Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries

Sébastien Orange; Guénaël Renault; Kazuhiro Yokoyama

doi:10.1007/s11786-012-0112-y

Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries

Sébastien Orange, Guénaël Renault, Kazuhiro Yokoyama

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	217-233
Number of pages	17
Journal	Mathematics in Computer Science
Volume	6
Issue number	3
DOIs	https://doi.org/10.1007/s11786-012-0112-y
Publication status	Published - 1 Sept 2012
Externally published	Yes

Keywords

Algebraic extension field
Algorithms
Arithmetic
Splitting field

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10.1007/s11786-012-0112-y

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title = "Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries",

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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year = "2012",

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AU - Renault, Guénaël

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AB - 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.

KW - Algebraic extension field

KW - Algorithms

KW - Arithmetic

KW - Splitting field

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DO - 10.1007/s11786-012-0112-y

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SP - 217

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JO - Mathematics in Computer Science

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Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries

Abstract

Keywords

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