This paper analyses the performances of an authentication system based on graphical printed codes. The authentica- tion system relies on the non-invertible degradation due to the stochastic nature of the printing and scanning processes. As- suming that the models of these processes are known, authen- tication is performed by a Neyman-Pearson test computed from the distributions of both original and copied print and scanned codes. The probabilities of false positive and false negative are then computed using Chernoff bounds. Consid- ering 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 assume 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 perfor- mance is better for dense noises than for sparse noises for both scenarios, and (ii) for both families of distribution, the op- ponent optimal parameters are close to the legitimate source parameters, and (iii) the legitimate source can find a configu- ration which maximize the authentication performance.