An on-demand fabrication method for additive physical unclonable functions (PUFs), a hardware-based security primitive, is inevitably required, especially considering increasingly miniaturized microelectronic devices. An optical printing approach is regarded as an alternative method to fabricate functional nano/microscale patterns against conventional methods due to its superior fabrication flexibility. However, owing to the Brownian motion of nanoparticles, achieving highly precise and selective printing persists an ongoing obstacle for the applicability of optical printing methods. Here, it is shown that the optical printing approach possesses plenty of room to fabricate on-demand PUFs by exploiting the obstacle from the perspective of randomness. To demonstrate this, an optical PUF based on a mesoscopic lattice pattern consisting of optically printed gold nanoparticles is proposed. Comprehensive analyses on physical features occurring naturally and multi-modal keys generated from them reveal that both exhibit randomness. Through a ternary bit system and key integration approach, the capability of the physical unclonable function using as few as 25 nanoparticles can be ensured in terms of the amount of information, complexity, uniqueness, and encoding capacity. The versatility of optical printing regarding the usability of a broad range of substrates and the ability to create arbitrary patterns with tunable dimensions are also shown.