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.
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