A quantum-secure partial parallel MAC QPCBC

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.