Call a noncommutative rational function r regular if it has no singularities, i.e., r(X) is defined for all tuples of self-adjoint matrices X. In this talk regular noncommutative rational functions r will be characterized via the properties of their (minimal size) linear systems realizations r = c∗L−1b. Our main result states that r is regular if and only if L = A0 + ∑ j Ajxj is privileged. Rou...

In this paper, the technique of foliations in characteristic p is used to investigate the difference between rational connectedness and separable rational connectedness in positive characteristic. The notion of being freely rationally connected is defined; a variety is freely rationally connected if a general pair of points can be connected by a free rational curve. It is proved that a freely r...

The Mafia fraud consists in an adversary transparently relaying the physical layer signal during an authentication process between a verifier and a remote legitimate prover. This attack is a major concern for certain RFID systems, especially for payment related applications. Previously proposed protocols that thwart the Mafia fraud treat relaying and nonrelaying types of attacks equally: whethe...