Information-theoretic security analysis of physical uncloneable functions

We propose a general theoretical framework to analyze the security of Physical Uncloneable Functions (PUFs). We apply the framework to optical PUFs. In particular we present a derivation, based on the physics governing multiple scattering processes, of the number of independent challenge-response pairs supported by a PUF. We find that the number of independent challenge-response pairs is proportional to the square of the thickness of the PUF and inversely proportional to the scattering length and the wavelength of the laser light. We compare our results to those of Pappu and show that they coincide in the case where the density of scatterers becomes very high.Finally, we discuss some attacks on PUFs, and introduce the Slow PUF as a way to thwart brute force attacks.