A PUF is expected to generate responses containing ideally the same number of logic-0s and logic-1s. Therefore, the uniformity metric (also called randomness by Yu et al. in [47]) can be exploited to estimate the distribution of logic-0 and logic-1 in PUF responses. Let N be the number of response bits, the percentage measure for uniformity of response r = (г,_{0}, гц, ... r_{itN}__{1}) can be defined as

A value of 100% means that all r response bits are logic-1. For true random bits, uniformity should be as close as possible to its ideal value of 50 %. Let R be the number of responses, resulting from the product between the amount of different

PUF instances and input challenges (if any). The average uniformity for a population or R devices can be calculated as

i

Bit Aliasing

The uniformity metric is not enough to qualify the randomness of PUFs responses. Indeed, even with a best value of bit uniformity, some homologous bits could turn out to be biased among the responses of the PUF population. This could happen whenever the manufacturing process introduces static variations which compromise all the homologous bits in the responses, causing a fixed preferred value. To this aim, we can compute the bit aliasing [30] (also called bias in [47]) as

If some homologous bits are biased, the bit-aliasing results in a value far from 50 %.