A Cryptography Classification Of Quasigroups Of Order 7

The paper studies mainly the quasigroup theory,classifies quasigroups of order 7and selects Latin squares which are appropriated for encryption based on applications in the cryptography.In Chapter 1,the development of Cryptography is presented.The application in the stream cipher of quasigroup of order 4 and the probability of weak-key of the cipher make it important about the classification of quasigroups of order 7 and the security of secret key.In Chapter 2,the definitions of quasigroup and an e-transformation based on quasigroup operation are presented.The Keystream is obtained from some e-transformations.In the analysis of e-transformations,it obtains concepts of period factor f*based on the period of sequence and the probability distribution of fk*.In Chapter 3,the concept of primitive group and relevant knowledge with quasigroups are presented.In Chapter 4,the classification of quasigroups of order 7 is presented.For Latin squares forming in the primitive group of lower order,classify Latin squares according to the cycle type of column permutations.For quasigroups forming in Alternating group T6 and Symmetric group T7,because the specific form of Latin square is not listed,hence,according to the basic condition with forming a Latin square we classify quasigroups based on the combination of cycle types which can form a Latin square.In Chapter 5,the period factor of quasigroups in every class is presented.In Chapter 6,make conclusions.we analysis the expected value of period factor of Latin squares forming in primitive groups and find that some Latin squares forming in T6 and T7 are appropriated for encryption.