In the literature, many silicon PUF architectures have been introduced and each one tries to enhance one of the properties illustrated in the Sect. 10.2. To compare them with objective measurements, some metrics have been introduced [31, 47]. The need for fair metrics to compare the quality of PUF proposals has generated some quality parameters.

Uniqueness

Ideally, due to the manufacturing variability, devices are unique in terms of physical quantities which characterize them. Silicon PUFs discretize such physical quantity to extract bit strings as responses from provided challenges, hence the uniqueness can be estimated trough responses comparison. Having a pair of PUF instances whichprovide N-bitresponses, respectively T_{j} = (T_{j},_{0}, T_{j},_{1}, ... T_{j},_{N}__{1}) and ^{r}j = (Tj,_{0}, Tj1, ... Tj,_{N}__{1}), the uniqueness can be estimated as the fractional Hamming distance between r_{j} and Tj. The Hamming distance (HD) is a function computed over two binary strings of equal length which returns the number of homologous bits that differ, or, in other words, the minimum amount of substitutions needed to change one string into the other. The fractional HD (fHD) normalizes the distance value on the string length and can be formalized as:

It returns a value in the range [0, 1], yielding the value 0 if T_{j} = Tj and the value 1 if

^{T}i = T.

Globally, for a population of R devices, we can estimate the uniqueness, also called inteT-chip HD, averaging fHD calculated for all (^{R}) responses pairs:

If PUFs provide uniformly distributed and independent response bits, the global uniqueness turns out to be close to 50 % on average. Values higher or lower than 50 % are symptoms of lower chip distinguishability.