Point compression for certificates of authenticity

This paper describes the point compression for certificates of authenticity (COA), which are digitally signed physical objects that have a random unique structure. The certificates of authenticity satisfies three requirements: (i) the cost of creating and signing original COAs is small (ii) the cost of exact of near-exact replication of COA's physical structure is several orders of magnitude larger than creating an original, and (iii) the cost of verifying the authenticity of a signed COA is small. The straightforward point compression algorithm is developed to address information about the random structure of the physical object.