A quick and dirty irreducibility Test for Multivariate Polynomials over   F_q
  We provide some statistics about an irreducibility/reducibility test for multivariate polynomials over finite fields based on counting points. The test works best for polynomials in a large number of variables and can also be applied to black box polynomials. 
H.-C. Graf v. Bothmer and F.-O. Schreyer