General Vector Instruction Extension for GF(2m) Polynomial Operation in Post-quantum Cryptography

We present a general vector instruction extension applicable for both ARM NEON and RISC-V Vector Extension. The extension targets efficient bit-manipulation and can provide considerable speedup for applications in GF(2
^m
) such as code-based post-quantum cryptography schemes. The effectiveness of the extension is evaluated by using the custom instructions to optimize the kernel operations in BIKE key-encapsulation schemes. We first innovate vectorized versions of bit-polynomial multiplication and inversion algorithms in GF(2
^m
) and propose vector instruction extension. Furthermore, a configurable hardware unit has been proposed to support custom operations of different bandwidths at little cost and constant latency. Both experiments on Xilinx UltraScale+ ZCU104 for ARM and simulations on gem5 for RISC-V have been carried out. Compared to portable C implementation, the result shows a speedup for bit-polynomial multiplication and inversion of up to 13x and 16x in ARM, 13x and 22x in RISC-V respectively.