Algorithms for finite fields

Karim Belabas (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 LFANT - Lithe and fast algorithmic number theory

This series of lectures concentrates on deterministic algorithms for finite fields. The emphasis is not on developing algorithms for practical use, but on viewing the quest for polynomial-time algorithms as a challenge of our structural understanding of finite fields. The topics treated include: representing finite fields, recognizing finite fields, constructing finite fields, constructing maps between finite fields and factoring polynomials.

Domaines: Théorie des nombres [math.NT]

Karim Belabas. Algorithms for finite fields. Explicit methods in number theory. Rational points and Diophantine equations, SMF, pp.1-18, 2012. ⟨hal-00932379⟩