Root optimization of polynomials in the number field sieve

Shi Bai; Richard P. Brent; Emmanuel Thomé

doi:10.1090/S0025-5718-2015-02926-3

Root optimization of polynomials in the number field sieve

Shi Bai, Richard P. Brent, Emmanuel Thomé

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

11 Citations (Scopus)

Abstract

The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.

Original language	English
Pages (from-to)	2447-2457
Number of pages	11
Journal	Mathematics of Computation
Volume	84
Issue number	295
DOIs	https://doi.org/10.1090/S0025-5718-2015-02926-3
Publication status	Published - 2015

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title = "Root optimization of polynomials in the number field sieve",

abstract = "The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.",

author = "Shi Bai and Brent, {Richard P.} and Emmanuel Thom{\'e}",

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AU - Bai, Shi

AU - Brent, Richard P.

AU - Thomé, Emmanuel

PY - 2015

Y1 - 2015

N2 - The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.

AB - The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.

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U2 - 10.1090/S0025-5718-2015-02926-3

DO - 10.1090/S0025-5718-2015-02926-3

M3 - Article

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VL - 84

SP - 2447

EP - 2457

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 295

ER -

Root optimization of polynomials in the number field sieve

Abstract

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