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 $\bK$, 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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Contributor : Jean-Marc Couveignes <>
Submitted on : Sunday, October 9, 2011 - 7:05:31 PM
Last modification on : Monday, April 29, 2019 - 4:17:05 PM

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  • HAL Id : hal-00630394, version 1
  • ARXIV : 0802.0282


Jean-Marc Couveignes, Reynald Lercier. Galois invariant smoothness basis. SAGA, May 2007, Papeete, France. pp.142-167. ⟨hal-00630394⟩



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