Galois invariant smoothness basis

Details Galois invariant smoothness basis Galois invariant smoothness basis

2008-02-03

arxiv.org/abs/0802.0282v1

Mathematics

Number Theory

Scientific paper

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 $\bK$, one looks for a smoothness basis for $\bK^*$ that is left invariant by automorphisms of $\bK$. 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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