Factoring polynomials over finite fields

Enver Ozdemir

doi:10.1142/S1793042121500469

Factoring polynomials over finite fields

Enver Ozdemir^*

^*Corresponding author for this work

Informatics Institute

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

1 Citation (Scopus)

Abstract

In this paper, we describe a new polynomial factorization algorithm over finite fields with odd characteristics. The main ingredient of the algorithm is special singular curves. The algorithm relies on the extension of the Mumford representation and Cantor's algorithm to these special singular curves.

Original language	English
Pages (from-to)	1517-1536
Number of pages	20
Journal	International Journal of Number Theory
Volume	17
Issue number	7
DOIs	https://doi.org/10.1142/S1793042121500469
Publication status	Published - Aug 2021

Bibliographical note

Publisher Copyright:
© 2021 World Scientific Publishing Company.

Keywords

finite fields
Hyperelliptic curves
Jacobian
Picard group
polynomial factorization

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10.1142/S1793042121500469

Cite this

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title = "Factoring polynomials over finite fields",

abstract = "In this paper, we describe a new polynomial factorization algorithm over finite fields with odd characteristics. The main ingredient of the algorithm is special singular curves. The algorithm relies on the extension of the Mumford representation and Cantor's algorithm to these special singular curves.",

keywords = "finite fields, Hyperelliptic curves, Jacobian, Picard group, polynomial factorization",

author = "Enver Ozdemir",

note = "Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",

year = "2021",

month = aug,

doi = "10.1142/S1793042121500469",

language = "English",

volume = "17",

pages = "1517--1536",

journal = "International Journal of Number Theory",

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T1 - Factoring polynomials over finite fields

AU - Ozdemir, Enver

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N2 - In this paper, we describe a new polynomial factorization algorithm over finite fields with odd characteristics. The main ingredient of the algorithm is special singular curves. The algorithm relies on the extension of the Mumford representation and Cantor's algorithm to these special singular curves.

AB - In this paper, we describe a new polynomial factorization algorithm over finite fields with odd characteristics. The main ingredient of the algorithm is special singular curves. The algorithm relies on the extension of the Mumford representation and Cantor's algorithm to these special singular curves.

KW - finite fields

KW - Hyperelliptic curves

KW - Jacobian

KW - Picard group

KW - polynomial factorization

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U2 - 10.1142/S1793042121500469

DO - 10.1142/S1793042121500469

M3 - Article

AN - SCOPUS:85100544889

SN - 1793-0421

VL - 17

SP - 1517

EP - 1536

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 7

ER -

Factoring polynomials over finite fields

Abstract

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Keywords

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