BF PUF: A Modeling Attack-Resistant Strong PUF Based on Bent Functions

Strong physical unclonable functions (PUFs) are promising circuits for lightweight Internet of Things (IoT) authentication and security. However, existing strong PUFs exhibit very low cryptographic nonlinearity (NL), making them vulnerable to machine learning (ML) modeling and cryptanalytic attack. To address this issue, we propose the Bent function PUF (BF PUF) based on Maiorana-McFarland (M-M) constructed Bent functions, which obfuscates the responses of the strong PUF to enhance resistance against modeling attacks. The core idea is to employ the M-M construction method for Bent functions to ensure maximum cryptographic NL to resist modeling attacks. A Feistel network is configured using weak PUF responses as keys to achieve device-specific and unpredictable mappings of input challenges while meeting the requirements of the M-M Bent function construction. A Python-based model of the BF PUF was developed, and simulation results indicate that the cryptographic NL of the proposed BF PUF outperforms <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xor</small> arbiter PUFs (APUFs) (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k} =2$</tex-math> </inline-formula>, 4, 6). The proposed BF PUF was also implemented and evaluated on the FPGA hardware platform. The experimental results show that under modeling attacks using four ML algorithms—logistic regression (LR), artificial neural networks (ANNs), deep neural networks (DNNs), and covariance matrix adaptation evolution strategies (CMA-ES)—the best prediction accuracy under these four modeling attack algorithms is 52.60%. The reliability under temperature fluctuations ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 10~^{\circ }$</tex-math> </inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$80~^{\circ }$</tex-math> </inline-formula>C is between 84.20% and 99.78%.