## Cryptology ePrint Archive: Report 2010/171

On Foundation and Construction of Physical Unclonable Functions

Jiang Wu and Maire O'Neill

Abstract: Physical Unclonable Functions (PUFs) have been introduced as a new cryptographic primitive, and whilst a large number of PUF designs and applications have been proposed, few studies has been undertaken on the theoretical foundation of PUFs. At the same time, several PUF designs have been found to be insecure, raising questions about their design methodology. Moreover, PUFs with efficient implementation are needed to enable many applications in practice.

In this paper, we present novel results on the theoretical foundation and practical construction for PUFs. First, we prove that, for an $\ell$-bit-input and $m$-bit-output PUF containing $n$ silicon components, if $n< \frac{m2^{\ell}}{c}$ where $c$ is a constant, then 1) the PUF cannot be a random function, and 2) confusion and diffusion are necessary for the PUF to be a pseudorandom function. Then, we propose a helper data algorithm (HDA) that is secure against active attacks and significantly reduces PUF implementation overhead compared to previous HDAs. Finally, we integrate PUF construction into block cipher design to implement an efficient physical unclonable pseudorandom permutation (PUPRP); to the best of our knowledge, this is the first practical PUPRP using an integrated approach.

Category / Keywords: physical unclonable function