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The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signal is concealed by two commutative private filters that are placed on each end of the communication channel. We demonstrate that when the transmitted signal is a convolution of the truncated time delayed output signals or some powers of the delayed output signals synchronization is still maintained. The task of a passive attacker is mapped onto Hilberts tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-Complete problems. This bridge between two different disciplines, synchronization in nonlinear dynamical processes and the realm of the NPC problems, opens a horizon for a new type of secure public-channel protocols.
We study the mutual coupling of chaotic lasers and observe both experimentally and in numeric simulations, that there exists a regime of parameters for which two mutually coupled chaotic lasers establish isochronal synchronization, while a third lase
We formulate a property $P$ on a class of relations on the natural numbers, and formulate a general theorem on $P$, from which we get as corollaries the insolvability of Hilberts tenth problem, Godels incompleteness theorem, and Turings halting probl
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize completely,
We relate the decidability problem for BS with unordered cartesian product with Hilberts Tenth problem and prove that BS with unordered cartesian product is NP-complete.
We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an autonomous system c