A Review of Multivariate Public Key Cryptography Algorithms in NIST Additional Digital Signature Schemes Standardization Evaluation

In recent years, a large amount of research has been conducted on quantum computers. Once large-scale quantum computers are introduced and put into practical scenarios, public key cryptography systems based on traditional cryptography will no longer be secure. As an excellent candidate for anti-quantum cryptography, multivariable public key cryptography has received widespread attention from the cryptography community. The purpose of this study is to evaluate the security and efficiency of the multivariable cryptographic algorithm in the first round of NIST additional digital signature standard candidate schemes, in order to determine its potential application in post quantum cryptography. This article will provide a brief overview of the current multivariable cryptographic algorithms participating in the first round of additional digital signature scheme selection. These 10 multivariable algorithms will be classified according to different trapdoor constructions. Then, a comparative analysis will be conducted between the multivariable algorithms in each classification and the NIST standardized cryptographic algorithms. Finally, based on the current research progress in multivariable cryptography, we will provide a prospect and summarize the prospects of multivariable cryptographic algorithms.