# Chaotic Map Functions

The Security of our proposed protocol is given in Section 5. of a single valued function on a compact space are closely linked to the dynamics of the shift map on the inverse limit with the function as the sole bonding 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. Introduction. Then, the permutation in inverse order can be executed to row and column accordingly. Plotting the bifurcation diagram of a chaotic dynamical system. , momentum and coordinate $$(p,x)$$. chaotic maps, a new Beta chaotic map was introduced to generate a key sequence which is based on Beta function [14]. This map has chaotic behavior in range [1. chaotic map, Rastrigin function whose dimensions are set to. The ebook and printed book are available for purchase at Packt Publishing. 4 and b = 0. The performance of that scheme is evaluated through statistical analysis. 4], for other values it. 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. Another hash function based on a Cat map, is deﬁned in [10]. 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. Ramafiarisona Hajasoa Malalatiana. Abstract: In this paper a dynamic Hash algorithm construction based on chaotic maps with controllable parameters is proposed and analyzed. We display several messages that collide to the same output for this hash function. 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. 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. Overall, the use of the uniform pseudorandom number distribution generated by the tent map produced the most accurate results. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. The output generated by the ﬂrst tent map is fed to the second tent map as the input (initial condition) and vice versa. Recently, many papers have been dedicated to exactly solvable chaotic maps [3-7, 18-21]. At the Crypto 2005 rump session, a new hash function based upon a chaotic map was presented. bit exchange technique, a fusion of two arbitrary functions, and a chaotic map. 1 Analysis of the improved logistic map. As r increases, there is a fold bifurcation point (rs,x∗s) at. Next, a novel chaotic maps problem is described in Section 3. I use the Pypy jit-compiler to speed up the Python code. The ﬁrst layer is a pre-processing layer, which is performed with the chaotic Baker map on the original image. The An Introduction to Chaotic Dynamical Systems (Studies in Nonlinearity) is not a book for the faint hearted however it does provide a very good mathematical overview of the subject. JERK FUNCTIONS Recently Gottlieb9 pointed out that the simplest ODE in a single variable that can exhibit chaos is third order, and he suggested searching for chaotic systems of the form ^x5j(x,x˙,x¨), where j is a jerk function ~time derivative of acceleration!. In case anyone else is interested, the following reference mentions it: C. Although there exist a wide range of chaos-based hash functions in literature, most of them are designed in an ad hoc manner rather than relying on well-established design paradigms. An image encryption scheme with a pseudorandom permutation based on chaotic maps. 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. The zeta function is a function of two variables, x and y which exist in the complex plane). Using Logistic map as a chaotic sequence generator and bitXOR operator for encrypting the image values an image. But ]0,1[ is isomorphic to is an isomorphism), so the cardinal of is greater or equal than the cardinality of R. You'll see that for 0 < r < 3 there's a singular peak in "accumulation", and from 3 < r < 4 there are two points, and at r = 4 there's zero accumulation in any region. Chaotic itinerancy based on attractors of one-dimensional maps where g is a chaotic map. It is described by the equations: $\tag{1} \begin{array}{lcr} \bar{p} = p+K\sin x \\ \bar{x} = x+\bar{p} \end{array}$ where the bars indicate the new values of variables after one map iteration and $$K$$ is a dimensionless parameter that influences the degree. So map square [1, 1, 2, 3, 5, 8] would yield the list [1, 1, 4, 9, 25, 64]. Shapour Mohammadi, 2009. In recent years, new discrete-time chaotic systems, based on the logistic map, have been proposed. In fact, many researchers have. 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. An extensive survey of the correspond-. Interest in chaotic dynamics has grown explosively in recent years. 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. The synchronization system is designed via Lyapunov theory and chaoticity proves via Poincar´e maps and Lyapunov exponents will be pro-. The statistical properties of chaotic binary sequences generated by the Bernoulli map and Walsh functions are discussed. For simplicity, we consider the reﬂecting symmetry in G(yn): G(2yn)5 2G(yn). Changing the system parameter or initial conditions alters the dynamics of the system, therefore, exhibiting chaotic behavior []. Unlike other functions and the return statement, Console() doesn't actually return a value; rather, it logs messages in a separate window for inspection purposes only. Maps may be parameterized by a discrete-time or a continuous-time parameter. The story of robotics over the past four decades is one of complicated machines that don't work - or, anyway, not for long. Chaotic maps are evolution functions that exhibits chaotic behavior. They are derived systematically by using multiplication formulas of the elliptic functions. binary sequences that are orthogonal to each other. The proposed new chaos map has a better BER performance according to analysis of probability density function. Then for some well-defined square matrix A¡, with entries either zero or one,. 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. A multiobjective fitness function for genetic algorithm is designed to find the optimal parameter of beta chaotic map. The logistic map models the evolution of a population, taking into account both reproduction and density-dependent mortality (starvation). Chaotic itinerancy based on attractors of one-dimensional maps where g is a chaotic map. Compared with the classical Quadratic map, the proposed Quadratic map demonstrates better chaotic properties for encryption such as a much larger maximal Lyapunov exponent. (a) Skew tent map fr(s); (b) the orbit s(n, 0. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Functions That Read and Write Files in Compressed Formats. Then, they propose to use other chaotic maps like Piece Wise Linear Chaotic Map (PWLCM). You'll see that for 0 < r < 3 there's a singular peak in "accumulation", and from 3 < r < 4 there are two points, and at r = 4 there's zero accumulation in any region. A chaos system also creates a random behavior subsequently, but at the same time a chaos system is wholly deterministic. Supporting Functions Map. 1 Logistic Map One of the simplest chaotic functions that have been studied. What makes the dynamical system “chaotic” is the fact that orbits arising from initial data which are arbitrarily close grow apart exponentially. Both transmitter and receiver use conversions between voltage and time to implement nonlinear tent-map functions. The Logistic map is a classic non-linear chaotic function which has complex chaotic behavior. Recently Li and Yorke introduced the notion of chaos for mappings from the class C°(/, /), where / is a compact real interval. Please don't PM a user in the channel without asking first, some find it rude. Itis to be emphasized that the existing chaotic hash functions in the literatureuse a multitude of chaotic maps whereas we show in this paperthat using two chaotic maps judiciously achieves a secure hash function. iter : It is a iterable which is to be mapped. Applications to practically every scientific field have had far-reaching impact. Chaotic systems have the property of being deterministic in microscopic space and behave randomly, when observed in a coarse-grained state-space. The Security of our proposed protocol is given in Section 5. What is Chaotic Map? Definition of Chaotic Map: Some kind of evaluation function that include chaotic behaviors. Microphone Mute Proximity com/education. 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. Shapour Mohammadi, 2009. A new hash function system, based on coupled chaotic map dynamics, is suggested. 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. binary sequences that are orthogonal to each other. Handle: RePEc:boc:bocode:t741513. UNIVERSITE DE NANTES, 2019. Digital video and image cryptography is based on non linear trigonometric functions sine and cosine chaotic map. Based on its Lyapunov exponents and entropy measure, the characteristics of the new mathematical function are better. Printing Mindmaps. The most attractive features of. We can see that for any value of the iterates will be quickly pushed below -1. 5 Exploring the logistic map We are now going to use a pre-written set of commands known as a “script” or a “function” do these repeated calculations for us. As such, researchers have utilized them in the design of algorithms such as hash functions. 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 functions numerically compute a solution of the fractional nonlinear differential equations, which describe the chaotic system. Those are chaotic systems, and it's true for this function when r = 4. Chaotic Robotics Mark Tilden is building them. We also show that the rounding operation and the finite precision arithmetic render the algorithm noninvertible. For most of our experiments, we used a 10 Volt peak-to-peak auditory oscillator set to 20 KHz. The algorithm uses permutations whose positions are computed and indexed by a standard chaotic function and a linear congruence. This technique is implemented in two layers to enhance the security level of the classical DRPE. Keywords: steganography, spatial domain, transform domain, DWT, chaos, logistic map, tent map, Henon map, embedding, extraction Abstract This article was withdrawn and retracted by the Journal of Fundamental and Applied Sciences and has been removed from AJOL at the request of the journal Editor in Chief and the organisers of the conference at. Sensitivity to initial condition and total chaotic range of FMM are medium. Here, as a newest. In order to generate chaotic behavior, f( ) must be a nonlinear function. But ]0,1[ is isomorphic to is an isomorphism), so the cardinal of is greater or equal than the cardinality of R. If f1(x 0;ﬁ) and f2(y ;ﬁ) are. In this paper, we propose a novel hash function based on irregularly decimated chaotic map. Devaney, 2003) where the logistic map is referred to as the quadratic map. Based on a chaotic system, a hash construction which. 1 Logistic Map One of the simplest chaotic functions that have been studied. The color map runs between 0 (white) and 8 (black). Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Further, a one-way coupled chaotic map lattice was used by Huaping et al [43] for generating pseudo-random numbers. So map square [1, 1, 2, 3, 5, 8] would yield the list [1, 1, 4, 9, 25, 64]. This paper serves as an introduction to the analysis of chaotic systems, with techniques being developed by working through two famous examples. Discrete maps usually take the form of iterated functions. Chaotic cryptography [1] deals with hiding and recover-ing of secret messages using algorithm which consists of encryption rule that uses chaotic functions (analog or di- gital). In the group of chaotic maps, the 1D chaotic maps have lots of applications because of their simple structure. map and is more security; besides, it is robust to the common signal attacks. The formulation of Logistic map is as follows, [mathematical expression not reproducible] (1). To generate more uniform density function maps, two modified versions of the proposed Mehrab map are also defined. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to. The formulation of Logistic map is as follows, [mathematical expression not reproducible] (1). 0979659811419. A secure image encryption algorithm based on chaotic maps and SHA-3 G. using chaotic maps in standard model. DNAG Decade Map blackwell91 0 324 Blanco, M. It is a recurrence relation, shown by:. Most PSO methods use the same chaotic map, namely a logistic map [16]. �tel-02271074�. We show that the encryption function is not well-defined for some values. JERK FUNCTIONS Recently Gottlieb9 pointed out that the simplest ODE in a single variable that can exhibit chaos is third order, and he suggested searching for chaotic systems of the form ^x5j(x,x˙,x¨), where j is a jerk function ~time derivative of acceleration!. Chaotic definition, completely confused or disordered: a chaotic mass of books and papers. The proposed methods use. 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. ; Just find the global maximum (or minimum) point. The hash function called SHAH is based on two Tinkerbell maps filtered with irregular decimation rule. For the canonical values the Hénon map is chaotic. The existence of a chaotic phase is a common property of large networks of neurons with random connectivity [1, 2]. 2 (The exponential map is chaotic). The system parameter for the both chaotic maps is kept same and is in the chaotic regime. For simplicity, we consider the reﬂecting symmetry in G(yn): G(2yn)5 2G(yn). (a) coverage under logistic map, (b) coverage under tent map. All of the chaotic maps listed in Table 1 are in real space domain. In the group of chaotic maps, the 1D chaotic maps have lots of applications because of their simple structure. 1 Logistic Map One of the simplest chaotic functions that have been studied. In order to improve the security performance of the image encryption algorithm, the concept of shuffling the positions of pixels in the. Please don't PM a user in the channel without asking first, some find it rude. dissipative chaotic system and can be used to reveal its dynamical properties. The inherent characteristics of chaos can improve PSO by enabling it to escape from local solutions, and thus boost the global search capability of PSO [15]. Firey Algorithm combined with chaotic map Masaki Moriyama, Masaki Takeuchi, Yoko Uwate and Yoshifumi Nishio Departmrnt of Electrical and Electronic Engineering, Tokushima University 2-1 Minami-Josanjima, Tokushima 770-8506, Japan more functions and insert other chaotic maps. fractional. 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. With this construction, is onto. In conjunction with a master thesis about chaotic maps I develop a Python code to analyze and plot these diagrams. Using Logistic map as a chaotic sequence generator and bitXOR operator for encrypting the image values an image. Dual Watermarking Technic using Chaotic Map And Discrete Wavelet Transform. The computation of a chaotic map M. 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 quasi-chaotic nonlinear filter was used in , and the piecewise linear chaotic map was used by Hasan and Wang et al. It is chaotic when its parameters have values of a = 1. mﬁle that you downloaded, using the menu items File → Open. Chaotic map synonyms, Chaotic map pronunciation, Chaotic map translation, English dictionary definition of Chaotic map. 1 Logistic Map One of the simplest chaotic functions that have been studied. Solvable chaotic maps having the given invariant measure ρ (x) = An / √{ 1 - x2n } of n = 2 and n = 3 are obtained. The An Introduction to Chaotic Dynamical Systems (Studies in Nonlinearity) is not a book for the faint hearted however it does provide a very good mathematical overview of the subject. DNAG Decade Map blackwell91 0 324 Blanco, M. CHAOTIC MAP AND WATERMARKING A chaotic map is an evaluation function that exhibits some sorts of chaotic behavior. (1) To employ 10 different chaotic maps through normalized function to propose chaotic variants of GOA. Next, a novel chaotic maps problem is described in Section 3. Using chaotic function scientists projected a theory that can be mathematically explained known as chaos theory [1. The hash functions are the most useful primitives in cryptography. Based on simplest 2-D chaotic maps, a new hash function has been proposed and analyzed in this paper. Due to the disadvantages of logistic map, different versions of chaotic maps have been developed. The Walsh functions are based on a 2 k × 2 k Hadamard matrix. This binary string is then hashed to produce a second binary string. Maps may be parameterized by a discrete-time or a continuous-time parameter. >>> main() This program illustrates a chaotic function Enter a number between 0 and 1:. For example, it has been shown that with Devaney’s de nition of chaos the bonding function is chaotic if and only if the shift map is chaotic. The coding technique to handle this sort of scatter-plot at speed is to avoid calling the graphics library functions from within the loops but just use Python's built-in "lists" to hold the plotting surface, and only call the graphics library when the whole image is complete and ready for output. One of the simplest examples of a chaotic maps is the so-called. 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. 1 Analysis of the improved logistic map. 1993 The P-wave velocity structure of the mantle below the Iberian Peninsula: evidence for subducted lithosphere below Southern Spain. During the last few years, considerable effort has been devoted to research on chaos-based hash functions. Chaotic maps are evolution functions that exhibits chaotic behavior. , the Bernoulli map and the tent map. 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. Changing the system parameter or initial conditions alters the dynamics of the system, therefore, exhibiting chaotic behavior []. A multiphase symmetric key encryption algorithm was proposed by the author using finite field cosine transformation (FFCT) in which A fractal is used as a source of one-time-pad keystream, provides a secure cryptosystem [15]. Chaotic system exhibit dynamics that are sensitive to initial conditions [1, 19]. In order to generate chaotic behavior, f( ) must be a nonlinear function. Diverse chaotic maps have been used for image encryption in different schemes. chaotic map, Rastrigin function whose dimensions are set to. Neotectonics of North America Geol. The principle of the method consists in mixing three chaotic maps produced from an input initial vector. What makes the dynamical system "chaotic" is the fact that orbits arising from initial data which are arbitrarily close grow apart exponentially. Maps may be parameterized by a discrete-time or a continuous-time parameter. Two things we might want to do with a function: Represent the whole function over its range. Discrete maps usually take the form of iterated functions. However, it requires certain parameters to encrypt these coefficients. 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. The study validates the proposed system's performance with a range of nonlinear test functions. 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. When the system is not in a proper order then it is said to exhibit chaos. At the same time, for any periodic point of the mapping function f(x), there is no correlation in all subsets. 999 (Completely Chaotic). Different from the other chaotic maps, Hénon map is a two-dimensional nonlinear system. 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. The proposed methods use. Graph of function (1) is a group of lines. The sensitivity of chaotic maps to initial conditions makes them optimum candidates to relate minimal critical information about the input, in the output sequence. JERK FUNCTIONS Recently Gottlieb9 pointed out that the simplest ODE in a single variable that can exhibit chaos is third order, and he suggested searching for chaotic systems of the form ^x5j(x,x˙,x¨), where j is a jerk function ~time derivative of acceleration!. Keywords: Chaotic functions, Entropy, Logistic Map, One Dimensional Chaotic functions, Tent Map. The researchers in [9], [10], proved that logistic map, that was widely used in the encryption domain, is not enough random and uniform. Here are the first 1000 iterations starting from each of $4. Fluctuations of absorption coefficient will be calculated as a function of temperature modeled in terms of these maps, and the emis- sion from flames will be quantified in terms of parameters of the chaotic maps. In the receiver side, a synchronizer reconstructs the chaotic oscillator signals, one of which is used for the decryption of the message. In geophysics, my background, it can help explain the reversals of Earth's magnetic field, for example. If the hash function is chaotic, then the seed data should have strange attractors. State space coverage by chaotic trajectories. 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. Three resourceful chaotic functions in the literature are evaluated to find the best strategy for ABO improvement. The formula of this function is as follows (N. Etemadi and Eshghi present a new permutation-substitution image encryption architecture using chaotic maps and Tompkins Paige algorithm [9]. The synchronization system is designed via Lyapunov theory and chaoticity proves via Poincar´e maps and Lyapunov exponents will be pro-. Discrete maps usually take the form of iterated functions. 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. 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. Neotectonics of North America Geol. For ease of analysis, this differential equation is first converted to a nondimensional form by defining , , , and , where is the pendulum's. Here are the first 1000 iterations starting from each of$4. As this situation is a discrete. Plotting the bifurcation diagram of a chaotic dynamical system. mﬁle that you downloaded, using the menu items File → Open. The statistical properties of chaotic binary sequences generated by the Bernoulli map and Walsh functions are discussed. We see that after one application of f c, there are no points in [-x 2 , c). 10, 20, 30, 40 and 50 resp ectively are used as the test. The study validates the proposed system's performance with a range of nonlinear test functions. 5 Exploring the logistic map We are now going to use a pre-written set of commands known as a “script” or a “function” do these repeated calculations for us. as a potential inherent nonlinearity in various chaotic maps. Then for some well-defined square matrix A¡, with entries either zero or one,. The Baker Map is an extension of 1D Tent map. 2, 1 (2008), 203-221. CBBO11 to CBBO20 have chaotic migration operator. 5 1 0 50 10 10 20 50 0. If so, then I may be able to map a seed to its attractor and "pre-mine" using attractor buckets. Discrete maps usually take the form of iterated functions. , momentum and coordinate $$(p,x)$$. State space coverage by chaotic trajectories. The proposed example is studied by using the -rst return map in I, which we prove to be chaotic in I making. Project of a chaotic map rng analog to previous ones, but including a von neumann corrector useful to force the probabilities of 0 and 1 to 0. fractional. Spakman, W. Further, a one-way coupled chaotic map lattice was used by Huaping et al [43] for generating pseudo-random numbers. The starting point is a pendulum consisting of two point masses, m, and m2, suspended by massless wires of length l1 and l2. The segment I c = [-x 2 , x 2] is mapped into itself (here x 2 is the right repelling fixed point). 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. At the same time, for any periodic point of the mapping function f(x), there is no correlation in all subsets. Novel chaos-based hash algorithm, which uses m-dimensional Cat map, is proposed in [16] and improved in [7]. For a more recent textbook for beginners, read Non Linear Dynamics and Chaos (Steven H. Published on Jan 29, 2020. The functions of two maps are shown as follows. 1 Proposed Algorithm for Hash Function Based on Combination of Chaotic Maps 136 5. 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. Chaotic Map Based DSSS (https: PROBLEM: Variable 'msg' is character type variable! Some functions in DSSS. Three resourceful chaotic functions in the literature are evaluated to find the best strategy for ABO improvement. Owing to the exceptionally desirable properties of mixing and sensitivity to initial conditions and parameters of chaotic maps, chaos-based encryption has suggested a new and efficient way to deal with the intractable problem of fast and highly secure image encryption. rng07-vhdl Same as previous project, but the file randgen_package. f ( x 1) ≠ f ( x 2) w h e n e v e r x 1 ≠ x 2. Michele Boldrin & Nicola Perisco, 1993. That mean the applicability of chaotic maps work with networks security, the algorithm improves Feistel network and build a cubic chaotic map function and its keys spaces was large, generated by the compound chaotic sequence (9). The sine and cosine chaotic map is generated for high-intense of chaos over most regions of image to increase confidentiality of information. Nonlinear dynamical systems, describing changes in variables over time, may appear. 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 , ,. 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. The performance of that scheme is evaluated through statistical analysis. iter : It is a iterable which is to be mapped. com: The design source for electronics engineers and managers worldw oversight, though, threaten to mute the volume. As is well-known, the mathematical form of the SLE can be transformed into the stochastic differential equation (SDE). Neotectonics of North America Geol. 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. Chaotic maps often generate fractals. Many of the proposed digital chaotic ciphers have used different chaotic maps, such as the 2-D Hénon attractor in and. 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. Using chaotic function scientists projected a theory that can be mathematically explained known as chaos theory [1. Then, the non-interactive twin chaotic maps-key exchange protocol is given in Section 4. DNAG Decade Map blackwell91 0 324 Blanco, M. Discrete maps usually take the form of iterated functions. The most attractive features of. 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]. A multiphase symmetric key encryption algorithm was proposed by the author using finite field cosine transformation (FFCT) in which A fractal is used as a source of one-time-pad keystream, provides a secure cryptosystem [15]. The chaos streams are generated by using various chaotic maps. where fis a smooth function on Rm. This is an extremely desirable property as the map function cannot be exactly realized due to process variations. The performance of that scheme is evaluated through statistical analysis. Among the various maps, four maps are investigated and their characteristics are analyzed. An image encryption scheme with a pseudorandom permutation based on chaotic maps. Application and Development of Enhanced Chaotic Grasshopper Optimization Algorithms 2D-SLMM is derived from two 1D chaotic maps , the Logistic and Sine maps. Here, as a newest. In order to improve the security performance of the image encryption algorithm, the concept of shuffling the positions of pixels in the. This model uses a novel parallel chaotic hashing model for single chaotic system to create an n-bit. However, it requires certain parameters to encrypt these coefficients. 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. In this paper, we introduce two simple chaotic 2D No Equilibria Maps (NEM). Chaotic cryptography [1] deals with hiding and recover-ing of secret messages using algorithm which consists of encryption rule that uses chaotic functions (analog or di- gital). The formulation of Logistic map is as follows, [mathematical expression not reproducible] (1). Logistic, Cubic and Ricker's (Chen and Huang, 2011) are one-dimensional maps while Hénon and Ikeda (Driebe, 1999) are in two dimensional space. "CHAOTICMAPS: MATLAB function to generate chaotic 1D and 2D discrete maps," Statistical Software Components T7415013, Boston College Department of Economics. 303213732397 0. If f1(x 0;ﬁ) and f2(y ;ﬁ) are. Advantages: Sensitivity to primary conditions Apparently accidental feature Deterministic work 7 Logistic Map Signal r=3. Our study shows that when the driver and the response systems are fed by common noise, the noise does not affect synchronization. With the development of image encryption technology, it is also about the. Chaotic functions Functions where "nearby" Input does not generate "nearby" Output. Digital video and image cryptography is based on non linear trigonometric functions sine and cosine chaotic map. 2013040102: Recently, a parallel hash function based on chaotic maps with changeable parameters was proposed by Li et al (2011, pp. chaotic maps used in the paper are: Logistic Map The system should be highly unpredictable. Chaotic functions. This map can be parameterized by discrete-time or continuous-time. They are derived systematically by using multiplication formulas of the elliptic functions. Logistic maps Chaotic sequences are generated using discrete chaotic functions. A chaotic map is, roughly speaking, a function that when iterated a large number of times behaves in unpredictable ways. scheme is constructed based on chaotic maps. Systems of diffusively coupled chaotic maps. Unlike a single-modal chaotic map, i. Graph of function (1) is a group of lines. algorithms based on chaotic maps like the Logistic map [5-7], the Standard map[8], the Baker map [9, 10], the PWNLCM [11] the Cat map [12, 13], the Chen map [6, 13], etc. However, it requires certain parameters to encrypt these coefficients. If f1(x 0;ﬁ) and f2(y ;ﬁ) are. map and is more security; besides, it is robust to the common signal attacks. 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. Recently, many papers have been dedicated to exactly solvable chaotic maps [3-7, 18-21]. 1 Introduction At the Crypto 2005 rump session [1], a new hash function was designed based upon chaos theory. The ﬁrst layer is a pre-processing layer, which is performed with the chaotic Baker map on the original image. In this section, we briefly review one of the named Logistic map. 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. 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]. chaotic maps with rational zeta function 707 a subset of the absorbing boundary of the interval, is contained in some compact subset of the interval, and this compact set does not contain critical points of f. Chui, A symmetric image encryption scheme based on 3D chaotic cat maps, Chaos Solitons Fractals, 21 (2004) 749-761. chaotic map, Rastrigin function whose dimensions are set to. We consider a chaotic time series derived by a logistic map (a demographic model of the population biomass of species in the presence of limiting factors such as food supply or disease) that is non-stationary in the sense that the underlying parameter is not fixed but is varying smoothly in time. A secure pseudo-random number generator three-mixer is proposed. Furthermore. The formulation of Logistic map is as follows, [mathematical expression not reproducible] (1). Chaotic maps often occur in the study of dynamical systems. Plotting the bifurcation diagram of a chaotic dynamical system. Printing Mindmaps. A function is preformed to each sub block of 4 by 4 of S, the result is noted T. The ﬁrst layer is a pre-processing layer, which is performed with the chaotic Baker map on the original image. A chaotic transmitter and a synchronized chaotic receiver have been designed in a 0. 6 and (c) Lyapunov exponent ofthe chaotic orbits as a function of a. Chaotic maps have various properties that mirror the security requirements of cryptographic algorithms. 19 synonyms for chaotic: disordered, confused, uncontrolled, anarchic, tumultuous, lawless, riotous. Logistic Map. 1 423-437 Geol. function, chaotic maps for the authentication, integrity, confidentiality. The logistic map models the evolution of a population, taking into account both reproduction and density-dependent mortality (starvation). We will draw the system's bifurcation diagram, which shows the possible long-term behaviors (equilibria, fixed points, periodic orbits, and chaotic trajectories) as a function of the system's parameter. Inverse problem in chaotic map theory is formulated. Chaotic itinerancy based on attractors of one-dimensional maps where g is a chaotic map. The quasi-chaotic nonlinear filter was used in , and the piecewise linear chaotic map was used by Hasan and Wang et al. Project of a chaotic map rng analog to previous ones, but including a von neumann corrector useful to force the probabilities of 0 and 1 to 0. Our analysis adapts to discrete-time (maps) the. 2 (The exponential map is chaotic). , it is not required that all maps in the ensemble are the same). DNAG Decade Map blackwell91 0 324 Blanco, M. The Chirikov standard map, is an area-preserving map for two canonical dynamical variables, i. In this section, we briefly review one of the named Logistic map. At the Crypto 2005 rump session, a new hash function based upon a chaotic map was presented. In the last decade, various hash functions based on chaotic maps are proposed. Any of various general mathematical theories of chaotic dynamical systems, such as the complex or nonlinear systems found in weather patterns,. 4: Fixed points and derivatives of f(x,r,γ)=rsinγ(πx)for different values of γ. We consider a chaotic time series derived by a logistic map (a demographic model of the population biomass of species in the presence of limiting factors such as food supply or disease) that is non-stationary in the sense that the underlying parameter is not fixed but is varying smoothly in time. The Security of our proposed protocol is given in Section 5. More detailed descriptions and properties of these chaotic maps can be found in [17, 29]. 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. In case anyone else is interested, the following reference mentions it: C. Moreover in this paper, an algorithm for one way hash function construction based on chaos theory is introduced. We chose an audio oscillator over a digital function generator because the synthesized sine waves produced by digital function. Functions This work embeds ten chaotic maps into the gravitational constant (G) of the recently proposed population-based meta-heuristic algorithm called Gravitational Search Algorithm (GSA). Overall, the use of the uniform pseudorandom number distribution generated by the tent map produced the most accurate results. A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. This map has chaotic behavior in range [1. General Chaotic Maps In general, chaotic maps are obtained by a deterministic rule: x t = f(x t-1,x t-2,). 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. K-Means Live k-means on a video feed with Lloyd's algorithm Moiré Just moiré Ikeda Map A discrete chaotic attractor Hertzsprung-Russell Diagram Star magnitudes and temperatures Mandelbrot Drawing the first iterations of the Mandelbrot set as a complex function Pulsar Signals and noise (no physical significance) Multiscale Turing Patterns Multiscale turing patterns, as described by Jonathan. Although a fractal may be constructed by an iterative. The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. From what I understand, hash functions are pseudorandomly generated based on the initial seed (the raw data). Application and Development of Enhanced Chaotic Grasshopper Optimization Algorithms 2D-SLMM is derived from two 1D chaotic maps , the Logistic and Sine maps. 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. Plotting the bifurcation diagram of a chaotic dynamical system. Numerical techniques to generate well defined random numbers with high quality are also demonstrated. The statistical properties of chaotic binary sequences generated by the Bernoulli map and Walsh functions are discussed. Graph of function (0) is a curve. The quasi-chaotic nonlinear filter was used in , and the piecewise linear chaotic map was used by Hasan and Wang et al. While the evolution of under the map is chaotic it is not entirely random. In mathematics, a chaotic map is a map (= evolution function) that exhibits some sort of chaotic behavior. Project of a chaotic map rng analog to previous ones, but including a von neumann corrector useful to force the probabilities of 0 and 1 to 0. 999 (Completely Chaotic). 10,11 He showed that case A in Ref. The essence of the chaotic system belongs to a nonlinear system, but compared with the usual nonlinear system, the. The Lyapunov number λ is also computed exactly for each map function, which is expressed commonly by λ = log m in terms of the. The paper is organized as follows: Section presents the 2 properties of keyed hash functions. Geospatial data, like other files, are frequently stored and transmitted in compressed or archive formats, such a tar, zip, or GNU zip. 8, x˙5y, y˙52x1yz, z˙512y2, ~4!. As we know, piecewise linear chaotic maps (PLCM) are the simplest kind of chaotic maps from the viewpoint of realization. Discrete maps usually take the form of iterated functions. 1 Logistic Map The logistic map takes places of chaotic behaviors of biological population [20]. Logistic maps Chaotic sequences are generated using discrete chaotic functions. 6 and (c) Lyapunov exponent ofthe chaotic orbits as a function of a. In this brief, we propose a new 2/spl lscr/ -bit iterated hash function based on chaotic tent maps. The hash function called SHAH is based on two Tinkerbell maps filtered with irregular decimation rule. Simple piecewise affine input-output (I/O) characteristics have been extensively used for the generation of random bits, e. Another hash function based on a Cat map, is deﬁned in [10]. In fact, many researchers have. ( 1) and ( 2. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. 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. (It is Xn+1 = f(Xn, Xn-1) type function. image encryption based on chaotic Baker map and Double Random Phase Encoding (DRPE). The system parameter for the both chaotic maps is kept same and is in the chaotic regime. Then, they propose to use other chaotic maps like Piece Wise Linear Chaotic Map (PWLCM). 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. function that maps the previous state to the next state. 42857129819234609814 and again, getting: 0. Inverse problem in chaotic map theory is formulated. 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. The ﬁrst layer is a pre-processing layer, which is performed with the chaotic Baker map on the original image. 1993 The P-wave velocity structure of the mantle below the Iberian Peninsula: evidence for subducted lithosphere below Southern Spain. Chaotic Time Series Modelling Description. Three different benchmark functions are selected from the IEEE CEC 2013 competition benchmark set. CBBO21 to CBB30 have chaotic mutation operator. The story of robotics over the past four decades is one of complicated machines that don't work - or, anyway, not for long. The inherent characteristics of chaos can improve PSO by enabling it to escape from local solutions, and thus boost the global search capability of PSO [15]. Chaos theory has found uses across a broad set of scientific fields to explain some complicated observed behavior. The coding technique to handle this sort of scatter-plot at speed is to avoid calling the graphics library functions from within the loops but just use Python's built-in "lists" to hold the plotting surface, and only call the graphics library when the whole image is complete and ready for output. Logistic, Cubic and Ricker's (Chen and Huang, 2011) are one-dimensional maps while Hénon and Ikeda (Driebe, 1999) are in two dimensional space. !6" demonstrates the existence of chaotic jerk functions with only quadratic nonlinearities, it is interesting to identify the simplest such function. 1 Selected Chaotic System The two-dimensional Hénon map was chosen as the chaotic system: (1) x n+1 = a–x n 2 +by yn+1 = xn. 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. The proposed method uses a new special case of discrete chaotic map based on the composition of permutations, in order to overcome the problem with potentially short length of the orbits. Unlike other functions and the return statement, Console() doesn't actually return a value; rather, it logs messages in a separate window for inspection purposes only. coupled chaotic maps. 303213732397 0. = For the canonical values the Hénon map is chaotic. Both transmitter and receiver use conversions between voltage and time to implement nonlinear tent-map functions. Although the function is extremely e cient, it. In 2004 Fu et al [42] proposed a chaos-based random number generator using piecewise chaotic map. 6) In the following arguments, we show that our model also reduces to Langevin-like. beclassified as chaotic. But if we sacrifice invariability temporarily, thereby introducing singularities, one dimensional chaotic map can be easily. We also show that the rounding operation and the finite precision arithmetic render the algorithm noninvertible. Spakman, W. The system parameter for the both chaotic maps is kept same and is in the chaotic regime. The map is chaotic on the real line. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre. The formula of this function is as follows (N. Akerlof September 26, 2012 The following notes describe the kinematics of the double pendulum. Both transmitter and receiver use conversions between voltage and time to implement nonlinear tent-map functions. chaotic map, Rastrigin function whose dimensions are set to. Media in category "Chaotic maps" The following 23 files are in this category, out of 23 total. Design, implementation and analysis of keyed hash functions based on chaotic maps and neural networks. 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. Chaotic Function Based ECG Encryption System: 10. 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. So map square [1, 1, 2, 3, 5, 8] would yield the list [1, 1, 4, 9, 25, 64]. 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. Due to the disadvantages of logistic map, different versions of chaotic maps have been developed. One example is the known Logistic map[representedinFig. Although the function is extremely e cient, it. Once the tissues are expanded, antibodies are used to tag target structures or molecules, allowing researchers to use common microscopes. 156257842027 0. 1) Logistic map function One of the most popular and useful chaotic functions is the logistic map function described in Eq. Included are functions to simulate different types of chaotic time series maps. 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. !6" demonstrates the existence of chaotic jerk functions with only quadratic nonlinearities, it is interesting to identify the simplest such function. 4], for other values it. 5 1 0 50 10 10 20 50 0. The logistic map connects fluid convection, neuron firing, the Mandelbrot set and so much more. 565661470088 0. Figures 1(b) and 2(b) show the bifurcation diagram and the Lyapunov Exponent of the improved chaotic map. In this paper, a new efficient scheme for parallel hash function based on high-dimensional chaotic map is proposed. 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. 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. create the running total using data step lag function during data building time. functions based on chaotic maps and neural networks Nabil Abdoun To cite this version: Nabil Abdoun. Then, the non-interactive twin chaotic maps-key exchange protocol is given in Section 4. For K = 0 the stretching of ﬂuid elements is homogeneous in space. 958185428249 0. function that maps the previous state to the next state. 6 and (c) Lyapunov exponent ofthe chaotic orbits as a function of a. Baldur's Gate Durlag's Tower B3 - Trapped and locked stone on the north wall of the fiery bridge room. A collection and description of functions to investigate the chaotic behavior of time series processes. rng07-vhdl Same as previous project, but the file randgen_package. compared with the existing sine map and logistic chaotic maps. If the hash function is chaotic, then the seed data should have strange attractors. Based on its Lyapunov exponents and entropy measure, the characteristics of the new mathematical function are better. Based on simplest 2-D chaotic maps, a new hash function has been proposed and analyzed in this paper. The Logistic Map Introduction One of the most challenging topics in science is the study of chaos. tigates TRI using a system of chaotic maps. INTRODUCTION Chaotic term is coined from the word chaos. 4: Fixed points and derivatives of f(x,r,γ)=rsinγ(πx)for different values of γ. 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. This paper proposes a new hybrid chaotic map and a different way of using optimization technique to improve the performance of encryption algorithms. In conjunction with a master thesis about chaotic maps I develop a Python code to analyze and plot these diagrams. A damped and driven pendulum is one of the simplest systems to use in the study of chaos. 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. 0979659811419. The functions of two maps are shown as follows. This map can be parameterized by discrete-time or continuous-time. Chaotic itinerancy based on attractors of one-dimensional maps where g is a chaotic map. Slight changes in the initial conditions therefore result in massive alterations in the final outcome. The proposed method uses a new special case of discrete chaotic map based on the composition of permutations, in order to overcome the problem with potentially short length of the orbits. For Sa˜o Paulo J. The chaotic maps used in numeric calculations are given below: 3. 1 423-437 Geol. (A) The average permutation Lyapunov exponent λ D as a function of the chaotic parameter of the underlying map T and the message length L. Chaotic map synonyms, Chaotic map pronunciation, Chaotic map translation, English dictionary definition of Chaotic map. The first map is the Chepyshev chaotic map, which is used for the permutation of the pixels of the image. dissipative chaotic system and can be used to reveal its dynamical properties. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. chaotic maps with rational zeta function 707 a subset of the absorbing boundary of the interval, is contained in some compact subset of the interval, and this compact set does not contain critical points of f. Hashing performances are evaluated in terms of original message condition changes, statistical analyses, and collision analyses. In this paper it is investigated the effect of tuning of control parameters of the Lozi Chaotic Map employed as a chaotic pseudo-random number generator for the particle swarm optimization algorithm. Discrete maps usually take the form of iterated functions. Khade and Prof. Hashing performances are evaluated in terms of original message condition changes, statistical analyses, and collision analyses. So the cardinal of the Cartesian. Graph of function (0) is a curve. So map square [1, 1, 2, 3, 5, 8] would yield the list [1, 1, 4, 9, 25, 64]. 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]. A function is preformed to each sub block of 4 by 4 of S, the result is noted T. Isola, Orderings of the rationals and dynamical systems, Colloquium Mathematicum 116, 2 (2009). A multiobjective fitness function for genetic algorithm is designed to find the optimal parameter of beta chaotic map. binary sequences that are orthogonal to each other. The same strategy is applied across the algorithms under study to provide an unbiased judgment. This function takes two arguments: a function f which maps as to bs, and a list xs of as. You'll see that for 0 < r < 3 there's a singular peak in "accumulation", and from 3 < r < 4 there are two points, and at r = 4 there's zero accumulation in any region. Published on Jan 29, 2020. Trajectories from six landmarks (two hands, two feet, the head, and the body center) on human body are used as input to our method. NOTE : You can pass one or more iterable to the map () function. The algorithm uses permutations whose positions are computed and indexed by a standard chaotic function and a linear congruence. "CHAOTICMAPS: MATLAB function to generate chaotic 1D and 2D discrete maps," Statistical Software Components T7415013, Boston College Department of Economics. 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 example is the known Logistic map[representedinFig. The improved chaotic map is examined by the bifurcation diagram and by Lyapunov exponent at the value of k= 8. 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. Michele Boldrin & Nicola Perisco, 1993. Chaotic maps are evolution functions that exhibits chaotic behavior. -1 100150 200 250. Project of a chaotic map rng analog to previous ones, but including a von neumann corrector useful to force the probabilities of 0 and 1 to 0. 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. 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. A novel chaotic pulse sequence generator is presented, which includes a tent map function subcircuit and an iterative operation subcircuit. 974215686851 0. Chaotic maps often generate fractals. (A) Map of the largest groove systems in the chaotic terrain antipodal to the Caloris basin. In this paper it is investigated the effect of tuning of control parameters of the Lozi Chaotic Map employed as a chaotic pseudo-random number generator for the particle swarm optimization algorithm. Design, implementation and analysis of keyed hash functions based on chaotic maps and neural networks. Electrocardiogram (ECG)) over insecure networks. DNAG Decade Map blackwell91 0 354 Blanco, M. 823973143043 0. Sensitivity to initial condition and total chaotic range of FMM are medium. 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 , ,. From what I understand, hash functions are pseudorandomly generated based on the initial seed (the raw data). 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. SMÍTAL Abstract.