Efficient and scalable FPGA design of GF(2m) inversion for post-quantum cryptosystems

Post-quantum cryptosystems based on QC-MDPC codes are designed to mitigate the security threat posed by quantum computers to traditional public-key cryptography. The polynomial inversion is the core operation of key generation in such cryptosystems and the adoption of ephemeral keys imposes the execution of key generation for each session. To this end, there is a need for efficient and scalable hardware implementations of binary polynomial inversion to support the key generation primitive across a wide range of computational platforms. This manuscript proposes an efficient and scalable architecture that supports binary polynomial inversion at the hardware level and that can deliver a performance-optimized implementation for each polynomial length and for each FPGA of the mid-range Xilinx Artix-7 family. The effectiveness of the proposed solution was validated by means of the BIKE and LEDAcrypt post-quantum QC-MDPC cryptosystems as representative use cases. Compared to the C11- and the optimized AVX2-based software implementations of LEDAcrypt, instances of the proposed architecture targeting the Artix-7 200 FPGA show an average performance improvement of 31.7 and 2.2 times, respectively. Moreover, the proposed architecture delivers a performance improvement up to 18.1 and 21.5 times for AES-128 and AES-192 security levels, respectively, compared to the BIKE hardware implementation.