A new model for estimating bit error probabilities of Ring-Oscillator PUFs

Embedded systems carry and process more and more sensitive information in untrusted environments, where an attacker can wiretap the external communication and also has unlimited physical access to the device. Cryptography protects systems against many of the threats and relies on the security of the cryptographic keys inside the system. Physical Unclonable Functions (PUFs) measure manufacturing variations inside integrated circuits, for example FPGAs, to generate a unique secret PUF response inside each device. Similar to deriving a biometric pattern from human features, the individual pattern inside an FPGA differs slightly from measurement to measurement. From these measurements, the PUF response is generated to derive a secure and reliable cryptographic key. The Ring-Oscillator (RO) PUF is a popular PUF type because of its high randomness and reliability. Frequencies of ROs are compared pairwise to derive one secret bit. So far, the reliability of RO PUFs was evaluated by counting bit flips in measured PUF responses. This work analyzes the distribution of frequency measurements to derive the behavior of the PUF. Analyzing the frequency distributions gives a more precise estimation of the PUF bit error rates than measuring the bit errors after the comparison of two oscillator frequencies. The evaluation of publicly available real world empirical FPGA data has shown that most error probabilities of RO PUF responses are so low that they cannot be measured in feasible time. For almost 200 evaluated FPGAs, more than 70% of the PUF outputs on every FPGA have bit error probabilities under 10^-20. We can even ensure this error probability for over 60% of the PUF outputs after a practicable number of frequency measurements with a confidence of 99.9%. Index Terms-Physical Unclonable Functions (PUFs), Ring Oscillator PUF, FPGA, Statistics.