The use of printed banknotes is widespread despite cashless payment methods: for example, more than 27 billion euro banknotes are currently in circulation, and this amount is constantly increasing. Unfortunately, many false banknotes are in circulation, too. Central banks worlwide are continuously striving to reduce the counterfeiting. To fight against the criminal practice, a range of security features are added to banknotes, such as watermarks, micro-printing, holograms, and embossed characters. Beside these well-known characteristics, the colored fibers inside every banknote have strong potential as a security feature, but have so far been poorly exploited. The mere presence of colored fibers does not guarantee the banknote genuineness, as they can be drawn or printed by counterfeiters. However, their random position can be exploited to uniquely identify the banknote. This paper presents a technique for automatically recognizing fibers and efficiently storing their positions, considering realistic application scenarios. The classification accuracy and fault tolerance of the proposed method are theoretically demonstrated, thus showing its applicability regardless of banknote wear or any implementation issue. This is a major advantage with respect to state-of-the-art anti-counterfeit approaches. The proposed security method is strictly topical, as the European Central Bank plans to redesign euro banknotes by 2024.