Point compression for the trace zero subgroup over a small degree extension field

DOI10.1007/s10623-014-9921-0zbMath1319.14033arXiv1403.0126OpenAlexW3104884073MaRDI QIDQ2340180

Maike Massierer, Elisa Gorla

Publication date: 16 April 2015

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

Full work available at URL: https://arxiv.org/abs/1403.0126

zbMATH Keywords

elliptic curvespoint compressiontrace zero varietysummation polynomialsdiscrete logarithm problem, elliptic curve cryptography

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Elliptic curves (14H52) Varieties over finite and local fields (11G25) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (2)

Index calculus in the trace zero variety ⋮ An optimal representation for the trace zero subgroup

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Endomorphisms for faster elliptic curve cryptography on a large class of curves
• Point compression for Koblitz elliptic curves
• Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem
• Computing pairings using \(x\)-coordinates only
• Using abelian varieties to improve pairing-based cryptography
• The Magma algebra system. I: The user language
• Constructive and destructive facets of Weil descent on elliptic curves
• Elliptic curve discrete logarithm problem over small degree extension fields
• On the Function Field Sieve and the Impact of Higher Splitting Probabilities
• Lambda Coordinates for Binary Elliptic Curves
• Solving a $$6120$$ -bit DLP on a Desktop Computer
• A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic
• High-Speed High-Security Signatures
• Trace Zero Varieties over Fields of Characteristic 2 for Cryptographic Applications
• Public-key cryptosystems based on cubic finite field extensions
• Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication
• Discrete Logarithm in GF(2809) with FFS
• Efficient and Secure Algorithms for GLV-Based Scalar Multiplication and Their Implementation on GLV-GLS Curves
• A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic
• Advances in Cryptology - CRYPTO 2003
• On the Discrete Logarithm Problem on Algebraic Tori
• Algorithmic Number Theory
• Algorithmic Number Theory

This page was built for publication: Point compression for the trace zero subgroup over a small degree extension field