能够实现\(H(V_i) \neq H(S)\)，而在之前的安全构造中\(H(V_i)=H(S)\)，其中\(H(V_i)\)和\(H(S)\)分别是每个份额和秘密的熵。
There are two types of threshold ramp secret sharing (TRSS) schemes: Linear function ramp and nonlinear function ramp. A linear (resp. nonlinear) function TRSS scheme reveals information of the secret linearly (resp. nonlinearly). There are many studies on the linear ones and various secure and efficient constructions have been proposed. In contrast, the notion of the nonlinear function scheme was recently introduced, and any previous construction is either insecure or inefficient. This paper first points out defects of the previous insecure construction, and then presents the first secure and efficient construction. The proposed construction can achieves H(V i) H(S) while in the previous secure construction H(V i) = H(S) where H(V i) and H(S) are the entropies of each share and the secret, respectively.