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On the Security of ``Golden'' Cryptography  [cached]
a?ngel Marti-n del Rey,Gerardo Rodri-guez Sa?nchez
International Journal of Network Security , 2008,
Abstract: In this paper the security of ``golden'' cryptography, which has been proposed recently, is tackled. Specifically, it is shown that the security of such cryptosystem is trivially compromised as it does not pass one of the basic cryptanalytic attacks: the chosen plaintext attack.
The Fast Haar Wavelet Transform for Signal & Image Processing  [PDF]
V. Ashok,T. Balakumaran,C. Gowrishankar,I. L. A. Vennila,A. Nirmal kumar
Computer Science , 2010,
Abstract: A method for the design of Fast Haar wavelet for signal processing and image processing has been proposed. In the proposed work, the analysis bank and synthesis bank of Haar wavelet is modified by using polyphase structure. Finally, the Fast Haar wavelet was designed and it satisfies alias free and perfect reconstruction condition. Computational time and computational complexity is reduced in Fast Haar wavelet transform.
Discrete differential operators in multidimensional Haar wavelet spaces
Carlo Cattani,Luis M. Sánchez Ruiz
International Journal of Mathematics and Mathematical Sciences , 2004, DOI: 10.1155/s0161171204307234
Abstract: We consider a class of discrete differential operators acting on multidimensional Haar wavelet basis with the aim of finding wavelet approximate solutions of partial differential problems. Although these operators depend on the interpolating method used for the Haar wavelets regularization and the scale dimension space, they can be easily used to define the space of approximate wavelet solutions.
Chaotic trigonometric haar wavelet with focus on image encryption  [PDF]
Sodeif Ahadpour,Yaser Sadra
Computer Science , 2014,
Abstract: In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling function of the Haar wavelet. With regard to applications of Haar wavelet transform in image processing, we introduce chaotic trigonometric Haar wavelet transform to encrypt the plain images. In addition, the encrypted images based on a proposed algorithm were made. To evaluate the security of the encrypted images, the key space analysis, the correlation coefficient analysis and differential attack were performed. Here, the chaotic trigonometric Haar wavelet transform tries to improve the problem of failure of encryption such as small key space and level of security.
The Haar Wavelet Transform of a Dendrogram: Additional Notes  [PDF]
Fionn Murtagh
Computer Science , 2007,
Abstract: We consider the wavelet transform of a finite, rooted, node-ranked, $p$-way tree, focusing on the case of binary ($p = 2$) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through translation and dilation of a wavelet function. We explore how this works in our tree context.
Solution of wave-like equation based on Haar wavelet  [cached]
Naresh Berwal,Dinesh Panchal,C. L. Parihar
Le Matematiche , 2012,
Abstract: Wavelet transform and wavelet analysis are powerful mathematical tools for many problems. Wavelet also can be applied in numerical analysis. In this paper, we apply Haar wavelet method to solve wave-like equation with initial and boundary conditions known. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number or variables. The results and graph show that the proposed way is quite reasonable when compared to exact solution.
Complete quantum circuit of Haar wavelet based MRA
Yuguo He,Jigui Sun
Chinese Science Bulletin , 2005, DOI: 10.1360/982004-694
Abstract: Wavelet analysis has applications in many areas, such as signal analysis and image processing. We propose a method for generating the complete circuit of Haar wavelet based MRA by factoring butterfly matrices and conditional perfect shuffle permutation matrices. The factorization of butterfly matrices is the essential part of the design. As a result, it is the key point to obtain the circuits of $I_{2t} \oplus W \oplus I_{2^n - 2t - 2} $ In this paper, we use a simple means to develop quantum circuits for this kind of matrices. Similarly, the conditional permutation matrix is implemented entirely, combined with the scheme of Fijany and Williams. The circuits and the ideas adopted in the design are simple and intelligible.
The Haar Wavelet Transform of a Dendrogram  [PDF]
Fionn Murtagh
Computer Science , 2006, DOI: 10.1007/s00357-007-0007-9
Abstract: We describe a new wavelet transform, for use on hierarchies or binary rooted trees. The theoretical framework of this approach to data analysis is described. Case studies are used to further exemplify this approach. A first set of application studies deals with data array smoothing, or filtering. A second set of application studies relates to hierarchical tree condensation. Finally, a third study explores the wavelet decomposition, and the reproducibility of data sets such as text, including a new perspective on the generation or computability of such data objects.
Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems  [PDF]
Harpreet Kaur, R.C. Mittal, Vinod Mishra
American Journal of Computational Mathematics (AJCM) , 2011, DOI: 10.4236/ajcm.2011.13020
Abstract: Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems. Through this analysis, solutions are found on the coarse grid points and refined towards higher accuracy by increasing the level of the Haar wavelets. A distinctive feature of the proposed method is its simplicity and applicability for a variety of boundary conditions. Numerical tests are performed to check the applicability and efficiency. C++ program is developed to find the wavelet solution.
Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram  [PDF]
Guy P. Nason,Kara N. Stevens
Statistics , 2013,
Abstract: It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet spectrum of a locally stationary wavelet time series. Our new method works by combining the advantages of a Haar-Fisz transformed spectrum with a simple, but powerful, Bayesian wavelet shrinkage method. Our new method produces excellent and stable spectral estimates and this is demonstrated via simulated data and on differenced infant ECG data. A major additional benefit of the Bayesian paradigm is that we obtain rigorous and useful credible intervals of the evolving spectral structure. We show how the Bayesian credible intervals provide extra insight into the infant ECG data.
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