Polynomial Factorisation using Drinfeld Modules

Anand Kumar Narayanan (1, 2)

1 ALMASTY - ALgorithms for coMmunicAtion SecuriTY
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

The arithmetic of Drinfeld modules have recently yielded novel algorithms for factoring polynomials over finite fields; a computational problem with applications to digital communication, cryptography and complexity theory. The following is a gentle invitation to these developments assuming no prior acquaintance with Drinfeld modules. Familiarity with finite fields and elliptic curves is helpful but not required.

Domaines: Théorie des nombres [math.NT]; Complexité [cs.CC]; Calcul formel [cs.SC]; Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]

Anand Kumar Narayanan. Polynomial Factorisation using Drinfeld Modules. Newsletter of the London Mathematical Society, 2019. ⟨hal-02368680⟩