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Variable-Length Bit Mapping and Error-Correcting Codes for Higher-Order Alphabet PUFs

  • Vincent Immler
  • Matthias Hiller
  • Qinzhi Liu
  • Andreas Lenz
  • Antonia Wachter-Zeh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10662)

Abstract

Device-specific physical characteristics provide the foundation for Physical Unclonable Functions (PUFs), a hardware primitive for secure storage of cryptographic keys. So far, they have been implemented by either directly evaluating a binary output or by mapping outputs from a higher-order alphabet to a fixed-length bit sequence. However, the latter causes a significant bias in the derived key when combined with an equidistant quantization.

To overcome this limitation, we propose a variable-length bit mapping that reflects the properties of a Gray code in a different metric, namely the Levenshtein metric instead of the classical Hamming metric. Subsequent error-correction is therefore based on a custom insertion/deletion correcting code. This new approach effectively counteracts the bias in the derived key already at the input side.

We present the concept for our scheme and demonstrate its feasibility based on an empirical PUF distribution. As a result, we increase the effective output bit length of the secret by over \(40\%\) compared to state-of-the-art approaches while at the same time obtaining additional advantages, e.g., an improved tamper-sensitivity. This opens up a new direction of Error-Correcting Codes (ECCs) for PUFs that output responses with symbols of higher-order output alphabets.

Keywords

Physical Unclonable Functions Fuzzy extractor Secrecy leakage Coding theory Quantization Varshamov-Tenengolts (VT) code 

Notes

Acknowledgements

The authors from Fraunhofer AISEC have been supported by the Fraunhofer Internal Programs under Grant No. MAVO 828 432. A. Lenz and A. Wachter-Zeh have been supported by the Technical University of Munich–Institute for Advanced Study, funded by the German Excellence Initiative and European Union Seventh Framework Programme under Grant Agreement No. 291763. Many thanks to Aysun Önalan for preparing the numbers of the RS-based fuzzy commitment scheme.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Vincent Immler
    • 1
  • Matthias Hiller
    • 1
  • Qinzhi Liu
    • 1
    • 2
  • Andreas Lenz
    • 3
  • Antonia Wachter-Zeh
    • 3
  1. 1.Fraunhofer Institute for Applied and Integrated Security (AISEC)Garching bei MünchenGermany
  2. 2.RWTH Aachen UniversityAachenGermany
  3. 3.Institute for Communications EngineeringTechnical University of Munich (TUM)MunichGermany

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