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形式作为差分族的变体，被提出用于构造新的无条件安全非弹性门限方案，其本身具有独立的组合学意义。本文给出了（强）循环外差分族在构造与不存在性方面的新结果，从而解决了该领域若干开放问题。