2 citations · 3 across the 4 of their papers we have counts for
4 papers
Normal Elliptic Bases and Torus-Based Cryptography
Clement Dunand, Reynald Lercier
We consider representations of algebraic tori over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers and infi…
Elliptic periods and primality proving
Jean-Marc Couveignes, Tony Ezome, Reynald Lercier
We define the ring of elliptic periods modulo an integer and give an elliptic version of the AKS primality criterion.
On Elkies subgroups of l-torsion points in elliptic curves defined over a finite field
Reynald Lercier, Thomas Sirvent
As a subproduct of the Schoof-Elkies-Atkin algorithm to count points on elliptic curves defined over finite fields of characteristic p, there exists an algorithm that computes, for…
Galois invariant smoothness basis
Jean-Marc Couveignes, Reynald Lercier
This text answers a question raised by Joux and the second author about the computation of discrete logarithms in the multiplicative group of finite fields. Given a finite residue…