Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction

Nir Drucker; Shay Gueron; Vlad Krasnov

doi:10.1109/ARITH.2018.8464777

Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction

Nir Drucker, Shay Gueron, Vlad Krasnov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 language	English
Title of host publication	Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	115-119
Number of pages	5
ISBN (Print)	9781538626122
DOIs	https://doi.org/10.1109/ARITH.2018.8464777
State	Published - 13 Sep 2018
Event	25th International Symposium on Computer Arithmetic, ARITH 2018 - Amherst, United States Duration: 25 Jun 2018 → 27 Jun 2018

Publication series

Name	Proceedings - Symposium on Computer Arithmetic
Volume	2018-June

Conference

Conference	25th International Symposium on Computer Arithmetic, ARITH 2018
Country/Territory	United States
City	Amherst
Period	25/06/18 → 27/06/18

Bibliographical note

Publisher Copyright:
© 2018 IEEE.

ASJC Scopus subject areas

Theoretical Computer Science
Software
Hardware and Architecture

Access to Document

10.1109/ARITH.2018.8464777

Cite this

Drucker, N., Gueron, S., & Krasnov, V. (2018). Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction. In Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018 (pp. 115-119). Article 8464777 (Proceedings - Symposium on Computer Arithmetic; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ARITH.2018.8464777

@inproceedings{be2666512ca644fba16b7a28ddcac64f,

title = "Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction",

abstract = "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.",

author = "Nir Drucker and Shay Gueron and Vlad Krasnov",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 25th International Symposium on Computer Arithmetic, ARITH 2018 ; Conference date: 25-06-2018 Through 27-06-2018",

year = "2018",

month = sep,

day = "13",

doi = "10.1109/ARITH.2018.8464777",

language = "English",

isbn = "9781538626122",

series = "Proceedings - Symposium on Computer Arithmetic",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "115--119",

booktitle = "Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018",

address = "United States",

}

Drucker, N, Gueron, S & Krasnov, V 2018, Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction. in Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018., 8464777, Proceedings - Symposium on Computer Arithmetic, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 115-119, 25th International Symposium on Computer Arithmetic, ARITH 2018, Amherst, United States, 25/06/18. https://doi.org/10.1109/ARITH.2018.8464777

Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction. / Drucker, Nir; Gueron, Shay; Krasnov, Vlad.
Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 115-119 8464777 (Proceedings - Symposium on Computer Arithmetic; Vol. 2018-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction

AU - Drucker, Nir

AU - Gueron, Shay

AU - Krasnov, Vlad

PY - 2018/9/13

Y1 - 2018/9/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85054323766&partnerID=8YFLogxK

U2 - 10.1109/ARITH.2018.8464777

DO - 10.1109/ARITH.2018.8464777

M3 - Conference contribution

AN - SCOPUS:85054323766

SN - 9781538626122

T3 - Proceedings - Symposium on Computer Arithmetic

SP - 115

EP - 119

BT - Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 25th International Symposium on Computer Arithmetic, ARITH 2018

Y2 - 25 June 2018 through 27 June 2018

ER -

Drucker N, Gueron S, Krasnov V. Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction. In Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 115-119. 8464777. (Proceedings - Symposium on Computer Arithmetic). doi: 10.1109/ARITH.2018.8464777

Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this