Helper Data Schemes for Coded Modulation and Shaping in Physical Unclonable Functions

We consider the generation and utilization of helper data for physical unclonable functions (PUFs) that provide real-valued, Gaussian distributed readout symbols. A coded modulation and signal shaping scheme that matches this distribution is employed, extracting more than one bit of entropy from each basic building block (PUF node). Compared to classical binary PUFs, longer keys/fingerprints are obtained and/or higher reliabilities (lower error ratios) are possible. A new helper data scheme is proposed that works with any type of coded modulation/shaping scheme. Compared to the permutation scheme known from the literature, in the conversion scheme, a smaller amount of helper data needs to be generated, yet a higher reliability is achieved. Additionally, the recently proposed idea of a two-metric helper data scheme is generalized to coded modulation and a general S-metric scheme. We demonstrate how to generate additional helper data to enhance decodability resulting in the desired lower word error ratios. The proposed schemes are assessed through numerical simulations and evaluation of measurement data. We compare multi-level codes employing a newly proposed rate design strategy with bit-interleaved coded modulation and trellis shaping with a distribution matcher. It is demonstrated that when selecting a suitable design, the rate per PUF node that can be reliably extracted can be as high as 2 bit/node.