A Secure and Robust PUF-based Key Generation with Wiretap Polar Coset Codes

Millions of small and resource constrained devices are expected to connect in the fifth-generation (5G) network. To secure the devices, physical unclonable functions (PUFs) offer a practical solution of secret key generations. Polar codes have been considered in PUF-based key generation schemes to ensure robustness and security. However, we have proven that helper data errors have catastrophic effects on the hard-in min-sum based successive cancellation decoding in the scheme, which leads to decoding failures no matter how strong the polar codes are. In this paper, a new polar-based fuzzy extractor is proposed to securely and robustly generate secret keys from unstable and biased PUF bits. To handle the secrecy leakage caused by bias, we design an OR-based debiasing to control the resulting bias in $$[2-g,0.5]$$ , where $$g$$  is the golden ratio, and then the secrecy leakage caused by the resulting bias is hidden by wiretap polar coset codes. We evaluate the upper bound of the secrecy leakage using the Hamming weights of polar codewords and then determine the length of mask for meeting certain security and robustness requirements. In addition, we give a secure and robust polar construction algorithm for our key generation scheme based on Reed-Muller codes. Simulation results show that our design needs fewer PUF bits than other state-of-the-arts.