Séminaires : Séminaire Théorie des Nombres

Equipe(s) : fa, tn, tga,
Responsables :Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel
Email des responsables : cathy.swaenepoel@imj-prg.fr
Salle :
Adresse :



Orateur(s) Anand Kumar Narayanan - IMJ-PRG,
Titre Drinfeld Modules, Hasse Invariants and Factoring Polynomials over Finite Fields
Horaire14:00 à 15:00
RésumeWe present three novel algorithms to factor polynomials in
one variable over finite fields using the arithmetic of Drinfeld modules.
The first algorithm estimates the degree of an irreducible factor of
a polynomial from Euler-Poincare characteristics of random Drinfeld
modules. Knowledge of a factor degree allows one to rapidly extract
all factors. The second algorithm is a random Drinfeld module analogue of Berlekamp’s algorithm, partly inspired by Lenstra’s elliptic
curve method for integer factorization. The third algorithm employs
Drinfeld modules with complex multiplication and will be the primary
focus of the talk. The main idea is to compute a lift of the Hasse invariant with Deligne’s congruence playing a critical role. We will discuss
practical implementations and complexity theoretic implications of the