Not All Feed-Forward MUX PUFs Generate Unique Signatures

A fundamental property of physical unclonable functions (PUFs) is that they generate unique outputs that cannot be reproduced by another chip, even with an identical circuit and layout design. Several configurations of feed-forward PUFs (FF PUFs) are evaluated in terms of their interchip variation, a measure of uniqueness. In general, PUFs are considered to be unique due to symmetry in their path delay distributions, which are typically Gaussian. In this paper, we prove that certain FF PUFs can result in skewed path delay distributions leading to poor uniqueness. In these PUFs, the total delay difference is sum of a symmetric Gaussian distribution and an asymmetric half-Gaussian distribution. We also compute empirical estimates and verify our observations by simulating 200 PUFs in each FF configuration. It is observed that (1) FF PUFs with one intermediate arbiter and odd number of feed-forward loops and (2) FF PUFs in cascade or separate configurations have degraded interchip variation. This is the first study to observe and prove the non-uniqueness property of such PUFs.