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 for the receiver is to perform a statistical test in order to recognize and accept an original code corrupted by noise and reject any illegal copy or a counterfeit. This study highlights the fact that the probability of type I and type II errors can be better approximated, by several orders of magnitude, when using the Cramér-Chernoff theorem instead of a Gaussian approximation. The practical computation of these error probabilities is also possible using Monte Carlo simulations combined with the importance sampling method. By deriving the optimal test within a Neyman-Pearson setup, a first theoretical analysis shows that a thresholding of the received code induces a loss of performance. A second analysis proposes to find the best parameters of the channels involved in the model in order to maximize the authentication performance. This is possible not only when the opponent's channel is identical to the legitimate channel but also when the opponent's channel is different, leading this time to a min-max game between the two players. Finally, we evaluate the impact of an uncertainty for the receiver on the opponent channel, and we show that the authentication is still possible whenever the receiver can observe forged codes and uses them to estimate the parameters of the 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.
This paper combines the principles of statistical estimation and hypothesis testing to analyze the impact of parameter estimation on an authentication system based on graphical codes. The studied authentication system uses the fact that a code, once printed, undergoes a stochastic and non invertible alteration. A statistical test applies a likelihood ratio between the model of the authentic printed and scanned image and the model of the reproduced one, with the particularity here that the later model is unknown. The proposed solution consists in using an optimal estimation of the image model coming from observed fake codes in order to perform the likelihood test. Using a second order expansion, we derive a linear relation between the quadratic error of the estimated parameters and the probability of type II error. We are then able to formulate analytically and practically the error spread region of the Receiver Operating Characteristic (ROC) curves, and to compute the average authentication performance when the receiver has to estimate the opponent print and scan channel.
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