Short vectors of planar lattices via continued fractions

Authors:
Friedrich Eisenbrand
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany
Venue:
Information Processing Letters
Year:
2001

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Abstract

We show that a shortest vector of a 2-dimensional integral lattice with respect to the lsub-infinity-norm can be computed with a constant number of extended-gcd computations, one common-convergent computation and a constant number of arithmetic operations. It follows that in two dimensions, a fast basis-reduction algorithm can be solely based on Schönhage's classical algorithm on the fast computation of continued fractions and the reduction algorithm of Gauss.