  A physically unclonable function (PUF) is an electronic circuit that produces
an intrinsic identifier in response to a challenge. These identifiers depend on
uncontrollable variations of the manufacturing process, which make them hard to
predict or to replicate. Various security protocols leverage on such intrinsic
randomness for authentification, cryptographic key generation,
anti-counterfeiting, etc. Evaluating the entropy of PUFs (for all possible
challenges) allows one to assess the security properties of such protocols.
  In this paper, we estimate the probability distribution of certain kinds of
PUFs composed of $n$ delay elements. This is used to evaluate relevant R\'enyi
entropies and determine how they increase with $n$. Such a problem was known to
have extremely high complexity (in the order of $2^{2^n}$) and previous entropy
estimations were carried out up to $n=7$. Making the link with the theory of
Boolean threshold functions, we leverage on the representation by Chow
parameters to estimate probability distributions up to $n=10$. The resulting
Shannon entropy of the PUF is close to the max-entropy, which is asymptotically
quadratic in $n$.
