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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.