测量和重新编程技术2.0：多轮菲亚特-沙米尔和更多
The Measure-and-Reprogram Technique 2.0: Multi-Round Fiat-Shamir and More
摘要：
我们回顾了Don、Fehr、Majenz和Schaffner以及Liu和Zhandry最近关于量子随机预言模型（QROM）中$Σ$ -协议的Fiat-Shamir变换的安全性的工作。在这种情况下出现的两个自然的问题是：（1）结果是否扩展到多轮交互式证明的Fiat-Shamir变换，以及（2）Don等人。的$O(q^2)$损失的安全性是最佳的。首先，我们对问题（1）的回答是肯定的。作为解决证明这一结果的技术困难的副产品，我们稍微改进了Don等人的结果，为它配备了更干净的装订和更简单的校样。我们将我们的结果应用到数字签名方案中，表明它可以用来证明QROM中MQDSS等方案的强安全性。作为另一个应用，我们证明了Liu，Wei和Wong的一个非交互OR证明的QROM安全性。对于问题（2），我们通过基于Grover搜索的攻击表明Don et al.的二次安全损失的Fiat-Shamir变换的$Σ$ -协议是最佳的小常数因子。这扩展到我们的新的多轮结果，证明它紧到一个因素，只取决于轮数，即是恒定的任何恒定轮交互式证明。
英文摘要：
We revisit recent works by Don, Fehr, Majenz and Schaffner and by Liu and Zhandry on the security of the Fiat-Shamir transformation of $Σ$-protocols in the quantum random oracle model (QROM). Two natural questions that arise in this context are: (1) whether the results extend to the Fiat-Shamir transformation of multi-round interactive proofs, and (2) whether Don et al.'s $O(q^2)$ loss in security is optimal. Firstly, we answer question (1) in the affirmative. As a byproduct of solving a technical difficulty in proving this result, we slightly improve the result of Don et al., equipping it with a cleaner bound and an even simpler proof. We apply our result to digital signature schemes showing that it can be used to prove strong security for schemes like MQDSS in the QROM. As another application we prove QROM-security of a non-interactive OR proof by Liu, Wei and Wong. As for question (2), we show via a Grover-search based attack that Don et al.'s quadratic security loss for the Fiat-Shamir transformation of $Σ$-protocols is optimal up to a small constant factor. This extends to our new multi-round result, proving it tight up to a factor that depends on the number of rounds only, i.e. is constant for any constant-round interactive proof.
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。
