Document authentication using graphical codes: impacts of the channel model

This paper proposes to investigate the impact of the channel model for authentication systems based on codes that are corrupted by a physically unclonable noise such as the one emitted by a printing process. The core of such a system is the comparison for the receiver between an original binary code, an original corrupted code and a copy of the original code. We analyze two strategies, depending on whether or not the receiver use a binary version of its observation to perform its authentication test. By deriving the optimal test within a Neyman-Pearson setup, a theoretical analysis shows that a thresholding of the code induces a loss of performance. This study also highlights the fact that the probability of the type I and type II errors can be better approximated, by several orders of magnitude, computing Chernoff bounds instead of the Gaussian approximation. Finally we evaluate the impact of an uncertainty for the receiver on the opponent channel and show that the authentication is still possible whenever the receiver can observe forged codes and uses them to estimate the parameters of the model.