Faster integer multiplication using short lattice vectors

02/22/2018
by   David Harvey, et al.
0

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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