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arXiv · 1802.07932

Faster integer multiplication using short lattice vectors

David Harvey·Joris van der Hoeven
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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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David Harvey, Joris van der Hoeven. 2018-02-22. Faster integer multiplication using short lattice vectors. https://doi.org/10.2140/obs.2019.2.293

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