Various notions of non-malleable secret sharing schemes have been considered. In this paper, we review the existing work on non-malleable secret sharing and suggest a novel game-based definition. We provide a new construction of an unconditionally secure non-malleable threshold scheme with respect to a specified relation. To do so, we introduce a new type of algebraic manipulation detection code and construct examples of new variations of external difference families, which are of independent combinatorial interest.

中文翻译：

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无条件安全的不可延展的秘密共享和循环外部差异族

已经考虑了不可延展的秘密共享方案的各种概念。在本文中，我们回顾了有关不可延展秘密共享的现有工作，并提出了一种新颖的基于游戏的定义。我们提供了关于指定关系的无条件安全的不可延展阈值方案的新构造。为此，我们引入了一种新型代数操作检测代码，并构造了具有独立组合兴趣的外部差分族新变体的示例。