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 known threshold change regimes that are realized by (optimal) TCSS schemes or (optimal) uTCSS schemes. In this work, by combining the frequently used two methods in previous constructions: folding shares of a given secret sharing scheme and packing shares of multiple secret sharing schemes, we construct an optimal TCSS scheme and an optimal uTCSS scheme with a new threshold change regime, respectively. This helps us determine the full threshold change range that 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.

设计了一种阈值可变秘密共享（TCSS）方案，用于在经销商向参与者分配份额后将隐私阈值和重建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）方案是阈值可更改为多个新的阈值对。我们专注于在没有经销商的情况下与外部对手和参与者之间缺乏安全渠道的阈值可变性。有一些已知的阈值变化机制是通过（最优）TCSS 方案或（最优）uTCSS 方案实现的。在这项工作中，通过结合以前构造中经常使用的两种方法：给定秘密共享方案的折叠份额和打包共享多个秘密共享方案，我们分别构建了一个最优 TCSS 方案和一个具有新阈值变化机制的最优 uTCSS 方案。这有助于我们分别确定最佳 TCSS 方案和最佳 uTCSS 方案可以实现的完整阈值变化范围。此外，我们构建了一些接近最优的 TCSS 方案，以表明 TCSS 方案的整个阈值变化范围（不需要最优性）完全被我们的接近最优 TCSS 方案的阈值变化机制以及最优 TCSS 方案的整个阈值变化范围所覆盖.