Théorie de l’information et méthodes statistiques pour l’analyse des systèmes d’authentification utilisant des codes graphiques

The problem of authentication is investigated from an information theoretic security point of view. An authentication model is analyzed using two settings, namely non-channel coding and channel coding based authentication. In the former, a reliable performance measurements of an authentication system relying on a Neyman–Pearson test is provided. Specifically, an asymptotic expression using Sanov's theorem is first proposed to compute the probabilities of false alarm and non-detection, then a practical method based on Monte-Carlo using importance sampling is given to estimate these small probabilities. Thanks to these accurate computation of probabilities, we show that it is possible to optimize the authentication performance when the model of the print and scan channel is known. In the latter, we study the setup where the authentication message is coded by the deterministic channel codes. We show that using channel coding is possible to enhance the authentication performance. Precisely, it is possible to find codes making the two error probabilities simultaneously arbitrarily small. Such codes have rates between the capacity of main channel and that of the opponent channel. It should be noted that the legitimate receiver does not know whether the observed message comes from the legitimate or from the opponent. Therefore it is the objective of the legitimate receiver to use a decoding rule matching with the distribution law of the main channel but mismatching with the opponent channel. Finally, a practical scheme Turbo codes is proposed. The analysis of the EXIT chart is discussed to choose channel parameters so that the authentication performance is optimized.