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

Extended Version
: Immler, V.; Hiller, M.; Liu, Q.; Lenz, A.; Wachter-Zeh, A.


Journal of hardware and systems security 3 (2019), Nr.1, S.78-93
ISSN: 2509-3428
ISSN: 2509-3436
Fraunhofer AISEC ()

evice-specific physical characteristics provide the foundation for physical unclonable functions (PUFs), a hardware primitive for secure storage of cryptographic keys. Thus far, they have been implemented by either directly evaluating a binary output or by mapping symbols from a higher-order alphabet to a fixed-length bit sequence. However, when combined with equidistant quantization, this causes significant bias in the derived secret which is a security issue. 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 error-correcting code (ECC). This new approach effectively counteracts the bias in the derived key already at the input side of the ECC. 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. In addition to that, we investigate different segmentation approaches which is important due to the variable length of the considered values. Practical implementation results demonstrate that the proposed scheme requires only a fraction of the execution time compared to Bose-Chaudhuri-Hocquenghem (BCH) codes. This opens up a new direction of ECCs for PUFs that output responses with symbols of a higher-order alphabet.