While the amount of data created and stored continues to increase at striking rates, data protection and concealment increases its importance as a field of scientific study that requires more effort. It is essential to protect critical data at every stage while it is being stored and transferred. One cryptographic tool that is of interest and can be widely used in this medium is zero-knowledge proof systems. This cryptographic structure allows one party to securely guarantee the authenticity and accuracy of the data at hand, without leaking any confidential information during communication. The strength of zero-knowledge protocols is mostly based on a few hard-to-solve problems. There is a need to design more secure and efficient zero-knowledge systems. This need brings the necessity of determining suitable difficult problems to design secure zero-knowledge schemes. In this study, after a brief overview of zero-knowledge proof systems, the relationship of these structures to group-theoretic algorithmic problems and an annotated list of intractable algorithmic problems in group theory are given.
翻译:虽然创建和储存的数据数量继续以惊人的速度增加,但数据保护和隐藏却增加了其作为科学研究领域的重要性,而科学研究领域需要更加努力。在储存和转让时,必须在每个阶段保护关键数据。一个令人感兴趣并可广泛用于这一媒介的加密工具是零知识验证系统。这种加密结构使一方能够保证手头数据的真实性和准确性,在通信过程中不泄露任何机密信息。零知识协议的力量主要基于几个难以解决的问题。需要设计更安全、效率更高的零知识系统。这就需要确定设计保证零知识计划的适当困难问题。在本研究中,在简单概述零知识验证系统之后,给出了这些结构与群体理论的理论中棘手的算法问题和附加说明的清单之间的关系。