The quantum security of message authentication codes (MACs) has been gaining increasing attention in recent years, particularly with regard to proving the quantum security of classical MACs, which has emerged as a significant area of interest. In this work, we present two variants of classical MACs: QPMAC, a quantum-secure parallel version of PMAC, and QCBCMAC, a quantum-secure variant of CBCMAC and NMAC that supports variable-length input. We demonstrate that QPMAC is a parallel quantum-secure MAC, with an inverse relationship between its degree of parallelism and its level of quantum security. On the other hand, QCBCMAC provides quantum security for variable-length inputs. To achieve an optimal balance between parallelism and quantum security, we propose QPCBC, a hybrid construction that combines the strengths of QPMAC and QCBCMAC. We also provide an instantiation of QPCBC using tweakable block ciphers.

近年来，消息身份验证码 （MAC） 的量子安全性越来越受到关注，尤其是在证明经典 MAC 的量子安全性方面，这已成为一个重要的关注领域。在这项工作中，我们提出了经典 MAC 的两种变体：QPMAC，PMAC 的量子安全并行版本，以及 QCBCMAC，CBCMAC 和 NMAC 的量子安全变体，支持可变长度输入。我们证明 QPMAC 是一种并行量子安全 MAC，其并行度和量子安全级别之间存在反比关系。另一方面，QCBCMAC 为可变长度输入提供量子安全性。为了实现并行性和量子安全性之间的最佳平衡，我们提出了 QPCBC，这是一种结合了 QPMAC 和 QCBCMAC 优势的混合结构。我们还提供了使用可调整分组密码的 QPCBC 实例化。