The Periodicity Of Pseudo Random Sequence Based On Quasigroups

Pseudo random sequence play an important role in the technical fields of communication, automation, computation and cryptography, the candidate algorithm in third of eSTREAM—Edon80 was a kind of nonlinear pseudo random sequence based on quasigroups. Many scholars study the periodicity from the point of view of experiment, however, the study about the periodicity of pseudo random sequence based on quasigroups in the terms of theory are rareIn this paper, we study the the period of pseudo random sequence based on quasigroups from a viewpoint of theory and the character of quasigroups with large periods, the main work as follow:(1) Given and proved a series of conceptions of the coefficient of period growth; The period of pseudo random sequence based on quasi-groups was decided by the quasigroups. Proved that the coefficient of period growth of quasigroups was accordant with the coefficient of period growth of their generated subgroup.(2) Discussed the coefficient of pseudo random sequence when the quasigroups generated by the cyclic groups regarded as the cipher stream obtained the formula of the coefficient of period growth of the cyclic groups and their generated quasigroups. (3) Discussed the coefficient of pseudo random sequence when the quasigroups generated by the non-cyclic groups regarded as the cipher stream, obtained the formula of the coefficient of period growth of the alternative group and the cyclic group.(4)Discussed relationship between the coefficient of period growth of the quasigroups and (3,2,1)-conjugate r-orthogonal, obtained the for-mula when the order n was even number and n was odd number.