Return-Map Cryptanalysis Revisited

As a powerful cryptanalysis tool, the method of return-map attacks can be used to extract secret messages masked by chaos in secure communication schemes. Recently, a simple defensive mechanism was presented to enhance the security of chaotic parameter modulation schemes against return-map attacks. Two techniques are combined in the proposed defensive mechanism: multistep parameter modulation and alternative driving of two different transmitter variables. This paper re-studies the security of this proposed defensive mechanism against return-map attacks, and points out that the security was much over-estimated in the original publication for both ciphertext-only attack and known/chosen-plaintext attacks. It is found that a deterministic relationship exists between the shape of the return map and the modulated parameter, and that such a relationship can be used to dramatically enhance return-map attacks thereby making them quite easy to break the defensive mechanism.Comment: 11 pages, 7 figure

Adaptive sliding mode observers in uncertain chaotic cryptosystems with a relaxed matching condition

We study the performance of adaptive sliding mode observers in chaotic synchronization and communication in the presence of uncertainties. The proposed robust adaptive observer-based synchronization is used for cryptography based on chaotic masking modulation (CM). Uncertainties are intentionally injected into the chaotic dynamical system to achieve higher security and we use robust sliding mode observer design methods for the uncertain nonlinear dynamics. In addition, a relaxed matching condition is introduced to realize the robust observer design. Finally, a Lorenz system is employed as an illustrative example to demonstrate the effectiveness and feasibility of the proposed cryptosyste

Breaking a chaos-based secure communication scheme designed by an improved modulation method

Recently Bu and Wang [Chaos, Solitons & Fractals 19 (2004) 919] proposed a simple modulation method aiming to improve the security of chaos-based secure communications against return-map-based attacks. Soon this modulation method was independently cryptanalyzed by Chee et al. [Chaos, Solitons & Fractals 21 (2004) 1129], Wu et al. [Chaos, Solitons & Fractals 22 (2004) 367], and \'{A}lvarez et al. [Chaos, Solitons & Fractals, accepted (2004), arXiv:nlin.CD/0406065] via different attacks. As an enhancement to the Bu-Wang method, an improving scheme was suggested by Wu et al. by removing the relationship between the modulating function and the zero-points. The present paper points out that the improved scheme proposed by Wu et al. is still insecure against a new attack. Compared with the existing attacks, the proposed attack is more powerful and can also break the original Bu-Wang scheme. Furthermore, it is pointed out that the security of the modulation-based schemes is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.Comment: elsart.cls, 18 pages, 9 figure

Breaking a chaos-noise-based secure communication scheme

This paper studies the security of a secure communication scheme based on two discrete-time intermittently-chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) the key space can be remarkably reduced; 2) the decryption is insensitive to the mismatch of the secret key; 3) the key-generation process is insecure against known/chosen-plaintext attacks. The first two defects mean that the scheme is not secure enough against brute-force attacks, and the third one means that an attacker can easily break the cryptosystem by approximately estimating the secret key once he has a chance to access a fragment of the generated keystream. Yet it remains to be clarified if intermittent chaos could be used for designing secure chaotic cryptosystems.Comment: RevTeX4, 11 pages, 15 figure

Impulsive Control and Synchronization of Chaos-Generating-Systems with Applications to Secure Communication

When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area

Digital Communication System with High Security and High Immunity

Today, security issues are increased due to huge data transmissions over communication media such as mobile phones, TV cables, online games, Wi-Fi and satellite transmission etc. for uses such as medical, military or entertainment. This creates a challenge for government and commercial companies to keep these data transmissions secure. Traditional secure ciphers, either block ciphers such as Advanced Encryption Standard (AES) or stream ciphers, are not fast or completely secure. However, the unique properties of a chaotic system, such as structure complexity, deterministic dynamics, random output response and extreme sensitivity to the initial condition, make it motivating for researchers in the field of communication system security. These properties establish an increased relationship between chaos and cryptography that create strong and fast cipher compared to conventional algorithms, which are weak and slow ciphers. Additionally, chaotic synchronisation has sparked many studies on the application of chaos in communication security, for example, the chaotic synchronisation between two different systems in which the transmitter (master system) is driving the receiver (slave system) by its output signal. For this reason, it is essential to design a secure communication system for data transmission in noisy environments that robust to different types of attacks (such as a brute force attack). In this thesis, a digital communication system with high immunity and security, based on a Lorenz stream cipher chaotic signal, has been perfectly applied. A new cryptosystem approach based on Lorenz chaotic systems was designed for secure data transmission. The system uses a stream cipher, in which the encryption key varies continuously in a chaotic manner. Furthermore, one or more of the parameters of the Lorenz generator is controlled by an auxiliary chaotic generator for increased security. In this thesis, the two Lorenz chaotic systems are called the Main Lorenz Generator and the Auxiliary Lorenz Generator. The system was designed using the SIMULINK tool. The system performance in the presence of noise was tested, and the simulation results are provided. Then, the clock-recovery technique is presented, with real-time results of the clock recovery. The receiver demonstrated its ability to recover and lock the clock successfully. Furthermore, the technique for synchronisation between two separate FPGA boards (transmitter and receiver) is detailed, in which the master system transmits specific data to trigger a slave system in order to run synchronously. The real-time results are provided, which show the achieved synchronisation. The receiver was able to recover user data without error, and the real-time results are listed. The randomness test (NIST) results of the Lorenz chaotic signals are also given. Finally, the security analysis determined the system to have a high degree of security compared to other communication systems

Digital Communication System with High Security and High Immunity

Today, security issues are increased due to huge data transmissions over communication media such as mobile phones, TV cables, online games, Wi-Fi and satellite transmission etc. for uses such as medical, military or entertainment. This creates a challenge for government and commercial companies to keep these data transmissions secure. Traditional secure ciphers, either block ciphers such as Advanced Encryption Standard (AES) or stream ciphers, are not fast or completely secure. However, the unique properties of a chaotic system, such as structure complexity, deterministic dynamics, random output response and extreme sensitivity to the initial condition, make it motivating for researchers in the field of communication system security. These properties establish an increased relationship between chaos and cryptography that create strong and fast cipher compared to conventional algorithms, which are weak and slow ciphers. Additionally, chaotic synchronisation has sparked many studies on the application of chaos in communication security, for example, the chaotic synchronisation between two different systems in which the transmitter (master system) is driving the receiver (slave system) by its output signal. For this reason, it is essential to design a secure communication system for data transmission in noisy environments that robust to different types of attacks (such as a brute force attack). In this thesis, a digital communication system with high immunity and security, based on a Lorenz stream cipher chaotic signal, has been perfectly applied. A new cryptosystem approach based on Lorenz chaotic systems was designed for secure data transmission. The system uses a stream cipher, in which the encryption key varies continuously in a chaotic manner. Furthermore, one or more of the parameters of the Lorenz generator is controlled by an auxiliary chaotic generator for increased security. In this thesis, the two Lorenz chaotic systems are called the Main Lorenz Generator and the Auxiliary Lorenz Generator. The system was designed using the SIMULINK tool. The system performance in the presence of noise was tested, and the simulation results are provided. Then, the clock-recovery technique is presented, with real-time results of the clock recovery. The receiver demonstrated its ability to recover and lock the clock successfully. Furthermore, the technique for synchronisation between two separate FPGA boards (transmitter and receiver) is detailed, in which the master system transmits specific data to trigger a slave system in order to run synchronously. The real-time results are provided, which show the achieved synchronisation. The receiver was able to recover user data without error, and the real-time results are listed. The randomness test (NIST) results of the Lorenz chaotic signals are also given. Finally, the security analysis determined the system to have a high degree of security compared to other communication systems