Recent results on recursive nonlinear pseudorandom number generators (Invited paper)

Abstract

This survey article collects recent results on recursive nonlinear pseudorandom number generators and sketches some important proof techniques. We mention upper bounds on additive character sums which imply uniform distribution results. Moreover, we present lower bounds on the linear complexity profile and closely related lattice tests and thus results on the suitability in cryptography. Finally, we give bounds on multiplicative character sums from which one can derive results on the distribution of powers and primitive elements. © 2010 Springer-Verlag.