基于半欺骗概率的MinRank问题的三遍识别方案
Three-Pass Identification Scheme Based on MinRank Problem with Half Cheating Probability
摘要：
在Asiacrypt 2001中，Courtois基于MinRank问题提出了第一个三遍零知识识别方案。然而，在单轮Courtois的ID方案中，欺骗概率，即，作弊证明者的成功概率为2/3，大于一半。虽然Courtois也提出了一个变体方案，声称有一半的欺骗概率，其安全性没有正式证明，它需要另一个硬度假设上的一个特定的单向函数和验证者总是根据一个特定的非均匀分布产生的挑战。在本文中，我们提出了第一个三遍零知识ID方案的MinRank问题的基础上，欺骗概率正好为每一轮的一半，即使只有两个比特的挑战空间，没有任何额外的假设。在相同的安全级别下，与Curtois相比，我们提出的ID方案需要更少的轮数和更少的总平均通信开销。
英文摘要：
In Asiacrypt 2001, Courtois proposed the first three-pass zero-knowledge identification (ID) scheme based on the MinRank problem. However, in a single round of Courtois' ID scheme, the cheating probability, i.e., the success probability of the cheating prover, is 2/3 which is larger than half. Although Courtois also proposed a variant scheme which is claimed to have half cheating probability, its security is not formally proven and it requires another hardness assumption on a specific one-way function and that verifier always generates challenges according to a specific non-uniform distribution. In this paper, we propose the first three-pass zero-knowledge ID scheme based on the MinRank problem with the cheating probability of exactly half for each round, even with only two-bit challenge space, without any additional assumption. Our proposed ID scheme requires fewer rounds and less total average communications costs compared to Curtois' under the same security level against impersonation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
