Full threshold change range of threshold changeable secret sharing

Full threshold change range of threshold changeable secret sharing
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DOI：
10.1007/s10623-023-01205-9
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发表时间：
2023-03
期刊：
Designs, Codes and Cryptography
影响因子：
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通讯作者：
Jian Ding;Changlu Lin;Fuchun Lin;Huaxiong Wang
Jian Ding;Changlu Lin;Fuchun Lin;Huaxiong Wang
中科院分区：
其他
文献类型：
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作者：
Jian Ding;Changlu Lin;Fuchun Lin;Huaxiong Wang

文献摘要

相似文献

设计了一种阈值可变秘密共享（TCSS）方案，将隐私阈值和重构阈值的初始阈值对更改为给定的阈值对，而通用阈值可变秘密共享（uTCSS）方案是将阈值更改为多个新阈值对。我们将重点关注具有外部对手和参与者之间缺乏安全通道的无经销商场景中的阈值可变性。有一些已知的阈值变化机制是由（最优）TCSS方案或（最优）uTCSS方案实现的。本文结合以往构建中常用的两种方法：对给定的秘密共享方案进行折叠共享和对多个秘密共享方案进行打包共享，分别构建了具有新阈值变化机制的最优TCSS方案和最优uTCSS方案。这有助于我们确定最优TCSS方案和最优uTCSS方案分别可以实现的完整阈值变化范围。此外，我们构造了一些近最优TCSS方案，证明了TCSS方案的全阈值变化范围（不要求最优性）完全被我们的近最优TCSS方案的阈值变化范围和最优TCSS方案的全阈值变化范围所覆盖。
A threshold changeable secret sharing (TCSS) scheme is designed for changing the initial threshold pair of the privacy threshold and reconstruction threshold to a given threshold pair after the dealer distributes shares to participants, while a universal threshold changeable secret sharing (uTCSS) scheme is threshold changeable to multiple new threshold pairs. We focus on the threshold changeability in a dealer-free scenario with an outside adversary and the absence of secure channels among participants. There are some knownthreshold change regimesthat are realized by (optimal) TCSS schemes or (optimal) uTCSS schemes. In this work, by combining the frequently used two methods in previous constructions:foldingshares of a given secret sharing scheme andpackingshares of multiple secret sharing schemes, we construct an optimal TCSS scheme and an optimal uTCSS scheme with anewthreshold change regime, respectively. This helps us determine thefull threshold change rangethat can be realized by optimal TCSS schemes and optimal uTCSS schemes, respectively. Moreover, we construct some near optimal TCSS schemes to show that the full threshold change range of TCSS schemes (without requiring optimality) is completely covered by the threshold change regimes of our near optimal TCSS schemes together with the full threshold change range of optimal TCSS schemes.