The circular external difference family and its strong version, which themselves are of independent combinatorial interest, were proposed as variants of the difference family to construct new unconditionally secure non-malleable threshold schemes. In this paper, we present new results regarding the construction and non-existence of (strong) circular external difference families, thereby solving several open problems on this topic.

翻译：循环外差分族及其强版本本身具有独立的组合学意义，它们作为差分族的变体被提出，用于构造新型无条件安全的非延展门限方案。本文提出了关于（强）循环外差分族构造与不存在性的新结果，从而解决了该领域的若干开放问题。