Y QC-MDPC Decoders with Several Shades of Gray

QC-MDPC code-based KEMs rely on decoders that have a small or even negligible Decoding Failure Rate (DFR). These decoders should be efficient and implementable in constant-time. One example for a QC-MDPC KEM is the Round-2 candidate of the NIST PQC standardization project, "BIKE". We have recently shown that the Black-Gray decoder achieves the required properties. In this paper, we define several new variants of the Black-Gray decoder. One of them, called Black-Gray-Flip, needs only 7 steps to achieve a smaller DFR than Black-Gray with 9 steps, for the same block size. On current AVX512 platforms, our BIKE-1 (Level-1) constant-time decapsulation is 1.9x faster than the previous decapsulation with Black-Gray. We also report an additional 1.25x decapsulating speedup using the new AVX512-VBMI2 and vector-PCLMULQDQ instructions available on "Ice-Lake" micro-architecture.