Hash Function Based On Quasigroups And The Security Study Of A Message Authentication Code

Hash functions are used as the encryption algorithm in the field of information securityand Hash functions are usually used to construct the data’s "short fingerprint "in cryptogra-phy. Once the data has changed, the fingerprint is no longer correct. By recalculating thedata fringerprint and verifying fingerprint, one will be able to detect the integrity of the da-ta even though putting the date on unsafe place. It ’s range of applications widely and incl-ud error detection, message authentication, data integrity verification and public key crypt-ography. In recent decade the rapid development of the Convention cryptography and digi-tal gnaturscheme, Hash function is becoming increasingly important.The properties of Hash functions such as one-way was brought by Diffie and Hellman.Importantly security properties of one-way, and anti-collision, are very important to Hashfunctions. All the time, finding Hash functions with such nature attract many resarchers. B-ecause of quasigroup can be used to encrypt and produce pseudo-random number, it can beused to construct Hash function. In1992, Denes and Keedwell propose a new class of Ha-sh function using the theorm of Hash function firsrly. Subsequent, Dswson and Donovan a-nalysis the secrity of such Hash function. Message which divided into " blocks " has an im-portant impact on the security of the Hash fu-nction. In2006, Meyey construct a messageauthentication code based on the quasigroup (Non-associative).In this paper, we construct a Hash function which has good collision based on the res-idue ring and finite field theory. And analysising the security of such Hash function with k-ey which called message authentication code.Chapter Ⅰ In this chapter, we introduce the backgrounds and developments of inves-stigate on of Hash function, present the concept of Hash function and quasigroup and giveknown results. And we introduce the Hash function based on discrete logarithms and blockcipher.Chapter Ⅱ In this chapter, According to the nature of the quasigroup and the method of calculati-on we give how to construct Hash function based on quasigroup. And we proof the charact- eristic such as the strong anti-collision and the one-way nature of such function. And anal-ysising the security of such hash function.Chapter ⅢIn this chapter, we give the message authentication code based on the q-uasigroup. Particularly, we introduce the way how message authentication code workingwith mathematical language and explain that the key space should be big enough. And a-nalysising the security of the message authentication code.