On the power generator and its multivariate analogue

Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators

“…Another class of algebraic dynamical systems which can be useful for designing good pseudorandom number generators is the class of polynomial systems such that their iterations have certain sparsity with respect to some variables (and with strictly positive algebraic entropy). For example, such are the polynomial systems constructed in [15], for which we have F…”

“…We recall the following result given in [15,Lemma 4], which can easily be shown by induction on k: where, for i = 1, . .…”

“…We note that the method of [15,Theorem 2], which works for m = 1, does not seem to apply to the more general systems (19) with m ≥ 2. Hence, the proof of [15,Theorem 8], that applies to the systems (16) is based on different arguments.…”

“…Hence, the proof of [15,Theorem 8], that applies to the systems (16) is based on different arguments. This same approach also works for the more general systems (19).…”

“…. , e m , compared to that used in the proof of [15,Theorem 8], but typically leads to stronger bounds.…”