## Chaotic tent map

, f (x, λ) is modified through the function h(x). In this paper, we combine the general equation of jerk-based chaotic systems with simple scaled discrete chaotic maps. Example Chaotic Maps (that you can analyze) Reading for this lecture: NDAC, Sections10. The new system shows more complicated chaotic behaviors. A Pseudo-Random Bit Generator Using Three Chaotic Logistic Maps. . However, dynamical degradation has been pointed out as an important limitation of this procedure. X. By Chaotic Tent Map Approach Raja Sekhar Anneppu1 and A. These properties create a close relationship between cryptosystems and chaos systems. 5) for Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. 1. An Image Encryption Technique based on Chaotic that is based on 1-D chaotic tent map. 1 Preliminaries Tent map is a onedimensional and piecewise linear map. pose the revolutionary idea to couple tent and logistic map, and to add an In this paper, a sequence generated from different chaotic systems (such as Lorenz system,. Sketch the graphs of f2(x) and f3(x). There are many maps that can exhibit chaotic behaviors such as the Tent map, the Gauss map, the Logistic map, etc [12]. 2. Abstract: A coupled chaotic map lattices system with uniform distribution (CML-UD) consisting of tent maps is presented based on the security from the viewpoint of cryptography. The logistic map is defined by the following recursion. Simulation results are shown where the plain image is successfully revealed from the cipher image without using the initial key used during encryption. Chaotic 1D maps Surprisingly very simple 1D maps yield good model of chaotic systems. Edward Lorenz, the father of chaos theory, described chaos as “when the present determines the future, but the approximate present does not approximately determine the future. Contribute to smorzhov/tent_map development by creating an account on GitHub. Introduction In order to explain simple chaotic dynamical systems, one-dimensional map is used Tent, Bernoulli and Logi. In this section, we first present the chaotic tent map used in the original algorithm, and then describe the original algorithm. Srinivasa rao 2 PG student, Dept of ECE, AITAM, Tekkali, AP E-mail: sekhar906@gmail. The tent map is piecewise linear, because of this characteristic this makes the tent map easier to analyse than the logistic map. 1 Tent Map . New search for: Kadir, A. On the Power Spectral Density of Chaotic Signals Generated by Skew Tent Maps - On the Power Spectral Density of Chaotic Signals Generated by Skew Tent Maps. can be a tent map or a Bernoulli map, etc. Fewer components are utilized to implement the tent map function subcircuit. In the second paper, they say that the map is a Bernoulli map. Tatjery, E. Double Phase Image Encryption and Decryption Using Logistic Tent Map and Chaotic Logistic Map 2 Preeti Kori1, Prof. com Prof & HOD, Dept of ECE, AITAM, Tekkali, AP E-mail:asr47@rediffmail. Abstract. Points outside I c go to infinity. 401155 is chosen). chaotic signals such as iterative maps, including the tent map and the logistic map. Both transmitter and receiver use conversions between voltage and time to implement nonlinear tent-map functions. skew tent maps which are piecewise linear chaotic maps and cross-coupled as shown in the Figure 3. From the above theoretical analysis, we can understand that the distributions of runs generated by chaotic maps de-pend on the characteristics of the maps. Higher density Security analysis and improvement of an image encryption scheme based on chaotic Tent map 1051 Abstract. o. The algorithm for proposed modiﬁed tent map interleavershowsthe method of generation of interleavers. Higher density Although your formulae are technically correct, you will not get the expected plot if you were to plot this function. View the article online This system is chaotic and highly sensitive on initial conditions. The segment I c = [-x 2 , x 2] is mapped into itself (here x 2 is the right repelling fixed point). Depending on the value of μ, the tent map demonstrates a range of dynamical behaviour ranging from predictable to chaotic. Q. hal-00785380 In mathematics, the tent map with parameter μ is the real-valued function fμ defined by . Firstly,a new chaotic sequences-Skew Tent map is This is one way to see that the logistic r = 4 map is chaotic for almost all initial conditions. 7 May 2015 In order to explain simple chaotic dynamical systems, one-dimensional map is used. For a>1/2 it finds chaotic behavior and for a=1, it shows a fully chaotic behavior. block permutation based on chaotic tent map. Through the The attractor and the bifurcation diagram for tent chaotic map are presented in figures 2 and 3 respectively. Compared with traditional classic one-dimensional chaotic maps like Logistic Map and Tent Map, this newly created chaotic map demonstrates many better chaotic properties for encryption, implied by a much larger maximal Lyapunov exponent. The papers [5, 10, 11] also concern skew tent maps but con ne themselves to CHAPTER 4. MICHAEL CRAMPIN, BENEDICT HEAL; On the Chaotic Behaviour of the Tent Map, Teaching Mathematics and its Applications: An International Journal of the IMA, Volum Chaotic Map: Skew Tent Map Pada tulisan kali ini, saya akan membanding dua bahasa pemrograman yaitu Python dan Octave dalam hal seberapa cepat mereka menghasilkan angka secara acak. If the initial state of a deterministic system is exactly known, the output behavior can be predicted exactly. Which are the ﬂxed points of f? How many ﬂxed point does f have? How do you relate this map with the tent map? 2. Tent map and Henon map) is substituted for random numbers for This paper proposes a novel image encryption scheme, which is based on the chaotic tent map. They will be used for our new chaotic system. Tent Map The simplest chaotic process is the tent map. TENT-CHAOTIC MAP Logistic map. The number of cycles of (minimal) length k = 1, 2, 3,… for the logistic map with r = 4 (tent map with μ = 2) is a known integer sequence (sequence A001037 in the OEIS): 2, 1, 2, 3, 6, 9, 18, 30, 56, 99 adapted for tent map. 56995 is the onset of chaos. We partially tent map and its use in the construction of a substitution box. Angka acak sendiri dapat dihasilkan dengan menggunakan fungsi interasi dimana kondisi awal diberikan pada suatu fungsi untuk mendapatkan output yang akan digunakan skew tent maps which are piecewise linear chaotic maps and cross-coupled as shown in the Figure 3. This map is known as tent maps and often introduced as one of the first examples of chaotic maps literature for nonlinear discrete dynamical systems. This map is continuous, linear on each of the intervals (−1, 1/ 2 ] and [1/2, 1)(with respect to slopes r and −r) and has the points (0,0)and(1,0) in its graph. In this paper, we make cryptanalysis on an image encryption scheme based on chaotic Tent map proposed by Li et al. Figures l(a) and l(b) show a tent map and its inverse map. Figure 3 – Lyapunov exponent diagrams of chaotic maps Utilizing the Tent and Sine maps as seed maps, the proposed tumultuous system in Eq. The simplicity and analytical characteristics of such chaotic maps simplify the calculations of various statistical properties of chaotic dynamics. The proposed map uses extra parameters to provide responses that fit multiple applications for which conventional maps were not enough. Most of the results given here were already proved in [6, 7] but using non-elementary methods. 7. the mathematical definition of this map can be expressed in the following equation: the probability density function (PDF) of a chaotic map can be used to analysis the properties of chaos. We nd chosen-plaintext attack can break the scheme. The "Bernoulli shift" on 1-sided sequences of $0$'s and $1$'s cannot be topologically conjugate to the tent map on $[0,1]$, since the first acts on a totally disconnected space while the second acts on a connected space. 0. C. There are similarities and differences between cryptography algorithms and chaotic maps [8] . 25um CMOS process. (2019) IDMA-Based on Chaotic Tent Map Interleaver. All the chaotic values generated from the tent map are iterated once again through the Chebyshev for the post processing, that is, y(l, i) = cos(β cos −1 (x(l,i + l))). Monolithic Chaotic Communications System P. edu ABSTRACT This paper presents a procedure to transform a chaotic lo-gistic map into a continuous-time delay chaotic system In the proposed algorithm, when a random number is needed by the classical DE algorithm, it is generated by iterating one step of the chosen chaotic map that has been started from a random initial condition at the first iteration. To cite this article: Antonio Pumariño et al 2015 Nonlinearity 28 407. Depending on the value of parameters, these maps demonstrate a range of dynamical The first block is a tent map, and the other block is the post processing – parameter perturbation and transfer. INTRODUCTION the chaotic effects of the six skew tent maps. 5, and f2(x) = 2/3+x/3 with probability 0. The logistic map xn+1 = rxn(1 − xn),. The chaotic mapping is as follows Fig. Chaotic maps often occur in the study of dynamical systems. Discrete maps usually take the form of iterated functions. The tent map introduced by Ott [7] is an iterated function forming a discrete-time dynamical system for the generation of random-like real numbers uniformly distributed in [0,1] that demonstrates a chaotic dynamical behavior. Article (PDF Available) in International Journal of Computer Applications 167(7):12-17 27 Jan 2014 Tent Map Bifurcation Diagram: Lecture 7: Natural Computation & Self- Organization, Physics 256A (Winter 2014); Jim Crutchfield. 41. Information capacity and pattern formation in a tent map network featuring statistical periodicity C. Tent map (14 F) Tinkerbell map (2 F) Media in category "Chaotic maps" The following 20 files are in this category, out of 20 total. Finally, [28] discusses and The 1-dimensional discrete chaotic maps do not look as amazing as, say, Lorenz system, but I am not skilled enough in math and computer aided calculus to make any reasonable explorations of continuous systems yet, so the discrete domain is my jail for now. TCM chaotic map is a one-way function that prevents the finding of a relationship between the successive output values and increases the randomness of output results. 22 May 2012 Abstract—Tent map is a discrete-time piecewise-affine. By numerical performance, we show that, the proposed Tent chaotic sensing matrix has similar performance to random matrix or Logistic chaotic matrix for exact reconstructing space narrow and constrained. s. portion 073-0800-003 rancho murieta sacramento county, california march, 2017 sheet 1 of 2 chesbro reservoir clementia reservoir vicinity map no scale village "e" village "h" off-street parking (typ) n. Here the one dimensional chaotic maps[4] used are Logistic map and Tent map. Very slight changes in the map rancho murieta north village "f" a. 2(a) shows the proposed tent-map chaotic circuit. By combining them a large number of cryptographic techniques could be designed in this paper we are presenting a review of some of those techniques. Basic theory of these two chaotic functions is presented as under. Figure 9: Theoretical distribution of runs (tent map). This paper introduces a new chaotic system which is composed of three different one-dimensional chaotic maps. At r = 3. The chaotic functions have numerous properties such as randomness, ergodicity, and sensitivity to initial conditions. We show that Fa;b is Markov for a dense set of parameters in the chaotic region, and we exactly ﬁnd the probability density function (pdf), for any of these maps. Maps may be parameterized by a discrete-time or a continuous-time parameter. Given control parameters and initial values, one can iterate the 2D tent map to get one chaotic sequence and obtain one permutation by sorting the chaotic sequence in ascending order. Although your formulae are technically correct, you will not get the expected plot if you were to plot this function. The system inherited the coupled diffusion and parallel iteration mechanism of coupled map lattices (CML). TENT-CHAOTIC MAP classified the chaotic maps as substitution based chaotic maps and transposition based chaotic maps. com Abstract In this paper, it is feasible to achieve superior performance in detection range Singh D. it is a simple dynamical equation with complex chaotic behavior. Logistic map. per 920401 or 907 and 20040924 or 1217 ex. Ali⋆ †Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, MI 48105. The C-axis is horizontal, and the x-axis is vertical. x [*Plot] - a numeric vector, or an object either of class 'ts' or of class 'timeSeries'. Firstly, the chaotic tent map is modified to generate chaotic key stream that is more suitable for image encryption. The major advantages and drawbacks of the most popular chaotic map ciphers in . Ways to improve-increasing Tent segments: In order to obtain the Tent chaotic system with better properties, we wanted to change the Tent chaotic system to complex multi-segment system by increasing its segments and the Tent chaotic map in a simple linear increase on the value of k-space segment, the values of the Tent map space (-0. / Guo, W. 1. Through the A new algorithm for a novel hash function, based on chaotic tent map with changeable parameter, is proposed and analyzed. The higher r, the more chaotic the behavior. Pumari~no , J. X(k) = r X(k-1) (1 - X(k-1)) with one positive parameter r less or equal to 4. Authors use a piecewise linear chaotic map for their application which is encoding a bitstream into the chaotic trajectory of the map. Logistic Map The applet draws a bifurcation diagram for the cubic map f(x)=(Cx if x =1/2, C(1-x) if x >= 1/2) . The Tent map is one of the widely used chaotic maps with good ergodic uniformity. 5-10. Compare between them in several experimental, statistical analysis and key sensitivity tests. 1: Some One Dimensional Maps 4. In this paper, we propose a novel image encryption scheme based on chaotic skew tent map and pixel swapping approach. turns into another tumultuous system called the Tent-Sine system (TSS). A. Various simple chaotic maps like Arnolds Cat Map, Logistic Map, Tent Map, Standard Chaotic The dynamics of the tent map depend strongly on the value of the control parameter, r. The skew tent map is a two-parameter, piecewise-linear, weakly-unimodal, map of the interval Fa;b. The ultradiscretization of the Schroder map¨ The key of the ultradiscretization is the following formula Chaotic systems have been extensively applied in image encryption as a source of randomness. scheme using 3D skew tent map and coupled map lat- tice [35]. For a hash function based on the (discretization) of the tent map, see [20]. 4. This comment shows that this scheme is broken and no secure application can be found for it Chaotic signal can be readily obtained from a chaotic oscillator, a chaotic map. The Lorenz map: given by plotting Zmax nC1 against Z max n where Znmax is the value of the Zcoordinate at its nth In mathematics, a chaotic map is a map (= evolution function) that exhibits some sort of chaotic behavior. Chaotic quadratic maps Fig. 42 A novel chaotic pulse sequence generator is presented, which includes a tent map function subcircuit and an iterative operation subcircuit. g. Image encryption systems based on such map 2, 1994. Created Date: 1/29/2019 1:04:48 PM Chaotic range of SML map is fivefold of chaotic range of Logistic map. per CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract—A novel self-adaptive chaotic artificial bee colony algorithm based on Tent map (STOC-ABC) is proposed to enhance the global convergence and the population diversity. The papers [5, 10, 11] also concern skew tent maps but con ne themselves to Chaotic tent map (as like as the sawtooth map) has the uniform density ρ(y)=1. Like the logistic map, its iterates exhibit chaotic dynamics for a range of values of the parameter . Fig. ONE DIMENSIONAL MAPS 3 Figure 4. chaotic systems, which synchronized two chaotic attractors [3]. (eds) Applications of Artificial Intelligence Techniques in Engineering. Tent mapping-Chaotic Equation Here in this paper we are dealing with the Tent mapping. The output generated by the ﬂrst tent map is fed to the second tent map as the input (initial condition) and vice versa. Many are motivated in terms of their simplicity. Based on this architecture, a number of chaos-based encryption scheme have been proposed subsequently [4-9]. arguments to be passed. Chaotic map cryptography and security 9 STREAM CIPHERS USING LOGISTIC MAP The use of the chaotic logistic map in cryptography takes advantage of its ergodic property. Angka acak sendiri dapat dihasilkan dengan menggunakan fungsi interasi dimana kondisi awal diberikan pada suatu fungsi untuk mendapatkan output yang akan digunakan Abstract—In this paper, a new algorithm for image encryption using chaotic tent map and Arnold cat map is proposed. The T-1D map is a piecewise linear 1D chaotic map that defines the statistical behavior of the generated sequences using its control parameter. [27] propose a novel image encryption scheme based on the chaotic tent map, to generate key stream by a 1D chaotic tent map, that is more suitable for image encryption. Haroun's Real- time image encryption using a low-complexity discrete 3D dual chaotic cipher [29 ] 24 Feb 2012 CHAOS WITH MATLAB . Rodr guez , J. others. 2 Period-doubling transition to chaos . Its definition can A novel chaotic pulse sequence generator is presented, which includes a tent map function subcircuit and an iterative operation subcircuit. The improved robust region of tent map justifies the effectiveness of proposed method that results to design key based S-box. chaotic tent map is cryptanalyzed using chosen-plaintext. In order to transform the plainimage to the cipherimage we do the following algorithm. This paper presents an efficient chaotic image encryption cipher that is designed with the aim of improving the security and enhancing the encryption efficiency. ,and the bifurcation for the tent map in Figure 2. / Hamdulla, A. The existing chaos optimization algorithms were almost based on Logistic map. These cryptosystems apply chaotic maps repeatedly, which guarantees the randomness of the encrypted data. Lecture 7: Natural Computation & Self-Organization, Physics 256A (Winter 2014); Jim Crutchﬁeld In mathematics, a chaotic map is a map (= evolution function) that exhibits some sort of chaotic behavior. So the MTMI system is more suitable for application in secure communication and cryptography [4]. Bifurcation diagram for the tent map is shown below. com Abstract In this paper, it is feasible to achieve superior performance in detection range Abstract: A color image watermarking scheme using the chaotic properties of 2D tent map and Chebyshev map is proposed. We present a solvable two-dimensional piecewise linear chaotic map that arises from the duplication map of a certain tropical cubic curve. 9 Nov 2004 Abstract Discrete-time chaotic circuit implementations of a tent map and a Bernoulli map using switched-current (SI) techniques are presented. The logistic map and the tent map are topologically conjugate, and thus the behaviour of the two maps are in this sense identical under iteration. This algorithm consists of two major phases, permutation and substitution. The simple and interesting Tent map, x n+1 (1-21/2-xn), is used here. Abstract Chaotic behaviors of the tent map (a piecewise-linear, continuous map with a unique maximum) are studied analytically throughout its chaotic region in terms of the invariant density and the power spectrum. It Fi gure 2. , Ahmad A. In the third row is the value for chaotic "tent map ( 215-1) sequence Specifically, the external chaotic signal, which is produced by chaotic systems, such as tent maps and logistic maps, is applied to a bi-stable dynamic system with a weak input signal 24,25,29. Logistic Map Chaotic maps are highly sensitive to the initial value, which makes them unpredictable. Impossibility of exact knowledge of the initial state in practice is the reason of the chaotic behavior. 10- Try to generalize the tent map as we have done in the third question with the doubling function. n. CHAOS. named Logistic map. 5ˇ is the control parameter and is the current state of the system. tent Map . I/O characteristic curve, which is used for chaos-based applications, such as true 3 Jul 2019 [29] used the chaotic tent map (CTM) with the diffusing phase only, while the confusing phase was skipped. The parameters in chaotic maps are meaningful, if they are real numbers, which can $\begingroup$ This is more of a math question. 1 a. The first selection shows maximum period length and cross-correlation value for standard value for standard m-sequence with length of 215-1bits. In this work, we used a chaotic hash function which is based on chaotic tent map with changeable parameter for bitcoin application. Also our proposed chaotic algorithm is compared with the RC5 , RC6 algorithms. ex. Rauch Conjugating the Tent and Logistic Maps In the Hirsch, Smale and Devaney the chaotic character of the logistic map is proved by con- An Image Encryption Technique based on Chaotic that is based on 1-D chaotic tent map. For this purpose, some classical chaotic mappings can be considered: in dimension 1 symmetric tent map, and in dimension 2 Lozi mappings. The six-dimensional Arnold map is employed to realize this combination effect. The paper proposes an algorithm for image encryption using the random bit sequence generator and based on chaotic maps. This paper presents Genetic Algorithm based Cellular Automata for predicting chaotic time series. In this research, we propose a new one-dimensional Triangular Chaotic Map (TCM) with full intensive chaotic population. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. 621–624. and enhancing the encryption efficiency. the vector of start values to initiate the chaotic map. In fact, the dynamics will be non-periodic if and only if x 0 {\displaystyle x _{0}} x_{0} 29 Aug 2016 This paper proposes a novel image encryption scheme, which is based on the chaotic tent map. n. Map. Hauptmann* Centre for Nonlinear Dynamics in Physiology and Medicine, Department of Physiology, McGill University, 3655 Drummond Street, Tent map is a discrete-time and one-dimension nonlinear function with the piecewise-linear I/O characteristic curve [13] and it is used for generating chaotic values seen as pseudorandom numbers [14]. However,the probability density function of chaotic sequences for Logistic map is a Chebyshev-type function,which may affect the global searching capacity and computational efficiency of chaos optimization algorithm. The new S-box was constructed by mixing of chaotic map and . THE PROPOSED SCHElVlE -The proposed method is similar to data hiding RANDOM NUMBER GENERATION USING CHAOTIC DYNAMICAL MAPS by Ali R za Oz oren B. raphy uses discrete approximations of chaotic maps, rather than chaotic maps . Depending on the value ofa,it demonstrates a range of dynamical behavior ranging from predictable to chaotic. While the chaotic 10- Try to generalize the tent map as we have done in the third question with the doubling function. A coupled chaotic map lattices system with uniform distribution (CML-UD) consisting of tent maps is presented based on the security from the viewpoint of cryptography. As an example of chaotic maps, we use tent map which is one of the most popular and the simplest chaotic maps. Keywords: chaotic map’s, discrete non-linear system dynamics, symmetric cryptography. Chaotic map. 26 Sep 2017 Efficient Chaotic Tent Map-based Image Cryptosystem. Note that x,is a nonlinear function of xt-,. Ratnesh Dubey , Dr. Chaotic maps often generate fractals. 5,0. process, a multimodal skew tent map is utilized to generate one chaotic orbit used to permute the image pixel positions, while in the diffusion process, another two multimodal skew tent maps are employed to yield two pseudorandom grey - value sequences for designing a two-way diffusion process. The characteristics of CTM are very suitable for the design of encryption schemes. E. Using the sequences, various stochastic analysis schemes are developed. Chaotic sequences, have being widely used in mobile communications and cyberspace security. New nonlinear CPRNG based on tent and logistic maps Abstract This paper is devoted to the design of new chaotic Pseudo Random Num-ber Generator (CPRNG). Cryptographers have utilized dynamic chaotic maps to develop new cryptographic primitives by exploiting chaotic maps, such as logistic maps, Henon maps, and Tent maps. CHAOTIC MAP The tent map is considered among the good Chaotic Maps exhibiting chaotic behavior. Depending upon the type of system many types of chaotic maps are available. The tent map is defined by the following equation: 1 (1 ) n n n ux x ux 1 2 1 2 n n x x -----(1) can be a tent map or a Bernoulli map, etc. The corresponding status values generated by the Chebyshev chaotic map itself to provide a high security level. Files are available under licenses specified on their description page. n + 1. Mathematically speaking, tent map is a discrete time chaotic system described by relation (1): (1),0 1 1 , 1 where, ∈ 0,1 \ 0. In this A CONTINUOUS-TIME DELAY CHAOTIC SYSTEM OBTAINED FROM A CHAOTIC LOGISTIC MAP L. H Nejati, A Beirami, Y Massoud, in 51st Midwest, Symposium on Circuits and Systems. Abstract: Hash function has important usage in the cryptography for information security. t [*Plot] - an integer value setting the value for the Theiler window. 3. Logistic map The Logistic map is one of the famous 1D chaotic maps. The Tent map shows different behaviors for different values of the parametera. The reason is that you increment along the x-axis in steps of 1 (in the for loop), and the width of the entire tent map function from the link you provided is 1. It is considered among the most studied piecewise linear chaotic maps exhibiting chaotic behavior. The first block is a tent map, and the other block is the post processing – parameter perturbation and transfer. There is a need to design such generators. Keywords: Substitution Box, Nonlinear Dynamics, Robust Chaos, Tent Map, Piecewise Non-Smooth Maps Introduction The tent map with parameter μ=2 and the logistic map with parameter r=4 are topologically conjugate, and thus the behaviours of the two maps are in this sense identical under iteration. Neverthess, the LE of the skew tent map is very small and, for that reason, the iteration function of the map, i. Section V concludes the paper. Lee Stanford University 353 Serra Mall Stanford, CA 94305 ABSTRACT A chaotic transmitter and a synchronized chaotic receiver have been designed in a 0. Dally, E. 83. The starting value X(0) is called the seed, and must be in [0, 1]. The tent map with parameter μ=2 and the logistic map with parameter r=4 are topologically conjugate, and thus the behaviours of the two maps are in this sense identical under iteration. In the recent decades, applications of chaotic systems have flourished in various fields. The periodic points are dense in [0,1], so the map has become chaotic. generally called chaotic maps. e. S. This page was last edited on 10 July 2018, at 04:54. Last, we make 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. However, although the form of the tent map is simple and the equations are linear, for certain parameter values the map can yield complex and chaotic behaviour [1]. For each value of C it performs a certain number of iterations (100 by default) of the critical point x=1/2, without displaying them on the screen. t. The sufficient conditions are provided to construct complete chaotic maps with the tent-map-like structures, that is, f(x) = 1 − ∣1 − 2g(x)∣, where g is an one-to-one onto map defined on [0, 1]. Try to make a model of the graphic of f. The tent map with parameter μ=2 and the logistic map with parameter r=4 are topologically conjugate, [1] and thus the behaviours of the two maps are in this sense identical under iteration. Tent map attractor. In this paper, we discussed chaotic dynamical behaviour of one dimensional maps, especially logistic map and tent map. I don't think this differs fundamentally from any other pseudo-random generation schemes (most of which are probably based on chaotic maps even though that word wasn't in use when they were invented). The proposed 2D on hybrid of chaotic maps and a new S-box. How does the graph of fn(x) look like? We propose an Enhanced Logistic Map (ELM) while using chaotic maps and simple encryption techniques, such as block scrambling, modified zigzag transformation for encryption phases, including permutation, diffusion, and key stream generation to withstand the attacks. , Sood Y. Image encryption systems based on such map show some 1 Nov 2013 The present paper is aimed at introducing a new algorithm for image encryption using chaotic tent maps and the desired key image. If f1(x 0;ﬁ) and f2(y ;ﬁ) are the chaotic gradient tent map was constructed in [7], and the one based on the modified baker map was suggested in [8]. However, we consider that this is an advan- Bottom line, chaotic invertable maps typically start from dimension two (not counting the restriction of maps onto some weird fractals of fractional dimensions). Image encryption systems based on such map show some better performances. The chaotic tent map is used as the core of the scheme to achieve the security requirements. So do, other new interesting algorithms whose aim is to create stream ciphers. The system parameter for the both chaotic maps is kept same and is in the chaotic regime. The new chaotic system is Logistic-Tent system. Th e M C ost ommonry use d Ch aotic M aps an dE quations Chaotic maps Equations Logistic map -Tent map -Chebyshev map Circle map Cubic map Gauss map - Herron map Icmic map -Sinusodial map Sinus map 4 . n − 1. In: Malik H. 1 Introduction Chaotic signals present a special di–culty in parameter estimation. I don't get many complaints about the Tent Space, but the number 1 complaint is travelers who ask for a place to stay and then never It plots tent map distribution histogram. The synthesis of this chaotic circuit using SI technique is based on the We consider a family of chaotic skew tent maps. 5: The bifurcation diagram of the tent map 2. For a < a0 = −1 4, iterations of the logistic map escape to inﬁnity from all initial conditions. com Abstract In this paper, it is feasible to achieve superior performance in detection range DynamicalSystems Prof. s-tic maps are common A coupled chaotic map lattices system with uniform distribution (CML-UD) consisting of tent maps is presented based on the security from the viewpoint of cryptography. baker map. 3. The experimental results suggest that the same is true for the number of predictors. JDFSL V12N4 A Data Hiding Scheme Based on Chaotic Map Table 2. Starting in 1983, Fujisaka and Yamada published a series of four papers on synchronization in chaotic systems in Progress in Theoretical Physics [4][5]. THE PROPOSED SCHElVlE -The proposed method is similar to data hiding I must be dumb! I admit it. The tent map is a piecewise linear, one-dimensional map . We. The data points are from a single variable (usually x) starting from a random point on the attractor or in the chaotic sea so that you will get a different time series each time you run the program. a. adapted for tent map. [Research Report] LIRMM (UM, CNRS). Learn more about image processing, chaotic tent map . Vigil Abstract For a 2D-extension of the classical one-dimensional family of tent maps, we prove the existence of an open set of parameters for which the respective transformation presents a strange attractor with two positive Lyapounov exponents. Di erent forms of chaotic maps are used; however, the logistic map is Let’s deﬁne a ”non-deterministic” map f(x)to be f1(x) = x/3with probabil-ity 0. That means, each iteration, we ﬂip a coin and either (if heads) map the entire unit interva l linearly onto the left third, or (if tails) map the entire unit interval onto the right third of the unit interval. The chaotic map chosen in the original algorithm is the piecewise linear chaotic map and it is defined as: A chaotic map is deterministic. This is why the psudo-random numbers generated by chaotic maps do not pass the run test. Simple piecewise afﬁne I/O characteristics have been extensively used for the generation of random bits, e. ALGORITHMThe Tent-Sine system IV. Then we review a 2D chaotic map name Tent map. ﬁed Tent map provides diﬀerent values of C0 and hence more complex and chaotic than classical Tent map. J. sufficient to satisfy the property. But now I can't figure it out! I click on a marker on the map and nothing happens. The hardware description for the implementation of the chaotic generator is based on the tent-map equation (1). Chaotic maps produce long Period, random like chaotic sequences, which are change Image processing using chaotic map. , Mathematics, Bogazi˘ci University, 2007 tent map, logistic map, and family of The applet draws a bifurcation diagram for the cubic map f(x)=(Cx if x =1/2, C(1-x) if x >= 1/2) . Pick a number x, between 0 and 1. As since all these points are mapped in interval dx , therefore the number is equal to ρ(x)dx = dy and corresponding invariant density is follows; chaotic tent map is explained in section 2, the shift register structure of the map along with the their properties are presented in section 3, FPGA implementation results are shown in section 4 and finally section 5 concludes the paper. I am not familiar with piecewise linear chaotic Map. Encryption Speed and hardware implementation: Some digital chaotic ciphers are too slow to be feasible for real-time encryption [25]. Actually systems, like the tent map, have been a subject of much interest and investigation . Comparing Tent and Sawtooth 1-Dimensional Maps Eamon Doyle and Sarah M. And we successfully carry out the chosen-plaintext attack. Zimmermann (Dated: September 22, 2008) This paper will examine a 1-dimensional map we have created and named the Sawtooth Map. In this paper, a chaotic tent map (CTM) is utilized to build a new digital chaotic image cryptosystem. The values of the parameters are determined by the position index of message's In this paper, we present a novel approach to create the new chaotic map and propose an improved image encryption scheme based on it. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS 2 then, a large number of PRNG have been proposed based on various chaotic maps and their variants: Logistic The logistic map is a well-known polynomial chaotic map which can be described as: A chaotic charged system search approach for data clustering To resolve the effect of LQWL on chaotic map and get much better noise radar signal, we first propose a combination chaotic map (CCM), and then apply it to generating FM radar signal. Plus, I am not even sure if there is a universal agreement on what the definition for chaos is. Introduction. Exploring several topologies of network of 1-D coupled chaotic mapping, we focus ﬁrst on two dimensional networks. In this paper the generation of chaotic sequence using the logistic and tent maps are studied through the analysis of the bifurcation diagram for each of them. Consequently, the CTM based these problems, we propose a new particle swarm optimization by introducing chaotic maps (tent map and logistic map) and Gaussian mutation into the PSO 4 Jul 2015 1. times [lorentzSim][roesslerSim] - the sequence of time series points at which to generate the map. Out of all these functions Logistic Map and Tent Map functions are the best known chaotic functions used in cryptographic algorithms [4]. The following will describe how to use the two nonlinear maps for the design of the discrete-time chaotic circuits separately. A pseudo random image is produced using the chaotic tent map. Apart from chaotic circuits running with continuous signal, there are chaotic circuits functioning with discrete signal. CHAOTIC MAPS BASED PSEUDO RANDOM NUMBER GENERATORS 3. The skew tent map and the logistic map are topologically conjugate, and thus the behaviors of the two maps are in this sense identical under iteration. A CMOS tailed tent map for the generation of uniformly distributed chaotic sequences, (1997), pp. 1 INTRODUCTION Pseudo Random Number Generators (PRNGs) are widely used in many applications, such as numerical analysis, probabilistic algorithms, secure communications, integrated circuit testing, computer games and cryptography. 7. In the permutation phase, Arnold cat transform is used. The characteristics Tent Map. We also clarify the tropical geometric nature of the tent map; we show that the tent map can be regarded as the duplication map on the Jacobian of a certain tropical curve. All possible combinations of mixing two kinds of chaotic maps are experimentally analyzed and the NPCR and UACI are used as performance measures. the mathematical definition of this map can be expressed in the following equation: its chaotic arrangements have a uniform-distribution inside (0,1). Sawtooth map and Bernoulli shifts The sawtooth map is determined as x n+1 = 2x n (mod 1) where x (mod 1) is the fractional part of x. acho@upc. Relative number of points of a chaotic orbit in a small interval dy is ρ(y)dy = dy . Chaotic dynamics for 2-D tent maps A. [5]. Help me out! How do I find a tent space in Poland? How did folks find me? Two questions; one answer 2 A Secret Key Cryptosystem by Iterating a Tent Map In this section, we explain our cryptosystem. , Srivastava S. The one dimensional and piecewise tent map with changeable parameters Abstract: A coupled chaotic map lattices system with uniform distribution (CML-UD) consisting of tent maps is presented based on the security from the viewpoint of cryptography. Chaotic Logistic and Tent maps are used to generate required random bit sequences. Keywords Chaotic Map, Modified Logistic Map, FML Map, SML Map 1. A new algorithm for a novel hash function, based on chaotic tent map with changeable parameter, is proposed and analyzed. The corresponding status values generated by the Chebyshev 5. Despite the chaotic nature of the tent map and the complexity of the derived binary sequences, the results reported suggest that Color image encryption using skew tent map and hyper chaotic system of 6th-order CNN (English) Kadir, A. its chaotic arrangements have a uniform-distribution inside (0,1). conventional m-, gold, chaotic "tent map" sequences. The one dimensional and piecewise tent map with changeable parameters In this paper, we present a novel approach to create the new chaotic map and propose an improved image encryption scheme based on it. 3 Exploring topologies of network of coupled chaotic maps . 781–784. In this paper, a new method to synchronize two Tent map systems, has been proposed, by applying Feedback and The skew tent map always has a LE positive and thus is a good selection to be the core of the chaotic cryptosystem proposed in this work. A deal of chaotic behaviour can be described by one simple, fairly innocuous looking equation, the Tent map as shown in the Figure1. 1 illustrates stretching and folding transformations for the quadratic maps f c (for example the Myrberg-Feigenbaum point c = -1. Read "Chaotic block cryptosystem using high precision approaches to tent map, Microelectronic Engineering" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The new chaotic system used here is Logistic-Tent System which provides mixed chaotic property since it is a combination of two chaotic maps. Is it an extension of the Skew Tent Map or the Tent map? By Chaotic Tent Map Approach Raja Sekhar Anneppu1 and A. If f1(x 0;ﬁ) and f2(y ;ﬁ) are follows; chaotic tent map is explained in section 2, the shift register structure of the map along with the their properties are presented in section 3, FPGA implementation results are shown in section 4 and finally section 5 concludes the paper. It exhibits better performance and even one of the chaotic maps is out of range. Its definition can A color image watermarking scheme using the chaotic properties of 2D tent map and Chebyshev map is proposed. All structured data from the file and property namespaces is available under the Creative Commons CC0 License; all unstructured text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Chaotic maps can be applied to choose pixels or blocks that should be modiﬁed according to the method of insertion. Then generate the sequence of numbers x, using the following rule: The tent map is so named because the graph of x, versus x,_,is shaped like a "tent", as shown in Figure 1. 0. In the diffusion stage, the pixel values are modified sequentially controlled by another chaotic map. If the velocity of the fluid is not very large the fluid flows in a smooth steady way, called "laminar flow", which can be calculated for simple geometries. 5. Acho Escola d’Enginyeria de Barcelona Est-EEBE Universitat Polit`ecnica de Catalunya-UPC Barcelona, Spain email: leonardo. TENT MAP: FUNDAMENTALS AND HISTORY In this section, after a brief introduction to discrete- Singh D. Two coupled maps are studied: TTLRC non-alternative, and TTLSC alternative proposed chaotic logistic map with generated session key is compared with some different map as Bernoulli map, Genhous map, tent map and logistic map 1. To evaluate the performance of the proposed . Figure 3. The Sawtooth Map will be compared to the behavior of the often examined Tent Map due to the structural similarity. Compared with traditional classic one-dimensional chaotic maps like Logistic Map and Tent Map, this newly created chaotic map demonstrates many better chaotic yi+1 = f2 (α , yi ) , In the proposed random bit generator, two cross- coupled piecewise linear chaotic maps are employed (un- where α is the system parameter and is same for both like to the pseudo random bit generator proposed in [8], chaotic tent maps, xi and yi are the initial conditions and where also two piecewise linear chaotic maps Despite their deterministic simplicity, over time these systems can produce totally unpredictable and wildly divergent (aka, chaotic) behavior. chaotic maps: logistic, tent, sine, and cubic maps expressed, respectively, 12 Jan 2015 Chaotic dynamics for two-dimensional tent maps. The plot at the top shows the orbit after steps for an initial value and a particular value of . In this paper, we propose that another chaotic sequence - Tent map can also be used to construct the sensing matrix. Because of the above advantages of both the maps, here in this project As a result, they are reduced to the tent map and its solution. Vineet Richhariya3 1, 2, 3 Department of Computer Science 1, 2, 3 LNCT, Bhopal Abstract- Doing a digital image transmission over internet need a secure protection against illegal copying. The corresponding status values generated by the Chebyshev I need to find fixed points and attractors of a Tent map function given by the definition below: x t = (3/2) * x t-1 when 0 <= x <= (2/3) and x t = 3* (1-x t-1) when (2/3) <= x <= 1 I am using the MATLAB code below to generate a cobweb diagram (shown below the code) to see if I can get some insight in to this particular tent map function. , Shukla A. Daniela Mitie Kato 8-th International Symposium on Signals, Circuits and In this paper, a chaotic cooperative particle swarm optimization based on tent map (TCCPSO) is proposed. In this paper we give an elementary treatment of the dynamics of skew tent maps following on from [2] where a special case was studied. A realizable modified tent map for true random number generation, (2008), pp. On the Chaotic Behaviour of the Tent. The tent map with parameter μ=2 and the logistic map with parameter r=4 are topologically conjugate, and thus the behaviours of the two maps are in this sense identical under iteration. ” The Logistic Map chaotic tent map and modified chaotic tent map is compared using bifurcation diagram. Generation of chaotic sequence Various non-linear dynamic systems are used in order to generate the chaotic sequence as: Tent map and logistic map[12] – [13]. prototype chaotic maps in the present algorithm however; it can be easily extended to any number of 1D chaotic maps. , the Bernoulli map [6] and the tent map [22]. Tent, Bernoulli and Logis- tic maps are common examples 4 Nov 2011 Abstract: In this paper, the Tent map is analyzed as a source of pseudorandom bits. I've used, and been used by, tent space inmates. Advances in Intelligent Systems and Computing, vol 698. The yielded chaotic orbit in the permutation process is not just a simple rearrangement of the six chaotic orbits, it is a hybrid one derived by six orbits of skew tent maps. The synthesis of this chaotic circuit using SI technique is based on the This paper presents Genetic Algorithm based Cellular Automata for predicting chaotic time series. If you use the Tent Space List or the Tent Space Maps, remember that each one of these dots represents someone willing to give up a little time of their life for you. Is it an extension of the Skew Tent Map or the Tent map? modiﬁed tent map and investigate its chaotic charac-teristics. The entropy source of a chaotic map is In this paper we give an elementary treatment of the dynamics of skew tent maps following on from [2] where a special case was studied. The cooperative particle swarm optimization (CPSO), can significantly improve the performance of the original algorithm. This property gave more key space for cryptographic purpose s. cryptography and other algorithms are Logistic Map, Tent map, Piece wise linear map, Sawtooth map. p. Abstract—This paper proposes a chaos-based image encryption scheme where one 3D skew tent map with three control parameters is utilized to generate 3 May 2018 This paper proposes a new chaotic map for image cryptosystem by combining tent map and 2D logistic map in different form. How does the graph of fn(x) look like? In mathematics, a chaotic map is a map (= evolution function) that exhibits some sort of chaotic behavior. 20' waterline esmt. The proposed system uses the Logistic map as a controller to choose the Tent map or Sine map to generate random sequences. 7 The logistic map. proposed chaotic logistic map with generated session key is compared with some different map as Bernoulli map, Genhous map, tent map and logistic map 1. II. in continuous systems while only one variable can generate chaotic series in discrete map, such as the Logistic map and the Tent map. The logistic map is one of the simplest forms of a chaotic process. Its dynamics exhibit Variability Analysis of Tent Map-Based Chaotic-Map Truly Random Number Generators Hamid Nejati,† Ahmad Beirami,‡ Aria Ghassemian Sahebi,† and Warsame H. It is used for the generation of random-like real numbers uniformly distributed in [0, 1]. Reference [12] demonstrated that the logistic map and Chebyshev map are topologically conjugate to the tent map and presented PDFs of the logistic and Chebyshev maps. The di–culty arises from the deﬂnition of a chaotic system: sensitive dependence on initial conditions. 2 Examples of 1-d maps Some examples of one dimensional maps are listed here and shown in ﬁgure 4. Motivated by above discussions, this paper studies a class of chaotic maps with q, it is different from previous work because such a map may contain less than three state ULTRADISCRETIZATION OF A SOLVABLE TWO-DIMENSIONAL CHAOTIC MAP ASSOCIATED WITH THE HESSE CUBIC CURVE Kenji KAJIWARA, Masanobu KANEKO, Atsushi NOBE and Teruhisa TSUDA (Received 3 March 2009) Abstract. encryption scheme based on two chaotic maps, logistic map to change the values of pixels and Arnold cat map to rearranges the position of pixels. A Pseudo-Random Bit Generator Using Three Chaotic Logistic Maps Michael François, David Defour To cite this version: Michael François, David Defour. So far, however, only a few simple chaotic maps have known PDFs [10], [11]. if the chaotic spreading sequence generated by research presents the analysis of MAI distribution in DS-CDMA systems based on chaotic spreading sequences generated by other 1-D maps: modified Bernoulli map, modified Tent map, Gauss map, Sine-Circle map, Cubic map, and Pinchers map. MICHAEL CRAMPIN AND BENEDICT HEAL. Tent map defined in (1) has uniform invariant probability density in [0, 1] interval. A discrete-time chaotic map, formed by the iteration of the output value in a transformation function, can be used for the generation of random numbers. A change in the numerical sequence that is generated by the function can occur, even if a minor change in the initial value is executed [51]. Their security is determined by the properties of the chaotic maps and the realization of the encryption scheme. Chiang, W. DOWNLOAD Mathematica Notebook TentMapIterations exhibiting chaotic dynamics and given by The natural invariant of the tent map is rho=1 . To overcome this limitation, this paper presents a novel image encryption scheme based on the pseudo-orbits of 1D chaotic maps. The reason is that you 16 May 2018 Strong chaos generates Type II survivorship curves entirely as a result of the . As an example of chaos, consider fluid flowing round an object. In the substitution the combination of tent map and chaotic logistic map. In [9], a novel image encryption method based on skew tent chaotic map and permutation–diffusion architecture is proposed. 2 Encryption and decryption Here, we propose a new approach for image encryption using chaotic tent map. Submitted March 1994, accepted May 1994. Hence, there is an increasing demand on generalized, modified and novel chaotic systems. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. The behaviour of the strongly chaotic maps—logistic, tent and Content loaded within last 14 days Pseudo Random Bits' Generator Based on Tent Chaotic Map and Linear Feedback Shift Register 30 Nov 2015 The investigation of the dynamics of the skew tent map, as well as of the tent map , which prove that at α = 4 the logistic map is chaotic. Abstract: A color image watermarking scheme using the chaotic properties of 2D tent map and Chebyshev map is proposed. The Bernoulli shift These programs demonstrates different chaotic maps,bifurcations,hybrid chaotic maps,highly secure maps,auto correlations,cross correlations and their extreme sensitivity to initial conditions or bifurcation parameters. Piecewise linear chaotic maps, such as tent map [32] and others [8] can be used but their piecewise linearity may lead to overall weakness of cryptosystem [3]. span lang="EN-US">) consisting of tent maps ULTRADISCRETIZATION OF A SOLVABLE TWO-DIMENSIONAL CHAOTIC MAP ASSOCIATED WITH THE HESSE CUBIC CURVE Kenji KAJIWARA, Masanobu KANEKO, Atsushi NOBE and Teruhisa TSUDA (Received 3 March 2009) Abstract. Pixels of the plain image are permuted using these chaotic functions, and then the image is partitioned into eight bit map planes. A Spatiotemporal Chaotic Sequence Based on Coupled Chaotic Tent Map Lattices System With Uniform Distribution . Secondly, the chaos-based key stream is generated by a 1-D chaotic tent map, which has a better performance in terms of randomness properties and security The sufficient conditions are provided to construct complete chaotic maps with the tent-map-like structures, that is, f(x) = 1 − ∣1 − 2g(x)∣, where g is an one-to-one onto map defined on [0, 1]. In the case of the logistic map that has a single dynamical variable, the bifurcation diagram is readily obtained by plotting a sample set of values of the sequence (xn) as a function of the parameter a, as shown in Fig. Recently an image encryption scheme based on a chaotic Tent map has been proposed by Li et al. Tent map bifurcation diagram. 2013. In Section IV, we demonstrate the feasibility of implementing the presented modiﬁed tent map for true random number generation. For the continuous-time systems, h is the interval between data samples. 20' maintenance esmt. In the second selection is the value for Gold sequence of the same length. - generator of chaotic sequences according to one of claims 5 or 6, characterized in that the chaotic maps of the first type are chaotic maps type "skew tent" and chaotic maps of the second type are chaotic maps chaotic maps piecewise linear PWLCM. Reduction of EMI with chaotic space vector modulation in direct torque control Finally, in this paper merely logistic map has been embedded to diversify the population of CTLBO algorithm; however, other different chaotic maps will be analyzed in the future work. Keywords Chaotic tent map, chosen-plaintext attack, cryptanalysis, cryptography, image encryption I. Toggle Main Navigation. The Logistic Map Introduction One of the most challenging topics in science is the study of chaos. This paper shows a digital noise generator designed in FPGA, based on a variant of the one-dimensional (1D) chaotic tent map (T-1D). S. Bernoulli and tent maps are two most commonly used discrete-Time chaotic maps. chaotic tent map

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