Tent Map Research Articles

Chaos-Based Simultaneous Compression and Encryption for Hadoop.

Data compression and encryption are key components of commonly deployed platforms such as Hadoop. Numerous data compression and encryption tools are presently available on such platforms and the tools are characteristically applied in sequence, i.e., compression followed by encryption or encryption followed by compression. This paper focuses on the open-source Hadoop framework and proposes a data storage method that efficiently couples data compression with encryption. A simultaneous compression and encryption scheme is introduced that addresses an important implementation issue of source coding based on Tent Map and Piece-wise Linear Chaotic Map (PWLM), which is the infinite precision of real numbers that result from their long products. The approach proposed here solves the implementation issue by removing fractional components that are generated by the long products of real numbers. Moreover, it incorporates a stealth key that performs a cyclic shift in PWLM without compromising compression capabilities. In addition, the proposed approach implements a masking pseudorandom keystream that enhances encryption quality. The proposed algorithm demonstrated a congruent fit within the Hadoop framework, providing robust encryption security and compression.

Multi-objective thermal power load dispatch using chaotic differential evolutionary algorithm and Powell’s method

In this work, a chaotic differential evolutionary and Powell’s pattern search (CDEPS) algorithm is proposed to solve multi-objective thermal power load dispatch (MTPLD) problem. The chaotic differential evolutionary method is responsible for the diversification, and Powell’s pattern search is dedicated to exploitation. Further, the performance of two CDEPS variants based on Gauss map and Tent map is investigated. The proposed MTPLD solution procedure either identifies a solution close to Pareto front or diversifies the existing Pareto frontier and finally selects a suitable compromising solution among the available options. In order to select the best compromising solution, a combination of surrogate worth trade-off approach and fuzzy theory is proposed as choice of objectives is ambiguous. The uniformity of Pareto front is evaluated by exploiting a quality measure approach. The performance analysis is done using generalized benchmark test functions and complex MTPLD problems. The ability of CDEPS to diversify Pareto front is verified by uniformity analysis of Pareto front. The one-sample Wilcoxon’s test and two-sample Mann Whitney’s test are used to analyze the experimental results. The exhaustive analysis shows that the Tent map-based CDEPS has better ability to generate quality generation schedule with uniform Pareto front quality and faster convergence rate.

Direct coupling: a possible strategy to control fruit production in alternate bearing

We investigated the theoretical possibility of applying phenomenon of synchronization of coupled nonlinear oscillators to control alternate bearing in citrus. The alternate bearing of fruit crops is a phenomenon in which a year of heavy yield is followed by an extremely light one. This phenomenon has been modeled previously by the resource budget model, which describes a typical nonlinear oscillator of the tent map type. We have demonstrated how direct coupling, which could be practically realized through grafting, contributes to the nonlinear dynamics of alternate bearing, especially phase synchronization. Our results show enhancement of out-of-phase synchronization in production, which depends on initial conditions obtained under the given system parameters. Based on these numerical experiments, we propose a new method to control alternate bearing, say in citrus, thereby enabling stable fruit production. The feasibility of validating the current results through field experimentation is also discussed.

Adding machine maps and minimal sets for iterated function systems

ABSTRACTIn this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be conjugated to an adding machine map. It is proved that every minimal iterated function system which has some non-periodic regular point is semi-conjugate to an adding machine map. Furthermore, we investigate the topological conjugacy of an infinite family of tent maps, as well as the restriction of a map to its ω—limit set with an iterated function system.

Generalized Smooth Transition Map Between Tent and Logistic Maps

There is a continuous demand on novel chaotic generators to be employed in various modeling and pseudo-random number generation applications. This paper proposes a new chaotic map which is a general form for one-dimensional discrete-time maps employing the power function with the tent and logistic maps as special cases. The proposed map uses extra parameters to provide responses that fit multiple applications for which conventional maps were not enough. The proposed generalization covers also maps whose iterative relations are not based on polynomials, i.e. with fractional powers. We introduce a framework for analyzing the proposed map mathematically and predicting its behavior for various combinations of its parameters. In addition, we present and explain the transition map which results in intermediate responses as the parameters vary from their values corresponding to tent map to those corresponding to logistic map case. We study the properties of the proposed map including graph of the map equation, general bifurcation diagram and its key-points, output sequences, and maximum Lyapunov exponent. We present further explorations such as effects of scaling, system response with respect to the new parameters, and operating ranges other than transition region. Finally, a stream cipher system based on the generalized transition map validates its utility for image encryption applications. The system allows the construction of more efficient encryption keys which enhances its sensitivity and other cryptographic properties.

An Image Encryption Technique based on Chaotic S-Box and Arnold Transform

In recent years, chaos has been extensively used in cryptographic systems. In this regard, one dimensional chaotic maps gained increased attention because of their intrinsic simplicity and ease in application. Many image encryption algorithms that are based on chaotic substitution boxes (S-boxes) have been studied in the last few years but some of them appear to be vulnerable to robustness. We, in this paper, propose an efficient scheme for image encryption that utilizes a composition of chaotic substitution based on tent map with the scrambling effect of the Arnold transform. The proposed construction algorithm for substitution box is, on one hand, straightforward and saves omputational labour, while on the other, it provides highly efficient performance outcomes. The understudy scheme uses an S-box, that is based on 1-D chaotic tent map. We partially encrypt the image using this S-box and then apply certain number of iterations of the Arnold transform to attain the fully encrypted image. For decryption we apply the reverse process. The strength of the proposed method is determined through the most significant techniques used for the statistical analysis and it is proved that the anticipated algorithm shows coherent results.

A novel colour image encryption scheme using rectangular transform-enhanced chaotic tent maps

In recent years, the chaos-based cryptographic algorithms have attracted a lot of attention. Specially, chaotic tent map (CTM)-based schemes show some good performances in randomness properties and security level. However, several shortcomings still can be found from them. In this paper, based on the security analysis of the pure CTM-based scheme, we propose a novel image encryption algorithm by using the combination of the rectangular transform and the CTM principle. It encrypts the three channels of the plain image at the same time, and these channel encryptions associate with each other. In addition, by generating the key streams related to both the secret keys and the plain image, its key-sensitivity has been further improved. The security of the proposed scheme has been verified by security analysis and experimental evaluations, and our results show that many drawbacks of pure CTM-based schemes have been overcome.

Design and efficient implementation of a chaos-based stream cipher

We designed and implemented a stream cipher cryptosystem based on an efficient chaotic generator of finite computing precision (N = 32). The proposed structure of the chaotic generator is formed by a Key-setup, an IVsetup, a non-volatile memory, an output and an internal state function. The cryptographic complexity mainly lies in the internal state containing two recursive filters, with one, two or three delays. Each recursive filter includes a perturbation technique using a linear feedback shift register. The first recursive filter includes a discrete skew tent map, and the second one includes a discrete piecewise linear chaotic map. The chaotic generator is implemented in sequential and parallel versions using Pthread library in a secure manner. The proposed Stream ciphers have very good performance in terms of security and execution time. Experimental results highlight the robustness of the proposed system against known cryptographic and statistical attacks.

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT.

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment.

Allowed Patterns of Symmetric Tent Maps via Commuter Functions

We introduce a new technique to study pattern avoidance in dynamical systems, namely, the use of a commuter function between nonconjugate dynamical systems. We investigate the properties of such a commuter function, specifically $h : [0,1] \to [0,1]$ satisfying $T_1 \circ h = h \circ T_\mu$, where $T_\mu$ denotes a symmetric tent map of height $\mu$. We make use of this commuter function to prove strict inclusion of the set of allowed patterns of $T_\mu$ in the set of allowed patterns of $T_1$.

Memory Matters in Synchronization of Stochastically Coupled Maps

Synchronization of stochastically coupled chaotic oscillators is a topic of intensive research for its ubiquitous application across natural and technological systems. Several breakthroughs have been made over the last decade in understanding the underpinnings of stochastic synchronization. Yet, most of the literature has focused on memoryless switching, where the coupling between the oscillators intermittently changes independently of the switching history. Here, we analytically investigate the synchronization of two one-dimensional coupled nonlinear maps under Markovian switching. We linearize the system in the vicinity of the synchronous solution and examine the mean square asymptotic stability of the error dynamics. By leveraging state-of-the-art techniques in jump linear systems, fundamentals of ergodic theory, and perturbation analysis, we elucidate the potential of Markovian switching in manipulating the stability of synchronization. We focus on chaotic tent maps, for which we compute exact, closed...

Statistical and deterministic dynamics of maps with memory

We consider a dynamical system to have memory if it remembers the current state as well as the state before that. The dynamics is defined as follows: $x_{n+1}=T_{\alpha }(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha )\cdot x_{n-1}),$ where $\tau$ is a one-dimensional map on $I=[0,1]$ and $0<\alpha <1$ determines how much memory is being used. $T_{\alpha}$ does not define a dynamical system since it maps $U=I\times I$ into $I$. In this note we let $\tau $ to be the symmetric tent map. We shall prove that for $0<\alpha <0.46,$ the orbits of $\{x_{n}\}$ are described statistically by an absolutely continuous invariant measure (acim) in two dimensions. As $\alpha $ approaches $0.5$ from below, that is, as we approach a balance between the memory state and the present state, the support of the acims become thinner until at $\alpha=0.5$, all points have period 3 or eventually possess period 3. For $0.5<\alpha <0.75$, we have a global attractor: for all starting points in $U$ except $(0,0)$, the orbits are attracted to the fixed point $(2/3,2/3).$ At $\alpha=0.75,$ we have slightly more complicated periodic behavior.

A Chaos-Based Authenticated Cipher with Associated Data

In recent years, there has been a rising interest in authenticated encryption with associated data (AEAD) which combines encryption and authentication into a unified scheme. AEAD schemes provide authentication for a message that is divided into two parts: associated data which is not encrypted and the plaintext which is encrypted. However, there is a lack of chaos-based AEAD schemes in recent literature. This paper introduces a new 128-bit chaos-based AEAD scheme based on the single-key Even-Mansour and Type-II generalized Feistel structure. The proposed scheme provides both privacy and authentication in a single-pass using only one 128-bit secret key. The chaotic tent map is used to generate whitening keys for the Even-Mansour construction, round keys, and random s-boxes for the Feistel round function. In addition, the proposed AEAD scheme can be implemented with true random number generators to map a message to multiple possible ciphertexts in a nondeterministic manner. Security and statistical evaluation indicate that the proposed scheme is highly secure for both the ciphertext and the authentication tag. Furthermore, it has multiple advantages over AES-GCM which is the current standard for authenticated encryption.

A visually secure image encryption scheme based on compressive sensing

A novel visually secure image encryption scheme based on compressive sensing (CS) is proposed. Firstly, the plain image is transformed into wavelet coefficients, and then confused by a zigzag path and encrypted into a compressed cipher image using compressive sensing. Next, the cipher image is embedded into a carrier image, and finally a visually secure cipher image is obtained. SHA 256 hash function of the original image is generated to calculate the parameters for zigzag confusion and one-dimensional skew tent map, and the map is used to produce the measurement matrix for CS. Therefore, the proposed algorithm is highly sensitive to the plain image, and it can effectively withstand known-plaintext and chosen-plaintext attacks. Besides, our algorithm can achieve the image data security and image appearance security simultaneously, and the size of the cipher image and original image is equal, it does not require additional transmission bandwidth and storage space. Simulation results and performance analyses both demonstrate excellent encryption performance of the proposed encryption scheme.

A Fast Color Image Encryption Algorithm Using 4-Pixel Feistel Structure.

Algorithms using 4-pixel Feistel structure and chaotic systems have been shown to resolve security problems caused by large data capacity and high correlation among pixels for color image encryption. In this paper, a fast color image encryption algorithm based on the modified 4-pixel Feistel structure and multiple chaotic maps is proposed to improve the efficiency of this type of algorithm. Two methods are used. First, a simple round function based on a piecewise linear function and tent map are used to reduce computational cost during each iteration. Second, the 4-pixel Feistel structure reduces round number by changing twist direction securely to help the algorithm proceed efficiently. While a large number of simulation experiments prove its security performance, additional special analysis and a corresponding speed simulation show that these two methods increase the speed of the proposed algorithm (0.15s for a 256*256 color image) to twice that of an algorithm with a similar structure (0.37s for the same size image). Additionally, the method is also faster than other recently proposed algorithms.

A Novel Image Stream Cipher Based On Dynamic Substitution

Recently, many chaos-based stream cipher algorithms have been developed. Traditional chaos stream cipher is based on XORing a generated secure random number sequence based on chaotic maps (e.g. logistic map, Bernoulli Map, Tent Map etc.) with the original image to get the encrypted image, This type of stream cipher seems to be vulnerable to chosen plaintext attacks. This paper introduces a new stream cipher algorithm based on dynamic substitution box. The new algorithm uses one substitution box (S-box) and a chaotic shuffling process. Each byte in the plain image vector is substituted using a different S-box to get the cipher image vector. This algorithm is designed to be invulnerable to chosen plaintext attacks. In addition, this algorithm is more secured compared to conventional stream cipher.

Epileptic Seizure Prediction Using a New Similarity Index for Chaotic Signals

Epileptic seizures are generated by abnormal activity of neurons. The prediction of epileptic seizures is an important issue in the field of neurology, since it may improve the quality of life of patients suffering from drug resistant epilepsy. In this study a new similarity index based on symbolic dynamic techniques which can be used for extracting behavior of chaotic time series is presented. Using Freiburg EEG dataset, it is found that the method is able to detect the behavioral changes of the neural activity prior to epileptic seizures, so it can be used for prediction of epileptic seizure. A sensitivity of 63.75% with 0.33 false positive rate (FPR) in all 21 patients and sensitivity of 96.66% with 0.33 FPR in eight patients were achieved using the proposed method. Moreover, the method was evaluated by applying on Logistic and Tent map with different parameters to demonstrate its robustness and ability in determining similarity between two time series with the same chaotic characterization.

A Novel Joint for Image Encryption and Coding Using Piecewise Linear Chaotic Map

Due to the features of chaotic maps, they are widely used into encrypting and coding information. Inspired by the tent map which is used to code and encrypt binary data, a novel joint for image encryption and coding based on piecewise linear chaotic map is proposed in this paper. We divide piecewise linear chaotic map into 256 parts according to the property of gray level image. In order to enhance the security of image, the image is subsequently encrypted by the piecewise linear chaotic map in which the secret key of image encryption is determined by the initial of chaotic map. This stage of image encryption possesses high key and plain-image sensitivities which results from the secret key related to plain-image. Finally, the encrypted image is coded by the piecewise linear chaotic map with a different initial value. The experimental results validate the effect of the proposed system and demonstrate that the encrypted and coded image is secure for transmission.

Singular SRB Measures for a Non 1–1 Map of the Unit Square

We consider a map of the unit square which is not 1--1, such as the memory map studied in \cite{MwM1}. Memory maps are defined as follows: $x_{n+1}=M_{\alpha}(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha )\cdot x_{n-1}),$ where $\tau$ is a one-dimensional map on $I=[0,1]$ and $0<\alpha <1$ determines how much memory is being used. In this paper we let $\tau $ to be the symmetric tent map. To study the dynamics of $M_\alpha$, we consider the two-dimensional map $$ G_{\alpha }:[x_{n-1},x_{n}]\mapsto [x_{n},\tau (\alpha \cdot x_{n}+(1-\alpha )\cdot x_{n-1})]\, .$$ The map $G_\alpha$ for $\alpha\in(0,3/4]$ was studied in \cite{MwM1}. In this paper we prove that for $\alpha\in(3/4,1)$ the map $G_\alpha$ admits a singular Sinai-Ruelle-Bowen measure. We do this by applying Rychlik's results for the Lozi map. However, unlike the Lozi map, the maps $G_\alpha$ are not invertible which creates complications that we are able to overcome.

Sistem Presensi Dosen Menggunakan IMEI dan GPS Smartphone dengan Data Terenkripsi

The improvement of education quality is determined not only by student's attendance but also lecturer's attendance in class. In this paper, control system of lecturer's attendance has been developed. This system requires two types of users, which are administrator and lecturer. The administrator is responsible for data analysis and report. The lecturer confirms his/her attendance using smartphone by utilising IMEI (International Mobile Equipment Identity) and GPS (Global Positioning System). The security of the data flow in this attendance system is built using the stream cipher algorithm with three key randomization methods: odd parity Hamming code, tent map and session keys. Research finds that this contol system of lecturer's attendance is secure because of the following reasons. First, it has been built using three-tier architecture. Second, there is a security check from software system. And lastly data flow is encrypted with low correlation between plaintext and ciphertext. Furthermore, the sytem is reliable because when internet and/or GPS is lost, data between client and server is kept and is delivered once there is internet and/or GPS connection. Report of lecturer's attendance from this system is reliable and hence it is recommended to be used for lecturers' attendance report.