We provide the first $\mathit{constant}$-$\mathit{round}$ construction of post-quantum non-malleable commitments under the minimal assumption that $\mathit{post}$-$\mathit{quantum}$ $\mathit{one}$-$\mathit{way}$ $\mathit{functions}$ exist. We achieve the standard notion of non-malleability with respect to commitments. Prior constructions required $\Omega(\log^*\lambda)$ rounds under the same assumption. We achieve our results through a new technique for constant-round non-malleable commitments which is easier to use in the post-quantum setting. The technique also yields an almost elementary proof of security for constant-round non-malleable commitments in the classical setting, which may be of independent interest. When combined with existing work, our results yield the first constant-round quantum-secure multiparty computation for both classical and quantum functionalities $\mathit{in}$ $\mathit{the}$ $\mathit{plain}$ $\mathit{model}$, under the $\mathit{polynomial}$ hardness of quantum fully-homomorphic encryption and quantum learning with errors.

翻译：我们给出了在最小假设——存在后量子单向函数——下，后量子不可延展承诺的第一个常数轮构造。我们实现了关于承诺的标准不可延展性概念。先前在同一假设下的构造需要Ω(log^*\lambda)轮。我们通过一种新的常数轮不可延展承诺技术实现结果，该技术在后量子环境下更易使用。该技术还在经典环境下为常数轮不可延展承诺提供了一种近乎初等的安全性证明，这或许具有独立意义。当与现有工作结合时，我们的结果首次在多项式假设下（基于量子全同态加密和量子学习误差问题的困难性）实现了对经典和量子功能在明文模型中的常数轮量子安全多方计算。