Galois invariant smoothness basis

Abstract : 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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Contributor : Marie-Annick Guillemer <>
Submitted on : Monday, April 6, 2009 - 11:37:00 AM
Last modification on : Friday, April 12, 2019 - 4:22:50 PM

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Jean-Marc Couveignes, Reynald Lercier. Galois invariant smoothness basis. Series on Number Theory and its Applications, 2008, 5, pp.142-167. ⟨10.1142/9789812793430_0008⟩. ⟨hal-00373511⟩



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