Encryption Techniques Based On Quasigroups

The researches on quasigroup have been fruitful result since the concept of quasi-group was given. Nowadays, the application of quasigroup in cryptology was concerned,Candidate Algorithm in third round of eSTREAM—Edon80 was a kind of sequenceciphers based on quasigroup. However, the study about sequence ciphers based on postcommutative quasigroup are rare.In this paper, we study the sequence ciphers system based on post–commutativequasigroup, the main work as follow:(1) Given the encryption and decryption algorithm of sequence ciphers based onpost–commutative quasigroup, and introduce the basic principle of multiple EncryptionSystem.(2) Discuss the relationship between the size of key space of ciphers based on post–commutative quasigroup and quantity of symmetric latin square, given the enumerationtheorem about symmetric latin square and the number of symmetric latin square oforder n 11 by computer searches, in general case, given the related enumerationformula.(3) Discuss the security of the sequence ciphers based on post–commutative quasi-group, and focuses the resistance of brute-force attack, proved it has the resistance ofbrute-force attack by an illustration. Given a brief introduction about resistance ofprobability attack.(4) Given the construction of post–commutative quasigroup of odd number or-der using by base block set, and the method of the post–commutative quasigroupof even number order generate by the post–commutative quasigroup of odd numberorder, and the method get more di?erent post–commutative quasigroup from one post–commutative quasigroup.(5) Discuss the Algorithm of symmetric latin square searching and the Algorithmof generating post commutative quasigroup, given the source code of post–commutative quasigroup cipher.