Ivan Boyer Language : fr | en

Research activities

• Ph.D Thesis

  1. Master 2 Thesis : Diverses applications de la géométrie algébrique à la théorie de l’information under the supervision of Jean-François Mestre.
     I discuss here classical efficient methods to count rational points on elliptic curves (Schoof, Elkies and Atkin algorithm). I provide some applications for cryptography and error correcting codes.
  2. Ph.D Thesis : Variétés abéliennes et jacobiennes de courbes hyperelliptiques, en particulier à multiplication réelle ou complexe under the supervision of Jean-François Mestre.
     This work is based on general tools in the theory of abelian varieties and I provide several of their applications. Some of these fundamental tools are
     • functions thêta theory linked with Schottky problem ;
     • the notion of correspondence and induced isogenies, which are used to construct abelian varieties with complex multiplication ;
     • the use of complex multiplication curves for the factorization in polynomial time of cyclotomic polynomials in finite fields.
     • We also deal with real multiplication curves by subfields of cyclotomic fields.
     Download links : Thesis Memoir and slides.

• Articles

  1. 2-2-2 Isogenies between Jacobians of Hyperelliptic Curves
     Submitted to AGCT14 proceedings.
  2. Courbes à multiplication réelle par des sous-corps cyclotomiques
     In preparation ; arXiv link
  3. Factorisation en temps polynomial dans F_p[x].
     In preparation.

• Presentations in conferences

  1. AGCT13 : Arithmetic, Geometry, Cryptography and Coding Theory 13
     From March 14 to 18, 2011 at CIRM, organized by Yves Aubry, Christophe Ritzenthaler and Alexey Zykin.
     Factorization of polynomials over finite fields in deterministic polynomial-time
  2. AGCT14 : Arithmetic, Geometry, Cryptography and Coding Theory 14
     From du June 3 to 7, 2013 at CIRM, organized by Stéphane Ballet, Marc Perret and Alexey Zaytsev.
     Families of genus 3 hyperelliptic curves whose jacobians are 2−2−2 isogenous