Even faster integer multiplication

@article{Harvey2016EvenFI,
  title={Even faster integer multiplication},
  author={David Harvey and Joris van der Hoeven and Gr{\'e}goire Lecerf},
  journal={ArXiv},
  year={2016},
  volume={abs/1407.3360}
}
We give a new algorithm for the multiplication of n-bit integers in the bit complexity model, which is asymptotically faster than all previously known algorithms. More precisely, we prove that two n-bit integers can be multiplied in time O(n log n K log ∗ n), where K = 8 and log n = min  k ∈ N : log k× . . . log n 6 1  . Assuming standard conjectures about the distribution of Mersenne primes, we give yet another algorithm that achieves K = 4. The fastest previously known algorithm was due to… CONTINUE READING
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