In this paper, we consider the generation and utilization of helper data for physical unclonable functions (PUFs) that provide real-valued readout symbols. Compared to classical binary PUFs, more entropy can be extracted from each basic building block (PUF node), resulting in longer keys/fingerprints and/or a higher reliability. To this end, a coded modulation and signal shaping scheme that matches the (approximately) Gaussian distribution of the readout has to be employed. A new helper data scheme is proposed that works with any type of coded modulation/shaping scheme. Compared to the permutation scheme from the literature, less amount of helper data has to be generated and a higher reliability is achieved. Moreover, the recently proposed idea of a two-metric helper data scheme is generalized to coded modulation and a general S-metric scheme. It is shown how extra helper data can be generated to improve decodability. The proposed schemes are assessed by numerical simulations and by evaluation of measurement data. We compare multi-level codes using a new rate design strategy with bit-interleaved coded modulation and trellis shaping with a distribution matcher. By selecting a suitable design, the rate per PUF node that can be reliably extracted can be as high as 2~bit/node.

翻译：本文研究了为具备实值读出符号的物理不可克隆函数（PUF）生成和利用辅助数据的方法。相较于经典二进制PUF，该方法可从每个基本构建块（PUF节点）中提取更多熵，从而生成更长的密钥/指纹并/或实现更高可靠性。为此，需要采用与读出值（近似）高斯分布相匹配的编码调制与信号成形方案。本文提出了一种适用于任意类型编码调制/成形方案的新型辅助数据方案。与文献中的置换方案相比，该方案所需生成的辅助数据量更少，且可靠性更高。此外，本文将近期提出的双度量辅助数据方案推广至编码调制领域，并提出了通用S度量方案。本文展示了如何生成额外辅助数据以提升可解码性。通过数值仿真及实测数据评估，对所提方案进行了验证。我们采用新型速率设计策略比较了多级码、比特交织编码调制以及结合分布匹配器的网格成形。通过选取合适的设计，每个PUF节点可可靠提取的速率高达2比特/节点。