Construction of authentication codes with distrust arbitration from polynomials over finite fields

The authentication codes with arbitration are able to solve dispute between the sender and the receiver. The authentication codes with trusted arbitration are called A2-codes, the authentication codes with distrust arbitration are called A3-codes. As an expansion of A2-codes, an A3-codes is an authentication system which is closer to the reality environment. Therefore, A3-codes have more extensive application value. In this paper, we construct a class of A3-codes based on polynomials over finite fields, give the parameters of the constructed codes, and calculate a variety of cheating attacks the maximum probabilities of success. Especially, in a special case, the constructed A3-codes are perfect. Compared with a known type of codes, they have almost the same security level, however, our codes need less storage requirements. Therefore, our codes have more advantages.