门限方案的组合可修性
Combinatorial Repairability for Threshold Schemes
摘要：
在本文中，我们考虑的方法，其中一个子集的球员在$(k,n)$阈值计划可以“修复”另一个球员的份额的情况下，他们的份额已经丢失或损坏。这将在没有建立该计划的经销商参与的情况下进行。修复协议不应损害阈值方案的（无条件）安全性，并且它应该是高效的，其中效率是根据在修复过程期间交换的信息量来测量的。我们研究了两种修复方法。第一种方法是基于来自\cite{NSG}的“登记协议”，该协议最初被开发为在方案建立之后将新的玩家添加到阈值方案（没有经销商的参与）。第二种方法将“多个份额”分配给每个参与者，如由合适的组合设计定义的。与第一种方法相比，这种方法导致更大的份额，但降低了通信复杂度。
英文摘要：
In this paper, we consider methods whereby a subset of players in a $(k,n)$-threshold scheme can "repair" another player's share in the event that their share has been lost or corrupted. This will take place without the participation of the dealer who set up the scheme. The repairing protocol should not compromise the (unconditional) security of the threshold scheme, and it should be efficient, where efficiency is measured in terms of the amount of information exchanged during the repairing process. We study two approaches to repairing. The first method is based on the "enrollment protocol" from \cite{NSG} which was originally developed to add a new player to a threshold scheme (without the participation of the dealer) after the scheme was set up. The second method distributes "multiple shares" to each player, as defined by a suitable combinatorial design. This method results in larger shares, but lower communication complexity, as compared to the first method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
