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arXiv · 0802.0282

Galois invariant smoothness basis

Jean-Marc Couveignes·Reynald Lercier
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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 $\bK$, 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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Jean-Marc Couveignes, Reynald Lercier. 2008-02-03. Galois invariant smoothness basis. https://arxiv.org/abs/0802.0282

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