High-dimensional anticounterfeiting nanodiamonds authenticated with deep metric learning

Physical unclonable function (PUF) labels have emerged as a promising candidate for achieving unbreakable anticounterfeiting. Despite their significant progress, two challenges for developing practical PUF systems remain, namely 1) fairly few high-dimensional encoded labels with excellent material properties, and 2) existing authentication methods with poor noise tolerance or inapplicability to untrained labels. Herein, we employ the linear polarization modulation of randomly distributed fluorescent nanodiamonds (FNDs) to demonstrate, for the first time, three-dimensional encoding for diamond-based labels. Briefly, our 3D encoding scheme provides digitized images with an encoding capacity of 10 9771 and high distinguishability under a short readout time of 7.5 s. The ultrahigh photostability and inertness of FNDs endow our labels with high reproducibility and long-term stability. To address the second challenge, we employ a deep metric learning algorithm to develop a novel authentication methodology that computes the similarity of deep features of digitized images, exhibiting a superior noise tolerance than the classical point-by-point comparison method. Meanwhile, it overcomes the key limitation of existing artificial intelligence (AI)-driven classification-based methods, i.e., inapplicability to untrained PUF labels. Considering the high performance of both FND PUF labels and deep metric learning authentication, our work paves the way for developing practical PUF anticounterfeiting systems.