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Why attackers lose: design and security analysis of arbitrarily large XOR arbiter PUFs

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Abstract

In a novel analysis, we formally prove that arbitrarily many Arbiter PUFs can be combined into a stable XOR Arbiter PUF. To the best of our knowledge, this design cannot be modeled by any known oracle access attack in polynomial time. Using majority vote of arbiter chain responses, our analysis shows that with a polynomial number of votes, the XOR Arbiter PUF stability of almost all challenges can be boosted exponentially close to 1; that is, the stability gain through majority voting can exceed the stability loss introduced by large XORs for a feasible number of votes. Considering state-of-the-art modeling attacks by Becker and Rührmair et al., our proposal enables the designer to increase the attacker’s effort exponentially while still maintaining polynomial design effort. This is the first result that relates PUF design to this traditional cryptographic design principle.

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Notes

  1. For the sake of easier notation, we chose to model challenges as vectors in \(\{-1,1\}^{n}\) rather than \(\{0,1\}^{n}\). If desired, all results can be transformed into \(\{0,1\}^{n}\) challenges by “encoding” inputs bits with a function \(\rho :\{0,1\}\rightarrow \{-1,1\}\), where \(\rho (0)=1\) and \(\rho (1)=-1\). This way, we can write \(\rho (b)=(-1)^{b}\) and have the convenient property \(\rho (b_{1}\oplus b_{2})=\rho (b_{1})\cdot \rho (b_{2})\), where \(\oplus \) denotes addition modulo 2 and \(\cdot \) denotes multiplication over \({\mathbb {Z}}\). Any output of our model can be transformed by \(\rho ^{-1}\).

  2. Code at https://github.com/nils-wisiol/pypuf/tree/2019-why-attackers-lose.

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Acknowledgements

The authors would like to thank Christoph Graebnitz, Manuel Oswald, Tudor A. A. Soroceanu, and Benjamin Zengin for helpful comments and discussions.

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  1. Department for Mathematics and Computer Science, Freie Universität Berlin, Takustrasse 9, 14195, Berlin, Germany

    Nils Wisiol & Marian Margraf

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Wisiol, N., Margraf, M. Why attackers lose: design and security analysis of arbitrarily large XOR arbiter PUFs. J Cryptogr Eng 9, 221–230 (2019). https://doi.org/10.1007/s13389-019-00204-8

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