$A^3$-Codes Under Collusion Attacks

Abstract

An $A^3$-code is an extension of an $A$-code in which none of the three participants, transmitter, receiver, and arbiter, is trusted. In this paper, we extend the previous model of $A^3$-codes by allowing the transmitter and the receiver to not only individually attack the system, but also collude with the arbiter against the other. We derive information-theoretic lower bounds on the success probability of various attacks, and combinatorial lower bounds on the size of key spaces. We also study the combinatorial structure of optimal $A^3$-codes against collusion attacks and give a construction of an optimal code.