Recent results on fast multiplication

Abstract: Joris van der Hoeven and I recently proposed an algorithm that multiplies two $n$-bit integers in $O(n \log n)$ bit operations. I will explain the main ideas behind this algorithm, and discuss the difficulties that arise when trying to adapt this algorithm to multiplication of polynomials in $F[x]$ where $F$ is a finite field.

computational complexitymathematical softwarenumber theory

Audience: researchers in the topic

( chat | paper | slides )

Comments: This invited talk by David Harvey was chaired by Steven Galbraith.

There are two papers relevant to this talk:

• Integer multiplication in time $O(n\log n)$
• Polynomial multiplication over finite fields in time $O(n \log n)$

by David Harvey and Joris van der Hoeven.

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Algorithmic Number Theory Symposium (ANTS XIV)

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