On Constant-Time QC-MDPC decoders with negligible failure rate

Nir Drucker, Shay Gueron, Dusan Kostic

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


The QC-MDPC code-based KEM Bit Flipping Key Encapsulation (BIKE) is one of the Round-2 candidates of the NIST PQC standardization project. It has a variant that is proved to be IND-CCA secure. The proof models the KEM with some black-box (“ideal”) primitives. Specifically, the decapsulation invokes an ideal primitive called “decoder”, required to deliver its output with a negligible Decoding Failure Rate (DFR). The concrete instantiation of BIKE substitutes this ideal primitive with a new decoding algorithm called “Backflip”, that is shown to have the required negligible DFR. However, it runs in a variable number of steps and this number depends on the input and on the key. This paper proposes a decoder that has a negligible DFR and also runs in a fixed (and small) number of steps. We propose that the instantiation of BIKE uses this decoder with our recommended parameters. We study the decoder’s DFR as a function of the scheme’s parameters to obtain a favorable balance between the communication bandwidth and the number of steps that the decoder runs. In addition, we build a constant-time software implementation of the proposed instantiation, and show that its performance characteristics are quite close to the IND-CPA variant. Finally, we discuss a subtle gap that needs to be resolved for every IND-CCA secure KEM (BIKE included) where the decapsulation has nonzero failure probability: the difference between average DFR and “worst-case” failure probability per key and ciphertext.

Original languageEnglish
Title of host publicationCode-Based Cryptography - 8th International Workshop, CBCrypto 2020, Revised Selected Papers
EditorsMarco Baldi, Paolo Santini, Edoardo Persichetti
Number of pages30
ISBN (Print)9783030540739
StatePublished - 2020
Event8th International Workshop on Code-Based Cryptography, CBCrypto 2020 - Zagreb, Croatia
Duration: 9 May 202010 May 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12087 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Workshop on Code-Based Cryptography, CBCrypto 2020

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2020.


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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