Mathematics in Computer Science

, Volume 6, Issue 3, pp 217–233 | Cite as

Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries

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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.

Keywords

Algorithms Arithmetic Algebraic extension field Splitting field 

Mathematics Subject Classification

Primary 12Y05 Secondary 12F10 12-04 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.LMAH, Université du HavreLe HavreFrance
  2. 2.INRIA, Paris-Rocquencourt, POLSYS Project, CNRS, UMR 7606, LIP6UPMC, Univ. Paris 06ParisFrance
  3. 3.Rikkyo UniversityTokyoJapan

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