摘要
本文参考前人对于零知识证明问题相关研究，得出了若干设计协议的结论和方式。在此基础上，以降低零知识证明协议的欺骗概率为目标，使用离散对数问题作为数学支撑，结合分割选择技术作为基础进行设计。在最终验证环节引入一个随机数作为创新点，以及分割选择验证环节采取相邻数作差更为复杂的协议算法，设计出一种新式的零知识证明协议。经过对多种情况的假设进行推导，得到不同前提下的欺骗方案设计，运用概率积事件求出最终欺骗概率，与前人的成果进行比较，达成降低欺骗概率的目标。针对此协议还提出了个性化设计方案以降低协议欺骗概率，以及给出未来协议的应用和发展方向。
关键词： 零知识证明；离散对数；密码学
Abstract
In this paper, some conclusions and methods of designing protocols are obtained by referring to previous researches on zero-knowledge proof. On this basis, aiming at reducing the deception probability of the zero-knowledge proof protocol, the discrete logarithm problem is used as the mathematical support and the cut and choose technique is used as the basis for the design. A new zero-knowledge proof protocol is designed by introducing a random number as the innovation point in the final verification process and using a more complicated protocol algorithm to cut and choose process. After deducing the hypothesis of various situations, the deception scheme design under different premises is obtained. The final deception probability is obtained by using probability product events, and the goal of reducing the deception probability is achieved by comparing with the previous achievements. A personalized design scheme is proposed to reduce the probability of deception, and the future application and development direction of the protocol are given.
Key words： Zero-knowledge proof; Discrete logarithm; Cryptography
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