### Abstract

A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented whose asymptotic running time improves upon previous results. To factor a polynomial of degree n over F_{q}, the algorithm uses O((n^{2}+n log q)·(log n)^{2} log log n) arithmetic operations in F_{q}. 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) |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

Editors | Anon |

Publisher | Publ by ACM |

Pages | 97-105 |

Number of pages | 9 |

ISBN (Print) | 0897915119 |

State | Published - 1992 |

Event | Proceedings of the 24th Annual ACM Symposium on the Theory of Computing - Victoria, BC, Can Duration: May 4 1992 → May 6 1992 |

### Other

Other | Proceedings of the 24th Annual ACM Symposium on the Theory of Computing |
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City | Victoria, BC, Can |

Period | 5/4/92 → 5/6/92 |

### Fingerprint

### ASJC Scopus subject areas

- Software

### Cite this

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*(pp. 97-105). Publ by ACM.

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing.*Publ by ACM, pp. 97-105, Proceedings of the 24th Annual ACM Symposium on the Theory of Computing, Victoria, BC, Can, 5/4/92.

}

TY - GEN

T1 - Computing Frobenius maps and factoring polynomials

AU - von zur Gathen, Joachim

AU - Shoup, Victor

PY - 1992

Y1 - 1992

N2 - A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented whose asymptotic running time improves upon previous results. To factor a polynomial of degree n over Fq, the algorithm uses O((n2+n log q)·(log n)2 log log n) arithmetic operations in Fq. 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 whose asymptotic running time improves upon previous results. To factor a polynomial of degree n over Fq, the algorithm uses O((n2+n log q)·(log n)2 log log n) arithmetic operations in Fq. 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.

UR - http://www.scopus.com/inward/record.url?scp=0026999432&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026999432&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026999432

SN - 0897915119

SP - 97

EP - 105

BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

A2 - Anon, null

PB - Publ by ACM

ER -