Frequency Domain Authentication Using Piezoelectric PZT Disks as Hardware IDs

Abstract

The increasing interconnectedness of the modern world in the consumer, commercial, and military realms has emphasized the necessity of authenticating devices to prevent impostor attack vulnerabilities from being exploited. However, conventional digital methods used to store identification information in various devices are susceptible to various methods that can potentially expose the information to bad actors. Therefore, the avenue of hardware IDs, whose analog properties dictate its identity via in-situ bit string generation, is increasingly being explored as an alternative, given that they do not store a digital identifying key, are resistant to invasive attacks, can be cost-effective, are relatively tamper-evident, and can be difficult to clone. In this thesis, the focus will be on utilizing a lead zirconate titanate (PZT) thin cylinder (disk) as a hardware ID, based on the response of its various entropy sources to a frequency sweep. Those entropy sources explored by this work are the admittance peak magnitudes, resonance frequencies, quality factor of the admittance peaks, impedance peak magnitudes, anti-resonance frequencies, and quality factor of the impedance peaks. These sources exhibit a wide degree of variation in response to minute changes in the PZT disk dimensions, which are varied in this work. This experiment is conducted in the COMSOL Multiphysics simulation environment to obtain unique IDs for each disk. The entropy source values for each disk are digitized via bins of a corresponding continuous distribution constructed from the sample values by Gaussian kernel density estimation, in which six sets of 10-bit IDs—one for each entropy source—are created, and a set of 60-bit IDs is created via concatenation of the 10-bit sets. Then, these bits are evaluated for security, and demonstrate uniqueness values that consistently approach 0.5, average minimum entropies per bit around 0.9 bits, and maximum entropy and no collisions in the 60-bit ID set. The minimum sampling rate for a subsequent hardware implementation beyond the scope of this work is found to be 946528 Hz, with a minimum frequency resolution capability of 6 µHz, and a minimum magnitude resolution of 2799.9306 siemens and 3748.1494 ohms. Additionally, total correlation and dual total correlation is found to be low as a fraction of the 10 bits present in the 10-bit ID sets but is skewed in a negative direction due to the small sample size compared to the number of possible bit combinations in the 60-bit ID set. However, in all cases, these metrics prove to be useful for assessing the total information quantity and thus security of the set of devices in the context of Kerckhoff's principle. These results show that PZT disks, and the piezoelectric quirks associated with the material and geometry, are conducive to viable hardware IDs that can serve as the backbone for a secure system in the contemporary world.