### Abstract

A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented. To factor a polynomial of degree n over F_{q}, the number of arithmetic operations in F_{q} is O((n^{2}+nlog q). (log n)^{2} loglog n). The main technical innovation is a new way to compute Frobenius and trace maps in the ring of polynomials modulo the polynomial to be factored.

Original language | English (US) |
---|---|

Pages (from-to) | 187-224 |

Number of pages | 38 |

Journal | Computational Complexity |

Volume | 2 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1992 |

### Fingerprint

### Keywords

- Subject classifications: 68Q40, 11Y16, 12Y05

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Mathematics
- Mathematics(all)
- Computational Theory and Mathematics

### Cite this

*Computational Complexity*,

*2*(3), 187-224. https://doi.org/10.1007/BF01272074

**Computing Frobenius maps and factoring polynomials.** / von zur Gathen, Joachim; Shoup, Victor.

Research output: Contribution to journal › Article

*Computational Complexity*, vol. 2, no. 3, pp. 187-224. https://doi.org/10.1007/BF01272074

}

TY - JOUR

T1 - Computing Frobenius maps and factoring polynomials

AU - von zur Gathen, Joachim

AU - Shoup, Victor

PY - 1992/9

Y1 - 1992/9

N2 - A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented. To factor a polynomial of degree n over Fq, the number of arithmetic operations in Fq is O((n2+nlog q). (log n)2 loglog n). The main technical innovation is a new way to compute Frobenius and trace maps in the ring of polynomials modulo the polynomial to be factored.

AB - A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented. To factor a polynomial of degree n over Fq, the number of arithmetic operations in Fq is O((n2+nlog q). (log n)2 loglog n). The main technical innovation is a new way to compute Frobenius and trace maps in the ring of polynomials modulo the polynomial to be factored.

KW - Subject classifications: 68Q40, 11Y16, 12Y05

UR - http://www.scopus.com/inward/record.url?scp=0001605828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001605828&partnerID=8YFLogxK

U2 - 10.1007/BF01272074

DO - 10.1007/BF01272074

M3 - Article

AN - SCOPUS:0001605828

VL - 2

SP - 187

EP - 224

JO - Computational Complexity

JF - Computational Complexity

SN - 1016-3328

IS - 3

ER -