QC-MDPC Decoders with Several Shades of Gray

Nir Drucker, Shay Gueron, Dusan Kostic

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 currentplatforms, our BIKE-1 (Level-1) constant-time decapsulation is (Formula Presented) faster than the previous decapsulation with Black-Gray. We also report an additional (Formula Presented) decapsulating speedup using the newandinstructions available on “Ice-Lake” micro-architecture.

Original languageEnglish
Title of host publicationPost-Quantum Cryptography - 11th International Conference, PQCrypto 2020, Proceedings
EditorsJintai Ding, Jean-Pierre Tillich
Number of pages16
ISBN (Print)9783030442224
StatePublished - 2020
Event11th International Conference on Post-Quantum Cryptography, PQCrypto 2020 - Paris, France
Duration: 15 Apr 202017 Apr 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12100 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th International Conference on Post-Quantum Cryptography, PQCrypto 2020

Bibliographical note

Funding Information:
Acknowledgments. We thank Ray Perlner from NIST for pointing out that the mock-bits technique is not sufficient for security when using static keys, which drove us to change our BIKE implementation. This research was partly supported by: The Israel Science Foundation (grant No. 3380/19); The BIU Center for Research in Applied Cryptography and Cyber Security, and the Center for Cyber Law and Policy at the University of Haifa, both in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office.

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.


  • BIKE
  • Constant-time implementation
  • QC-MDPC codes
  • QC-MDPC decoders

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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