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：圆外差分族及其强版本作为差分族的变体，本身具有独立的组合学价值，最初被提出用于构造新型无条件安全的不可锻造门限方案。本文给出了关于（强）圆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。