Reynald Lercier

J.-M. Couveignes and R. Lercier. Galois invariant smoothness basis. Series on Number Theory and Its Applications, 5:142-167, May 2008. World Scientific.

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 field K, one looks for a smoothness basis for K^* that is left invariant by automorphisms of K. For a broad class of finite fields, we manage to construct models that allow such a smoothness basis. This work aims at accelerating discrete logarithm computations in such fields. We treat the cases of codimension one (the linear sieve) and codimension two (the function field sieve).

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