Inversive pseudorandom numbers over Galois rings

We provide a new construction of nonlinear pseudorandom number generators. We use the inversive method over Galois rings. This generalizes to the common setting of Galois rings both the works of Niederreiter et al. over finite fields and Eichenauer-Herrmann et al. over integers modulo a prime power. The main proof technique to bound the discrepancy from above is the local Weil bound on hybrid character sums over Galois rings. The estimates hold for the full period and also for certain parts of the period. Elementary p -adic analysis allows us to ensure maximal period length.