Index calculus in class groups of non-hyperelliptic curves of genus three

DOI10.1007/s00145-007-9014-6zbMath1167.11047OpenAlexW2086701118MaRDI QIDQ1021239

Claus Diem, Emmanuel Thomé

Publication date: 8 June 2009

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

Full work available at URL: https://doi.org/10.1007/s00145-007-9014-6

zbMATH Keywords

Jacobianclass groupindex calculusDLPnon-hyperelliptic curve

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Number-theoretic algorithms; complexity (11Y16) Computational aspects of algebraic curves (14Q05) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (13)

Fast subgroup membership testings for \(\mathbb{G}_1, \mathbb{G}_2\) and \(\mathbb{G}_T\) on pairing-friendly curves ⋮ Index calculus in the trace zero variety ⋮ On the discrete logarithm problem for plane curves ⋮ Cover attacks for elliptic curves over cubic extension fields ⋮ An \(L(1/3)\) discrete logarithm algorithm for low degree curves ⋮ Elliptic curve cryptography: the serpentine course of a paradigm shift ⋮ Group arithmetic in \(C_{3,5}\) curves ⋮ Using symmetries in the index calculus for elliptic curves discrete logarithm ⋮ A new method for decomposition in the Jacobian of small genus hyperelliptic curves ⋮ Non-hyperelliptic modular Jacobians of dimension 3 ⋮ Another look at non-standard discrete log and Diffie-Hellman problems ⋮ Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem ⋮ Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with \((\ell ,\ell ,\ell)\)-isogenies

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic function fields and codes
• Parallel collision search with cryptanalytic applications
• Computing Riemann-Roch spaces in algebraic function fields and related topics.
• Über die Automorphismengruppe eines algebraischen Funktionenkörpers von Primzahlcharakteristik. I: Eine Abschätzung der Ordnung der Automorphismengruppe
• A low-memory algorithm for point counting on Picard curves
• A general framework for subexponential discrete logarithm algorithms
• Fast Jacobian Group Operations for C_3,4 Curves over a Large Finite Field
• A double large prime variation for small genus hyperelliptic index calculus
• Fast addition on non-hyperelliptic genus 3 curves
• The arithmetic of Jacobian groups of superelliptic cubics
• Construction of CM Picard curves
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• Point counting on Picard curves in large characteristic
• Algorithmic Number Theory
• Algorithmic Number Theory
• Public Key Cryptography – PKC 2004
• The diameter of sparse random graphs

This page was built for publication: Index calculus in class groups of non-hyperelliptic curves of genus three