Secure multiparty computation (MPC) schemes allow two or more parties to conjointly compute a function on their private input sets while revealing nothing but the output. Existing state-of-the-art number-theoretic-based designs face the threat of attacks through quantum algorithms. In this context, we present secure MPC protocols that can withstand quantum attacks. We first present the design and analysis of an information-theoretic secure oblivious linear evaluation (OLE), namely ${\sf qOLE}$ in the quantum domain, and show that our ${\sf qOLE}$ is safe from external attacks. In addition, our scheme satisfies all the security requirements of a secure OLE. We further utilize ${\sf qOLE}$ as a building block to construct a quantum-safe multiparty private set intersection (MPSI) protocol.

翻译：安全多方计算（MPC）方案允许多个参与方在其私有输入集上协同计算函数，除输出外不泄露任何信息。现有基于数论的经典设计面临量子算法攻击的威胁。在此背景下，我们提出了能够抵御量子攻击的安全MPC协议。我们首先在量子领域设计并分析了一种信息论安全的无意识线性评估（OLE）方案，即${\sf qOLE}$，并证明我们的${\sf qOLE}$能够抵御外部攻击。此外，该方案满足安全OLE的所有安全需求。我们进一步将${\sf qOLE}$作为基础构件，构建了一种量子安全的多方隐私集合交集（MPSI）协议。