# Faster integer multiplication using short lattice vectors

(with Joris van der Hoeven)

Proceedings of the Thirteenth Algorithmic Number Theory Symposium (ANTS XIII), Open Book Series Vol 2 (2019), 293–310 (DOI).

arXiv preprint (February 2018).

## Abstract

We prove that *n*-bit integers may be multiplied in
*O*(*n* log *n* 4^{log* n})
bit operations.
This complexity bound had been achieved previously by several authors,
assuming various unproved number-theoretic hypotheses.
Our proof is unconditional, and depends in an essential way on
Minkowski's theorem concerning lattice vectors in symmetric convex sets.

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