Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction

Nir Drucker, Shay Gueron, Vlad Krasnov

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


Polynomial multiplication over binary fields F2n is a common primitive, used for example by current cryptosystems such as AES-GCM (with n=128). It also turns out to be a primitive for other cryptosystems, that are being designed for the Post Quantum era, with values ngg 128. Examples from the recent submissions to the NIST Post-Quantum Cryptography project, are BIKE, LEDAKem, and GeMSS, where the performance of the polynomial multiplications, is significant. Therefore, efficient polynomial multiplication over F2n, with large n, is a significant emerging optimization target. Anticipating future applications, Intel has recently announced that its future architecture (codename 'Ice Lake') will introduce a new vectorized way to use the current VPCLMULQDQ instruction. In this paper, we demonstrate how to use this instruction for accelerating polynomial multiplication. Our analysis shows a prediction for at least 2x speedup for multiplications with polynomials of degree 512 or more.

Original languageEnglish
Title of host publicationProceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Print)9781538626122
StatePublished - 13 Sep 2018
Event25th International Symposium on Computer Arithmetic, ARITH 2018 - Amherst, United States
Duration: 25 Jun 201827 Jun 2018

Publication series

NameProceedings - Symposium on Computer Arithmetic


Conference25th International Symposium on Computer Arithmetic, ARITH 2018
Country/TerritoryUnited States

Bibliographical note

Funding Information:
This research was supported by: The PQCRYPTO project, which was partially funded by the European Commission Horizon 2020 research Programme, grant #645622; The Israel Science Foundation (grant No. 1018/16); The Ministry of Science and Technology, Israel, and the Department of Science and Technology, Government of India; The BIU Center for Research in Applied Cryptography and Cyber Security, in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office; The Center for Cyber Law and Policy at the University of Haifa.

Publisher Copyright:
© 2018 IEEE.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Hardware and Architecture


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