Generating pairing-friendly elliptic curve parameters using sparse families

DOI10.1515/jmc-2017-0024zbMath1496.94043OpenAlexW2789331349MaRDI QIDQ1640702

Georgios Fotiadis, Elisavet Konstantinou

Publication date: 14 June 2018

Published in: Journal of Mathematical Cryptology (Search for Journal in Brave)

Full work available at URL: http://orbilu.uni.lu/handle/10993/39267

zbMATH Keywords

Pell equationpairing-based cryptographypairing-friendly elliptic curvessparse families

Mathematics Subject Classification ID

Cryptography (94A60) Elliptic curves (14H52) Curves over finite and local fields (11G20) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Cites Work

• Building curves with arbitrary small MOV degree over finite prime fields
• A new method of choosing primitive elements for Brezing-Weng families of pairing-friendly elliptic curves
• A taxonomy of pairing-friendly elliptic curves
• Ordinary Abelian varieties having small embedding degree
• Generating more MNT elliptic curves
• Elliptic curves suitable for pairing based cryptography
• Guide to Pairing-Based Cryptography
• Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case
• On the Efficient Generation of Generalized MNT Elliptic Curves
• Computing Hilbert class polynomials with the Chinese remainder theorem
• On Constructing Families of Pairing-Friendly Elliptic Curves with Variable Discriminant
• CONSTRUCTING PAIRING-FRIENDLY CURVES WITH VARIABLE CM DISCRIMINANT
• Generating Pairing-Friendly Curves with the CM Equation of Degree 1
• Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
• Constructing Pairing-Friendly Elliptic Curves Using Factorization of Cyclotomic Polynomials
• Pairing-Friendly Elliptic Curves of Prime Order
• Algorithmic Number Theory
• Simple continued fraction solutions for Diophantine equations

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