The point decomposition problem over hyperelliptic curves, Toward efficient computation of discrete logarithms in even characteristic

DOI10.1007/s10623-017-0449-yzbMath1400.14072OpenAlexW2774118421MaRDI QIDQ1671640

Jean-Charles Faugère, Alexandre Wallet

Publication date: 6 September 2018

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

Full work available at URL: https://doi.org/10.1007/s10623-017-0449-y

zbMATH Keywords

Gröbner basesalgebraic curvesdiscrete logarithmalgebraic attacksindex calculuscurve-based cryptography

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Finite ground fields in algebraic geometry (14G15) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Uses Software

• FGb
• Magma
• NTL
• CADO-NFS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Arithmetic on abelian and Kummer varieties
• Using symmetries in the index calculus for elliptic curves discrete logarithm
• 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 arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• The Magma algebra system. I: The user language
• Elliptic curve discrete logarithm problem over small degree extension fields
• Handbook of Finite Fields
• Cover and Decomposition Index Calculus on Elliptic Curves Made Practical
• Summation Polynomial Algorithms for Elliptic Curves in Characteristic Two
• On the discrete logarithm problem in elliptic curves
• Factorization of a 768-Bit RSA Modulus
• The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
• Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field
• Fast algorithm for change of ordering of zero-dimensional Gröbner bases with sparse multiplication matrices
• Symmetrized Summation Polynomials: Using Small Order Torsion Points to Speed Up Elliptic Curve Index Calculus
• Fast genus 2 arithmetic based on Theta functions
• Computation of a 768-Bit Prime Field Discrete Logarithm
• FGb: A Library for Computing Gröbner Bases
• Algorithmic Number Theory