New Constructions Of Authentication Codes With Multiple Arbiters

In a common authentication code with arbitration, the arbiter is powerful to solve the distrust between the transmitter and the receiver in communication, but the dishonest arbiter may make a great threat to the security of authentication system. In order to prevent deception of the arbiter in the communication, four constructions of authentication codes with multiple arbiters are given in this paper. An authentication code with single arbiter is constructed from projective geometry over finite fields, where all kinds of attacks succeed with the same probability, it means that participators of the system have no advantage over others even if they have secrets. An authentication code with double arbiters is constructed from finite sets, which can prevent not only attacks from single participator but also collusion attacks from arbiters and participators. An authentication code with multiple arbiters is constructed from linear codes, which does well in resisting both collusion attacks from arbiters and collusion attacks from arbiters and participators, then the code ensures the safety of the system in a larger range. An authentication code with double arbiters is constructed from symplectic geometry over finite fields, which changes the authentication system with single arbiter, and reduces requirements of arbiters’ honesty, the possible deception of the arbiters do not need to worry about, however. Probabilities of parameters and success of all possible attacks in every construction are computed. These codes limit the probabilities of possible attacks within the safety requirements, not only resist the deception of single participator of the communication, but also effectively limit collusion attacks from arbiters and participators, and ensure the relative security and stability of the system under any attack.