Classification of quasigroups based on period factors

Abstract

Edon80 is a stream cipher design that had advanced to the third and last phase of the eSTREAM project. The core of the cipher consists quasigroup string e-transformations and it employs four quasigroups of order 4. The employed quasigroups have influence on the period of the keystream. There are 576 quasigroups of order 4 in total which have different period factors. The four quasigroups used in Edon80 were chosen by numerous computer experiments. In this paper, based on permutation groups, we give a theory criterion for the determination of quasigroups and give a complete classification for the 576 quasigroups of order 4 according to their period factors.

Keywords:

• quasigroup
• Edon80
• Latin square
• period factor
• stream cipher

2010 AMS Subject Classifications::

• 05B15
• 94C30

Acknowledgment

The authors would like to acknowledge the support of the National Natural Science Foundation of China under Grant no. 61373007, 11371208 and Zhejiang Provincial Natural Science Foundation of China under Grant no. LY13F020039, and Sponsored by K.C. Wong Magna Fund in Ningbo University.