On the Confidence in Bit-Alias Measurement of Physical Unclonable Functions

Physical Unclonable Functions (PUFs) are modern solutions for cheap and secure key storage. The security level strongly depends on a PUF's unpredictability, which is impaired if certain bits of the PUF response tend towards the same value on all devices. The expectation for the probability of 1 at some position in the response, the Bit-Alias, is a state-of-the-art metric in this regard. However, the confidence interval of the Bit-Alias is never considered, which can lead to an overestimation of a PUF's unpredictability. Moreover, no tool is available to verify if the Bit-Alias is within given limits. This work adapts a method for the calculation of confidence intervals to Bit-Alias. It further proposes a statistical hypothesis test to verify if a PUF design meets given specifications on Bit-Alias or bit-wise entropy. Application to several published PUF designs demonstrates the methods' capabilities. The results prove the need for a high number of samples when the unpredictability of PUFs is tested. The proposed methods are publicly available and should improve the design and evaluation of PUFs in the future.