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).


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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