A Theoretical Model to Link Uniqueness and Min-Entropy for PUF Evaluations

Chongyan Gu, Weiqiang Liu, Neil Hanley, Robert Hesselbarth, Maire O'Neill

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)
550 Downloads (Pure)


Physical unclonable functions (PUFs) are security primitives which enable the extraction of digital identifiers from electronic devices, based on the inherent silicon variation between devices which occurs during the manufacturing process. Due to the intrinsic and lightweight nature of a PUF, they have been proposed to provide security at a low cost for many applications, e.g. IoT. Many
metrics have been proposed to evaluate the security and performance of PUF architectures, e.g. uniqueness and min-entropy. The uniqueness of a PUF response evaluates its ability to differentiate between different physical devices, while the entropy prediction is a measure of how much uncertainty the response provides. The min-entropy is a lower-bound of real entropy. When the uniqueness of a PUF design is close to the optimal, it is unclear if the design has a significantly high entropy. It would also be useful to ascertain the minimum uniqueness required to achieve a given entropy. To date, a thorough investigation of the relationship between uniqueness and entropy for PUF designs has not been conducted. In this paper, this relationship between the uniqueness and entropy is explored, and for the first time, to the authors’ knowledge, the relationship between them is modeled. To verify this model, both simulated and hardware-based experimental results are performed, with a test-bed containing 184 Xilinx Artix-7 FPGA based Basys3 boards providing a large dataset for granular results. The experimental results demonstrate that the proposed model accurately estimates the relationship between uniqueness and min-entropy. The hardware-based min-entropy and uniqueness results match closely with both theoretical analysis and software simulation.
Original languageEnglish
Pages (from-to)287
JournalIEEE Transactions on Computers
Issue number2
Publication statusPublished - 23 Aug 2018


  • Entropy
  • Physical Unclonable Functions
  • Uniqueness


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