The main property of a PUF is the unclonability, that can be formally described as the impossibility to obtain a PUF в' which is identical to в, such that the latter can replace the former. Being a physical object, the unclonability can be considered in a mathematical or physical manner. Mathematical unclonability implies that it is hard to find a mathematical procedure that is able to provide the same CRPs set of в (10.2a), while the physical unclonability indicates that it is hard to reproduce a device with a PUF в' which can be recognized as в (property 10.2b).

How these properties are guaranteed is determined by the manufacturing process and by the internal PUF design. The mathematical unclonability is guaranteed by the non-feasibility of modeling the manufacturing variability process and its impact on each physical parameter which determines the PUF behavior. The impossibility of producing two identical devices, even with the best knowledge on physical parameters affected by variability, is given by the noncontrollability of the manufacturing variability.