In the recent years, the copy detection patterns (CDP) attracted a lot of attention as a link between the physical and digital worlds, which is of great interest for the internet of things and brand protection applications. However, the security of CDP in terms of their reproducibility by unauthorized parties or clonability remains largely unexplored. In this respect, this paper addresses a problem of anti-counterfeiting of physical objects and aims at investigating the authentication aspects and the resistances to illegal copying of the modern CDP from machine learning perspectives. A special attention is paid to a reliable authentication under the real-life verification conditions when the codes are printed on an industrial printer and enrolled via modern mobile phones under regular light conditions. The theoretical and empirical investigation of authentication aspects of CDP is performed with respect to four types of copy fakes from the point of view of (i) multi-class supervised classification as a baseline approach and (ii) one-class classification as a real-life application case. The obtained results show that the modern machine-learning approaches and the technical capacities of modern mobile phones allow to reliably authenticate CDP on end-user mobile phones under the considered classes of fakes.