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：我们在后量子单向函数存在的最小假设下，首次构建了常数轮的后量子非弹性承诺方案。我们实现了关于承诺的标准非弹性概念。在相同假设下，先前的构造需要Ω(log*λ)轮。我们通过一种在量子设置中更易使用的新技术来实现常数轮非弹性承诺。该技术还在经典设置中为常数轮非弹性承诺提供了近乎初等的安全性证明，这可能具有独立的研究价值。与现有工作结合时，我们的结果在量子全同态加密和量子学习误差问题的多项式难度假设下，首次在普通模型中实现了针对经典和量子功能性的常数轮量子安全多方计算。