A New Construction of Multi-sender Authentication Codes from Polynomials over Finite Fields

Multisender authentication code was firstly constructed by Gilbert et al. [1] in 1974. Multisender authentication system refers towho a groupof senders, cooperatively send amessage to a receiver; then the receiver should be able to ascertain that the message is authentic. About this case, many scholars and researchers had made great contributions to multisender authentication codes, such as [2–6]. In the actual computer network communications, multisender authentication codes include sequential model and simultaneous model. Sequential model is that each sender uses his own encoding rules to encode a source state orderly, the last sender sends the encoded message to the receiver, and the receiver receives themessage and verifies whether the message is legal or not. Simultaneousmodel is that all senders use their own encoding rules to encode a source state, and each sender sends the encoded message to the synthesizer, respectively; then the synthesizer forms an authenticated message and verifies whether the message is legal or not. In this paper, we will adopt the second model. In a simultaneous model, there are four participants: a group of senders U = {U 1 , U 2 , . . . , U n }, the key distribution center, he is responsible for the key distribution to senders and receiver, including solving the disputes between them, a receiver R, and a synthesizer, where he only runs the trusted synthesis algorithm. The code works as follows: each sender and receiver has their own Cartesian authentication code, respectively. Let (S, E i , T i ; f i ) (i = 1, 2, . . . , n) be the senders’ Cartesian authentication code, (S, E R , T; g) be the receiver’s Cartesian authentication code, h : T 1 × T 2 × ⋅ ⋅ ⋅ × T n →