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| HAL: hal-00630394, version 1 |
| arXiv: 0802.0282 |
| Detailed view |  Export this paper |
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| SAGA, Papeete : France (2007) |
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| Galois invariant smoothness basis |
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| Jean-Marc Couveignes 1Reynald Lercier 2 |
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| (2008-04-03) |
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| 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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| 1: | Institut de Mathématiques de Toulouse (IMT) |
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Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219 |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Subject | : | Mathematics/Number Theory |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/0802.0282 |
| hal-00630394, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00630394 | |
| oai:hal.archives-ouvertes.fr:hal-00630394 | |
| From: Jean-Marc Couveignes | |
| Submitted on: Sunday, 9 October 2011 19:05:31 | |
| Updated on: Tuesday, 11 October 2011 10:24:06 | |
