Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography

Nir Drucker, Shay Gueron, Dusan Kostic

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


The NIST PQC standardization project evaluates multiple new designs for post-quantum Key Encapsulation Mechanisms (KEMs). Some of them present challenging tradeoffs between communication bandwidth and computational overheads. An interesting case is the set of QC-MDPC based KEMs. Here, schemes that use the Niederreiter framework require only half the communication bandwidth compared to schemes that use the McEliece framework. However, this requires costly polynomial inversion during the key generation, which is prohibitive when ephemeral keys are used. One example is BIKE, where the BIKE-1 variant uses McEliece and the BIKE-2 variant uses Niederreiter. This paper shows an optimized constant-time polynomial inversion method that makes the computation costs of BIKE-2 key generation tolerable. We report a speedup of$$11.8{\times }$$ over the commonly used NTL library, and$$55.5{\times }$$ over OpenSSL. We achieve additional speedups by leveraging the latest Intel’s Vector-instructions on a laptop machine,$$14.3{\times }$$ over NTL and$$96.8{\times }$$ over OpenSSL. With this, BIKE-2 becomes a competitive variant of BIKE.

Original languageEnglish
Title of host publicationCyber Security Cryptography and Machine Learning - 4th International Symposium, CSCML 2020, Proceedings
EditorsShlomi Dolev, Gera Weiss, Vladimir Kolesnikov, Sachin Lodha
Number of pages18
ISBN (Print)9783030497842
StatePublished - 2020
Event4th International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2020 - Beersheba, Israel
Duration: 2 Jul 20203 Jul 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12161 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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