A Construction of Multi-sender Authentication Codes from Pseudo-Symplectic Geometry over Finite Fields

Multisender authentication code was firstly constructed by Gilbert et al. in [1] in 1974.Multisender authentication system refers to a group of senders that cooperatively send amessage to the receiver, and then the receiver should be able to ascertain that the message is authentic. About this case, many scholars had also much researches and had made great contributions to multisender authentication codes [2–6]. In the actual computer network communications, multisender authentication codes include sequential model and simultaneous model. Sequential model is that each sender uses its own encoding message to the receiver, and the receiver receives the message and verifies whether the message is legal or not. Simultaneous model 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, and 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 P = {P 1 , P 2 , . . . , P n }, the keys distribution center, he is responsible for the key distribution to senders and receiver, including solving the disputes between them, a receiver R, a synthesizer, 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 → T