On the discrete logarithm problem in class groups of curves

DOI10.1090/S0025-5718-2010-02281-1zbMath1231.11142OpenAlexW2073916736MaRDI QIDQ3081294

Claus Diem

Publication date: 7 March 2011

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-2010-02281-1

zbMATH Keywords

discrete logarithm problemcurves over finite fields

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (10)

Fast cryptography in genus 2 ⋮ Summation Polynomial Algorithms for Elliptic Curves in Characteristic Two ⋮ On the discrete logarithm problem for plane curves ⋮ Cover attacks for elliptic curves over cubic extension fields ⋮ Recent progress on the elliptic curve discrete logarithm problem ⋮ Using symmetries in the index calculus for elliptic curves discrete logarithm ⋮ An optimal representation for the trace zero subgroup ⋮ On the use of expansion series for stream ciphers ⋮ Cover attacks for elliptic curves with cofactor two ⋮ Computing in Picard groups of projective curves over finite fields

Cites Work

• Algebraic function fields and codes
• Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem
• Index calculus attack for Jacobian of hyperelliptic curves of small genus using two large primes
• Computing Riemann-Roch spaces in algebraic function fields and related topics.
• Approximate formulas for some functions of prime numbers
• A general framework for subexponential discrete logarithm algorithms
• Nombre de points des jacobiennes sur un corps fini
• A double large prime variation for small genus hyperelliptic index calculus
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
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