Counterfeiting and piracy are among the main problems for modern society. Many traditional anti-counterfeiting technologies become quickly obsolete in view of the rapid technological progress that offers a wide range of modern high-tech tools and applications to the counterfeiters. At the same time, many new approaches to anti-counterfeiting such as printable graphical codes appear thanks to the advancement of modern mobile technologies and machine learning algorithms. The security of printable codes in terms of their reproducibility by unauthorized parties remains largely unexplored. Thesis 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 printable graphical codes from machine learning perspectives. A special attention is paid to a reliable authentication on the modern mobile phones. Also the robustness to adversarial examples in the digital world and training under the limited amount of labeled data are investigated.