An Improved Analysis of Reliability and Entropy for Delay PUFs

Physically unclonable functions (PUF) have been used in various applications, such as device authentication, secure storage of sensitive data, and anti-counterfeiting. Different applications require various levels of reliability from the PUF. However, as of today, no predictive model to characterize the PUF reliability has been developed. This is particularly a problem for PUFs with low error rates, because the lower the error rate, the larger the number of measurements required to obtain a good estimate. In this paper, we develop a predictive framework, which enables us to derive a closed-form expression of both entropy and reliability for several families of delay PUFs: the ring oscillator (RO) PUF, the RO sum PUF as well as the Loop PUF. Improving reliability with bit-filtering, we provide an explicit tradeoff between complexity, reliability and entropy. Error rates as low as 10^-9 or even lower can be achieved. Our theoretical results are validated by experiments on Loop PUFs implemented in 65 nm CMOS ASIC technology, also used to simulate the behavior of the RO PUF and the RO sum PUF.