Coding Theorems on the Threshold Scheme for a General Source
Coding Theorems on the Threshold Scheme for a General Source
复制标题
一般源阈值方案的编码定理
DOI：
10.1109/tit.2008.921860
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发表时间：
2008
影响因子：
2.5
通讯作者：
H. Koga
中科院分区：
文献类型：
--
作者：
H. Koga
本文讨论了一般信源的（t，m）-门限方案的编码定理，其中m为份额数，t为门限。本文提出的（t，m）-门限方案将n个源输出Xn同时加密为m个份额，并要求满足两个条件：1）Xn是从任意t个份额中复制出来的; 2）从任意t - 1个份额中几乎不泄露Xn的信息。证明了（t，m）-门限方案必须满足一定的不等式，包括概率上的极限不等式.其中一个不等式与用于实现（t，m）阈值方案的交易者所需的公平随机比特的最小长度密切相关。此外，还证明了Shamir门限方案的某种变化形式满足这两个条件。同样的方法也可以用于解决香农密码系统的完全保密性和固定长度信源编码的零译码错误概率的问题。结果表明，表明匡威编码定理的同一类不等式在两种情况下都成立。
In this paper, coding theorems on the (t, m) -threshold scheme for a general source are discussed, where m means the number of the shares and t means a threshold. The (t,m) -threshold scheme treated in this paper encrypts n source outputs Xn to m shares at once and is required to satisfy the two conditions that 1) Xn is reproduced from arbitrary t shares, and 2) almost no information of Xn is revealed from any t - 1 shares. It is shown that the (t,m) -threshold scheme must satisfy certain inequalities including the limit inferiors in probability. One of the inequalities is closely related to the minimum length of the fair random bits needed to a dealer for realizing the (t, m) -threshold scheme. In addition, it is shown that a certain variation of Shamir's threshold scheme meets the two conditions. The same approach can be taken to the problems of Shannon's cipher system with the perfect secrecy and fixed-length source coding with vanishing decoding error probability. It is shown that the same kind of inequalities, which indicate the converse coding theorems, hold in both two cases.
影响因子：
22.7
作者：
SHAMIR, A
通讯作者：
SHAMIR, A