Three Constructions of Authentication Codes from Power Function over Finite Fields with Perfect Secrecy

Abstract

In this paper, we present three algebraic constructions of authentication codes from power functions over finite fields with secrecy and realize an application of some properties about authentication codes in [1]. The first and the third class are optimal. Some of the codes in the second class are optimal, and others in the second class are asymptotically optimal. All authentication codes in the three classes provide perfect secrecy.