Showing papers on "Hartley transform published in 2020"

An asymmetric cryptosystem based on the random weighted singular value decomposition and fractional Hartley domain

Abstract: A new asymmetric encryption system for double random phase encoding based on random weighted singular value decomposition and fractional Hartley transform domain has been proposed. Random weighted singular value decomposition is purely based upon random weights, isometric matrix and orthogonal triangular decomposition and all these fragments enhances the security of double random phase encoding cryptosystem. Random weights and orthogonal triangular decomposition are considered as heart of this cryptosystem. This system is carried out in fractional Hartley domain, where fractional orders play a vital role. On the receiver side, it is only possible to decrypt the image if anyone knows all the three components, its multiplication order, fractional order of fractional Hartley transform. Proposed cryptosystem is efficiently compared with singular value decomposition and truncated singular value decomposition. Similar to singular value decomposition and truncated singular value decomposition, proposed cryptosystem also yields three components. Because of random weights, these three components are highly differing from traditional singular value decomposition and truncated singular value decomposition components. Some analysis is offered to authenticate the opportunity.

Faster image super-resolution by improved frequency-domain neural networks

Abstract: Recently, most deep learning-based studies have focused on elaborately developing various types of neural networks in the spatial domain to tackle super-resolution. These methods usually have numerous parameters and require a huge amount of memory and time to train their networks. A frequency-domain neural network for super-resolution (FNNSR) has been presented. It designs a primitive neural network that can be trained using back propagation in the frequency domain. In this paper, we propose an improved FNNSR. In our method, the parameters of four quadrants in the compact weighting layer are shared. This substantially reduces the number of parameters in this layer. We use multiple convolutional layers with activations instead of a single convolution operator in FNNSR, so that the underlying features in transformed images can be learned. The Hartley transform is computed directly rather than through the Fourier transform. We design a new weighted Euclidean loss, which pays more attention to reconstructing the high-frequency part that is difficult to recover. Extensive experiments show that our method runs faster and requires fewer parameters than FNNSR. Though our method is not better than state-of-the-art methods in terms of quantitative performance, it still reveals encouraging results.

A Novel 3D Vector Decomposition for Color-Image Encryption

Abstract: In this paper, a novel 3D vector decomposition is proposed for color-image encryption, in which a 3D vector is decomposed into two 3D vectors with random size in a random plane for providing a reliable security constraint. The technique of 3D vector decomposition, as far as we know, firstly offers a three-component encryption with one action, which fits well color-image encryption, and outputs a real ciphertext, which is convenient for recording and transmission. Furthermore, we employ an 1D chaos, which has strong chaotic properties, and reality-preserving fractional Hartley transform to cooperate 3D vector decomposition for constructing a color-image cryptosystem. Therefore, the proposed cryptosystem accomplishes improved security by reducing the single-channel attack risk in individual color-image encryption and avoiding the vulnerable channel in sequential color-image encryption as well as reduced the amount of data of transform-based cryptosystem by avoiding the complex output. Also, it has the advantages of strong chaotic performances, large key space and high key sensitivity, which is highly robust against various attacks. Experimental results show the effectiveness and superiority of the proposed cryptosystem.

Detection of Low-Rate Cloud DDoS Attacks in Frequency Domain Using Fast Hartley Transform

Abstract: Distributed Denial-of-Service (DDoS) attack has been a serious threat to the availability feature of cloud computing. As traditional DDoS attacks are implemented using a huge volume of malicious traffic, the detection of such attacks becomes a naive task. To evade this detection, attackers are moving towards the Low-Rate DDoS (LRDDoS) attacks. The stealthy behavior of LRDDoS attack makes it difficult to get detected due to its low volume traffic. The existing frequency-domain approaches for LRDDoS detection are not feasible in terms of computational and storage requirements. This paper aims to propose a lightweight, accurate, and adaptive approach for the detection of LRDDoS attacks in frequency-domain. In this paper, the LRDDoS attack is detected by analyzing the power spectral distribution. The novelty of the proposed approach is to calculate the power spectral density using Fast Hartley Transform (FHT). The FHT processes real-valued input data, and has low computational and storage complexities. The approach is implemented on OpenStack cloud platform, and the aggregate network traffic (external and internal) is captured and analyzed. Experimental results show that the computational and storage complexities involved in FHT are lower than other transformation algorithms’ complexities. Thus, the approach provides faster response with an average detection time of 60.16 s. The average true negative and true positive rates obtained by the proposed approach are 99.83% and 99.46% respectively, which are competitive.

Two level phase retrieval in fractional Hartley domain for secure image encryption and authentication using digital signatures

Abstract: A novel image authentication scheme based on two level phase retrieval algorithm (PRA) propagated in fractional Hartley transform (FrHT) to extract two phase-only masks (POMs) is proposed. PRA is based on iterative phase mask which uses nonlinear process to generate POMs which in turn makes the system immune to chosen plaintext attack (CPA) and known plaintext attack (KPA). Random amplitude mask (RAM) and random phase mask (RPM) are used as encryption keys which makes the system immune to special attack. Further multiple level of security leads to the achievement of non-convergence of MSE and good performance in the retrieval process. Apart from encrypting the information, authentication has also been included in the scheme. The features incorporated in any plaintext have been shown to provide unique signatures, which can be used to verify their authenticity. The content of the original images can be authenticated only if the authentication key is correct. The robustness of the proposed multiple level cryptosystem has been examined based on various parameters by simulating on MATLAB 9.4.0 (R2018a). The experimental results highlight the suitability and shows the attacker cannot recover the original image without the knowledge of POMs. The scheme has also been compared with similar algorithms which proves that the proposed two-level scheme is more secure, feasible and effective.

Image Compression Using Discrete Weyl-Heisenberg Transform

Abstract: This article proposes a new approach to raster image compression, based on the use of the two-dimensional real discrete Weyl-Heisenberg transform (DWHT) This discrete transform is orthogonal and is based on the optimal Weyl-Heisenberg signal basis, which has the best time-frequency localization The indicated properties are ensured by choosing the optimal forming function of the basis and the best ratio of its parameters In addition, to assess the potential possibilities of using the discrete Weyl-Heisenberg transform in compression problems, the main criteria for compression efficiency were formulated and DWHT was compared with other well-known orthogonal transforms – discrete cosine transform (DCT) and discrete Hartley transform (DHT) It is experimentally shown that the proposed method based on discrete Weyl-Heisenberg transform has much better compression characteristics The paper also presents the results of comparing three compression methods (DHT, DCT and DWHT) in the form of corresponding tables and figures of the restored images

Bargmann transform on the space of hyperplanes.

Abstract: We introduce a Bargmann transform on the space of hyperplanes by applying the Plancherel formula of the Radon transform to the definition of the Bargmann transform on the Euclidean space. Some basic facts on microlocal analysis are also discussed.

Сжатие изображений с использованием дискретного преобразования Вейля - Гейзенберга

Abstract: Предлагается новый подход к сжатию растровых изображений, основанный на использованиидвухстороннего вещественного дискретного преобразования Вейля – Гейзенберга. Данное преобразованиеявляется ортогональным и строится на основе оптимального сигнального базиса Вейля – Гейзенберга,обладающего наилучшей частотно-временной локализацией. Указанные свойства обеспечиваются за счетвыбора оптимальной функции формирования базисного эталона и наилучшего соотношения егопараметров. Кроме того, для оценивания потенциальных возможностей использования дискретногопреобразования Вейля – Гейзенберга (DWHT) в задачах сжатия были сформулированы основные критерииэффективности сжатия и проведено сравнение DWHT с другими известными ортогональнымипреобразованиями – дискретного косинусного преобразования (DCT) и дискретного преобразованияХартли (DHT). Экспериментально показано, что предложенный метод сжатия на основе DWHT обладаетлучшими характеристиками по всем введенным критериям. Приводятся результаты сравнения трехметодов сжатия в виде таблиц и восстановленных изображений.

Fast Recursive Computation of Sliding DHT with Arbitrary Step.

Abstract: Short-time (sliding) transform based on discrete Hartley transform (DHT) is often used to estimate the power spectrum of a quasi-stationary process such as speech, audio, radar, communication, and biomedical signals. Sliding transform calculates the transform coefficients of the signal in a fixed-size moving window. In order to speed up the spectral analysis of signals with slowly changing spectra, the window can slide along the signal with a step of more than one. A fast algorithm for computing the discrete Hartley transform in windows that are equidistant from each other is proposed. The algorithm is based on a second-order recursive relation between subsequent equidistant local transform spectra. The performance of the proposed algorithm with respect to computational complexity is compared with the performance of known fast Hartley transform and sliding algorithms.

The Integral Transform of N.I. Akhiezer

Abstract: We study the integral transform which appeared in a different form in Akhiezer’s textbook “Lectures on Integral Transforms”

Fast Hartley Transform based Elliptic Curve Cryptography for resource constrained devices

Abstract: The growing security and vulnerability threats in apps, software, etc., affect smart gadgets. But, it is computationally not feasible to run the advanced security algorithms in resource-constrained devices (smart gadgets). For example, the encryption and the decryption time of security algorithms in smart gadgets are higher than the workstation/servers. Therefore, there is a need to optimize the time complexity of efficient security algorithms without compromising its security. Elliptic Curve Cryptography (ECC) is computationally less complex among the existing security algorithms due to its less key size. In this paper, to reduce the complexity involved in the scalar multiplication operation of ECC, Fast Hartley transform (FHT) based Hybrid ECC is proposed. From the experimental results, it is evident that using FHT in ECC has an improvement (4% to 8%) over FFT based ECC in terms of encryption and decryption time.

Порівняння дискретних спектральних перетворень при використанні у задачі аналізу електроспоживання локального об’єкту

Abstract: The paper is devoted to the use and comparative analysis of discrete spectral transforms of Fourier, Hartley, Wilenkin-Crestenson and transform at the oriented basis (OB). These methods are considered for analysis of discrete time dependence of electrical energy consumption in local objects like MicroGrid. The prediction of electrical power consumption in such object is quite actual task. One of the ways to solve it is use of spectral and wavelet analysis methods. The non-stationary character of power consumption time dependence curve needs to fulfill preliminary stage of smoothing. This is why wavelet analysis could be effectively used here – as a result of its use we obtain smoothed and compressed version of initial signal (so called “trend”). And the core of wavelet is defined by the type of basic function. These could be, in particular, basic functions of spectral transforms. This is why it was decided to compare different spectral methods – Fourier, Hartley, Wilenkin-Krestenson, and spectral transform at oriented basis.Comparison of spectral methods was carried out according to the following criteria: number of computational operations, simplicity and accuracy of calculations. The amplitude-frequency and phase-frequency spectra of the investigated signal for different spectral methods are considered. The process of finding the spectrum for the above methods was considered for the interval from 0 to 26. The interval was chosen based on demands of the transform at oriented basis where it’s necessary to provide the lengths of initial discrete function dividable to 3 (N=33=27). For the rest methods the interval could be changes accordingly. Thus it gives more objective assessment of the use of spectral methods for the analysis of power consumption of a local object. During the analysis of different spectral methods it was taken into account that Fourier and Wilenkin-Crestenson transforms operate with complex values of the spectra, while Hartley and OB-transforms deal with the real numbers. At the same time, Wilenkin-Crestenson and OB-transforms operate with the number presented in m-ary counting system. It should be noted that the transition to the m-ary system makes it possible to significantly simplify the calculation process at the interval of determination for the Wilenkin-Crestenson method. The Hartley transform differs from the Fourier transform because it operates only with real values, that leads to significant decreasing of the values of basic function and therefore simplifies and accelerates the calculation of the spectrum. It was shown that, in contrast to the Fourier transform, the transform at the oriented basis is asymmetrical, that is, for direct conversion, the angle of inclination of the transformation axis is possible. Comparisons of the considered methods were made on the basis of the values of the required amount of memory for the operation and storage of the program for the calculation of the spectra, as well as the time of performing mathematical operations for the calculation of the spectra of the daily power consumption function. In this way, the transform at the oriented basis is most effective for simplifying and speeding up the calculations. Given that the analysis of fractional power consumption is advisable to perform at a sampling interval of less than one hour, the advantage of this method becomes indisputable, thus showing that the method at the oriented basis is the most appropriate among the considered ones, because with a certain set of parameters allows to accelerate significantly spectrum for analyzing the power consumption signal.

Semi-blind robust watermarking with dual complex tree wavelet based hybrid transform and SVD

Abstract: This paper presents an intelligent scheme for robust digital watermarking of image The inherent property of perfect reconstruction of dual complex tree wavelet transform and secret transform order in fractional Hartley transform is motivation to select these transforms These transformation in 2D are used to generate a hybrid transform The LL-sub band of this hybrid transform is further decomposed into SVD components for embedding watermark Only LL-band of original image is required during watermark extraction and therefore is considered as semi- blind watermarking scheme Experimental evaluation proves that the proposed scheme is robust against variety of attacks