Lattice basis reduction for indefinite forms and an application Original Research Article

In this paper we present an analogue of the lattice basis reduction algorithm of A.K. Lenstra, H.W. Lenstra and L. Lovász for the case of an indefinite non-degenerate symmetric bilinear form. The algorithm produces a reduced basis with similar size properties as in the Euclidean case. As an application, we present an algorithm, which finds zero divisors in rings isomorphic to M2(Z) in polynomial time.