Faster integer multiplication using short lattice vectors

Understand

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.