Implementing the 4-dimensional GLV method on GLS elliptic curves with \(j\)-invariant 0

DOI10.1007/s10623-011-9558-1zbMath1253.14027OpenAlexW2033553296MaRDI QIDQ411481

Zhi Hu, Patrick Longa, Mao-Zhi Xu

Publication date: 4 April 2012

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-011-9558-1

zbMATH Keywords

elliptic curvesGLS curvesGLV methodpoint multiplication

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items

Ready-made short basis for GLV+GLS on high degree twisted curves, Fast subgroup membership testings for \(\mathbb{G}_1, \mathbb{G}_2\) and \(\mathbb{G}_T\) on pairing-friendly curves, A new twofold Cornacchia-type algorithm and its applications, Refinement of the four-dimensional GLV method on elliptic curves, New point compression method for elliptic \(\mathbb{F}_{q^2}\)-curves of \(j\)-invariant 0, Four-dimensional Gallant-Lambert-Vanstone scalar multiplication

Uses Software

• MIRACL
• eBATS

Cites Work

• Endomorphisms for faster elliptic curve cryptography on a large class of curves
• Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves
• Hyperelliptic curves with compact parameters
• High-Speed High-Security Signatures
• The Eta Pairing Revisited
• Efficient Techniques for High-Speed Elliptic Curve Cryptography
• Exponentiation in Pairing-Friendly Groups Using Homomorphisms
• Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
• New Composite Operations and Precomputation Scheme for Elliptic Curve Cryptosystems over Prime Fields
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