Mathematical Model of Strong Physically Unclonable Functions Based on Hybrid Boolean Networks

TL;DR

The results suggest that the HBN-PUF is a true ‘strong’ PUF in the sense that its security properties depend exponentially on both the manufacturing variation and the challenge-response space.

Abstract

We introduce a mathematical framework for simulating Hybrid Boolean Network (HBN) Physically Unclonable Functions (PUFs, HBN-PUFs). We verify that the model is able to reproduce the experimentally observed PUF statistics for uniqueness $μ_{inter}$ and reliability $μ_{intra}$ obtained from experiments of HBN-PUFs on Cyclone V FPGAs. Our results suggest that the HBN-PUF is a true `strong' PUF in the sense that its security properties depend exponentially on both the manufacturing variation and the challenge-response space. Our Python simulation methods are open-source and available at https://github.com/Noeloikeau/networkm.

Figures (3)

• Figure 1: A Hybrid Boolean Network (HBN), depicted as an $N=32$ random regular graph of degree 3, in which each node executes the exclusive-or (XOR) function on the state of 3 random neighbors. The FPGA logic elements and wiring diagram are shown for a single node $n$. The identity of nodes $k-q$ are determined by the fixed topology of the HBN. The block diagram depicts the proposed differential equation \ref{['dxdt']} governing the analog node state $x_{n}$.
• Figure 2: Statistics of experimental (top row) and simulated (bottom row) $N=256$ HBN-PUFs. Light-colored curves are per-class, per-time statistics $\mu^{s}(t)$. Solid curves are an average over $s$, representing a typical HBN-PUF. The sample sizes for the experimental data are given in Table \ref{['indices']}. The simulated data use a noise amplitude $\varepsilon=0.01$ and manufacturing variation $\sigma=0.05$, with sample sizes $N_{s}=N_{i}=N_{c}=N_{r}=15$.
• Figure 3: Variation of the average simulated statistics in Fig. \ref{['fig2']} with respect to $\sigma$ and $\varepsilon$ evaluated at fixed $t_{opt}=6$ ns. The black curves are fits to the function $y=B-Ae^{-Cx}$. (a): Uniqueness as a function of $\sigma$, with a fixed $1\%$ noise floor $\mu_{inter}(\sigma,\varepsilon=0.01)$, having fit parameters $A=0.32\pm0.01$, $B=0.48\pm0.00$, $C=93.78\pm3.98$. (b): Reliability as a function of $\varepsilon$, with a fixed $5\%$ manufacturing variation $\mu_{intra}(\varepsilon,\sigma=0.05)$, having fit parameters $A=0.28\pm0.01$, $B=0.29\pm0.00$, $C=36.67\pm2.27$.