Effect of aging on linear and nonlinear MUX PUFs by statistical modeling

This paper addresses the effect of aging on linear and non-linear MUX physical unclonable functions (PUFs). It is well known that a PUF response can be modeled in terms of the delay difference of MUX stages. In this paper, we show that the aging effects can be modeled in terms of variations in delay-difference and arbiter delay. Specifically, with aging, the percent delay-difference variation of each MUX stage can be modeled as a ratio of two correlated Gaussian random variables. This ratio distribution is shown to be approximately Gaussian with zero mean and variance increasing with time. In case of the arbiter, the ratio distribution is modeled as a Gaussian with positive mean. The paper makes three contributions: modeling the effect of aging in terms of percent variations in delay-difference of the MUX stages and arbiter delay, analysis of authentication accuracy with aging, and approaches to increase the PUF's lifetime by either recalibrating it to obtain new delay-difference parameters, or by tuning a threshold based on the total delay-difference. A general approach for selecting the threshold values is described in the paper. It is shown that the authentication accuracy of a PUF is significantly affected due to aging effects of the arbiter itself. Therefore, under the assumption that the variations in arbiter delay are considerably more than in delay-differences, the performance degradation in the case of aging alone is prominent compared to noise alone. We show that the authentication accuracy of a feed-forward PUF is more degraded compared to linear or modified feed-forward PUF. Metrics like Jenson-Shannon and Henze-Penrose divergence are also used to analyze the effect of aging.