Fast unimodular reduction: planar integer lattices

The author shows that a shortest basis for the 2-dimensional lattice Λ(u, v) generated by an input pair u, v∈Z ² can be computed in O(M(n) log n) where n is the bit-size of the input numbers and M(n) is the complexity of multiplying two n-bit integers. This generalizes Schonhage´s technique (1971) for fast integer GCD to a higher dimension