While the amount of data produced and accumulated continues to advance at unprecedented rates, protection and concealment of data increase its prominence as a field of scientific study that requires more action. It is essential to protect privacy-sensitive data at every phase; at rest, at run, and while computations are executed on data. The zero-knowledge proof (ZKP) schemes are a cryptographic tool toward this aim. ZKP allows a party to securely ensure the data's authenticity and precision without revealing confidential or privacy-sensitive information during communication or computation. The power of zero-knowledge protocols is based on intractable problems. There is a requirement to design more secure and efficient zero-knowledge proofs. This demand raises the necessity of determining appropriate intractable problems to develop novel ZKP schemes. In this paper, we present a brief outline of ZKP schemes, the connection of these structures to group-theoretic intractable problems, and annotate a list of intractable problems in group theory that can be employed to devise new ZKP schemes.

翻译：尽管数据产生和积累的速度以空前水平持续增长，数据的保护与隐藏作为一项亟需深化研究的科学领域，其重要性日益凸显。在数据生命周期的每个阶段——静态存储、运行状态以及计算执行过程中，保护隐私敏感数据都至关重要。零知识证明方案正是实现这一目标的密码学工具。该方案允许参与方在通信或计算过程中，在不泄露机密或隐私敏感信息的前提下，安全地验证数据的真实性与精确性。零知识协议的安全性基于不可解问题。设计更安全、更高效的零知识证明方案已成为迫切需求，这进而要求我们甄选适用的不可解问题以开发新型ZKP方案。本文简要概述了零知识证明方案及其与群论中不可解问题的关联，并梳理了可用于设计新型ZKP方案的群论不可解问题清单。