Point counting on Picard curves in large characteristic

DOI10.1090/S0025-5718-05-01758-8zbMath1079.14040OpenAlexW2064619631MaRDI QIDQ5315429

Annegret Weng, Mark Bauer, Edlyn Teske

Publication date: 8 September 2005

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-05-01758-8

zbMATH Keywords

discrete logarithm problemJacobians

Mathematics Subject Classification ID

Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Special algebraic curves and curves of low genus (14H45)

Related Items (9)

Explicit bounds of polynomial coefficients and counting points on Picard curves over finite fields ⋮ Approximating Euler products and class number computation in algebraic function fields ⋮ Picard curves over with good reduction away from 3 ⋮ A low-memory algorithm for point counting on Picard curves ⋮ Galois representations attached to Picard curves ⋮ Index calculus in class groups of non-hyperelliptic curves of genus three ⋮ Hasse–Witt and Cartier–Manin matrices: A warning and a request ⋮ Decomposing Jacobians of curves over finite fields in the absence of algebraic structure ⋮ Computing 𝐿-polynomials of Picard curves from Cartier–Manin matrices

Uses Software

• Magma

Cites Work

• Algebraic function fields and codes
• Parallel collision search with cryptanalytic applications
• Ideal arithmetic and infrastructure in purely cubic function fields
• Endomorphisms of Abelian varieties over finite fields
• The parallelized Pollard kangaroo method in real quadratic function fields
• Explicit bounds and heuristics on class numbers in hyperelliptic function fields
• New directions in cryptography
• On the JACOBIan Varieties of PICARD Curves Defined over Fields of Characteristicp < 0
• An improved algorithm for computing logarithms over&lt;tex&gt;GF(p)&lt;/tex&gt;and its cryptographic significance (Corresp.)
• The arithmetic of certain cubic function fields
• Counting Points in Medium Characteristic Using Kedlaya's Algorithm
• Construction of CM Picard curves
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• Algorithmic Number Theory
• The Hasse-Witt matrix of an algebraic curve
• Abelian varieties over finite fields
• Public Key Cryptography – PKC 2004
• Advances in Cryptology - ASIACRYPT 2003
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Point counting on Picard curves in large characteristic