A point-set compression heuristic for fiber-based certificates of authenticity

A certificate of authenticity (COA) is an inexpensive physical object that has a random unique structure with high cost of near-exact reproduction. An additional requirement is that the uniqueness of COA´s random structure can be verified using an inexpensive device. Bauder was the first to propose COA created as a randomized augmentation of a set of fixed-length fibers into a transparent gluing material that randomly fixes once for all the position of the fibers within. Recently, Kirovski (2004) showed that linear improvement in the compression ratio of a point-set compression algorithm used to store fibers´ locations, yields exponential increase in the cost of forging a fiber-based COA instance. To address this issue, in this paper, we introduce a novel, generalized heuristic that compresses M points in an N-dimensional grid with computational complexity proportional to O(M²). We compare its performance with an expected lower bound. The heuristic can be used for numerous other applications such as storage of biometric patterns.