Can we beat the square root bound for ECDLP over \(\mathbb{F}_p^2\) via representation?

DOI10.1515/jmc-2019-0025zbMath1466.11091OpenAlexW3080625311MaRDI QIDQ2023309

Claire Delaplace, Alexander May

Publication date: 3 May 2021

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

Full work available at URL: https://doi.org/10.1515/jmc-2019-0025

zbMATH Keywords

representationselliptic curve discrete logarithm (ECDLP)multivariate polynomial zero-testing

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Arithmetic ground fields for curves (14H25) Number-theoretic algorithms; complexity (11Y16) Polynomials over finite fields (11T06) Finite ground fields in algebraic geometry (14G15) Computational algebraic geometry over arithmetic ground fields (14Q25)

Cites Work

• Improved elliptic curve hashing and point representation
• Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem
• Recent progress on the elliptic curve discrete logarithm problem
• The discrete logarithm problem on elliptic curves of trace one
• Constructive and destructive facets of Weil descent on elliptic curves
• Counting points on elliptic curves over finite fields
• Algebraic Approaches for the Elliptic Curve Discrete Logarithm Problem over Prime Fields
• Improved Generic Algorithms for Hard Knapsacks
• Powers of tensors and fast matrix multiplication
• New Generic Algorithms for Hard Knapsacks
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Evaluation of discrete logarithms in a group of 𝑝-torsion points of an elliptic curve in characteristic 𝑝
• Algorithms – ESA 2004
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item