### Abstract

In this paper we describe ideas used to accelerate the Searching Phase of the Berlekamp-Zassenhaus algorithm, the algorithm most widely used for computing factorizations in Z[x]. Our ideas do not alter the theoretical worst-case complexity, but they do have a significant effect in practice: especially in those cases where the cost of the Searching Phase completely dominates the rest of the algorithm. A complete implementation of the ideas in this paper is publicly available in the library NTL. We give timings of this implementation on some difficult factorization problems.

Original language | English (US) |
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Title of host publication | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |

Publisher | ACM |

Pages | 1-7 |

Number of pages | 7 |

State | Published - 2000 |

Event | Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000) - St Andrews, UK Duration: Aug 7 2000 → Aug 9 2000 |

### Other

Other | Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000) |
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City | St Andrews, UK |

Period | 8/7/00 → 8/9/00 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC*(pp. 1-7). ACM.

**Factorization in Z[x] : The Searching Phase.** / Abbott, John; Shoup, Victor; Zimmermann, Paul.

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

*Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC.*ACM, pp. 1-7, Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000), St Andrews, UK, 8/7/00.

}

TY - CHAP

T1 - Factorization in Z[x]

T2 - The Searching Phase

AU - Abbott, John

AU - Shoup, Victor

AU - Zimmermann, Paul

PY - 2000

Y1 - 2000

N2 - In this paper we describe ideas used to accelerate the Searching Phase of the Berlekamp-Zassenhaus algorithm, the algorithm most widely used for computing factorizations in Z[x]. Our ideas do not alter the theoretical worst-case complexity, but they do have a significant effect in practice: especially in those cases where the cost of the Searching Phase completely dominates the rest of the algorithm. A complete implementation of the ideas in this paper is publicly available in the library NTL. We give timings of this implementation on some difficult factorization problems.

AB - In this paper we describe ideas used to accelerate the Searching Phase of the Berlekamp-Zassenhaus algorithm, the algorithm most widely used for computing factorizations in Z[x]. Our ideas do not alter the theoretical worst-case complexity, but they do have a significant effect in practice: especially in those cases where the cost of the Searching Phase completely dominates the rest of the algorithm. A complete implementation of the ideas in this paper is publicly available in the library NTL. We give timings of this implementation on some difficult factorization problems.

UR - http://www.scopus.com/inward/record.url?scp=0033658634&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033658634&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0033658634

SP - 1

EP - 7

BT - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

PB - ACM

ER -