New results on quasi-subfield polynomials

Marie Euler; Christophe Petit

doi:10.1016/j.ffa.2021.101881

New results on quasi-subfield polynomials

Marie Euler, Christophe Petit

Computer Science

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Abstract

Quasi-subfield polynomials were introduced by Huang et al. together with a new algorithm to solve the Elliptic Curve Discrete Logarithm Problem (ECDLP) over finite fields of small characteristic. In this paper we provide both new quasi-subfield polynomial families and a new theorem limiting their existence. Our results do not allow to derive any speedup for the new ECDLP algorithm compared to previous approaches.

Original language	English
Article number	101881
Journal	Finite Fields and Their Applications
Volume	75
Early online date	11 Jun 2021
DOIs	https://doi.org/10.1016/j.ffa.2021.101881
Publication status	Published - Oct 2021

Keywords

Cryptography
Elliptic curve discrete logarithm problem
Linearized polynomials

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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10.1016/j.ffa.2021.101881Licence: None: All rights reserved

EulerM2021NewAccepted author manuscript, 486 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Isogeny-Based Cryptography: From Theory to Practice
Petit, C.
Engineering & Physical Science Research Council
25/03/19 → 24/03/22
Project: Research Councils

Cite this

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title = "New results on quasi-subfield polynomials",

abstract = "Quasi-subfield polynomials were introduced by Huang et al. together with a new algorithm to solve the Elliptic Curve Discrete Logarithm Problem (ECDLP) over finite fields of small characteristic. In this paper we provide both new quasi-subfield polynomial families and a new theorem limiting their existence. Our results do not allow to derive any speedup for the new ECDLP algorithm compared to previous approaches.",

keywords = "Cryptography, Elliptic curve discrete logarithm problem, Linearized polynomials",

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AB - Quasi-subfield polynomials were introduced by Huang et al. together with a new algorithm to solve the Elliptic Curve Discrete Logarithm Problem (ECDLP) over finite fields of small characteristic. In this paper we provide both new quasi-subfield polynomial families and a new theorem limiting their existence. Our results do not allow to derive any speedup for the new ECDLP algorithm compared to previous approaches.

KW - Cryptography

KW - Elliptic curve discrete logarithm problem

KW - Linearized polynomials

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VL - 75

JO - Finite Fields and Their Applications

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New results on quasi-subfield polynomials

Abstract

Keywords

ASJC Scopus subject areas

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Projects

Isogeny-Based Cryptography: From Theory to Practice

Cite this