Efficient Bound for Conditional MinEntropy of Physical Unclonable Functions Beyond IID The remaining minentropy of a secret generated by fuzzy extraction from a Physical Unclonable Function is typically estimated under the assumption of independent and identically distributed PUF responses, but this assumption does not hold in practice. This work analyzes the more realistic case that the responses are independent but not necessarily identically distributed. For this case, we extend the (nk) bound and a tighter bound by Delvaux et al. In particular, we suggest a grouping bound which provides a trade off for accuracy vs computational effort. Comparison to previous bounds shows the accuracy and efficiency of our bound. We also adapt the key rank (a tool from sidechannel analysis) to crossvalidate the stateoftheart and our proposed minentropy bounds based on publicly available PUF data from real hardware.

On the Confidence in BitAlias 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 PUFu0027s 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 BitAlias, is a stateoftheart metric in this regard. However, the confidence interval of the BitAlias is never considered, which can lead to an overestimation of a PUFu0027s unpredictability. Moreover, no tool is available to verify if the BitAlias is within given limits. This work adapts a method for the calculation of confidence intervals to BitAlias. It further proposes a statistical hypothesis test to verify if a PUF design meets given specifications on BitAlias or bitwise entropy. Application to several published PUF designs demonstrates the methodsu0027 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.