Stream Cipher Based On Quasigroups With Keystream Period Of Arbitrary Length

Technologies of cryptography are the core of information security. The study ofcryptography has been performed for thousands of years. Cryptography has playeda very important role in the world. On the whole, the cryptography mainly includestwo parts: symmetric cryptosystem and asymmetric cryptosystem. One of the sym-metric cryptosystem which express information by password in the encryption calledstream cipher. At present, the research of stream cipher has got a lot of outstandingachievements on theory and technology. The research of stream cipher has been usedwidely in mobile communications, military diplomatic fields, there is still need onextremely efcient stream ciphers in various applications.Edon80is a hardware binary additive synchronous stream cipher. It was submit-ted to the eSTREAM project as a stream cipher, and it was designed by Gligoroski,Markovski, Kocarev and Gusev [1]. It concatenates80basic building blocks derivedfrom four small quasigroups of order4. There are576quasigroups of order4[2],and384of them are appropriate,64of them are very appropriate [1]. It has beenanalyzed by many cryptographers since it was first published, and a new knowledgehas been obtained that deepened the comprehension of Edon80. By that time, thebest attack on Edon80have done by Hell and Johansson. They have used the analysisof the periods of the keystream sequences of Edon80to mount an attack that canregain the key after using272. It was broke for the period of the keystream sequenceto be short.A quasigroup Q is a set together with a binary operation*such that the equationsy*u=v and u*x=v have unique solutions for each u, v∈Q. In fact, quasigroupshave very useful properties which can be used for construction of functions for en-cryption and decryption. Quasigroups can be very useful for cryptographic purposes,mainly because there is a huge number of quasigroup operations on a given finite set. In this paper, we give a stream cipher based on quasigroup with keystream se-quence of arbitrary period, and discuss the character of quasigroup with large periodgrowth.The whole paper is divided into six chapters.Chapter1In this chapter, we introduce the backgrounds and developments ofthe Edon80, then point out its defect and improving direction.Chapter2In this chapter, we will describe the algorithms of the stream cipherbased on quasigroup, and makes some improvements in order to obtain keystreamsequence of arbitrary period.Chapter3Analyzing the efects towards the period growth of quasigroup fromdiferent aspects, we construct the quasigroup with large period growth.Chapter4In this chapter, we will proof some conclusions among the quasigroupand its conjugates.Chapter5We mainly analyze the security of the stream cipher in this chapter.Chapter6In this chapter, we summarize the main results of this paper.