Communicating with noise: How chaos and noise combine to generate secure encryption keys

An approach for the secure transmission of encrypted messages using chaos and noise is presented in this paper. The method is based on the synchronization of certain types of chaotic oscillators in response to a common noise input. This allows two distant oscillators to generate identical output which can be used as a key for encryption and decryption of a message signal. The noiselike synchronizing input-which contains no message information-is communicated to identical oscillators in the transmitter and the receiver over a public channel. The encrypted message is also sent over a public channel, while the key is never transmitted at all. The chaotic nature of the oscillators which generate the key and the randomness of the signal driving the process combine to make the recovery of the key by an eavesdropper extremely difficult. We evaluate system performance with respect to security and robustness and show that a robust and secure system can be obtained. (c) 1998 American Institute of Physics.     

Chaotic secure communication based on strong tracking filtering

A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate.     

光学双稳系统混沌驱动保密通讯原理研究

根据声光双稳系统混沌驱动下的动力学行为，提出利用系统的相位特性实现信息的混沌加密，并且由接收端混沌驱动产生的混沌信号完成信息提取的原理。发现在较大的噪声覆盖下仍然可以实现信息的安全传送，由于信息解密不需要与载波安全同步的混信号而只利用传输信号与接收端被驱动系统输出信号的相位关系，因此这种方法具有实际应用价值。     

基于现场可编程门阵列的手机短信息混沌加密系统设计方案及硬件实现

手机的普及使得个人信息安全问题受到广泛关注, 其中手机短信息的安全性尤为重要. 本文致力于设计实现手机短信息加密与安全传输的硬件系统, 采用混沌A5/1混合算法, 提出一种基于现场可编程门阵列(FPGA)的手机短信息加密系统设计方案. 使用由Logistic混沌序列做初始密钥而改进的A5/1混合算法作为加密算法, 分析其伪随机性并证明圆周相关与线性相关的关系; 采用SIM300模块设计实现手机功能, 仿真普通手机短信息和加密短信息的传输; 开发一套软件测试平台, 可以在计算机上呈现硬件系统的测试结果. 经测试表明, 本文提出并实现的硬件系统可以加密手机短信息并保证其正常传输, 从而提高了手机短信息的安全性.     

基于状态观测器的分数阶时滞混沌系统同步研究

研究分数阶时滞混沌系统同步问题,基于状态观测器方法和分数阶系统稳定性理论,设计分数阶时滞混沌系统同步控制器,使得分数阶时滞混沌系统达到同步,同时给出了数学证明过程.该同步控制器采用驱动系统和响应系统的输出变量进行设计,无需驱动系统和响应系统的状态变量,简化了控制器的设计,提高了控制器的实用性.利用Lyapunov稳定性理论和分数阶线性矩阵不等式,研究并给出了同步控制器参数的选择条件.以分数阶时滞Chen混沌系统为例,设计基于状态观测器的同步控制器,实现了分数阶时滞Chen混沌系统同步,并将其应用于保密通信系统中.仿真结果证明了该同步方法的有效性.     

Synchronization of the time—varying parameter chaotic system and its application to secure communication

In this paper we propose and investigate the synchronization of a new chaotic model with time-varying parameters and apply it to improve the security of chaotic communication. In this model, the chaotic system is modulated by both the message and the varying parameters. The varying parameters distort the phase space so heavily that they prevent the carrier from being broken by nonlinear dynamic forecasting method. Theory and simulation experiments with speech signal communication indicate that the receiver can gain a perfect synchronization with the transmitter, and the intruder cannot break down this communication system. We also discuss the robustness of the new communication system.     

延迟-非线性反馈控制混沌

提出了基于稳定性准则的延迟非线性反馈控制混沌的方法，即SC延迟非线性反馈控制法. 通过对混沌系统的适当分离，得到一个特殊的非线性函数，并利用混沌输出信号与其延迟信号的非线性函数的差，构造了连续反馈输入干扰，以控制混沌轨到某一期望的不稳周期轨上. 该方法继承了延迟反馈控制方法的优点，实现了自-控制过程. 另外由于该方法基于线性系统的稳定性准则，保证了控制的有效性. 控制过程可随时开始，具有简便、灵活性. 给出耦合Duffing振子的例子，数值模拟结果显示了SC延迟反馈方法控制的有效性. 关键词： 稳定性准则 混沌控制 延迟反馈 干扰     

Chaotic wavelength division multiplexing for optical communication

We demonstrate wavelength division multiplexing with chaotic subcarriers in two pairs of one-way-coupled Nd:YVO4 microchip lasers. Two individual digital messages are encoded on two chaotic carriers with different wavelengths in two transmitters by the chaotic masking method, and the mixed signals are sent to two receivers. Dual synchronization of chaos is used to obtain the original chaotic waveforms in the receivers. Two messages are decoded by filtering the difference of the laser outputs between the transmitter and the receiver by use of a low-pass filter for each pair of lasers. The message recovery can be achieved more easily when messages with small amplitude and low frequency are used.     

主副垂直腔面发射激光器动力学系统混沌输出的时延特征及带宽分析

基于垂直腔面发射激光器(VCSEL)的自旋反转模型, 数值研究了由一个光反馈VCSEL (定义为主VCSEL, M-VCSEL)输出的混沌光单向注入到另一个VCSEL (定义为副VCSLE, S-VCSEL)所构成的主副VCSELs系统的混沌动力学特性, 分析了注入强度、M-VCSEL与S-VCSEL之间的频率失谐以及M-VCSEL所受到的光反馈强度对系统混沌输出时延特征(包括强度时延特征(I-TDS) 和相位时延特征(P-TDS))以及输出带宽(BW)的影响. 结果显示: 通过调节注入强度和频率失谐, 该系统混沌输出的两个偏振分量(X-PC和Y-PC)的P-TDS和I-TDS可以同时得到抑制; 进一步分析注入强度和频率失谐对混沌BW的影响, 发现在较大负频率失谐区域, 系统可输出BW超过30 GHz 的X-PC和Y-PC混沌信号; 结合系统混沌输出信号的TDS与BW在注入强度和频率失谐参量空间下的演化特性, 可确定宽带宽、低时延特征混沌信号输出的参量空间区域. 此外, 通过合理调节M-VCSEL 所受到的光反馈强度, 可以显著优化系统的混沌输出信号质量.     

Non-standard finite-difference time-domain method for solving the Schrödinger equation

The literature on chaos has highlighted several chaotic systems with special features. In this work, a novel chaotic jerk system with non-hyperbolic equilibrium is proposed. The dynamics of this new system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, we investigate the time-delay effects on the proposed system. Realisation of such a system is presented to verify its feasibility.     

A NEW SLIDING MODE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY CHAOTIC SYSTEMS

We propose a new sliding mode control scheme for a class of uncertain time-delay chaotic systems. It is shown that a linear time invariant system with the desired system dynamics is used as a reference model for the output of a time-delay chaotic system to track. A sliding mode controller is then designed to drive the output of the time-delay chaotic system to track the desired linear system. On the sliding mode, the output of the controlled time-delay chaotic system can behave like the desired linear system. A simulation example is given in support of the proposed control scheme.     

Cryptanalyzing chaotic secure communications using return maps

In chaotic secure communications, message signals are scrambled by chaotic dynamical systems. The interaction between the message signals and the chaotic systems results in changes of different kinds of return maps. In this paper, we use return map based methods to unmask some chaotic secure communication systems; namely, chaotic shift keying (chaotic switching), chaotic parameter modulation and non-autonomous chaotic modulation. These methods are used without knowing the accurate knowledge of chaotic transmitters and without reconstructing the dynamics or identifying the parameters of chaotic transmitters. These methods also provide a criterion of deciding whether a chaotic secure communication scheme is secure or not. The effects of message signals on the changes of different return maps are studied. Fuzzy membership functions are used to characterize different kinds of changes of return maps. Fuzzy logic rules are used to extract message signals from the transmitted signal. The computer experimental results are provided. The results in this paper show that the security of chaotic secure communication not only depends on the complexity of the chaotic system but also depends on the way the message is scrambled. A more complex chaotic system is not necessary to provide a higher degree of security if the transmitted signal has simple and concentrated return maps. We also provide examples to show that a chaotic system with complicated return maps can achieve a higher degree of security to the attacks presented in this paper.     

Recovery of parameters of delayed-feedback systems from chaotic time series

Methods for reconstructing a delay differential equation from the time series of an observable quantity are proposed for various classes of time-delay systems. The methods rely on knowledge of the distributions of extrema of the time series of observed oscillations and projection of the infinite-dimensional phase spaces of time-delay systems onto special low-dimensional subspaces. The effectiveness of the proposed methods is demonstrated by reconstructing delay differential equations from their chaotic solutions, including those corrupted by noise, and by constructing models of real time-delay systems from chaotic time series.     

Adaptive synchronization with nonlinear input

This paper considers the adaptive synchronization problem of the drive—response type chaotic systems. Using a transmitted scalar signal with an unknown time-delay, a response system is constructed. By appropriately selecting the observer gain and designing the controller, synchronization can be achieved in the presence of the drive system's disturbances and unknown parameters. A well-known chaotic system, Chua's circuit, is considered as an illustrative example to demonstrate the effectiveness of the proposed approach.     

Time-delayed chameleon: Analysis,synchronization and FPGA implementation

In this paper we report a time-delayed chameleon-like chaotic system which can belong to different families of chaotic attractors depending on the choices of parameters. Such a characteristic of self-excited and hidden chaotic flows in a simple 3D system with time delay has not been reported earlier. Dynamic analysis of the proposed time-delayed systems are analysed in time-delay space and parameter space. A novel adaptive modified functional projective lag synchronization algorithm is derived for synchronizing identical time-delayed chameleon systems with uncertain parameters. The proposed time-delayed systems and the synchronization algorithm with controllers and parameter estimates are then implemented in FPGA using hardware–software co-simulation and the results are presented.     

基于双光反馈垂直腔面发射激光器的双信道混沌同步通信

利用双光反馈垂直腔面发射半导体激光器(VCSELs) 两个正交偏振模式输出的两个混沌信号作为混沌载波, 构建了一个双信道的混沌保密通信系统, 并对该系统的通信性能进行了数值仿真研究.研究结果表明: 通过合理的选取反馈参量, 双光反馈VCSELs两个偏振模式输出的混沌信号能很好地隐藏外腔反馈延时特性; 双光反馈VCSEL两个偏振模式输出的混沌信号通过偏振保持注入到接收VCSEL中, 在强注入锁定条件下可以实现很好的混沌同步, 同步性能对频率失谐的容忍性随着注入强度的增加而加强; 在附加混沌调制加密方式下, 500 Mbit/s的信号在传输过程中能够得到很好的隐藏, 同时在接收端可以成功解调; 随着通信速率的增加, Q因子呈现下降的趋势, 但对于 6 Gbit/s的信息, Q因子仍大于6. 关键词： 垂直腔面发射激光器 双光反馈 双信道 混沌通信     

一阶时滞混沌的参数辨识

估计混沌系统的未知参数是混沌控制与同步中必须解决的关键问题.针对两种不同类型的时滞混沌系统中的未知参数的辨识问题，将系统的未知参数看作系统的未知状态，利用非线性状态观测器理论进行参数估计，通过选取观测器中非线性增益函数，使得闭环误差系统指数或渐进稳定，从而给出参数估计器存在的充分条件.以典型的时滞Logistic系统为例进行了数值模拟，数值仿真结果表明，使用该方法可以对时滞混沌系统的未知参数进行有效地估计.     

Decoding information by following parameter modulation with parameter adaptive control

It has been proposed to realize secure communication using chaotic synchronization via transmission of a binary message encoded by parameter modulation in the chaotic system. This paper considers the use of parameter adaptive control techniques to extract the message, based on the assumptions that we know the equation form of the chaotic system in the transmitter but do not have access to the precise values of the parameters which are kept secret as a secure set. In the case in which a synchronizing system can be constructed using parameter adaptive control by the transmitted signal and the synchronization is robust to parameter mismatches, the parameter modulation can be revealed and the message decoded without resorting to exact parameter values in the secure set. A practical local Lyapunov function method for designing parameter adaptive control rules based on originally synchronized systems is presented.     

Adaptive synchronization of a switching system and its applications to secure communications

This paper studies the adaptive synchronization of a switching system with unknown parameters which switches between the R?ssler system and a unified chaotic system. Using the Lyapunov stability theory and adaptive control method, the receiver system will achieve synchronization with the drive system and the unknown parameters would be estimated by the receiver. Then the proposed switching system is used for secure communications based on the communication schemes including chaotic masking, chaotic modulation, and chaotic shift key strategies. Since the system switches between two chaotic systems and the parameters are almost unknown, it is more difficult for the intruder to extract the useful message from the transmission channel. In addition, two new schemes in which the chaotic signal used to mask (or modulate) the transmitted signal switches between two components of a chaotic system are also presented. Finally, some simulation results are given to show the effectiveness of the proposed communication schemes.     

基于一阶时滞混沌系统参数辨识的保密通信方案

基于参数调制原理,针对一阶时滞Logistic混沌系统设计了相应的参数观测器,仅传递单路信号就可以成功辨识出系统中的未知参数,从而恢复出调制在参数中的模拟信号,并在此基础上采用不同频率信号代替“0”或“1”,设计出具体的数字保密通信方案.数值仿真验证了本方法的有效性. 关键词： 观测器 混沌保密通信 参数调制 滤波