Paper 2019/1423

QC-MDPC decoders with several shades of gray

Nir Drucker, Shay Gueron, and Dusan Kostic


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 deffine 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.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
BIKEQC-MDPC codesconstant-time implementationQC-MDPC decoders
Contact author(s)
drucker nir @ gmail com
shay gueron @ gmail com
dusan kostic @ epfl ch
2019-12-10: received
Short URL
Creative Commons Attribution


      author = {Nir Drucker and Shay Gueron and Dusan Kostic},
      title = {QC-MDPC decoders with several shades of gray},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1423},
      year = {2019},
      note = {\url{}},
      url = {}
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