Analog Chaos-based Secure Communications and Cryptanalysis: A Brief Survey
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paper_title: Some basic cryptographic requirements for chaos-based cryptosystems

paper_content:

In recent years, a large amount of work on chaos-based cryptosystems have been published. However, many of the proposed schemes fail to explain or do not possess a number of features that are fundamentally important to all kind of cryptosystems. As a result, many proposed systems are difficult to implement in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a thorough security analysis. Consequently, it is difficult for other researchers and end users to evaluate their security and performance. This work is intended to provide a common framework of basic guidelines that, if followed, could benefit every new cryptosystem. The suggested guidelines address three main issues: implementation, key management and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements. Meanwhile, several recommendations are made regarding some practical aspects of analog chaos-based secure communications, such as channel noise, limited bandwith and attenuation.
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paper_title: Error function attack of chaos synchronization based encryption schemes.

paper_content:

Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor.
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paper_title: Theoretical and experimental studies of parameter estimation based on chaos feedback synchronization.

paper_content:

In this paper, we perform theoretical and experimental studies of parameter estimation based on chaos feedback synchronization. The Chua chaotic system is applied as the original system, and its time series of a single variable is applied as a feedback variable to drive a simulative system. The simplex method is employed to minimize the synchronization error in the simulative system to iteratively approach the original system parameters. Furthermore, the effects of feedback function, feedback weight, and noise are investigated. The parameter estimation method based on feedback synchronization shows its robustness to noise perturbation. Finally, the circuit experiment of parameter estimation is implemented in order to examine its practical applicability. The original Chua circuit parameters can be well approached from its recorded time series of a single variable. The results show the parameter estimation method based on feedback synchronization may be capable of estimating real system parameters from a chaotic time series.
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paper_title: Identifiability and Identification of Chaotic Systems Based on Adaptive Synchronization

paper_content:

This paper deals with the problem of synchronization of chaotic systems when the driven (slave, receiver) system has the same structure as the master (driving, emitter) system but its parameters are unknown. It is shown that the concept of synchronization provides an efficient way to find the unknown slave system parameters. Parameter mismatch between master and slave systems and high sensitivity of response to changes of these parameters were so far considered as crucial for security issues. This paper shows evidence that this claimed advantage becomes in fact a major drawback in chaos communication schemes since parameters ran easily be found using adaptive synchronization and optimization tools. The general problem of identifiability of chaotic systems is defined and discussed in the context of possibilities for finding the unknown chaotic receiver parameters. Several typical systems used in experiments in chaos communication are tested for identifiability showing direct applications of the introduced concepts. In particular examples of the skew tent map, Henon map, Markov maps and Chua's circuit are considered in detail illustrating the problems of global and local identifiability.
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paper_title: A New Approach to Breaking Down Chaotic Secure Communication

paper_content:

In this paper, we propose the time-varying stable fixed point concept to advance the generalized synchronization and present a general approach to calculating the value of chaotic system parameters according to some signal data. It provides a new approach to studying an unknown chaotic attractor and unmask the chaotic communication. We break down two chaotic communication schemes as examples with this approach.
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paper_title: Cryptanalysis of Cryptosystems Based on Remote Chaos Replication

paper_content:

In the last five years, many cryptosystems based on the chaos phenomenon have been proposed. Most of them use chaotic maps, i.e., the discrete-time chaos. The recent announcement of a cryptosystem based on continuous-time chaos that is generated by a very simple electronic circuit known as Chua's circuit passed unrecognized by a large part of the cryptographic community. It is an analog to the VERNAM-cipher system, but uses auto-synchronization through remote replication of the chaotic masking signal. After the introductory description of continuous-time chaotic systems and their synchronization a general definition and discussion of cryptosystems based on remote chaos replication is given. A cryptanalytic attack for these systems is developed that can break the cryptosystem using Chua's circuit for all types of information-bearing signals.
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paper_title: Breaking a chaos-based secure communication scheme designed by an improved modulation method

paper_content:

Recently Bu and Wang [Bu S, Wang B-H. Chaos, Solitons & Fractals 2004;19(4):919–24] 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. [Chee CY, Xu D, Bishop SR. Chaos, Solitons & Fractals 2004;21(5):1129–34], Wu et al. [Wu X, Hu H, Zhang B. Chaos, Solitons & Fractals 2004;22(2):367–73], and Alvarez et al. [Alvarez G, Montoya F, Romera M, Pastor G. Chaos, Solitons & Fractals, in press, arXiv:nlin/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 proposed by Wu et al. is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.
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paper_title: Estimating system parameters of Chua's circuit from synchronizing signal

paper_content:

Recently, Vaidya and Angadi proposed a new method to find the parameters of Lorenz system in a very rapid manner from synchronizing signal by using its derivatives. In this Letter, we extended it to analysis of Chua's circuit. An example of this approach to decode chaotic shift keying is presented.
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paper_title: Chosen ciphertext attack on chaos communication based on chaotic synchronization

paper_content:

In this brief, we analyze the secure property of a chaos-communication system based on chaotic synchronization using the chosen-ciphertext attack under the Kerckhoff principle. We point out that a secure communication system based on chaotic synchronization is not highly secure. We can resolve the parameters (keys) of the secure communication system by the chosen-ciphertext attack.
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paper_title: UNMASKING A MODULATED CHAOTIC COMMUNICATIONS SCHEME

paper_content:

This paper will address the problem of unmasking a new chaotic communication scheme using synchronizing circuits, where the Lorenz system is modulated by the message and the x-coordinate of the modulated system is added to the message and transmitted to the receiver. The receiver is driven into perfect synchrony with the transmitter even in the presence of the message, and since the message becomes part of the dynamics it provides very little distortion to the phase space of the dynamical system. However, this paper will demonstrate that it is still possible to extract a sinusoidal message from the transmitted signal. It will also be shown that it is possible to extract the sinusoidal signal solely from the x-coordinate, without secondarily adding back the message sinusoid before transmission. The message extraction is also shown to work for simple frequency-modulated and phase-modulated message signals. The modulated communication scheme does effectively nullify a multi-step unmasking technique which had been somewhat successful when applied to chaotic communication schemes which employed additive message signals.
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paper_title: STEPS TOWARD UNMASKING SECURE COMMUNICATIONS

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This work tests the level of security in secure communication systems based on nonlinear dynamics (NLD), or chaos. In these systems, a chaotic carrier signal is used in a type of spread-spectrum signaling system, with the added benefit that the hidden information signal is buried at something of the order of −30 dB with respect to the chaotic carrier. To investigate the level of security in such systems, an examination was conducted on a test set of chaotic carriers and hidden information signals prepared by the NLD research group at the Naval Research Lab. The hidden signals included a triangle wave, a period doubled signal, and a chaotic signal that was different from the chaotic carrier. The analysis process was to use NLD forecasting to predict the carrier dynamics, and then subtract away the predicted values to reveal the hidden signal or at least increase its signal-to-noise ratio with respect to the carrier. In each case, it was a simple task to determine the power spectrum of the hidden signal once the prediction of the carrier was removed. This was then used to create a “comb” filter to extract the correct frequencies from the FFT of the first two signals. When this was done, the hidden signals were recreated with almost perfect accuracy. In the third case, the hidden chaotic signal had a broadband component, so the spectrum was used to develop a Weiner filter which enabled the hidden signal to be reconstructed with only moderate accuracy, where the overall structure of the hidden chaotic signal was preserved, but the fine structure was lost. As a further test, the processing approach was applied to a voice signal hidden in one-dimensional Lorenz data at −35 dB. After subtracting away the carrier model, the voice signal was reconstructed with reasonable accuracy, and had the same characteristic structure. In this case, no secondary filtering was applied. The forecasting approach was then extended to allow for dynamic signal estimation using threshold detection, so that whenever a signal was detected, multiple predictions of the carrier behavior were made into the future. This was tested on a square wave embedded at −42 dB in Lorenz data. The extended approach was able to reveal the square wave with almost perfect precision, except in a few regions where it temporarily lost synchrony with the carrier. This allowed for the elimination of the secondary filtering requirement entirely. The final conclusion is that the secure communications systems based on chaotic carriers may be useful to increase privacy, but are not yet capable of providing a high level of security. The paper concludes with a discussion of measures which may be taken to improve the security of such systems so that they may be applicable to areas where higher security is required.
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paper_title: Extracting Messages Masked by Chaos

paper_content:

This chapter highlights how to extract messages that are masked by a chaotic signal in a system of two Lorenz oscillators. This mask removal is done for two different modes of transmission: a digital one, where a parameter of the sender is switched between two values, and an analog mode, where a small amplitude message is added to the carrier signal. It can be achieved without using a second Lorenz oscillator as a receiver, and without doing a full reconstruction of the dynamics. This method is robust with respect to transformations that impede the unmasking using a Lorenz receiver, and is not affected by the broadband noise that is inherent to the synchronization process. The chapter also discusses the limitations of this way of extraction for messages in high frequency bands.
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paper_title: Breaking parameter modulated chaotic secure communication system

paper_content:

Abstract This paper describes the security weakness of a recently proposed secure communication method based on parameter modulation of a chaotic system and adaptive observer-based synchronization scheme. We show that the security is compromised even without precise knowledge of the chaotic system used.
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paper_title: Topological Characterization of Reconstructed Attractors Modding Out Symmetries

paper_content:

Topological characterization is important in understanding the subtleties of chaotic behaviour. Unfortunately it is based on the knot theory which is only efficiently developed in 3D spaces (namely IR 3 or in its one-point compactification S 3 ). Consequently, to achieve topological characterization, phase portraits must be embedded in 3D spaces, i.e. in a lower dimension than the one prescribed by Takens' theorem. Investigating embedding in low-dimensional spaces is, therefore, particularly meaningful. This paper is devoted to tridimensional systems which are reconstructed in a state space whose dimension is also 3. In particular, an important case is when the system studied exhibits symmetry properties, because topological properties of the attractor reconstructed from a scalar time series may then crucially depend on the variable used. Consequently, special attention is paid to systems with symmetry properties in which specific procedures for topological characterization are developed. In these procedures, all the dynamics are projected onto a so-called fundamental domain, leading us to the introduction of the concept of restricted topological equivalence, i. e. two attractors are topologically equivalent in the restricted sense, if the topological properties of their fundamental domains are the same. In other words, the symmetries are moded out by projecting the whole phase space onto a fundamental domain.
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paper_title: Inherent Frequency and Spatial Decomposition of the Lorenz Chaotic Attractor

paper_content:

This letter suggests a new way to investigate 3-D chaos in spatial and frequency domains simultaneously. After spatially decomposing the Lorenz attractor into two separate scrolls with peaked spectra and a 1-D discrete-time zero-crossing series with a wide-band spectrum, it is found that the Lorenz chaotic attractor has an inherent frequency uniquely determined by the three system parameters. This result implies that chaos in the Lorenz attractor is mainly exhibited when the trajectory crosses from one scroll to another, not within the two scrolls. This is also true for some other double-scroll Lorenz-like chaotic attractors, such as Chua's attractor. Some possible applications of the inherent frequency and the spatial decomposition are also discussed.
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paper_title: Breaking a chaos-based secure communication scheme designed by an improved modulation method

paper_content:

Recently Bu and Wang [Bu S, Wang B-H. Chaos, Solitons & Fractals 2004;19(4):919–24] 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. [Chee CY, Xu D, Bishop SR. Chaos, Solitons & Fractals 2004;21(5):1129–34], Wu et al. [Wu X, Hu H, Zhang B. Chaos, Solitons & Fractals 2004;22(2):367–73], and Alvarez et al. [Alvarez G, Montoya F, Romera M, Pastor G. Chaos, Solitons & Fractals, in press, arXiv:nlin/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 proposed by Wu et al. is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.
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paper_title: Return-Map Cryptanalysis Revisited

paper_content:

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.
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paper_title: Breaking chaotic switching using generalized synchronization: examples

paper_content:

In a chaotic switching scheme, a binary message signal is scrambled by two chaotic attractors. In this paper we present examples to show how generalized chaotic synchronization (GS) can be used to break chaotic switching schemes. Since GS is a very robust phenomenon, we find that an intruder can recover the binary information signal from chaotic switching schemes without knowing both the structure and parameters of the chaotic transmitter. The breaking method presented in this paper is not sensitive to the order of the transmitter, which means that even in a chaotic switching scheme which uses two hyperchaotic systems, the degree of security may still be low. The simulation results for both low order and high order transmitters are presented.
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paper_title: Estimating short-time period to break different types of chaotic modulation based secure communications

paper_content:

In recent years, chaotic attractors have been extensively used in the design of secure communication systems. One of the preferred ways of transmitting the information signal is binary chaotic modulation, in which a binary message modulates a parameter of the chaotic generator. This paper presents a method of attack based on estimating the short-time period of the ciphertext generated from the modulated chaotic attractor. By calculating and then filtering the short-time period of the transmitted signal it is possible to obtain the binary information signal with great accuracy without any knowledge of the parameters of the underlying chaotic system. This method is successfully applied to various secure communication systems proposed in the literature based on different chaotic attractors.
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paper_title: Detection and classification of nonlinear dynamic switching events.

paper_content:

A method is proposed for detecting chaotic switching events. Switching events are classified by the time of the event and by parameter value. Classifications are based on the density of localized dynamics about a test trajectory. This method is shown to be successful in tracking short-time parameter modulation and hyperchaotic key shifting used in otherwise secure communications.
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paper_title: Inherent Frequency and Spatial Decomposition of the Lorenz Chaotic Attractor

paper_content:

This letter suggests a new way to investigate 3-D chaos in spatial and frequency domains simultaneously. After spatially decomposing the Lorenz attractor into two separate scrolls with peaked spectra and a 1-D discrete-time zero-crossing series with a wide-band spectrum, it is found that the Lorenz chaotic attractor has an inherent frequency uniquely determined by the three system parameters. This result implies that chaos in the Lorenz attractor is mainly exhibited when the trajectory crosses from one scroll to another, not within the two scrolls. This is also true for some other double-scroll Lorenz-like chaotic attractors, such as Chua's attractor. Some possible applications of the inherent frequency and the spatial decomposition are also discussed.
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paper_title: Decoding Digital Information from the Cascaded Heterogeneous Chaotic Systems

paper_content:

In this paper, we propose a new approach to breaking down chaotic communication scheme by attacking its encryption keys. A remarkable advancement is that it can decode the hidden message exactly. This makes it become possible to break down some cascaded chaotic communication systems. We also decode digital information from the cascaded heterogeneous chaotic communication system and give the simulation results.
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paper_title: UNMASKING CHAOTIC MASK BY A WAVELET MULTISCALE DECOMPOSITION ALGORITHM

paper_content:

A method is proposed for extracting a useful signal hidden in a deterministic chaotic signal using a wavelet multiscale decomposition algorithm that can separate two signals with different wavelet scales. The mask removal is done without resorting to chaos synchronization. It is a noise reduction method without knowing the dynamical model of chaotic system, and restricting the modulation ratio of the chaos signal and useful signal. So this method is effective for unmasking chaotic mask through the quantitative analyses and the numerical simulations of three examples.
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paper_title: Unmasking a hyperchaotic communication scheme

paper_content:

This paper will consider the use of nonlinear dynamic forecasting techniques to extract message signals from a six-dimensional, message-modulated hyperchaotic communication scheme. It will be shown that a variety of messages can be successfully extracted using only a three-dimensional reconstruction. Further, the robustness of the signal extraction is demonstrated by extracting a speech message with the speech amplitude varied by over an order of magnitude. In all cases intelligible speech was extracted, so security was not greatly improved by going to a hyperchaotic system or larger amplitude signals.
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paper_title: Breaking a secure communication scheme based on the phase synchronization of chaotic systems.

paper_content:

A security analysis of a recently proposed secure communication scheme based on the phase synchronization of chaotic systems is presented. It is shown that the system parameters directly determine the cipher text waveform, hence it can be readily broken by system parameter estimation from the cipher text signal.
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paper_title: Cryptography based on chaotic systems

paper_content:

In this letter, a new chaos-based secure communication scheme is proposed in an attempt to thwart the attacks proposed recently. Instead of encoding the message signal in a chaotic system directly, we use two chaotic signals in our scheme. One of the chaotic signals is used to synchronize the chaotic encrypter and the chaotic decrypter. The other is used to encrypt the plain signal by using a multishift cipher scheme. Thus the transmitted signal is not used to encrypt the message and a more complicated method of encryption is used.
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paper_title: Reconstructing the keystream from a chaotic encryption scheme

paper_content:

A new technique of secure communication was developed which uses a synchronizing chaotic communication channel to transmit an encrypted message. The important feature of this system is that the keystream used in the encryption stage is not transmitted but may be dynamically reconstructed by the intended receiver. Since an additional level of encryption is employed, it was claimed that an eavesdropper may have limited success using nonlinear dynamic (NLD) forecasting techniques to extract the message. In this paper we show that there may be sufficient geometric information in the transmission to extract an estimate of the keystream (although it could require a difficult search) as well as characteristics of the encrypting function. Consequently, it may be possible to recover the hidden message with good accuracy.
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paper_title: Decoding Digital Information from the Cascaded Heterogeneous Chaotic Systems

paper_content:

In this paper, we propose a new approach to breaking down chaotic communication scheme by attacking its encryption keys. A remarkable advancement is that it can decode the hidden message exactly. This makes it become possible to break down some cascaded chaotic communication systems. We also decode digital information from the cascaded heterogeneous chaotic communication system and give the simulation results.
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paper_title: Digital signal transmission with cascaded heterogeneous chaotic systems.

paper_content:

A new chaos based secure communication scheme is proposed to transmit digital signals by combining the concepts of chaotic-switching and chaotic-modulation approaches. In this scheme two heterogeneous chaotic circuits are used both at the transmitter and receiver modules. First a binary message signal is scrambled by two chaotic attractors produced by a set of chaotic systems (No. 1) of the drive module. The so produced small amplitude scrambled chaotic signal is further directly injected or modulated by different chaotic system (No. 2) within the drive module. Then the chaotic signal generated by this second chaotic system No. 2 is transmitted to the response module through the channel. An appropriate feedback loop is constructed in the response module to achieve synchronization among the variables of the drive and response modules and the binary information signal is recovered by using the synchronization error followed by low-pass filtering and thresholding. Simulation results are reported in which the quality of the recovered signal is higher and the encoding of the information signal is potentially secure. The effect of perturbing factors like channel noise and nonidentity of parameters are also considered.
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paper_title: Heterogeneous chaotic systems based cryptography

paper_content:

Abstract A new chaos based cryptosystem is proposed to transmit digital information signal by using the conventional synchronization approach with cascaded heterogeneous chaotic systems. In this scheme two heterogeneous chaotic circuits (hyperchaotic and chaotic) are used both at the transmitter and receiver modules. The hyperchaotic system is used to mask the information signal and to produce a plaintext signal. The chaotic system acts as an encrypter in the transmitter module. Similarly the receiver module consists a chaotic decrypter and a hyperchaotic system. A multishift cipher scheme is considered both at the encrypter and the decrypter for respective encrypting and decrypting the plaintext messages. An appropriate feedback loop is constructed in the response-module to acheive synchronization among the variables of the drive and response-modules. Simulation results are reported in which the quality of the recovered signal is higher and the encoding is potentially secure. The effect of perturbing factors like channel noise and nonidentity of parameters are also considered.
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paper_title: 1 Lorenz System Parameter Determination and Application to Break the Security of Two-channel Chaotic Cryptosystems

paper_content:

This Letter describes how to determine the parameter of the chaotic Lorenz system used in a two-channel cryptosystem. First the geometrical properties of the Lorenz system are used to reduce the parameter search space. Second the parameters are exactly determined—directly from the ciphertext—through the minimization of the average jamming noise power created by the encryption process.
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paper_title: Analyzing and improving a chaotic encryption method

paper_content:

Abstract To resist the return map attack [Phys. Rev. Lett. 74 (1995) 1970] presented by Perez and Cerdeira, Shouliang Bu and Bing-Hong Wang proposed a simple method to improve the security of the chaotic encryption by modulating the chaotic carrier with an appropriately chosen scalar signal in [Chaos, Solitons & Fractals 19 (2004) 919]. They maintained that this modulating strategy not only preserved all appropriate information required for synchronizing chaotic systems but also destroyed the possibility of the phase space reconstruction of the sender dynamics such as a return map. However, a critical defect does exist in this scheme. This paper gives a zero-point autocorrelation method, which can recover the parameters of the scalar signal from the modulated signal. Consequently, the messages will be extracted from the demodulated chaotic carrier by using return map. Based on such a fact, an improved scheme is presented to obtain higher security, and the numerical simulation indicates the improvement of the synchronizing performance as well.
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paper_title: Cryptanalyzing an improved security modulated chaotic encryption scheme using ciphertext absolute value

paper_content:

Abstract This paper describes the security weakness of a recently proposed improved chaotic encryption method based on the modulation of a signal generated by a chaotic system with an appropriately chosen scalar signal. The aim of the improvement is to avoid the breaking of chaotic encryption schemes by means of the return map attack introduced by Perez and Cerdeira. A method of attack based on taking the absolute value of the ciphertext is presented, that allows for the cancellation of the modulation scalar signal and the determination of some system parameters that play the role of system key. The proposed improved method is shown to be compromised without any knowledge of the chaotic system parameter values and even without knowing the transmitter structure.
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paper_title: Improving the security of chaotic encryption by using a simple modulating method

paper_content:

Abstract In recent years, synchronization of chaotic systems has aroused much interest due to its potential application to secure communications. However, it is found by Perez and Cerdeira that an intruder, without the knowledge of the parameters of the system or even of the nonlinear system itself, may extract the messages from the carrier signal by producing a return map where the dynamics is attracted to an almost 1D set. To eliminate the weakness, in this letter, a simple but efficient method for synchronizing chaotic systems by modulating the transmitted signal with an appropriately choosing scalar signal is proposed. It turns out that this modulating strategy not only preserves all appropriate information required for synchronizing chaotic systems but also destroys the possibility of the phase space reconstruction of the sender dynamics such as a return map.
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paper_title: A zero-crossing approach to uncover the mask by chaotic encryption with periodic modulation

paper_content:

Abstract We present a so-called zero-crossing identification method that can crack the security shell of the chaotic encryption method [Chaos, Solitons & Fractals 19 (2004) 919] with periodic modulation. By collecting a special set of truncated data from the zero-crossing incidents of the modulated signal, we can detect the modulating function from chaotic signal. Furthermore we extend the technique to extract modulating function from noise and discuss the potential applications of this method in engineering.
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paper_title: Breaking a chaos-based secure communication scheme designed by an improved modulation method

paper_content:

Recently Bu and Wang [Bu S, Wang B-H. Chaos, Solitons & Fractals 2004;19(4):919–24] 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. [Chee CY, Xu D, Bishop SR. Chaos, Solitons & Fractals 2004;21(5):1129–34], Wu et al. [Wu X, Hu H, Zhang B. Chaos, Solitons & Fractals 2004;22(2):367–73], and Alvarez et al. [Alvarez G, Montoya F, Romera M, Pastor G. Chaos, Solitons & Fractals, in press, arXiv:nlin/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 proposed by Wu et al. is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.
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paper_title: CHAOTIC ENCRYPTION WITH TRANSIENT DYNAMICS INDUCED BY PSEUDO-RANDOM SWITCHING KEYS

paper_content:

A chaotic encryption method is proposed for digital communication using a pseudo-random switching key in which parameters irregularly adjust to a rule related to chaotic variables. The scheme derived two features — pseudo-random false switching events are densely produced to mask up binary switching and the transmitted signal possesses a transient nature thus diffusing any deterministic characteristics used by interceptors. The robustness of synchronization is discussed when the mismatch of parameters or keys occurs under erratic switching events.
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paper_title: Secure digital signal transmission by multistep parameter modulation and alternative driving of transmitter variables

paper_content:

The idea of secure communication of digital signals via chaos synchronization has been plagued by the possibility of attractor reconstruction by eavesdroppers as pointed out by Perez and Cerdeira. In this Letter, we wish to present a very simple mechanism by which this problem can be overcome, wherein the signal is transmitted via a multistep parameter modulation combined with alternative driving of different transmitter variables, which makes the attractor reconstruction impossible. The method is illustrated by means of the Lorenz system and Chua's circuit as examples.
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paper_title: Return-Map Cryptanalysis Revisited

paper_content:

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.
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Title: Analog Chaos-based Secure Communications and Cryptanalysis: A Brief Survey

Section 1: INTRODUCTION
Description 1: Provide background information on chaos-based cryptography and its evolution, introduce the types of chaos-based cryptosystems, and outline the purpose and organization of the paper.

Section 2: CHAOS SYNCHRONIZATION
Description 2: Explain the concept of chaos synchronization, types of driving modes, and various forms of chaos synchronization techniques relevant to analog chaos-based secure communications.

Section 3: ANALOG CHAOS-BASED SECURE COMMUNICATIONS
Description 3: Discuss the three basic types of analog chaos-based secure communication systems (chaotic masking, chaotic switching, and chaotic modulation) and provide a brief summary of their security.

Section 4: CRYPTANALYTIC RESULTS
Description 4: Explore the different cryptanalytic techniques used to evaluate the security of chaos-based secure communication systems, categorizing them into several types and highlighting specific methods and their implications.

Section 5: NEW COUNTERMEASURES AGAINST KNOWN ATTACKS
Description 5: List and describe various countermeasures that have been proposed to address the security problems of traditional chaos-based secure communication systems, including their strengths and weaknesses.

Section 6: CONCLUDING REMARKS
Description 6: Summarize the challenges and potential solutions in the field of analog chaos-based secure communications and suggest directions for future research.