Counting points on \(C_{ab}\) curves using Monsky-Washnitzer cohomology

DOI10.1016/j.ffa.2005.01.003zbMath1104.11032OpenAlexW2120966850MaRDI QIDQ814764

Frederik Vercauteren, Jan Denef

Publication date: 7 February 2006

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2005.01.003

zbMATH Keywords

cryptographyzeta functionMonsky-Washnitzer cohomologyKedlaya's algorithm\(C_{ab}\) curves

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15)

Related Items (17)

A generalized Kiepert formula for \(C_{ab}\) curves ⋮ Counting points on curves using a map to \(\mathbf P^1\). II. ⋮ Approximating Euler products and class number computation in algebraic function fields ⋮ Computing zeta functions of superelliptic curves in larger characteristic ⋮ Computing zeta functions of cyclic covers in large characteristic ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ An extension of Kedlaya's algorithm for hyperelliptic curves ⋮ On the exact evaluation of certain instances of the Potts partition function by quantum computers ⋮ Computing Zeta Functions in Families of C a,b Curves Using Deformation ⋮ On infiniteness of integral overconvergent de Rham-Witt cohomology modulo torsion ⋮ 𝑝-adic point counting on singular superelliptic curves ⋮ Algebraic independence in positive characteristic: A $p$-adic calculus ⋮ Fast arithmetic in unramified \(p\)-adic fields ⋮ Counting points on curves using a map to $\mathbf {P}^1$ ⋮ Curves in characteristic \(2\) with non-trivial \(2\)-torsion ⋮ The uniqueness of Weierstrass points with semigroup \(\langle a;b\rangle \) and related semigroups ⋮ Computing zeta functions of algebraic curves using Harvey's trace formula

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