Exploiting Weak PUFs From Data Converter Nonlinearity—E.g., A Multibit CT $\Delta\Sigma$ Modulator

This paper presents a novel approach of deriving physical unclonable functions (PUF) from correction circuits measuring and digitizing nonlinearities of data converters. The often digitally available correction data can then be used to generate a fingerprint of the chip. The general concept is presented and then specifically evaluated on an existing Delta-Sigma (ΔΣ) modulator whose outermost feedback DAC mismatches are greatly influencing the overall performance and thus need correction. The applied mixed-signal correction scheme reveals the intrinsic mismatches which are firstly used to linearize the ΔΣ modulator, but which can also be further analyzed. The intra-Hamming distance is initially determined to values less than 6% at nominal conditions and could be further reduced to less than 2% by applying different encodings. Regarding the distinctness of devices, the inter-Hamming distance is highly stable under all circumstances with a value very close to 50%. Though the influence of varying environmental conditions on the stability of repeated PUF readouts is negligible, inevitable deviations in the correction coefficients increase the intra-Hamming distance with respect to nominal conditions. As a result, 80 highly stable identification bits are obtained from the exemplarily used ΔΣ modulator.

I. Introduction

Over the last decade, physical unclonable functions (PUF) became a topic of increasing interest in cryptographic and authentication applications. Utilizing physical variations in the silicon resulting from limited fabrication accuracy, PUFs offer great characteristics for this field namely uniqueness, unpredictability and unclonability [1], [2]. When stimulated with a digital input, they generate an individual digital response based on their unique mismatches. So called “weak PUFs” [3] are capable of generating only few or even a single response. Their outputs usually cannot be used directly in an authentication scheme based on challenge-response-pairs (CRP) as the secrecy of the information is revealed in that process. Still weak PUFs can be used for either identification purposes (fingerprinting) or as sources of randomness for key generation in cryptographic hardware.