Authentication using graphical codes: Optimisation of the print and scan channels

In this paper we propose to cast the problem of authentication of printed documents using binary codes into an optimization game between the legitimate source and the opponent, each player tries to select the best print and scan channel to minimize/maximize his authentication performance. It is possible to solve this game by considering accurate computations of the type I and type II probability errors and by using additive stochastic processes to model the print and scan channel. Considering the print and scan models as Lognormal or Generalized gaussian additive processes, we maximize the authentication performances for two different security scenarios. The first one considers the opponent as passive and assumes that his print-and-scan channel is the same as the legitimate channel. The second scenario devises a minimax game where an active opponent tries to maximize the probability of non-detection by choosing appropriate parameters on his channel. Our first conclusions are the facts that (i) the authentication performance is better for dense noises than for sparse noises for both scenarios, and (ii) for both families of distribution, the opponent optimal parameters are close to the legitimate source parameters, and (iii) the legitimate source can find a configuration which maximizes the authentication performance.