Fast Hardware Architecture With Efficient Matrix Computations for the Key Generation of Classic McEliece

Classic McEliece, with a remarkably stable security level, has been selected as one of the four key-establishment algorithms in the fourth-round evaluation of the post-quantum cryptography (PQC) standardization process of national institute of standards and technology (NIST). However, its memory-intensive and time-consuming key generation poses an obstacle to widespread use. In this paper, we propose a fast hardware implementation of the key generation incorporating several architectural optimizations. For the Gaussian elimination, we optimize the scheduling of computing resources and the memory access process and present a high-performance and flexible systemizer with multiple low fan-out systolic arrays. Besides, an algorithmic-level parallelized design for entry generation and Gaussian elimination is proposed to reduce the redundant computation time. A compact entry generator with a multi-level feedback mechanism and a 2-D high-speed FFT module facilitates continuous streaming the generated entries into the systemizer.FPGA implementation results show that our designs for the key generation improve time-area efficiency by 11.9% to 43.2% compared to the state-of-the-arts. Moreover, compared to the hardware implementations for the key generation of the other two quasi-cyclic code-based PQC algorithms, ours for Classic McEliece based on the random code achieves close to or better results in several metrics.