The equivariant complexity of multiplication in finite field extensions

Jean-Marc Couveignes (1, 2, 3) , Tony Ezome (4)

1 UB - Université de Bordeaux
2 Bordeaux INP - Institut Polytechnique de Bordeaux
3 LFANT - Lithe and fast algorithmic number theory
4 USTM - Université des Sciences et Techniques de Masuku

We study the complexity of multiplication of two elements in a finite field extension given by their coordinates in a normal basis. We show how to control this complexity using the arithmetic and geometry of algebraic curves.

Domaines: Théorie des nombres [math.NT]

Jean-Marc Couveignes, Tony Ezome. The equivariant complexity of multiplication in finite field extensions. 2021. ⟨hal-03410146v1⟩