## Faster Integer Multiplication (2007)

by
Martin Fürer

Venue: | STOC'07 |

Citations: | 41 - 0 self |

### BibTeX

@MISC{Fürer07fasterinteger,

author = {Martin Fürer},

title = {Faster Integer Multiplication},

year = {2007}

}

### Years of Citing Articles

### OpenURL

### 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 Ω(n log n) lower bound. The prevailing conjecture has always been that the complexity of an optimal algorithm is Θ(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.