A cartesian product construction for unconditionally secure authentication codes that permit arbitration

Abstract

An authentication code consists of a collection of encoding rules associating states of an information source with messages that are to be used to communicate the state to a designated receiver. In order for a collection of encoding rules to be useful as an authentication code there must also exist one or more probability distributions on the rules which, if used by the receiver and transmitter (the insiders) to choose secretly the encoding rule they use, will result in the receiver being able to (probably) detect fraudulent messages sent by an outsider or modifications by him of legitimate messages. Authentication codes that permit arbitration are codes that in addition to protecting the insiders from deception by outsiders, also protect against some forms of insider deception. This is accomplished by making it possible for an arbiter to resolve (again in probability) certain disputes between the transmitter and receiver: the transmitter disavowing a message that he actually sent or the receiver claiming to have received a message that the transmitter did not send. An infinite class of authentication codes that permit arbitration is constructed and some bounds on the probability of a deception going undetected are proven. These codes are shown to be unconditionally secure, i.e., it is shown that the probability of a deception either going undetected or else of being unjustly attributed to an innocent party is independent of the computing capability or investment that a would-be cheater is willing to make. © 1990 International Association for Cryptologic Research.