Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem

From MaRDI portal
Publication:733510

DOI10.1016/j.jsc.2008.08.005zbMath1177.94148OpenAlexW2083052384MaRDI QIDQ733510

Pierrick Gaudry

Publication date: 16 October 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.08.005




Related Items (43)

A simple method for obtaining relations among factor basis elements for special hyperelliptic curvesThe Supersingular Isogeny Problem in Genus 2 and BeyondOn index calculus algorithms for subfield curvesSemi-Regular Sequences and Other Random Systems of EquationsA SAT-Based Approach for Index Calculus on Binary Elliptic CurvesA Note on Diem’s ProofLast Fall Degree, HFE, and Weil Descent Attacks on ECDLPFiat-Shamir and correlation intractability from strong KDM-secure encryptionSolving degree, last fall degree, and related invariantsThe point decomposition problem over hyperelliptic curves, Toward efficient computation of discrete logarithms in even characteristicSummation Polynomial Algorithms for Elliptic Curves in Characteristic TwoField extensions and index calculus on algebraic curvesQuasi-subfield polynomials and the elliptic curve discrete logarithm problemIndex calculus in the trace zero varietyAcceleration of Index Calculus for Solving ECDLP over Prime Fields and Its LimitationCover attacks for elliptic curves over cubic extension fieldsThe complexity of solving Weil restriction systemsElliptic curve cryptography: the serpentine course of a paradigm shiftElliptic curve discrete logarithm problem over small degree extension fieldsRecent progress on the elliptic curve discrete logarithm problemEndomorphisms for faster elliptic curve cryptography on a large class of curvesUsing symmetries in the index calculus for elliptic curves discrete logarithmSolving multivariate polynomial systems and an invariant from commutative algebraNew results on quasi-subfield polynomialsOn the discrete logarithm problem for prime-field elliptic curvesAn optimal representation for the trace zero subgroupCan we beat the square root bound for ECDLP over \(\mathbb{F}_p^2\) via representation?A generic approach to searching for JacobiansCryptographic implications of Hess' generalized GHS attackComplexity bounds on Semaev's naive index calculus method for ECDLPCover attacks for elliptic curves with cofactor twoOn the complexity of computing Gröbner bases for weighted homogeneous systemsA Variant of the F4 AlgorithmImprovement of FPPR method to solve ECDLPOn the discrete logarithm problem in class groups of curvesEndomorphisms for Faster Elliptic Curve Cryptography on a Large Class of CurvesGenerating Genus Two Hyperelliptic Curves over Large Characteristic Finite FieldsOn the Security of Pairing-Friendly Abelian Varieties over Non-prime FieldsFaster Halvings in Genus 2Using abelian varieties to improve pairing-based cryptographyKoblitz curves over quadratic fieldsComputing $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curvesPoint compression for the trace zero subgroup over a small degree extension field


Uses Software


Cites Work


This page was built for publication: Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem