Theoretical Enumeration of Deployable Single-Output Strong PUF Instances Based on Uniformity and Uniqueness Constraints

Uniqueness and Uniformity are two important quality metrics that determine the practical usability of a strong Physically Unclonable Function ("strong PUF") instance, or an ensemble of strong PUF instances. In this paper, we consider the strong PUF instance as a Boolean function, and theoretically enumerate the total number of usable single-output practical strong PUF instances, assuming commonly acceptable thresholds of the Uniqueness and Uniformity metrics. We have computed the number of possible strong PUF instances with ideal Uniformity (= 0.50), and Uniformity within an acceptable range of the ideal value, and the same for Uniqueness. Additionally, given an ideal Uniformity, we have enumerated the number of strong PUF instances with ideal Uniqueness (= 0.50), and Uniqueness within an acceptable range. Our analysis is completely generic and applicable to any PUF variant, independent of its structure and operating principle.