Mathematical Modeling Analysis of Strong Physical Unclonable Functions

Physical unclonable function (PUF) is a technique to produce secret keys or complete authentication in integrated circuits (ICs) by exploiting the uncontrollable randomness due to manufacturing process variations. For better PUF applications, efficient analysis of different designs is important. In this article, a mathematical model to analyze the performance of typical strong PUF designs is proposed and applied to arbiter PUF, ring oscillator (RO) PUF, and duty cycle (DC) PUF. For better reliability, a new PUF design, DC multiplexer (DC MUX) PUF proposed in our previous work is analyzed. The proposed model indicates that DC MUX PUF achieves 2% higher reliability than arbiter PUF under environment influences. It also shows that DC PUF achieves 10% higher reliability than RO PUF. For verification, the aforementioned four PUF designs are testified using HSPICE. As our model analysis indicates, for reliability DC MUX PUF outperforms arbiter PUF, and DC PUF outperforms RO PUF. For randomness, DC MUX PUF and DC PUF outperform arbiter PUF and RO PUF, respectively. For security, LR attacks on DC MUX PUF and arbiter PUF are performed. The training time for DC MUX PUF is 40 000 times of arbiter PUF.