Selection of an error-correcting code for FPGA-based physical unclonable functions

This paper explores error-correcting codes for fuzzy extractor applications with Physical Unclonable Functions. We investigate BCH codes and compare them to convolutional codes using criteria of remaining entropy, probability of decoder failure, and hardware requirements. Parallel BCH coding is analyzed with a comprehensive search performed to find the smallest BCH code which satisfies the criteria in a parallel design to produce 128, 192, and 256-bit keys. A convolutional code is selected for comparison against the BCH codes found in this analysis. Application of the selected codes to a fuzzy extractor design is analyzed. Hardware requirements for FPGA implementations of each code is compared, with a BCH decoder design implemented for Artix-7 and Spartan-6 FPGA families. We find that a (127, 22, 47) parallel BCH code or (2, 1, 12) convolutional code is capable of performing as well as a single large BCH code, while requiring fewer FPGA resources when block RAMs can be leveraged. The convolutional code additionally requires the least amount of PUF ID bits.