Volodymyr Lynnyk

Robust synchronization of a class of chaotic networks

This paper studies synchronization of a dynamical complex network consisting of nodes being generalized Lorenz chaotic systems and connections created with transmitted synchronizing signals. The focus is on the robustness of the network synchronization with respect to its topology. The robustness is analyzed theoretically for the case of two nodes with two-sided (bidirectional) connections, and numerically for various cases with large numbers of nodes. It is shown that, unless a certain minimal coherent topology is present in the network, synchronization is always preserved. While for a minimal network where synchronization is global, the resulting synchrony reduces to semi-global if redundant connections are added.

DESYNCHRONIZATION CHAOS SHIFT KEYING METHOD BASED ON THE ERROR SECOND DERIVATIVE AND ITS SECURITY ANALYSIS

This paper describes the chaos shift keying method based on the second derivative desynchronization error and provides its security analysis, especially against the attacks by power and return map analysis. Desynchronization chaos shift keying method (DECSK) uses methods to detect the correct bit by detecting the wrong bit. Various modifications are possible, here the method using sharp increase of error in the second derivative of synchronizing signal is used. The proposed method requires very reasonable amount of data to encrypt and time to decrypt one bit. Basically, to encrypt one bit, only one iteration (i.e. only one real number of six valid digits) is needed. At the same time, thanks to the desynchronization detection based on the synchronization error second derivative, almost 100% of the carrying chaotic signal can be used. The security of the proposed method can be systematically investigated showing its good resistance against typical decryption attacks. More detailed analysis is devoted to its analysis via power and return map analysis. Conclusion is that the DECSK method cannot be broken by the above two methods which together with other arguments developed there serves as a good basis for the DECSK security.

Observer-based chaos synchronization in the generalized chaotic Lorenz systems and its application to secure encryption

This paper studies the application of the observer-based chaos synchronization in the so-called generalized Lorenz systems to secure encryption. More precisely, a modified version of the chaos shift keying (CSK) scheme for secure encryption and decryption of data is proposed. Recall, that the classical CSK method determines the correct value of binary signal through checking which unsynchronized system is getting synchronized. On the contrary, our novel method, called as the anti-synchronization chaos shift keying (ACSK) method, determines wrong value of binary signal through checking which already synchronized system is loosing synchronization. Even when using two very close each to other chaotic systems, the anti-synchronization is thousand times faster than synchronization. As a consequence, unlike the classical CSK, the method proposed here requires very reasonable amount of data to encrypt and time to decrypt a single bit. Moreover, its security can be systematically investigated showing its good resistance against typical decryption attacks

Message Embedded Chaotic Masking Synchronization Scheme Based on the Generalized Lorenz System and Its Security Analysis

This paper focuses on the design of the novel chaotic masking scheme via message embedded synchronization. A general class of the systems allowing the message embedded synchronization is presented here, moreover, it is shown that the generalized Lorenz system belongs to this class. Furthermore, the secure encryption scheme based on the message embedded synchronization is proposed. This scheme injects the embedded message into the dynamics of the transmitter as well, ensuring thereby synchronization with theoretically zero synchronization error. To ensure the security, the embedded message is a sum of the message and arbitrary bounded function of the internal transmitter states that is independent of the scalar synchronization signal. The hexadecimal alphabet will be used to form a ciphertext making chaotic dynamics of the transmitter even more complicated in comparison with the transmitter influenced just by the binary step-like function. All mentioned results and their security are tested and demonstrated by numerical experiments.

ANTI-SYNCHRONIZATION CHAOS SHIFT KEYING METHOD BASED ON GENERALIZED LORENZ SYSTEM

Abstract In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data is proposed. The proposed scheme uses the effect of anti-synchronization, rather than synchronization. More specifically, the classical CSK method determines the correct value of binary signal through checking which unsynchronized system is getting synchronized. On the contrary, our novel method determines wrong value of binary signal through checking which already synchronized system is loosing synchronization. The advantage of the proposed method is two-fold. First, it requires very reasonable amount of data to encrypt and time to decrypt a single bit. Secondly, its security can be investigated and estimated as practically unbreakable. The main reason for both advantages is that anti-synchronization is thousand times faster than synchronization, even when using two close each to other chaotic systems. Our method is implemented and thoroughly tested on the recently introduced generalized Lorenz system (GLS) family making advantage of its special parametrization.

Message Embedded Synchronization for the Generalized Lorenz System and Its Use for Chaotic Masking

This paper implements and analyzes the well-known message embedded synchronization scheme for the case of the generalized Lorenz system. Such a synchronization may be used for chaotic masking scheme using a single channel only. This method was already discussed in the earlier literature for the particular classes of systems. In this paper, a more general class wheremessage embedded synchronization is possible is described. Then, it is shown that the generalized Lorenz system falls within that class. Furthermore, using the resulting synchronization, the novel secure encryption scheme is proposed. It requires very reasonable amount of data to encrypt and time to decrypt one bit. Basically, to encrypt one bit, only one iteration (i.e. only one real number of 6 valid digits) is needed. At the same time, 100 percent of the carrying chaotic signal can be used. The method is also demonstrated by numerical simulations of a digital data encryption and decryption.

Efficient chaos shift keying method based on the second error derivative anti-synchronization detection

This paper studies yet another improvement of the anti-synchronization chaos shift keying scheme for the secure encryption and decryption of the digital data. A new concept of the detection of the correct binary value in the receiver is introduced here. The proposed method requires very reasonable amount of data to encrypt and time to decrypt one bit. Basically, to encrypt one bit, only one iteration (i.e. only one real number of 6 valid digits) is needed. At the same time, thanks to the anti-synchronization detection based on the synchronization error second derivative, almost 100% of the carrying chaotic signal can be used. The security of the proposed method can be systematically investigated showing its good resistance against typical decryption attacks. The theoretical analysis of the introduced method is supported by the numerical experiments with digital data encryption.

Anti-synchronization chaos shift keying method: error derivative detection improvement.*

Abstract This paper studies a new modification of the anti-synchronization chaos shift keying scheme for the secure encryption and decryption of data. A new concept of the detection of the correct/incorect binary value in the receiver is used. The method proposed here requires very reasonable amount of data to encrypt and time to decrypt a single bit. Basically, to encrypt a single bit, only one iteration is needed. Moreover, the security of this method is systematically investigated showing its good resistance to typical decryption attacks. Theoretical results are supported by the numerical simulations.

ROBUST STRUCTURAL SYNCHRONIZATION IN DYNAMICAL COMPLEX NETWORKS

Abstract The aim of this paper is to study synchronization of a dynamical complex network consisting of nodes being generalized Lorenz chaotic systems and connections are created with transmitted synchronizing signals. Focus is on the robustness of the network synchronization with respect to its connectional structure. This robustness is analyzed theoretically for the case of two nodes with two-sided (bidirectional connections), and numerically for various cases with many nodes. It is shown that unless a certain minimal coherent connectional structure is present in network, the synchronization is always preserved. While for a minimal connectional configuration where the synchronization is global, the resulting synchronization is only semi-global when some redundant connections are added.

Network-based control of nonlinear large-scale systems composed of identical subsystems

Abstract This paper deals with a control of coupled nonlinear identical systems that admit full exact feedback input-output linearization. The subsystems are linearized using this nonlinear transformation. In the next step, an auxiliary low-dimensional system is derived whose stability implies stability of the original large-scale system. The control law is designed so that the control loops are only local, no information exchange between subsystems is required. Unknown time delay in the feedback are allowed. Two cases are studied: equal time delay for all subsystems or different delay in all subsystems. Results are illustrated by two examples.