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

TL;DR

This work considers the generation and utilization of helper data for physical unclonable functions (PUFs) that provide real-valued, Gaussian distributed readout symbols and demonstrates how to generate additional helper data to enhance decodability resulting in the desired lower word error ratios.

Abstract

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.

Figures (11)

• Figure 1: The concept of helper data generation in the initialization phase (left part) and the usage of this helper data in the reproduction phase (right part).
• Figure 2: Model of the PUF as communication system with $M$-ary ($M = 2^\mu$) signaling and readout process modeled as transmission over an AWGN channel. Upper part: operations in the initialization phase.; Lower part: interpretation for the readout process in the reconstruction phase.
• Figure 3: Regions $4$-ary and $8$-ary uniform signaling, $8$-ary shaped signaling (top to bottom). Natural labeling.
• Figure 4: Example for helper schemes. The PUF reference readout ${\hbox{\boldmath$x$}}_\mathrm{puf}$ (top left) is given. The elements of the word in the signal space should lie in the regions indicated by the columns of the codematrix ${\hbox{\boldmath$\ff{C}$}}$ (bottom right). A permutation and possibly a sign flip of the elements leads to the word ${\hbox{\boldmath$x$}}$ (top right), which matches the demands except for $x_1$. The proposed helper scheme indicates which bits of ${\hbox{\boldmath$\ff{C}$}}$ have to be flipped in order to obtain the matrix ${\hbox{\boldmath$\ff{Q}$}}$ (bottom left), whose columns indicate in which regions the elements of ${\hbox{\boldmath$x$}}_\mathrm{puf}$ lie.
• Figure 5: Regions and pdf the readout. Top: conventional case ($M=4$, uniform signaling); Bottom: $S=2$ and subregions/pdfs for $s=0$ and $s=1$. The centroid of the subregions are indicated by the black ticks.