Multivariate Quadratic Quasigroups (MQQs) as a suitable class of quasigroups for multivariate public key cryptography recently have been an important mathematical tool in information security field. In this paper, we propose a necessary and sufficient condition to verify whether a quasigroup given by its multiplication table is a bilinear MQQ, which shows that checking whether an arbitrary quasigroup is a bilinear MQQ is equivalent to solving a simple matrix equation. Based on this condition, a deterministic algorithm is proposed to judge whether a given quasigroup is a bilinear MQQ and then obtain the corresponding Boolean functions if it is. An example is given to show the validity of our results.
Zhang, Ying and Zhang, Huisheng
"An Algorithm for Judging and Generating Bilinear Multivariate Quadratic Quasigroups,"
Applied Mathematics & Information Sciences: Vol. 07:
5, Article 48.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss5/48