Multivariate permutation polynomial systems and nonlinear pseudorandom number generators

In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques studied previously for inversive generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates “on average” over all initial values than in the general case and thus can be of use for pseudorandom number generation.