A Comparison of NIST 2nd Round Candidates’ MQ-based Signature Schemes

With the development of quantum computers, the security of public-key cryptosystems currently in use is now under serious threat. The National Institute of Standards and Technology (NIST) has initiated a process to standardize one or more quantum-resistant public-key cryptographic algorithms. Compared to code-based, lattice-based or hash-based cryptography, multivariate cryptography has much better performance in low-cost devices. In this paper, we compare the four NIST 2nd round candidates multivariate quadratic based signature schemes: GeMSS, LUOV, MQDSS and Rainbow. Also, we summarize several known attacks against the security of multivariate cryptography using classical and quantum approaches.