Families of Explicit Isogenies of Hyperelliptic Jacobians

Benjamin Smith 1
1 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : We construct three-dimensional families of hyperelliptic curves of genus 6, 12, and 14, two-dimensional families of hyperelliptic curves of genus 3, 6, 7, 10, 20, and 30, and one-dimensional families of hyperelliptic curves of genus 5, 10 and 15, all of which are equipped with an an explicit isogeny from their Jacobian to another hyperelliptic Jacobian. We show that the Jacobians are generically absolutely simple, and describe the kernels of the isogenies. The families are derived from Cassou--Noguès and Couveignes' explicit classification of pairs $(f,g)$ of polynomials such that $f(x_1) - g(x_2)$ is reducible.
Document type :
Conference papers
Liste complète des métadonnées

Cited literature [24 references]  Display  Hide  Download

https://hal.inria.fr/inria-00420605
Contributor : Benjamin Smith <>
Submitted on : Tuesday, September 29, 2009 - 2:07:46 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:29 PM
Document(s) archivé(s) le : Wednesday, June 16, 2010 - 12:11:53 AM

Files

isogenies.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00420605, version 1
  • ARXIV : 0909.5406

Collections

Citation

Benjamin Smith. Families of Explicit Isogenies of Hyperelliptic Jacobians. Arithmetic, Geometry, Cryptography and Coding Theory 2009, Mar 2009, Luminy, France. pp.121-144. ⟨inria-00420605⟩

Share

Metrics

Record views

490

Files downloads

196