  We design and analyze an algorithm for computing rational points of
hypersurfaces defined over a finite field based on searches on "vertical
strips", namely searches on parallel lines in a given direction. Our results
show that, on average, less than two searches suffice to obtain a rational
point. We also analyze the probability distribution of outputs, using the
notion of Shannon entropy, and prove that the algorithm is somewhat close to
any "ideal" equidistributed algorithm.
