Counterfeiting poses a significant threat to global trade and public health. Effectively combating counterfeiting involves benefiting from stochastic physical processes to build physically unclonable functions (PUFs). Polymers, as low-cost materials with a wide range of functionalities, hold huge potential for PUF applications. In this context, while there are ongoing applications and studies related to PUF systems today, the development of PUF systems that provide high stochastic characteristics and robustness through simple and low-cost production methods remains critically important. In this regard, we propose stable and addressable polymer PUFs, utilizing a cross-linkable poly(2-vinylpyridine) (P2VP). The Rayleigh instability phenomenon occurring in electrohydrodynamic processes is used to fabricate randomized polymeric features. A brief thermal annealing process enhances adhesion with the substrate, while UV-ozone treatment cross-links P2VP. When applied through stencil masks, UV-ozone treatment results in localized cross-linking, yielding addressable randomized features. Structural and chemical analysis is employed to examine the cross-linked polymer features. Adjusting the conditions of electrospraying and cross-linking leads to PUFs with outstanding stability against solvents, oxygen plasma, and thermal heating. The randomized response of polymer features is evaluated through various statistical criteria. Feature matching algorithms enable direct authentication of images captured under different rotations and lighting conditions. This study demonstrates a versatile strategy for creating polymer-based PUFs with remarkable stability and addressability, enabled by a cross-linkable polymer system.