In the past decades, the advent of electronic computers and, later, of the network of such computers, presently known as the World Wide Web, has exponentially increased the amount of data exchanged among the most diverse people, areas and organizations, all over the world. This has brought about many advantages to the academic institutions, to the military structures to the financial institutions, to banks and corporations of all sizes, to the public administrations, governments etc. A detailed list of all those interested in the exchange of information over the internet is presently impossible. One simply observes that practically everybody in the industrialized world is directly or indirectly interested in that, while larger and larger fractions of the populations from the emerging economies are rapidly becoming interested in that.
In particular, sensitive information and information protected by privacy laws constitute a
large fraction of the total information being transmitted by all forms of telecommunication
equipments. Therefore, the development of secure communication has become impelling, in order to prevent an-authorized people from intercepting and embezzling information meant to others.
The most obvious way of achieving this goal is to encrypt the data that is to be transmitted.
Among the most promising encrypting techniques, we find those based on chaotic synchronized
dynamics, which constitute the subject of the present timely collection of research papers.
Chaos is one type of deterministic, hence in principle fully predictable, dynamic behaviour,
which, however, turns out to be as unpredictable as a stochastic process, in practice. This
is related to the impossibility of knowing with infinite precision the initial state of the
system at hand. Also, a chaotic signal enjoys the characteristics of e.g. aperiodicity.
Interacting chaotic oscillators are of interest in many areas of physics, biology, and engineering.
For instance, one challenging problem, faced by the current biological sciences, concerns our
understanding of the emergence of collective coherent behaviours, from groups of interacting functional units, separately displaying complicated behaviours. In particular, it is remarkable that chaotic systems can be synchronized letting them communicate only a part of the information concerning their state.
When this phenomenon was discovered, it became immediately clear that it could have been used to create keys for cryptography using the unsent state spaces. Indeed, by using the proper keys, or interactions, the sender may be synchronized with the receiver, and only part of the data needs to be transmitted, for the whole message to be delivered. This significantly reduces the possibility that the message be understood by an-authorized people.
As perfect, 100% secure, ways of encrypting a message may not be realizable, even chaotic
synchronization needs to be tested and further developed, while remaining one of the most promising tools for secure communication in the years to come. This makes the present collection of papers especially timely and useful.