论文标题
测量和原程技术2.0：多轮菲亚特 - 沙米尔等等
The Measure-and-Reprogram Technique 2.0: Multi-Round Fiat-Shamir and More
论文作者
论文摘要
我们对Don，Fehr，Majenz和Schaffner以及Liu和Zhandry的最新作品进行了有关Fiat-Shamir Transformation在Quantum Random Oracle模型（QROM）中的安全性。在这种情况下出现的两个自然问题是：（1）结果是否扩展到多轮交互式证明的菲亚特 - 沙米尔转换，以及（2）Don等人的$ O（q^2）$安全性损失是否最佳。 首先，我们在肯定中回答问题（1）。作为解决这一结果的技术困难的副产品，我们稍微改善了Don等人的结果，为其装备了清洁剂的绑定和更简单的证明。我们将结果应用于数字签名方案，表明它可以用来证明QROM中MQDS等方案的强大安全性。作为另一种应用，我们证明了刘，魏和黄的非交互式或证明的QROM - 安全性。 至于问题（2），我们通过基于Grover-Search的攻击显示Don等人的二次安全损失$σ$ -protocols的Fiat-Shamir转换是最佳的，最多是一个小的常数因素。这扩展到了我们的新多轮结果，证明它紧密到仅取决于回合数量的因素，即，对于任何恒定的连续互动证明，都恒定。
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.
