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 (AMD) code and construct examples of new variations of external difference families, which are of independent combinatorial interest.

翻译：各类非弹性秘密共享方案的概念已被广泛研究。本文回顾了非弹性秘密共享的现有工作，并提出了一种新颖的基于博弈论的定义。针对特定关系，我们构建了一种无条件安全的非弹性门限方案。为实现这一目标，我们引入了一种新型代数操作检测（AMD）码，并构造了外部差分族新变体的示例，这些变体本身具有独立的组合学意义。