## Cryptology ePrint Archive: Report 2009/277

On the Foundations of Physical Unclonable Functions

Ulrich Rührmair and Jan Sölter and Frank Sehnke

Abstract: We investigate the foundations of Physical Unclonable Functions from several perspectives. Firstly, we discuss formal and conceptual issues in the various current definitions of PUFs. As we argue, they have the effect that many PUF candidates formally meet no existing definition. Next, we present alternative definitions and a new formalism. It avoids asymptotic concepts like polynomial time, but is based on concrete time bounds and on the concept of a security experiment. The formalism splits the notion of a PUF into two new notions, Strong $t$-PUFs and Obfuscating $t$-PUFs.

Then, we provide a comparative analysis between the existing definitions and our new notions, by classifying existing PUF implementations with respect to them. In this process, we use several new and unpublished machine learning results. The outcome of this comparative classification is that our definitions seem to match the current PUF landscape well, perhaps better than previous definitions. Finally, we analyze the security and practicality features of Strong and Obfuscating $t$-PUFs in concrete applications, obtaining further justification for the split into two notions.

Category / Keywords: implementation / Physical Unclonable Functions, Foundations of Cryptography, Machine Learning