Entropy estimation of physically unclonable functions via Chow parameters

Alexander Schaub , Olivier Rioul , Joseph J. Boutros

A physically unclonable function (PUF) is an elec- tronic 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 Re ́nyi entropies and determine how they increase with n. Such a problem was known to have extremely high complexity (in the order of 22n ) 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.

Domaines: Théorie de l'information [cs.IT]; Cryptographie et sécurité [cs.CR]; Probabilités [math.PR]; Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]; Mathématiques générales [math.GM]; Mathématique discrète [cs.DM]; Traitement du signal et de l'image [eess.SP]; Statistiques [math.ST]

Alexander Schaub, Olivier Rioul, Joseph J. Boutros. Entropy estimation of physically unclonable functions via Chow parameters. 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton'19), Sep 2019, Monticello, IL, United States. pp.698-704. ⟨hal-02300791⟩