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AbstractLattice sieving in two dimensions has proven to be an indispensable practical aid in integer factorization and discrete log computations involving the number field sieve. The main contribution of this article is to show that a different method of lattice sieving in three dimensions will provide a significant speedup in medium characteristic. Our method is to use the successive minima and shortest vectors of the lattice instead of transition vectors to iterate through lattice points. Wedoi:10.1515/jmc-2020-0008 fatcat:t5rj4mip6za4xiztfjrjmfenjm