Faster integer multiplication using short lattice vectors

(with Joris van der Hoeven)

To appear in proceedings of ANTS XIII.

arXiv preprint (February 2018).

Abstract

We prove that n-bit integers may be multiplied in O(n log n 4log* 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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