On the Performance and Security of Multiplication in GF(2N)

Danger, Jean-Luc; El Housni, Youssef; Facon, Adrien; Gueye, Cheikh T.; Guilley, Sylvain; Herbel, Sylvie; Ndiaye, Ousmane; Persichetti, Edoardo; Schaub, Alexander

doi:10.3390/cryptography2030025

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El Housni, Y
Facon, A
Gueye, CT.
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Herbel, S
Ndiaye, O
Persichetti, E
Schaub, A

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Facon, A
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Facon, A
Gueye, CT.
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With following keywords

finite field arithmetic

tower fields

post-quantum cryptography

code-based cryptography

cache-timing attacks

secure implementation

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Jean-Luc Danger

Youssef El Housni

Adrien Facon

Cheikh T. Gueye

Sylvain Guilley

Sylvie Herbel

Ousmane Ndiaye

Edoardo Persichetti

Alexander Schaub

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Open AccessArticle

Cryptography 2018, 2(3), 25; https://doi.org/10.3390/cryptography2030025

On the Performance and Security of Multiplication in GF(2^N)

Jean-Luc Danger¹

, Youssef El Housni^2,*

, Adrien Facon^2,3

, Cheikh T. Gueye⁴

, Sylvain Guilley^1,2,3

, Sylvie Herbel²

, Ousmane Ndiaye⁴

, Edoardo Persichetti^5,*

and Alexander Schaub¹

LTCI, Télécom ParisTech, Université Paris-Saclay, 75013 Paris, France

Secure-IC S.A.S., 35510 Cesson-Sévigné, France

Département d’Informatique, École Normale Supérieure, CNRS, PSL Research University, 75005 Paris, France

⁴

Département Mathématique et Informatique, Université Cheikh Anta Diop, Dakar 5005, Senegal

⁵

Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA

Authors to whom correspondence should be addressed.

Received: 2 August 2018 / Revised: 4 September 2018 / Accepted: 13 September 2018 / Published: 18 September 2018

(This article belongs to the Special Issue Code-Based Cryptography)

Full-Text | PDF [357 KB, uploaded 19 September 2018]

Abstract

Multiplications in

G F (2^{N})

can be securely optimized for cryptographic applications when the integer N is small and does not match machine words (i.e.,

N < 32

). In this paper, we present a set of optimizations applied to DAGS, a code-based post-quantum cryptographic algorithm and one of the submissions to the National Institute of Standards and Technology’s (NIST) Post-Quantum Cryptography (PQC) standardization call. View Full-Text

Keywords: finite field arithmetic; tower fields; post-quantum cryptography; code-based cryptography; cache-timing attacks; secure implementation finite field arithmetic; tower fields; post-quantum cryptography; code-based cryptography; cache-timing attacks; secure implementation

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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MDPI and ACS Style

Danger, J.-L.; El Housni, Y.; Facon, A.; Gueye, C.T.; Guilley, S.; Herbel, S.; Ndiaye, O.; Persichetti, E.; Schaub, A. On the Performance and Security of Multiplication in GF(2^N). Cryptography 2018, 2, 25.

AMA Style

Danger J-L, El Housni Y, Facon A, Gueye CT, Guilley S, Herbel S, Ndiaye O, Persichetti E, Schaub A. On the Performance and Security of Multiplication in GF(2^N). Cryptography. 2018; 2(3):25.

Chicago/Turabian Style

Danger, Jean-Luc; El Housni, Youssef; Facon, Adrien; Gueye, Cheikh T.; Guilley, Sylvain; Herbel, Sylvie; Ndiaye, Ousmane; Persichetti, Edoardo; Schaub, Alexander. 2018. "On the Performance and Security of Multiplication in GF(2^N)." Cryptography 2, no. 3: 25.

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