  Strong physical unclonable functions (PUFs) provide a low-cost authentication
primitive for resource constrained devices. However, most strong PUF
architectures can be modeled through learning algorithms with a limited number
of CRPs. In this paper, we introduce the concept of non-monotonic response
quantization for strong PUFs. Responses depend not only on which path is
faster, but also on the distance between the arriving signals. Our experiments
show that the resulting PUF has increased security against learning attacks. To
demonstrate, we designed and implemented a non-monotonically quantized
ring-oscillator based PUF in 65 nm technology. Measurement results show nearly
ideal uniformity and uniqueness, with bit error rate of 13.4% over the
temperature range from 0 C to 50 C.
