Chaotic Map Functions



INTRODUCTION Chaotic term is coined from the word chaos. Functions 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. Itshouldbenoted that Jafari et al. The chaotic nature of the standard map and the good statistical properties of the ECF map motivate us to design a new PRBG for stream cipher applications. 1 Analysis of the improved logistic map. If f1(x 0;fi) and f2(y ;fi) are. CHAOTIC MAPS AND GENETIC ALGORITHM. The beta chaotic map is used to develop pseudo-random key that encrypts the coefficients of subbands. Deterministic stochastic resonance in a piecewise linear chaotic map Sitabhra Sinha1 and Bikas K. For instance, in [3], some modified logistic maps of arbitrary power are studied. This map has chaotic behavior in range [1. The hash functions are the most useful primitives in cryptography. As we know, piecewise linear chaotic maps (PLCM) are the simplest kind of chaotic maps from the viewpoint of realization. The algorithm uses permutations whose positions are computed and indexed by a standard chaotic function and a linear congruence. Strogatz, 2015, 2nd Edition. 42857129819234609814 and again, getting: 0. A novel chaotic pulse sequence generator is presented, which includes a tent map function subcircuit and an iterative operation subcircuit. : Encryption Applications of a Generalized Chaotic Map Fig. The sensitivity of chaotic maps to initial conditions makes them optimum candidates to relate minimal critical information about the input, in the output sequence. In this paper, we introduce two simple chaotic 2D No Equilibria Maps (NEM). The INDEX function in Excel is very similar to this. maps in this paper, we believe that these examples may serve as a starting point for a more general understanding of higher-order correlations of strongly chaotic dynamical systems. Based on the high-dimensional (HD) chaotic maps and the sine function, a new methodology of designing new chaotic maps using dimension expansion is proposed. This is an extremely desirable property as the map function cannot be exactly realized due to process variations. The Chirikov standard map, is an area-preserving map for two canonical dynamical variables, i. Here, we have analyzed the common chaotic maps. The obtained results of the conducted numerical experiments show that the use of chaotic maps instead of other commonly used high-quality PRNGs can speed up the algorithm, and the incorporated exponential step decay can improve the accuracy of the obtained solution. The hash function called SHAH is based on two Tinkerbell maps filtered with irregular decimation rule. 3, which is a classic parameter setting. Chaotic maps can easily be implemented and avoid entrapment in local optima [13-17]. Thus, the design of secure hash functions is crucial. Cases where such surfaces can be found are rare enough. In: Communications in Nonlinear Science and It is commonly believed that a chaotic map can be used as a good candidate of a nonlinear component for. CBBO11 to CBBO20 have chaotic migration operator. >>> main() This program illustrates a chaotic function Enter a number between 0 and 1:. A new compound two dimensional chaotic function is built using two one dimensional chaotic functions which are switched randomly and used for chaotic sequence generator, the said method is proposed by Xiaojun Tong et al. By combining floating point computation of chaos and some simple algebraic operations, the system reaches very high. There are two widely-used chaotic maps for encryption, namely the Logistic map and the Chebyshev map. 2, 1 (2008), 203-221. Parameter settings of CDSA are P=50, Spee d=1, T=10. As for the plot on the right: Watch and compare it to the left graph, watching the r-value. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to. maps in this paper, we believe that these examples may serve as a starting point for a more general understanding of higher-order correlations of strongly chaotic dynamical systems. The collision performance compares favorably with that of chaotic hash functions proposed in the recent literature. However, it requires certain parameters to encrypt these coefficients. Chaotic functions Functions where "nearby" Input does not generate "nearby" Output. Functions With cycles of order not a power of 2 are often considered as the chaotic functions since they share a number of properties not possessed by other maps and since in some sense they behave more wildly. 3D Chaotic Functions for Image Encryption Pawan N. The new MAP technology builds upon CLARITY and follows 2014 work from the groups of Deisseroth and Gradinaru showing the method can powerfully expand tissue samples, while still preserving the proteins inside. The proposed image encryption scheme is based on two chaotic maps. Shapour Mohammadi, 2009. Chaos users evaluate the BER performance according to chaos modulation system [5] [6]. It canbeshown [II] thattheLyapunov 0 exponent ofalmosteveryorbit. The essence of the chaotic system belongs to a nonlinear system, but compared with the usual nonlinear system, the. Theory background: is a second-order nonlinear differential equation that models the motion of a simple pendulum subject to a forcing function , where is the damping coefficient, is the length of the pendulum, and is its angular position. Furthermore, the environmental variations affect the map characteristic in real-time operation. 4], for other values it behave as periodic or convergence. Suppose that the function g 0 has k simple zeros where k≥2. This is a side project of mine, learning more about chaotic time series analysis. @article{osti_22391119, title = {Performance of Multi-chaotic PSO on a shifted benchmark functions set}, author = {Pluhacek, Michal and Senkerik, Roman and Zelinka, Ivan}, abstractNote = {In this paper the performance of Multi-chaotic PSO algorithm is investigated using two shifted benchmark functions. In pulse compression technique of pulse radars, the. CHAOTIC FUNCTIONS WITH ZERO TOPOLOGICAL ENTROPY J. Graph of function (1) is a group of lines. 32323 and parameter b = 0. A general method is presented for generating feedback functions for maps. A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. 5 1 0 50 10 10 20 50 0. Antonyms for chaotic. Hashing performances are evaluated in terms of original message condition changes, statistical analyses, and collision analyses. The proposed example is studied by using the -rst return map in I, which we prove to be chaotic in I making. SECURE HASH FUNCTIONS BASED ON CHAOTIC MAPS FOR E-COMMERCE APPLICATIONS. The researchers in [9], [10], proved that logistic map, that was widely used in the encryption domain, is not enough random and uniform. An encryption process comprising: choosing a secret key and a set of permutable functions defined on a phase space for encrypting/decrypting messages; and choosing a code for encoding messages to be sent as a number belonging to the phase space, the set of permutable functions comprising chaotic maps generated by a composite function of first and second functions and an inverse of the first. The essence of the chaotic system belongs to a nonlinear system, but compared with the usual nonlinear system, the. This function can be especially useful for inspecting variable values within a custom function at runtime. One example is the known Logistic map[representedinFig. It canbeshown [II] thattheLyapunov 0 exponent ofalmosteveryorbit. Only the trusted server can determine the real identity of a user during the authentication, and any other entities including other users of the system get nothing about the user's. An encryption process comprising: choosing a secret key and a set of permutable functions defined on a phase space for encrypting/decrypting messages; and choosing a code for encoding messages to be sent as a number belonging to the phase space, the set of permutable functions comprising chaotic maps generated by a composite function of first and second functions and an inverse of the first. The proposed image encryption scheme is based on two chaotic maps. However that map was "discon-tinuous" [Fig. the chaotic signals, different from that sent on the first channel. [01:08] alsamixer: function snd_ctl_open failed for default: No such file or directory [01:08] !pm | Shaba2 [01:08] Shaba2: Please ask your questions in the channel so that other people can also benefit AND help you. A damped and driven pendulum is one of the simplest systems to use in the study of chaos. especially in the optimization of functions that are in very-high. as a potential inherent nonlinearity in various chaotic maps. 43 In this paper, we propose an adaptive equalizer for a chaotic synchronization 44 scheme in a master-slave configuration using the H´enon map, which ensures that 45 the transmitted signal is in fact chaotic, as we shall see. Topological transitivity is a mathematician's way of saying that the function meanders. Keywords: Chaotic functions, Entropy, Logistic Map, One Dimensional Chaotic functions, Tent Map. By applying SHA‐3 function to the matrix Q 1, we can generate the chaotic matrix Q 2 from 1D Logistic map with new control parameter and initial condition. As for the plot on the right: Watch and compare it to the left graph, watching the r-value. Baker map The Baker map is a chaotic map from unit square M x M into itself. Mathematically this is the same as saying, f (x1) ≠ f (x2) whenever x1 ≠ x2. Chaos based cryptographic algorithms are efficient approaches to create secure image. for WSN , depend upon compound chaotic map. To generate more uniform density function maps, two modified versions of the proposed Mehrab map are also defined. Graph of function (0) is a curve. ch013: Remote health-care monitoring systems communicate biomedical information (e. SBA Experiences Chaotic Rollout to 'Unprecedented' Stimulus Program Lawmakers on both sides and business owners alike criticized the Trump administration for a rocky implementation of a new. Again there are number of ways through which digital chaos-based cryptosystems be realized: block ciphers based on forward and/or reverse iterations of chaotic maps [4, 20-23], block ciphers based on chaotic round functions [24-27], stream ciphers implementing chaos-based pseudo random bit generators (PRBG) [28-33] etc. In 2004 Fu et al [42] proposed a chaos-based random number generator using piecewise chaotic map. The essence of the chaotic system belongs to a nonlinear system, but compared with the usual nonlinear system, the. The same strategy is applied across the algorithms under study to provide an unbiased judgment. This may lead to an urgent need for more and better chaotic maps. Overall, the use of the uniform pseudorandom number distribution generated by the tent map produced the most accurate results. ANALYSIS OF CHAOTIC SYSTEMS JUSTIN GUO Abstract. Then, the non-interactive twin chaotic maps-key exchange protocol is given in Section 4. A chaotic map-based mutual authentication scheme with strong anonymity is proposed in this paper, in which the real identity of the user is encrypted with a shared key between the user and the trusted server. tity functions and this means there exists at least one equilibrium. In this section, we briefly review one of the named Logistic map. In this brief, we propose a new 2/spl lscr/ -bit iterated hash function based on chaotic tent maps. The most attractive features of. Our analysis allows for arbitrary map functions, the inclusion of noise, and the treatment of en-sembles that are heterogeneous (i. The essence of the chaotic system belongs to a nonlinear system, but compared with the usual nonlinear system, the. 1 1 1 Apositive his a sufficient condition for an aperiodic signal to (e) 0 0. 3, which is a classic parameter setting. , it is not required that all maps in the ensemble are the same). It canbeshown [II] thattheLyapunov 0 exponent ofalmosteveryorbit. In mathematics, a chaotic map is a map (= evolution function) that exhibits some sort of chaotic behavior. chaotic map, hop based image steganography, different cryptographic hash function, a dynamic cryptographic hash function, chaotic maps for the authentication, integrity, confidentiality. vhd is created by a c++ code useful to specify in a programmatic way the number of bits of the chaotic map state, and the number of. fractional. 1 Proposed Chaotic Map Chaotic system is typically a dynamic system that pos-sesses some signi cant properties, involving the sensitive dependence on initial conditions and system parameters, the density of the set of all periodic points, and topologi-cal transitivity. The treatment of this case can be found at:. Sensitivity to initial condition and total chaotic range of FMM are medium. The unprecedented popular interest shown in recent years in the chaotic behavior of discrete. Graph of function (1) is a group of lines. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. Next, a novel chaotic maps problem is described in Section 3. scheme is constructed based on chaotic maps. One of the simplest examples of a chaotic maps is the so-called. "A Chaotic Map Arising in the Theory of Endogenous Growth," Discussion Papers 1071, Northwestern University, Center for Mathematical Studies in Economics and Management Science. Image Encryption Using Chaotic Based Artificial Neural Network. In the second layer, the classical DRPE is utilized. The proposed image encryption scheme is based on two chaotic maps. Parameter settings of CDSA are P=50, Spee d=1, T=10. It disregards. The formulation of Logistic map is as follows, [mathematical expression not reproducible] (1). In this work, we study the dynamical system which can be transformed into a difference equation of the form εg(xt-n2,. In some of these papers, the authors not only find the explicit functions Xn that solve the maps, but also they discuss the statistical properties of the sequences generated by the chaotic maps. Section is devoted to 3. 1 423-437 Geol. At the same time, for any periodic point of the mapping function f(x), there is no correlation in all subsets. We see that after one application of f c, there are no points in [-x 2 , c). Rixon's site map showing how it is laid out and where to find what you need Site map - Menu - Door Control Accessories, Floor Closers, Speicalty Closers, Overhead Concealed Closers This website uses cookies. Different from the other chaotic maps, Hénon map is a two-dimensional nonlinear system. The transmitter outputs chaotic pulse position modulated (C-PPM) data as a stream of 2. 000001$ to $4. The main principle of the proposed method is to combine the results of the input. Then, they propose to use other chaotic maps like Piece Wise Linear Chaotic Map (PWLCM). To attain this aim, a Lorenz-like system is proposed and rigorouslyproved chaotic for exemplified analysis. More detailed descriptions and properties of these chaotic maps can be found in [17, 29]. The hash function called SHAH is based on two Tinkerbell maps filtered with irregular decimation rule. The logistic map is a nonlinear function that is known to create chaotic dynamics. A bounded sequence of values fx ig1. One of the simplest examples of a chaotic maps is the so-called. Functions 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. The hash functions are the most useful primitives in cryptography. Using delay and q-deformations, some chaotic logistic maps are studied in [8]. A chaotic map function is deterministic. A chaotic map is, roughly speaking, a function that when iterated a large number of times behaves in unpredictable ways. 401155 is chosen). In the second layer, the classical DRPE is utilized. Antonyms for chaotic. Looking for chaotic attractor? Find out information about chaotic attractor. Compared to other chaotic functions, the proposed chaotic map establishes an excellent randomness performance and sensitivity. Unlike a single-modal chaotic map, i. where fis a smooth function on Rm. / An image encryption scheme with a pseudorandom permutation based on chaotic maps. rng07-vhdl Same as previous project, but the file randgen_package. A bounded sequence of values fx ig1. One example is the known Logistic map[representedinFig. Published on Jan 29, 2020. The Lyapunov number λ is also computed exactly for each map function, which is expressed commonly by λ = log m in terms of the. 142857129819234609814 Multiply by 10, and drop the whole-number part: 0. One way to model this mathematically is with the function f(x) = fractional part of 10x That is, start with any number, for instance: 0. The collision performance compares favorably with that of chaotic hash functions proposed in the recent literature. Minor change to the non-linear system parameters produces different signals that can be used as an alternate spreading sequence in multiple access spread spectrum communication. 8, x˙5y, y˙52x1yz, z˙512y2, ~4!. Based on a chaotic system, a hash construction which. Fasthosts Techie Test competition is now closed! Learn more about. One of the most common utilizing is the logistic maps that can be given by the two following equations [6, 7]: x r x x n n n 1 (1 ) (1) 2 xx nn 1 12 (2) In equation (1), xn n @0,1 0,1,)>, and 04 dr is called the bifurcation parameter, for r @3. This map has chaotic behavior in range [1. Functions 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. Thus after saving you can easily view your mindmap as image from the stored location. The essence of the chaotic system belongs to a nonlinear system, but compared with the usual nonlinear system, the. all chaotic map functions in the sense that it asymptotically (in k ) achieves the binary metric entropy for any given map. But ]0,1[ is isomorphic to is an isomorphism), so the cardinal of is greater or equal than the cardinality of R. Two things we might want to do with a function: Represent the whole function over its range. It returns a list of bs which are the results of applying f to every member of xs. But if we sacrifice invariability temporarily, thereby introducing singularities, one dimensional chaotic map can be easily. Synonyms for chaotic in Free Thesaurus. Chaotic Mixing in a Torus Map – p. where fis a smooth function on Rm. A chaotic map is, roughly speaking, a function that when iterated a large number of times behaves in unpredictable ways. The chaotic nature of the standard map and the good statistical properties of the ECF map motivate us to design a new PRBG for stream cipher applications. Home > On the convergence rate of the autocorellation function of 1-D chaotic maps On the convergence rate of the autocorellation function of 1-D chaotic maps. To generate more uniform density function maps, two modified versions of the proposed Mehrab map are also defined. Chaotic dynamics has been proposed as a mechanism for internally-generated cortical variability [3–5] and the richness of the dynamics at the edge of chaos has been exploited to learn complex tasks involving generation of temporal patterns [6–12]. In addition, they. Abstract — Cryptography is the science to transform the information in secure way. Fasthosts Techie Test competition is now closed! Learn more about. The functions numerically compute a solution of the fractional nonlinear differential equations, which describe the chaotic system. Misiurewicz's proof. As is well-known, the mathematical form of the SLE can be transformed into the stochastic differential equation (SDE). In the second layer, the classical DRPE is utilized. Minal Chauhan. Futhermore, we. Digital video and image cryptography is based on non linear trigonometric functions sine and cosine chaotic map. DNAG Decade Map blackwell91 0 324 Blanco, M. 514181182445 0. Looking for chaotic attractor? Find out information about chaotic attractor. They are derived systematically by using multiplication formulas of the elliptic functions. 142857129819234609814 Multiply by 10, and drop the whole-number part: 0. Another hash function based on a Cat map, is defined in [10]. 10, 20, 30, 40 and 50 resp ectively are used as the test. �tel-02271074�. Thus, the design of secure hash functions is crucial. The improved chaotic map is examined by the bifurcation diagram and by Lyapunov exponent at the value of k= 8. , momentum and coordinate \( (p,x)\). The map M is area-preserving and chaotic. Is unifying chaotic map functions possible? Does anybody know about a chaotic map with no equilibria or only stable equilibria? (k+1)=f(x(k),y(k)), where the function f and its related. In this paper, we introduce two simple chaotic 2D No Equilibria Maps (NEM). (1) To employ 10 different chaotic maps through normalized function to propose chaotic variants of GOA. In pulse compression technique of pulse radars, the. Baldur's Gate Durlag's Tower B3 - Trapped and locked stone on the north wall of the fiery bridge room. 1 Proposed Chaotic Map Chaotic system is typically a dynamic system that pos-sesses some signi cant properties, involving the sensitive dependence on initial conditions and system parameters, the density of the set of all periodic points, and topologi-cal transitivity. This definition certainly is directly connected to SD and is one physicists often use to characterize systems as chaotic. UNIVERSITE DE NANTES, 2019. Based on its Lyapunov exponents and entropy measure, the characteristics of the new mathematical function are better. Chaotic system exhibit dynamics that are sensitive to initial conditions [1, 19]. A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition The long-anticipated revision of this well-liked textbook offers many new additions. Keywords: Chaotic functions, Entropy, Logistic Map, One Dimensional Chaotic functions, Tent Map. A more comprehensive reference on the subject is the textbook Chaotic Dynamical Systems (Robert L. Chaotic Image Encryption Using Logistic Map Acronis True Image - Activex Image - Adobe Image Wri - Africa Map - Africa Map Wmf - Ai Image Editor - Ai Image File Code 1-20 of 60 Pages: Go to 1 2 3 Next >> page. From Vim to Emacs+Evil chaotic migration guide Septiembre 20 2014 I’ve been using Vim for 18 years, and for me it was the only option for serious text work (like programming or writing) because I’m totally addicted to modal text editing to the point that I feel crippled when I’ve to edit text in a non-modal editor. Chaotic function Chaotic functions are similar to noise signals, but they are completely certain; that is, if we have the primary quantities and the drawn function, the exact signal can be reproduced. Nine different actions are used from the dataset provided by [12]. suitability of chaotic maps, we used all traces (including those which were not used in the model development) and compared the distribution functions of run and burst lengths produced by chaotic maps and several other models (ranging from simple to complex) with measured data using a metric expressing the difference of two distribution functions. The Logistic map is a classic non-linear chaotic function which has complex chaotic behavior. Again there are number of ways through which digital chaos-based cryptosystems be realized: block ciphers based on forward and/or reverse iterations of chaotic maps [4, 20-23], block ciphers based on chaotic round functions [24-27], stream ciphers implementing chaos-based pseudo random bit generators (PRBG) [28-33] etc. function, chaotic maps for the authentication, integrity, confidentiality. For ease of analysis, this differential equation is first converted to a nondimensional form by defining , , , and , where is the pendulum's. The functions numerically compute a solution of the fractional nonlinear differential equations, which describe the chaotic system. They are derived systematically by using multiplication formulas of the elliptic functions. Logistic maps Chaotic sequences are generated using discrete chaotic functions. Baldur's Gate Durlag's Tower B3 - Trapped and locked stone on the north wall of the fiery bridge room. The map M is area-preserving and chaotic. Maps X and Y are summed and converted to decimal numbers by an approximation, we obtain the map S. , the Bernoulli map and the tent map. Simple Chaotic Circuit The signal supplied to drive the circuit is a sinusoid with variable peak-to-peak amplitude. We will focus on a particular class of such maps, namely piecewise linear functions from [0,1] to [0,1]. Definition 2 f is said to be topologically transitive if, for. I think some of them are chaotic, whereas others are clearly periodic. In addition, they. Chaotic Map In order to investigate switching phenomena, two kinds of one-dimensional maps are investigated in this study. This method accepts N dimensions of any existing HD chaotic map as inputs to generate new dimensions based on the combined results of those inputs. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. Dual Watermarking Technic using Chaotic Map And Discrete Wavelet Transform. 3, which is a classic parameter setting. When the system is not in a proper order then it is said to exhibit chaos. A New Chaos-Based Color Image Encryption Scheme with an Efficient Substitution Keystream Generation Strategy. Supporting Functions Map. 4], for other values it. Overall, the use of the uniform pseudorandom number distribution generated by the tent map produced the most accurate results. Then for some well-defined square matrix A¡, with entries either zero or one,. A collection and description of functions to investigate the chaotic behavior of time series processes. This hash function can be expected to have at least the same computational security against target attack, free-start. Map Medieval City Medieval City Map Merchant Planet Portal Tavern Names Fantasy-Style Names Modern Names Name Jumbler Name Mixer Place Names Accessories Animal Companion Armor Art Object Car Charm Currency Familiar Futuristic Spare Part Gemstone Insignias Magic Artifact Magic Weapon Magical Component Musical Instrument Potions Spaceship Small. Matlab and Chaos: Solving Diff. Based on its Lyapunov exponents and entropy measure, the characteristics of the new mathematical function are better. CHAOTIC MAP AND WATERMARKING A chaotic map is an evaluation function that exhibits some sorts of chaotic behavior. What makes the dynamical system "chaotic" is the fact that orbits arising from initial data which are arbitrarily close grow apart exponentially. Moreover in this paper, an algorithm for one way hash function construction based on chaos theory is introduced. CHAOTIC FUNCTIONS WITH ZERO TOPOLOGICAL ENTROPY J. More detailed descriptions and properties of these chaotic maps can be found in [17, 29]. A discrete-time chaotic map, formed by the iteration of the output value in a transformation function, known as map, can be used for the generation of random numbers. 2013040102: Recently, a parallel hash function based on chaotic maps with changeable parameters was proposed by Li et al (2011, pp. the vector of start values to initiate the chaotic map. Chaotic maps often occur in the study of dynamical systems. functions based on chaotic maps and neural networks Nabil Abdoun To cite this version: Nabil Abdoun. 303213732397 0. Now you can type logisticin the command line and hit the “Enter ←-” key to run this script. All of the chaotic maps listed in Table 1 are in real space domain. Google Scholar Cross Ref; bib0300. Michele Boldrin & Nicola Perisco, 1993. The ebook and printed book are available for purchase at Packt Publishing. x n+1 = ¡ ax 3 + ax n: (1) x n +1 = ¡ ax n + a jx n + 1 2 j¡ a jx n ¡ 1 2 j: (2) Figures 1 and 2 show the one-dimensional maps derived by Eqs. The following chaotic maps have been integrated to the BBO algorithm: Chebyshev map Circle map Gauss/mouse map Iterative map Logistic map Piecewise map Sine map Singer map Sinusoidal map Tent map. 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. In this paper, we introduce two simple chaotic 2D No Equilibria Maps (NEM). Chaotic function Chaotic functions are similar to noise signals, but they are completely certain; that is, if we have the primary quantities and the drawn function, the exact signal can be reproduced. Chaotic maps have various properties that mirror the security requirements of cryptographic algorithms. An extensive survey of the correspond-. From what I understand, hash functions are pseudorandomly generated based on the initial seed (the raw data). Discrete maps usually take the form of iterated functions. where f(xn) is a nonlinear map that generates a chaotic at-tractor, h(x,p) is a scalar driving function, and G(yn)isa vector function that possesses symmetry. [2016a] proposed a 1D chaotic map with no equilibria. as a potential inherent nonlinearity in various chaotic maps. In the receiver side, a synchronizer reconstructs the chaotic oscillator signals, one of which is used for the decryption of the message. A function is called one-to-one if no two values of x. CHAOTIC FUNCTIONS WITH ZERO TOPOLOGICAL ENTROPY J. Hénon map, which presents a simple 2-D chaotic map with quadratic nonlinearity, depends on two parameters, r and b, which for the canonical Hénon map have values of r = 1. 10,11 He showed that case A in Ref. 42857129819234609814 and again, getting: 0. coupled chaotic maps. (Both are Xn+1 = f(Xn) type functions. The sensitivity of chaotic maps to initial conditions makes them optimum candidates to relate minimal critical information about the input, in the output sequence. However, repetition of values (many-to-one function) conflicts with the requirement of invariability. Baldur's Gate Durlag's Tower B3 - Trapped and locked stone on the north wall of the fiery bridge room. Interest in chaotic dynamics has grown explosively in recent years. Bonanno and S. Image Encryption with The Cross Diffusion of Two Chaotic Maps Shah continued, 'SUPARCO has been told to send chaotic politicians to space and to ensure that once they are sent there they cannot return. The rst is the logistic map, a rst-order discrete dynamical system, and the second is the Lorenz system, a three-dimensional system of di erential. This map has chaotic behavior in range [1. Figure 4 shows the simulation of the chaotic piecewise linear map iterating 50 times with the initial value x 0 = 0. 958185428249 0. 4 A summary of the cryptographic primitives based on 3D chaotic maps 134 5. ( 1) and ( 2. 1 Introduction At the Crypto 2005 rump session [1], a new hash function was designed based upon chaos theory. 4 show that there are no nontrivial fixed points for small values of r. Chaotic systems have the property of being deterministic in microscopic space and behave randomly, when observed in a coarse-grained state-space. Also, an adaptive normalization method is proposed to transit from the exploration phase to the exploitation phase smoothly. Chaotic Mixing in a Torus Map – p. Among the various maps, four maps are investigated and their characteristics are analyzed. rng07-vhdl Same as previous project, but the file randgen_package. Nevertheless, the corresponding analysis of them lag far behind. Electronics. This can be better visualized by plotting a histogram of all the values of in the evolution under the map for 20000 iterations. Functions With cycles of order not a power of 2 are often considered as the chaotic functions since they share a number of properties not possessed by other maps and since in some sense they behave more wildly. Chaotic maps often generate fractals. beclassified as chaotic. Figures 1(b) and 2(b) show the bifurcation diagram and the Lyapunov Exponent of the improved chaotic map. The rst is the logistic map, a rst-order discrete dynamical system, and the second is the Lorenz system, a three-dimensional system of di erential. After then, chaotic hash functions are gradually attracting more and more researchers to study ranging from the use of simple maps, such as tent map , , and logistic map , , to the use of more complicated maps of the sine map , standard map , piecewise linear or nonlinear chaotic maps , , , , and high-dimensional chaotic maps , ,. However that map was “discon-tinuous” [Fig. In this paper, the security. chaotic: /cha·ot·ic/ ( ka-ot´ik ) completely confused, disorganized, or irregular. State space coverage by chaotic trajectories. 1 Analysis of the improved logistic map. Open the logistic. beclassified as chaotic. map and is more security; besides, it is robust to the common signal attacks. Overall, the use of the uniform pseudorandom number distribution generated by the tent map produced the most accurate results. Chaotic system exhibit dynamics that are sensitive to initial conditions [1, 19]. Khade and Prof. 42857129819234609814 and again, getting: 0. Based on a chaotic system, a hash construction which. 1 423-437 Geol. Such a cryptosystem. Chaotic Henon map In 1989, Matthews suggested a new efficient way to deal with the intractable problem of fast and highly secure encryption by proposing the chaotic encryption algorithm. This function displays the chaotic map "in motion", so you can see how it gets filled in over time. �tel-02271074�. Simple Chaotic Circuit The signal supplied to drive the circuit is a sinusoid with variable peak-to-peak amplitude. A general method is presented for generating feedback functions for maps. Is unifying chaotic map functions possible? Does anybody know about a chaotic map with no equilibria or only stable equilibria? (k+1)=f(x(k),y(k)), where the function f and its related. Keywords: Chaotic functions, Entropy, Logistic Map, One Dimensional Chaotic functions, Tent Map. 42857129819234609814 and again, getting: 0. chaotic: /cha·ot·ic/ ( ka-ot´ik ) completely confused, disorganized, or irregular. A chaotic map is, roughly speaking, a function that when iterated a large number of times behaves in unpredictable ways. 156257842027 0. We see that after one application of f c, there are no points in [-x 2 , c). An image encryption scheme with a pseudorandom permutation based on chaotic maps. Because it improves the function of the nerves in the brain it has a calming, yet clarifying effect that can make getting through a chaotic work day much easier. Chaotic quadratic maps Fig. 000001$ to $4. Graph of function (0) is a curve. Only the trusted server can determine the real identity of a user during the authentication, and any other entities including other users of the system get nothing about the user's. If you know the equation for the function:. Definition 2 f is said to be topologically transitive if, for. A unimodal map f: [0, 1] → [0, 1] is said to be complete chaotic if it is both ergodic and chaotic in a probabilistic sense so as to preserve an absolutely continuous invariant measure. A method for generating a pseudo-random numbers Initially, the state of a chaotic system is digitized to form a binary string. It returns a list of bs which are the results of applying f to every member of xs. Because it improves the function of the nerves in the brain it has a calming, yet clarifying effect that can make getting through a chaotic work day much easier. Geospatial data, like other files, are frequently stored and transmitted in compressed or archive formats, such a tar, zip, or GNU zip. The Walsh functions are based on a 2 k × 2 k Hadamard matrix. rng07-vhdl Same as previous project, but the file randgen_package. Google Scholar Cross Ref; bib0305. Printing Mindmaps. There have been many literatures about implementation of chaotic oscillators using FPGA like FPGA based multiscroll attractor discussed in [32-39], digital chaotic oscillators and its FPGA model [36, 40], FPGA based four-wing chaotic attractor [37], and image cryptography with chaotic ciphers and its FPGA implementations and FPGA implemented memristor-based chaotic attractors [41]. Exact study has been provided on the novel scheme using distribution analysis, sensitivity analysis, static analysis of diffusion and confusion, and. Chaotic maps often generate fractals. Today I thought I'd share a chaotic system, called Gingerbreadman maps, whose equations make the system seem simple. The proposed image encryption scheme is based on two chaotic maps. Chaotic maps are evolution functions that exhibits chaotic behavior. The beta chaotic map is used to develop pseudo-random key that encrypts the coefficients of subbands. Parameter settings of CDSA are P=50, Spee d=1, T=10. 514181182445 0. A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. At the same time, for any periodic point of the mapping function f(x), there is no correlation in all subsets. 000001$ to $4. Chaotic itinerancy based on attractors of one-dimensional maps where g is a chaotic map. 4018/978-1-5225-0920-2. The researchers in [9], [10], proved that logistic map, that was widely used in the encryption domain, is not enough random and uniform. chaotic maps, a new Beta chaotic map was introduced to generate a key sequence which is based on Beta function [14]. There are preferred zones and which inhabits. Chaos users evaluate the BER performance according to chaos modulation system [5] [6]. Because it improves the function of the nerves in the brain it has a calming, yet clarifying effect that can make getting through a chaotic work day much easier. The mu-tual information between pairs of maps, in the stationary regime, is then used as the similarity index for clustering the data set. This function is a one-dimensional chaos function and receives only one single primary value as input and produces one chaotic sequence as output. map () function returns a map object (which is an iterator) of the results after applying the given function to each item of a given iterable (list, tuple etc. CHAOTIC MAP AND WATERMARKING A chaotic map is an evaluation function that exhibits some sorts of chaotic behavior. The chaos streams are generated by using various chaotic maps. We will propose a method to generate chaotic interleaver based on the generation of sequences having a chaotic behaviour using some chaotic maps such as logistic function and Henon map function. Chui, A symmetric image encryption scheme based on 3D chaotic cat maps, Chaos Solitons Fractals, 21 (2004) 749-761. They play an important role in data integrity, message authentication, digital signature and authenticated encryption. Then, the non-interactive twin chaotic maps-key exchange protocol is given in Section 4. chaotic maps used in the paper are: Logistic Map The system should be highly unpredictable. To generate more uniform density function maps, two modified versions of the proposed Mehrab map are also defined. The structures have prevailing NW and NE trends. An encryption process includes choosing a secret key and a set of permutable functions defined on a phase space for encrypting/decrypting messages, choosing a code for encoding messages to be sent as. Discrete maps usually take the form of iterated functions. 2013040102: Recently, a parallel hash function based on chaotic maps with changeable parameters was proposed by Li et al (2011, pp. The meaning of positivity here is that a global Lyapunov exponent is positive for almost all points in the specified set \(S\). chaotic: /cha·ot·ic/ ( ka-ot´ik ) completely confused, disorganized, or irregular. Further, a one-way coupled chaotic map lattice was used by Huaping et al [43] for generating pseudo-random numbers. This may lead to an urgent need for more and better chaotic maps. Is unifying chaotic map functions possible? Does anybody know about a chaotic map with no equilibria or only stable equilibria? (k+1)=f(x(k),y(k)), where the function f and its related. Matlab has some nice built-in functions for solving differential equations numerically and can do animations quite easily, so it's a handy way to explore chaotic systems (that can be represented by non-linear differential equations) without doing a whole lot of programming. The new MAP technology builds upon CLARITY and follows 2014 work from the groups of Deisseroth and Gradinaru showing the method can powerfully expand tissue samples, while still preserving the proteins inside. , to detect modification of an original message). The rest of the paper is organized as follows: Some pre-liminaries are given in Section 2. The Security of our proposed protocol is given in Section 5. Hénon map presents a simple 2-D chaotic map with quadratic nonlinearity, depends on two parameters, r and b, which for the canonical Hénon map have values of r = 1. Research on digital image encryption algorithm based on double logistic chaotic map Hailan Pan1,2,3*, Yongmei Lei1 and Chen Jian2,3 Abstract With the development of information technology, image information has become the main content of network information transmission. This map can be parameterized by discrete-time or continuous-time. Then, they propose to use other chaotic maps like Piece Wise Linear Chaotic Map (PWLCM). Matlab and Chaos: Solving Diff. Some map functions were found to fit data better than others. iter : It is a iterable which is to be mapped. A chaos system also creates a random behavior subsequently, but at the same time a chaos system is wholly deterministic. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Chaotic itinerancy is a closed-loop trajectory through high-dimensional state space of neural activity that directs the cortex in sequence of quasi-attractors. All create files in a folder for which you must have write permission. There are multplie plots that can extracted from chaotic maps (temporal evolution, coweb diagrams, bifurcation diagrams,). Chaotic Henon map In 1989, Matthews suggested a new efficient way to deal with the intractable problem of fast and highly secure encryption by proposing the chaotic encryption algorithm. 3 Description of the parallel Hash algorithm In this paper, the parallel Hash algorithm is developed by employing the high sensitivity to the initial conditions of a chaotic asymmetric tent map and a. The most general second-degree polynomial jerk function is j" !a 1! a 2 x! a 3 xú ! a 4 x¬"x¬! !a 5! a 6 x! a 7 xú "xú! !a 8! a 9 x "x! a 10, !8". (A) Map of the largest groove systems in the chaotic terrain antipodal to the Caloris basin. This technique is implemented in two layers to enhance the security level of the classical DRPE. Chaotic maps have various properties that mirror the security requirements of cryptographic algorithms. In the second layer, the classical DRPE is utilized. Finally, we sum the mark M with T to get the cipher. iter : It is a iterable which is to be mapped. Pareek et al, 2006): If we want to produce a chaotic. rng07-vhdl Same as previous project, but the file randgen_package. The hash function provides the necessary security in authentication methods and digital signature algorithms. General Chaotic Maps In general, chaotic maps are obtained by a deterministic rule: x t = f(x t-1,x t-2,). The Walsh functions are based on a 2 k × 2 k Hadamard matrix. This is a side project of mine, learning more about chaotic time series analysis. As an example of chaos, consider fluid flowing round an object. For instance, in [3], some modified logistic maps of arbitrary power are studied. The wave1 wave2 side jack jump run pjump walk bend Figure 1. Of a particular interest, a. posed Chaotic Map and Cellular Automata 2. Now you can type logisticin the command line and hit the "Enter ←-" key to run this script. The improved chaotic map is examined by the bifurcation diagram and by Lyapunov exponent at the value of k= 8. The system parameter for the both chaotic maps is kept same and is in the chaotic regime. Chaotic maps have various properties that mirror the security requirements of cryptographic algorithms. �tel-02271074�. Chaotic Henon map In 1989, Matthews suggested a new efficient way to deal with the intractable problem of fast and highly secure encryption by proposing the chaotic encryption algorithm. An encryption process comprising: choosing a secret key and a set of permutable functions defined on a phase space for encrypting/decrypting messages; and choosing a code for encoding messages to be sent as a number belonging to the phase space, the set of permutable functions comprising chaotic maps generated by a composite function of first and second functions and an inverse of the first. Michele Boldrin & Nicola Perisco, 1993. Pick any two points A and B. Chaotic maps can easily be implemented and avoid entrapment in local optima [13-17]. It disregards. In this section, we briefly review one of the named Logistic map. CBBO21 to CBB30 have chaotic mutation operator. I use the Pypy jit-compiler to speed up the Python code. A new compound two dimensional chaotic function is built using two one dimensional chaotic functions which are switched randomly and used for chaotic sequence generator, the said method is proposed by Xiaojun Tong et al. The sine and cosine chaotic map is generated for high-intense of chaos over most regions of image to increase confidentiality of information. >>> main() This program illustrates a chaotic function Enter a number between 0 and 1:. To attain this aim, a Lorenz-like system is proposed and rigorouslyproved chaotic for exemplified analysis. In this paper, the security. For ease of analysis, this differential equation is first converted to a nondimensional form by defining , , , and , where is the pendulum's. A chaotic map-based mutual authentication scheme with strong anonymity is proposed in this paper, in which the real identity of the user is encrypted with a shared key between the user and the trusted server. Abstract: In this paper a dynamic Hash algorithm construction based on chaotic maps with controllable parameters is proposed and analyzed. Design, implementation and analysis of keyed hash functions based on chaotic maps and neural networks. 823973143043 0. Maps may be parameterized by a discrete-time or a continuous-time parameter. Wang, A block cipher based on a suitable use of chaotic standard map, Chaos Solitons Fractals, 26 (2005) 117-129. This method accepts N dimensions of any existing HD chaotic map as inputs to generate new dimensions based on the combined results of those inputs. image encryption based on chaotic Baker map and Double Random Phase Encoding (DRPE). Hash function operations involve an initial stage when the chaotic map accepts initial conditions and a hashing stage that accepts input messages and generates the alterable-length hash values. Chaotic Commands is a 5th level priest spell. Going Off the Map: Exploring purrr's Other Functions January 9, 2019 I recently completed Colin Fay’s excellent DataCamp course, Intermediate Functional Programming with purrr (full disclosure: I work at DataCamp, but part of why I joined was that I was a big fan of the short, interactive course format). The Walsh functions are based on a 2 k × 2 k Hadamard matrix. The principle of the method consists in mixing three chaotic maps produced from an input initial vector. Today I thought I'd share a chaotic system, called Gingerbreadman maps, whose equations make the system seem simple. The discrete. In this paper, the nonlinear devices in the traditional block cipher S-box is used to construct variable parameters Hash algorithm composed of multiple chaotic maps. Only the trusted server can determine the real identity of a user during the authentication, and any other entities including other users of the system get nothing about the user's. [01:08] alsamixer: function snd_ctl_open failed for default: No such file or directory [01:08] !pm | Shaba2 [01:08] Shaba2: Please ask your questions in the channel so that other people can also benefit AND help you. Khade and Prof. It is represented by: 1 (1- )k k k X aX X (10) where k X is the th k chaotic number, k is iteration number. Application and Development of Enhanced Chaotic Grasshopper Optimization Algorithms 2D-SLMM is derived from two 1D chaotic maps , the Logistic and Sine maps. Baker-like map with in-nitely many branches, de-ned as a map of the interval I = [0;1] into itself with in-nitely branches due to expanding functions with range I except at most the rightmost one. However that map was "discon-tinuous" [Fig. , it is not required that all maps in the ensemble are the same). If its initial state is exactly known, its output behavior can be exactly predicted. Graph of function (0) is a curve. 2) Devaney’s chaotic dynamical systems: Consider a topo-logical space (X;˝) and a continuous function fon X. Baldur's Gate Durlag's Tower B3 - Trapped and locked stone on the north wall of the fiery bridge room. A general method is presented for generating feedback functions for maps. chaotic_maps. As in [24], the chaotic 46 synchronization scheme considered here feeds back the encoded message into the 47 CSG. Chaotic quadratic maps Fig. Figures 1(b) and 2(b) show the bifurcation diagram and the Lyapunov Exponent of the improved chaotic map. Cases where such surfaces can be found are rare enough. Synchronization of chaotic maps is studied using the method of variable feedback. Open the logistic. One of the most common utilizing is the logistic maps that can be given by the two following equations [6, 7]: x r x x n n n 1 (1 ) (1) 2 xx nn 1 12 (2) In equation (1), xn n @0,1 0,1,)>, and 04 dr is called the bifurcation parameter, for r @3. Our analysis allows for arbitrary map functions, the inclusion of noise, and the treatment of en-sembles that are heterogeneous (i. If f1(x 0;fi) and f2(y ;fi) are. Five pixels are selected as the encryption key for forming the initial value of the logical map function and for encrypting that part of the image. The performance of that scheme is evaluated through statistical analysis. In this paper, we introduce two simple chaotic 2D No Equilibria Maps (NEM). Exact study has been provided on the novel scheme using distribution analysis, sensitivity analysis, static analysis of diffusion and confusion, and. f ( x 1) ≠ f ( x 2) w h e n e v e r x 1 ≠ x 2. : Encryption Applications of a Generalized Chaotic Map Fig. The proposed image encryption scheme is based on two chaotic maps. Recently, many papers have been dedicated to exactly solvable chaotic maps [3-7, 18-21]. Antonyms for chaotic. Here, we have analyzed the common chaotic maps. Although the function is extremely e cient, it. Dual Watermarking Technic using Chaotic Map And Discrete Wavelet Transform. 1997-09-01 00:00:00 Exactly solvable iterative chaotic maps as a multiplicative congruential algorithm of random number generator is presented. Is unifying chaotic map functions possible? Does anybody know about a chaotic map with no equilibria or only stable equilibria? (k+1)=f(x(k),y(k)), where the function f and its related. That is, until you do some simulations. Microphone Mute Proximity com/education. When there are more than three markers, multilocus recombination probabilities cannot be uniquely determined by the defining property of map functions, and different methods have been proposed to permit the use of map functions to analyze multilocus data. State space coverage by chaotic trajectories. 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. What makes the dynamical system “chaotic” is the fact that orbits arising from initial data which are arbitrarily close grow apart exponentially. Open the logistic. two-dimensional (2D) Poincaré return map is rigorously derived for verifying the chaotic behaviors of the double-scroll chaotic at-tractor, which is a basic generator of various multiscroll chaotic attractors investigated in the paper. Logistic maps Chaotic sequences are generated using discrete chaotic functions. The formulation of Logistic map is as follows, [mathematical expression not reproducible] (1). Enhanced Chaotic Image Encryption Algorithm Based on Trigonometric functions International Journal of Image Processing and Vision Sciences (IJIPVS) ISSN(Print): 2278 - 1110, Vol-1 Iss-3,4 ,2012 74 In this paper, a new image encryption algorithm based on two different chaotic maps is proposed. for WSN , depend upon compound chaotic map. CHAOTIC MAP AND WATERMARKING A chaotic map is an evaluation function that exhibits some sorts of chaotic behavior. × To Support Customers in Easily and Affordably Obtaining Titles in Electronic Format IGI Global is Now Offering a 50% Discount on. Topological transitivity is a mathematician's way of saying that the function meanders. In the present paper we give a characterization of the class M c C°(7, /) of mappings chaotic in this sense. In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. A discrete map is chaotic if it has a positive global Lyapunov exponent. 1 Hash Function Based on Combination of Chaotic Maps 135 5. This implies that if you create two orbits with the identical initial data, x 0, then the orbits are the same. In this paper, to overcome these problems, we suggest a new chaotic image encryption algorithm, in which Secure Hash Algorithm (SHA)-3 function is used to simulate the effect of one-time pad. Although the function is extremely e cient, it. Interest in chaotic dynamics has grown explosively in recent years. In this paper, a new efficient scheme for parallel hash function based on high-dimensional chaotic map is proposed. (A) Map of the largest groove systems in the chaotic terrain antipodal to the Caloris basin. Devaney, 2003) where the logistic map is referred to as the quadratic map. Three different benchmark functions are selected from the IEEE CEC 2013 competition benchmark set. Based on simplest 2-D chaotic maps, a new hash function has been proposed and analyzed in this paper. 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. In this Comment, we point out three flaws in a previous proposal for chaotic encryption. 8, x˙5y, y˙52x1yz, z˙512y2, ~4!. The Lyapunov number λ is also computed exactly for each map function, which is expressed commonly by λ = log. In: Communications in Nonlinear Science and It is commonly believed that a chaotic map can be used as a good candidate of a nonlinear component for. An encryption process includes choosing a secret key and a set of permutable functions defined on a phase space for encrypting/decrypting messages, choosing a code for encoding messages to be sent as. Fast chaotic optimization algorithm based on spatiotemporal maps for global optimization Considering the statistical property such as the probability density function (PDF) of the chaotic sequences, the search ability of COA can improve the global searching capability by escaping the local solutions than classical stochastic optimization. vhd is created by a c++ code useful to specify in a programmatic way the number of bits of the chaotic map state, and the number of. Finally, we sum the mark M with T to get the cipher. Open the logistic. To download the map right-click the image and select "Save Image As". 1,0) 6000 times. Hénon map presents a simple 2-D chaotic map with quadratic nonlinearity, depends on two parameters, r and b, which for the canonical Hénon map have values of r = 1. This method accepts N dimensions of any existing HD chaotic map as inputs to generate new dimensions based on the combined results of those inputs. 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. 1 Introduction At the Crypto 2005 rump session [1], a new hash function was designed based upon chaos theory. A new hash function system, based on coupled chaotic map dynamics, is suggested. Moreover in this paper, an algorithm for one way hash function construction based on chaos theory is introduced. Logistic maps Chaotic sequences are generated using discrete chaotic functions. @article{osti_22391119, title = {Performance of Multi-chaotic PSO on a shifted benchmark functions set}, author = {Pluhacek, Michal and Senkerik, Roman and Zelinka, Ivan}, abstractNote = {In this paper the performance of Multi-chaotic PSO algorithm is investigated using two shifted benchmark functions. Pareek et al, 2006): If we want to produce a chaotic. Dual Watermarking Technic using Chaotic Map And Discrete Wavelet Transform. I found that this map is known as the modified Farey map. Neotectonics of North America Geol. Spakman, W. In mathematics, a chaotic map is a map (= evolution function) that exhibits some sort of chaotic behavior. When you realize that the list of bs that map returns can itself be a list of functions, things. Media in category "Chaotic maps" The following 23 files are in this category, out of 23 total. A novel chaotic pulse sequence generator is presented, which includes a tent map function subcircuit and an iterative operation subcircuit. 1,0) 6000 times. For a more recent textbook for beginners, read Non Linear Dynamics and Chaos (Steven H. The formula of this function is as follows (N. Media in category "Chaotic maps" The following 23 files are in this category, out of 23 total. The same strategy is applied across the algorithms under study to provide an unbiased judgment. Hash function operations involve an initial stage when the chaotic map accepts initial conditions and a hashing stage that accepts input messages and generates the alterable-length hash values. 1 Introduction At the Crypto 2005 rump session [1], a new hash function was designed based upon chaos theory. This is an extremely desirable property as the map function cannot be exactly realized due to process variations. CHAOTIC MAP AND WATERMARKING A chaotic map is an evaluation function that exhibits some sorts of chaotic behavior. The topics include efficient color image segmentation by a parallel optimized (ParaOptiMUSIG) activation function, chaotic map model-based interference employed in a quantum-inspired genetic algorithm to determine the optimum gray level image thresholding, multi-objective genetic and fuzzy approaches in rule mining problems of knowledge discovery in databases, concept generation in knowledge. The following chaotic maps have been integrated to the BBO algorithm: Chebyshev map Circle map Gauss/mouse map Iterative map Logistic map Piecewise map Sine map Singer map Sinusoidal map Tent map. One of the most famous functions which can have chaotic behavior is logistic map chaos function. You can normally easily represent it and find global optima. , the Bernoulli map and the tent map. This is one of the 100+ free recipes of the IPython Cookbook, Second Edition, by Cyrille Rossant, a guide to numerical computing and data science in the Jupyter Notebook. 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.
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