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Formal Analysis of PUF Instances Leveraging Correlation-Spectra in Boolean Functions

  • Durba ChatterjeeEmail author
  • Aritra Hazra
  • Debdeep Mukhopadhyay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11947)

Abstract

In this paper, we present a novel formal analysis scheme considering that the fabrication of a batch of \(N > 1\) PUFs is equivalent to drawing random instances of Boolean mappings. We model PUFs as black-box Boolean functions of dimension \(m \times 1\) and show combinatorially that random designs of such \(m \times 1\) functions exhibit correlation-spectra which can be used to characterize random and thus good designs of PUFs. We first develop theoretical results to quantize the correlation values and subsequently find the expected number of pairs of such Boolean functions which should belong in different regions of the spectra. We extend the concept of correlation to PUFs and theoretically prove that a randomly chosen sample of PUFs and Boolean functions follow the same distribution. In addition to this, we show through extensive experimental results that a randomly chosen sample of such PUFs also resembles the correlation-spectra property of the overall PUF population. We finally propose a formal analysis tool for evaluation of PUFs by observing the correlation-spectra of the PUF instances under test. We show through experimental results on 50 FPGAs that when the PUFs are infected by faults the usual randomness tests for the PUF outputs such as uniformity, fail to detect any aberration. However, the spectral-pattern is clearly shown to get affected, which we demonstrate by standard statistical measure like KL Divergence.

Keywords

Physically Unclonable Functions Formal analysis Boolean functions 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Indian Institute of Technology KharagpurKharagpurIndia

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