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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 

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Volumes > Volume 7 > No. 5

 
   

An Algorithm for Judging and Generating Bilinear Multivariate Quadratic Quasigroups

PP: 2071-2076
Author(s)
Ying Zhang, Huisheng Zhang,
Abstract
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.

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