### Abstract

For more than 35 years, the fastest known method for integer multiplication has been the Schönhage-Strassen algorithm running in time O(n log n log log n). Under certain restrictive conditions there is a corresponding (n log n) lower bound. The prevailing conjecture has always been that the complexity of an optimal algorithm is (n log n). We present a major step towards closing the gap from above by presenting an algorithm running in time n log n, 2 ^{O(log*n)}. The main result is for boolean circuits as well as for multitape Turing machines, but it has consequences to other models of computation as well.

Original language | English (US) |
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Title of host publication | STOC'07 |

Subtitle of host publication | Proceedings of the 39th Annual ACM Symposium on Theory of Computing |

Pages | 57-66 |

Number of pages | 10 |

DOIs | |

State | Published - Oct 30 2007 |

Event | STOC'07: 39th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States Duration: Jun 11 2007 → Jun 13 2007 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Other

Other | STOC'07: 39th Annual ACM Symposium on Theory of Computing |
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Country | United States |

City | San Diego, CA |

Period | 6/11/07 → 6/13/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*STOC'07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing*(pp. 57-66). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/1250790.1250800

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*STOC'07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing.*Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 57-66, STOC'07: 39th Annual ACM Symposium on Theory of Computing, San Diego, CA, United States, 6/11/07. https://doi.org/10.1145/1250790.1250800

**Faster integer multiplication.** / Furer, Martin.

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

TY - GEN

T1 - Faster integer multiplication

AU - Furer, Martin

PY - 2007/10/30

Y1 - 2007/10/30

N2 - For more than 35 years, the fastest known method for integer multiplication has been the Schönhage-Strassen algorithm running in time O(n log n log log n). Under certain restrictive conditions there is a corresponding (n log n) lower bound. The prevailing conjecture has always been that the complexity of an optimal algorithm is (n log n). We present a major step towards closing the gap from above by presenting an algorithm running in time n log n, 2 O(log*n). The main result is for boolean circuits as well as for multitape Turing machines, but it has consequences to other models of computation as well.

AB - For more than 35 years, the fastest known method for integer multiplication has been the Schönhage-Strassen algorithm running in time O(n log n log log n). Under certain restrictive conditions there is a corresponding (n log n) lower bound. The prevailing conjecture has always been that the complexity of an optimal algorithm is (n log n). We present a major step towards closing the gap from above by presenting an algorithm running in time n log n, 2 O(log*n). The main result is for boolean circuits as well as for multitape Turing machines, but it has consequences to other models of computation as well.

UR - http://www.scopus.com/inward/record.url?scp=35448968883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35448968883&partnerID=8YFLogxK

U2 - 10.1145/1250790.1250800

DO - 10.1145/1250790.1250800

M3 - Conference contribution

AN - SCOPUS:35448968883

SN - 1595936319

SN - 9781595936318

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 57

EP - 66

BT - STOC'07

ER -