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On the Entropy of Physically Unclonable Functions

Olivier Rioul 1, 2 Patrick Solé 1, 2 Sylvain Guilley 3, 2 Jean-Luc Danger 3, 2 
1 COMNUM - Communications Numériques
LTCI - Laboratoire Traitement et Communication de l'Information
3 SSH - Secure and Safe Hardware
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : A physically unclonable function (PUF) is a hard- ware device that can generate intrinsic responses from challenges. The responses serve as unique identifiers and it is required that they be as little predictable as possible. A loop-PUF is an architecture where n single-bit delay elements are chained. Each PUF generates one bit response per challenge. We model the relationship between responses and challenges in a loop-PUF using Gaussian random variables and give a closed- form expression of the total entropy of the responses. It is shown that n bits of entropy can be obtained with n challenges if and only if the challenges constitute a Hadamard code. Contrary to a previous belief, it is shown that adding more challenges results in an entropy strictly greater than n bits. A greedy code construction is provided for this purpose.
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Submitted on : Saturday, September 14, 2019 - 6:50:42 PM
Last modification on : Thursday, November 18, 2021 - 1:02:02 PM


  • HAL Id : hal-02288459, version 1


Olivier Rioul, Patrick Solé, Sylvain Guilley, Jean-Luc Danger. On the Entropy of Physically Unclonable Functions. 2016 IEEE International Symposium on Information Theory (ISIT'16), Jul 2016, Barcelona, Spain. ⟨hal-02288459⟩



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