AI 中文总结
本文针对后量子环境中预量子签名不安全的问题，研究多范式后量子签名，按范式分类构建N中选T门限方案的工具，还纳入FHE、MPC或ZKP的通用方法。
AI 中文摘要
门限签名方案将签名过程分配给N个参与方中的T个，支持多种应用，且受NIST近期征集的推动。但应用中主流是预量子签名，其效率更高却在后量子环境中不安全。本文研究基于格问题、单向（哈希）函数、密码群作用、同构和多元系统等多种范式的现有后量子签名，按范式对用于从数字签名构建N中选T方案的现有工具进行分类，还纳入基于全同态加密（FHE）、安全多方计算（MPC）或零知识证明（ZKP）的通用方法。
英文摘要
Threshold signature schemes distribute the signing process among $T$ parties out of $N$. They enable a variety of applications and their research is also motivated by a recent NIST call. However, applications are dominated by pre-quantum signatures, which are more efficient but not secure in the post-quantum setting. This paper investigates existing post-quantum signatures, based on a variety of paradigms: lattice problems, one-way (hash) functions, cryptographic group actions, isogenies and multivariate systems. We propose a classification (divided by paradigm) of existing tools that are used to build $T$-out-of-$N$ schemes from digital signatures. We also include general approaches based on FHE, MPC or ZKP.
