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Combinatorial constructions of repairable ramp schemes
Cryptography and Communications ( IF 1.4 ) Pub Date : 2024-01-17 , DOI: 10.1007/s12095-024-00695-1
Jinghui Zhao , Xiuling Shan , Zihong Tian

A repairable ramp scheme is a ramp scheme in which a player can securely reconstruct a lost share with the help from a subset of players. This will take place without the participation of the dealer who set up the scheme. The repairing protocol should not compromise the security of the ramp scheme. Distribution designs were introduced by Stinson and Wei (Des. Codes Cryptogr. 86, 195–210 2018) and can be used to construct repairable ramp schemes. In this paper, we first give the definitions of a \(\varvec{(\tau _{1},\tau _{2},l_{1},l_{2})}\)-distribution design and a repairable ramp scheme. And we use anti-Pasch Steiner triple systems as distribution designs to construct repairable ramp schemes. We determine the existence of an anti-Pasch Steiner triple system (QFSTS\(\varvec{(v)}\)) with a minimum basic repairing set for \(\varvec{v\equiv 1,3\pmod 6}\), \(\varvec{v\geqslant 9}\) and \(\varvec{v\ne 13}\). Then we obtain a \(\varvec{(2,4,n,3)}\)-repairable ramp scheme containing \(\varvec{n}\) players with \(\varvec{\lceil \frac{2v}{3}\rceil \leqslant n\leqslant \frac{v(v-1)}{6}}\).



中文翻译:

可修复坡道方案的组合施工

可修复斜坡方案是一种玩家可以在一部分玩家的帮助下安全地重建丢失份额的斜坡方案。这将在没有制定该计划的经销商参与的情况下进行。修复协议不应损害斜坡方案的安全性。分布设计由 Stinson 和 Wei 提出(Des. Codes Cryptogr. 86, 195–210 2018),可用于构建可修复的坡道方案。在本文中,我们首先给出\(\varvec{(\tau _{1},\tau _{2},l_{1},l_{2})}\)分布设计和可修复的定义坡道方案。我们使用反帕施斯坦纳三重系统作为分布设计来构建可修复的坡道方案。我们确定存在一个反 Pasch Steiner 三重系统 (QFSTS \(\varvec{(v)}\) ),其最小基本修复集为\(\varvec{v\equiv 1,3\pmod 6}\)\(\varvec{v\geqslant 9}\)\(\varvec{v\ne 13}\)。然后我们获得一个\(\varvec{(2,4,n,3)}\)可修复的斜坡方案,其中包含\(\varvec{n}\)个玩家,且\(\varvec{\lceil \frac{2v}{ 3}\rceil \leqslant n\leqslant \frac{v(v-1)}{6}}\)

更新日期:2024-01-18
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