Synchronizace chaotických oscilatorů pomocı́ nelineárnı́ rekonstrukce a jejı́ využitı́ k bezpečnému šifrovánı́ Chaos synchronization via nonlinear observers with application to secure encryption Summary

Synchronizace chaotick´ych oscilatorů pomocí nelineární rekonstrukce a její využití k bezpečnémušifrování Chaos synchronization via nonlinear observers with application to secure encryption Summary During previous decades, chaotic systems has been subjected to intensive research, in particular, using the methods of the automatic control theory. One of the prominent problems here is the so-called synchronization of two or more chaotic systems. Even in case, when having two identical copies of the same chaotic system with practically the same initial conditions, thanks to strong dependence on initial data, after some time their behavior may be very different. In such a way, chaotic oscillations tends to be de-synchronized, unless some synchronizing influence is being imposed. Synchronization is usually achieved by transferring certain synchronizing signal from one chaotic system into the other one. This signal should have the least possible dimension, preferable it should be a scalar time function. As a suitable theoretical framework for synchronization appears to be the notion of the observer introduced by automatic control theory. Synchronized chaotic systems may be used for various secure encryption schemes. For such a purpose, one of those synchronized chaotic systems is used on the transmitter side to encrypt the sensitive information while the other one is used on the receiver side to decrypt it. In this case, the notion of the so-called secure synchronization is important. The secure synchronization is the one which can be achieved only when knowing some crucial system parameter information. Such an information may later serve as a secure password. This lecture will give brief overview of possible secure encryption/decryption methods based on synchronized chaotic systems. Furthermore, it will define the above indicated secure synchronization and it will introduce the special class of chaotic systems, together with its efficient parame-trization enabling even the global exponential synchronization. Such a synchronization is based on nonlinear transformations and subsequent observer design having favorable error dynamics. Moreover, its security may be investigated thanks to the mentioned parametrization as well. Klíčová slova: Nelineární rekonstrukce, synchronizace chaosu, ˇ sifrování.