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Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries

Sébastien Orange 1 Guénaël Renault 2, 3 Kazuhiro Yokoyama 4
1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
3 LIP6 - Laboratoire d'Informatique de Paris 6
4 Department of Mathematics [Rikkyo]
Abstract : In this article, we present new results for efficient arithmetic operations in a number field K represented by successive extensions. These results are based on multi-modular and evaluation-interpolation techniques. We show how to use intrinsic symmetries in order to increase the efficiency of these techniques. Applications to splitting fields of univariate polynomials are presented.
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Sébastien Orange, Guénaël Renault, Kazuhiro Yokoyama. Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries. Mathematics in Computer Science, Springer, 2012, 6 (3), pp.217-233. ⟨10.1007/s11786-012-0112-y⟩. ⟨hal-00777860v2⟩

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