A SVD-Chaos Digital Image Watermarking Scheme Based on Multiple Chaotic System
20 Sep 2012-pp 9-18
TL;DR: In this paper, a new watermarking scheme for Gray scale image is proposed based on a family of chaotic maps and Singular Value Decomposition, Jacobian elliptic map is used to encrypt the watermark logo to improve the security of watermarked image.
Abstract: In this letter a new watermarking scheme for Gray scale image is proposed based on a family of the chaotic maps and Singular Value Decomposition. Jacobian elliptic map is used to encrypt the watermark logo to improve the security of watermarked image. Quantum map is also used to determine the location of image’s block for the watermark embedding. To test the robustness and effectiveness of our proposed method, several attacks are applied to the watermarked image and the best results have been reported. The purpose of this algorithm is to improve the shortcoming of watermarking such as small key space and low security. The experimental results demonstrate that the key space is large enough to resist the attack and the distribution of grey values of the encrypted image has a random-like behavior, which makes it a potential candidate for encryption of multimedia data such as images, audios and even videos.
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TL;DR: In this paper, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
Abstract: Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic Family Symbolic Dynamics Topological Conjugacy Chaos Structural Stability Sarlovskiis Theorem The Schwarzian Derivative Bifurcation Theory Another View of Period Three Maps of the Circle Morse-Smale Diffeomorphisms Homoclinic Points and Bifurcations The Period-Doubling Route to Chaos The Kneeding Theory Geneaology of Periodic Units Part Two: Higher Dimensional Dynamics Preliminaries from Linear Algebra and Advanced Calculus The Dynamics of Linear Maps: Two and Three Dimensions The Horseshoe Map Hyperbolic Toral Automorphisms Hyperbolicm Toral Automorphisms Attractors The Stable and Unstable Manifold Theorem Global Results and Hyperbolic Sets The Hopf Bifurcation The Hnon Map Part Three: Complex Analytic Dynamics Preliminaries from Complex Analysis Quadratic Maps Revisited Normal Families and Exceptional Points Periodic Points The Julia Set The Geometry of Julia Sets Neutral Periodic Points The Mandelbrot Set An Example: the Exponential Function
104 citations
Journal Article•
TL;DR: The emerging discipline known as chaos theory is a relatively new field of study with a diverse range of applications (i.e., economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for ''chaos'' as it applies to general dynamical systems.
Abstract: Abstract : The emerging discipline known as \"chaos theory\" is a relatively new field of study with a diverse range of applications (i.e., economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for \"chaos\" as it applies to general dynamical systems. Various approaches range from topological methods of a qualitative description; to physical notions of randomness, information, and entropy in ergodic theory; to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantitative measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems, it serves as a complement to the work done by Philip Beaver, which details chaotic dynamics for discrete systems.
85 citations
01 Jun 2020
TL;DR: The use of the bifurcation diagram and Lyapunov exponent analysis showed that the proposed chaos game has the dynamical behavior, and fully chaotic characteristic, and can be used as a secure PRNG in cryptography systems.
Abstract: In this paper, a digital image encryption algorithm is proposed based on the generalized model of the chaos game. The chaos game is a well-known fractal, which acts as a pseudo-random number generator (PRNG) in the proposed encryption algorithm. The foundation of the chaos game is based on basic points and its distance ratio that determine the basis of how they distribute random values in 2D or 3D space. These basic points are entered by the user interface and are the result of an encrypted image with a fractal structure. The use of the bifurcation diagram and Lyapunov exponent analysis showed that the proposed chaos game has the dynamical behavior, and fully chaotic characteristic, and can be used as a secure PRNG in cryptography systems. In the proposed method, the region of interest is determined by a number of Bases, and the fractal mechanism of chaos game for the encryption process is performed on the image. This process is very sensitive to any changes in keys and refers to confusion. The evaluation results of security and performance analysis on standard images confirm the efficiency of the proposed method and demonstrate that the proposed method is robust against attacks.
62 citations
TL;DR: It can be concluded that, the proposed novel watermarking scheme for image authentication can be applied for practical applications.
Abstract: Hierarchy of one-dimensional ergodic chaotic maps with Tsallis type of q -deformation are studied. We find that in the chaotic region, these maps with q -deformation are ergodic as the Birkhoff ergodic theorem predicts. q -deformed maps are defined as ratios of polynomials of degree N . Hence, by using the Stieltjes transform approach (STA), invariant measure is proposed. In addition, considering Sinai-Ruelle-Bowen (SRB) measure, Kolmogorov-Sinai (KS) entropy for q -deformed maps is calculated analytically. The new q -deformed scheme have ability to keep previous significant properties such as ergodicity, sensitivity to initial condition. By adding q -parameter to the hierarchy in order increase the randomness and one-way computation, we present a new scheme for watermarking. The introduced algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security. To illustrate the effectiveness of the proposed scheme, some security analyses are presented. By considering the obtained results, it can be concluded that, this scheme have a high potential to be adopted for watermarking. It can be concluded that, the proposed novel watermarking scheme for image authentication can be applied for practical applications.
25 citations
References
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Book•
01 Jan 1986
TL;DR: In this article, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
Abstract: Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic Family Symbolic Dynamics Topological Conjugacy Chaos Structural Stability Sarlovskiis Theorem The Schwarzian Derivative Bifurcation Theory Another View of Period Three Maps of the Circle Morse-Smale Diffeomorphisms Homoclinic Points and Bifurcations The Period-Doubling Route to Chaos The Kneeding Theory Geneaology of Periodic Units Part Two: Higher Dimensional Dynamics Preliminaries from Linear Algebra and Advanced Calculus The Dynamics of Linear Maps: Two and Three Dimensions The Horseshoe Map Hyperbolic Toral Automorphisms Hyperbolicm Toral Automorphisms Attractors The Stable and Unstable Manifold Theorem Global Results and Hyperbolic Sets The Hopf Bifurcation The Hnon Map Part Three: Complex Analytic Dynamics Preliminaries from Complex Analysis Quadratic Maps Revisited Normal Families and Exceptional Points Periodic Points The Julia Set The Geometry of Julia Sets Neutral Periodic Points The Mandelbrot Set An Example: the Exponential Function
3,589 citations
TL;DR: In this paper, the problem of approximating one matrix by another of lower rank is formulated as a least-squares problem, and the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another.
Abstract: The mathematical problem of approximating one matrix by another of lower rank is closely related to the fundamental postulate of factor-theory. When formulated as a least-squares problem, the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another. The solution of the problem is simplified by first expressing the matrices in a canonic form. It is found that the problem always has a solution which is usually unique. Several conclusions can be drawn from the form of this solution. A hypothetical interpretation of the canonic components of a score matrix is discussed.
3,576 citations
Book•
23 Nov 2007
TL;DR: This new edition now contains essential information on steganalysis and steganography, and digital watermark embedding is given a complete update with new processes and applications.
Abstract: Digital audio, video, images, and documents are flying through cyberspace to their respective owners. Unfortunately, along the way, individuals may choose to intervene and take this content for themselves. Digital watermarking and steganography technology greatly reduces the instances of this by limiting or eliminating the ability of third parties to decipher the content that he has taken. The many techiniques of digital watermarking (embedding a code) and steganography (hiding information) continue to evolve as applications that necessitate them do the same. The authors of this second edition provide an update on the framework for applying these techniques that they provided researchers and professionals in the first well-received edition. Steganography and steganalysis (the art of detecting hidden information) have been added to a robust treatment of digital watermarking, as many in each field research and deal with the other. New material includes watermarking with side information, QIM, and dirty-paper codes. The revision and inclusion of new material by these influential authors has created a must-own book for anyone in this profession.
*This new edition now contains essential information on steganalysis and steganography
*New concepts and new applications including QIM introduced
*Digital watermark embedding is given a complete update with new processes and applications
1,773 citations
01 Dec 1992
TL;DR: The emerging discipline known as chaos theory is a relatively new field of study with a diverse range of applications (i.e., economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for "chaos" as it applies to general dynamical systems.
Abstract: : The emerging discipline known as "chaos theory" is a relatively new field of study with a diverse range of applications (i.e., economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for "chaos" as it applies to general dynamical systems. Various approaches range from topological methods of a qualitative description; to physical notions of randomness, information, and entropy in ergodic theory; to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantitative measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems, it serves as a complement to the work done by Philip Beaver, which details chaotic dynamics for discrete systems.
1,220 citations
TL;DR: A new approach to mask the watermark according to the characteristics of the human visual system (HVS) is presented, which is accomplished pixel by pixel by taking into account the texture and the luminance content of all the image subbands.
Abstract: A watermarking algorithm operating in the wavelet domain is presented. Performance improvement with respect to existing algorithms is obtained by means of a new approach to mask the watermark according to the characteristics of the human visual system (HVS). In contrast to conventional methods operating in the wavelet domain, masking is accomplished pixel by pixel by taking into account the texture and the luminance content of all the image subbands. The watermark consists of a pseudorandom sequence which is adaptively added to the largest detail bands. As usual, the watermark is detected by computing the correlation between the watermarked coefficients and the watermarking code, and the detection threshold is chosen in such a way that the knowledge of the watermark energy used in the embedding phase is not needed, thus permitting one to adapt it to the image at hand. Experimental results and comparisons with other techniques operating in the wavelet domain prove the effectiveness of the new algorithm.
949 citations