Some Classes Of Perfect (2,1)-authentication And Secrecy Codes

Two main aspects of information security are secrecy and authentication. Secrecy is to prevent confidential information from being illegally authorized person to steal; authentica-tion is in order to confirm the identity of the information source, and if stored procedure had been tampered with in the transport. Secrecy and authentication are independent each other, we can only consider one, we can also consider both. Shannon in the1940s the first used the method of information theory to research secrecy issue, putting forward the rudi-ment of perfect secrecy system. Simmons used the method of information theory to research authentication issue in the1980s.When Stinson researched the (t, t-1)-rder optimal authentication and secrecy codes, he proved that can be characterized in terms of authentication perpendicular arrays. In this article, we will prove that (t, t-1)-order perfect authentication and secrecy codes can use the authentication partially balanced perpendicular arrays APBPA(t, k, v) to depict. We completely solve the existence of APBPA(2,3, v). For the existence of APBPA(2,5,v), when v is odd, we basically solve it, when v is even, we partially solve it. At the same time we also study the existence of APBPA(2,7, v), and we get several infinite classes. As their applications, we get some classes of (2,1)-order perfect authentication and secrecy codes.