We prove that Kilian's four-message succinct argument system is post-quantum secure in the standard model when instantiated with any probabilistically checkable proof and any collapsing hash function (which in turn exist based on the post-quantum hardness of Learning with Errors). At the heart of our proof is a new "measure-and-repair" quantum rewinding procedure that achieves asymptotically optimal knowledge error.

翻译：我们证明基里安的四点讯息简明论证系统在标准模型中具有后量级安全性,当它与任何概率的可核实证据和任何崩溃的散列函数(而散列功能又基于以错误学习后量级强度为基础而存在 ) 发生即时反应时。 我们证据的核心是一个新的“计量和修复”的量级回流程序,该程序实现了无源的最佳知识错误。