Quantum secure digital signature scheme based on multivariate quadratic quasigroups (MQQ)

In this paper, we propose a digital signature scheme, the MQQ-Sigv scheme, that relies on the difficulty of solving the multivariate quadratic (MQ) problem. The central map of the proposed scheme will be designed using the multivariate quadratic quasigroup (MQQ). We will prove that the MQQ-Sigv scheme is secure against various attacks including existential unforgeability under chosen message attack (EUF-CMA), Min-Rank attack, High-Rank attack, Direct attack, and Differential attack. Furthermore, we will prove that finding an equivalent good key for the MQQ-Sigv scheme is infeasible in polynomial time, and analyze the operating characteristics of the scheme.