Showing papers on "Hartley transform published in 2019"

Color Image Encryption Using Pixel Scrambling Operator and Reality-Preserving MPFRHT

Abstract: To ensure the confidentiality of color images during their storage or transmission on insecure networks, a number of encryption methods based on fractional transforms have been proposed and widely investigated. However, most of their outputs are complex values that are inconvenient for record and transmission. Also, those methods always deal with a whole color component with the same fractional-order and ignore the textural features that are contained in different image parts. In this paper, we first define a reality-preserving multiple-parameter fractional Hartley transform (RPMPFRHT), whose output is real value, and then a novel color image encryption method is proposed that divides the RGB components into different blocks and uses a constructed pixel scrambling operator to mix and hide the original color information. The outputs are transformed to different RPMPFRHT domains and further scrambled by a non-adjacent coupled map lattices system. Numerical simulations are performed to demonstrate that the proposed encryption algorithm is feasible, secure, sensitive to keys, and robust to potential attacks.

Asymmetric encryption algorithm for colour images based on fractional Hartley transform

Abstract: This paper presents a new scheme for encryption of single-channel colour images. The scheme uses amplitude- and phase-truncation approach to introduce non-linearity for enhanced security. Further, the colour image encryption is performed in the fractional Hartley domain, which is relatively less investigated. The encryption starts with an affine transform of each channel of the input colour image. Thereafter, one of the channels is considered as the input amplitude image while the other two are used as phase masks, one in the spatial and the other in the frequency domain. A detailed analysis of the scheme’s sensitivity to various encryption parameters has been carried out. In addition, security analysis of the scheme against attacks establishes the scheme’s robustness. The combined use of the affine transform and phase-truncation approach for colour image encryption in the fractional Hartley domain is attempted for the first time in this study. It is shown that the proposed scheme resists the spec...

Towards a Dictionary for the Bargmann Transform

Abstract: There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of $L^2(\R)$ to that of $F^2$. Examples include the Fourier transform, the Hilbert transform, Gabor frames, pseudo-differential operators, and the uncertainty principle.

Phase correlation functions: FFT vs. FHT

Abstract: The ability to process an image is a crucial skill in many measurement activities. In image processing or pattern recognition, Fast Fourier Transform (FFT) is widely used. In particular, the Phase Only Correlation (POC) method demonstrates high robustness and subpixel accuracy in pattern matching. However, there is a disadvantage in the required memory machine because of the calculation of 2D-FFT. In applications in which the use of memory is a critical element, Fast Hartley Transform (FHT) seems to be a good substitute. In this context, the use of Hartley’s transform can be of interest for apps implemented on portable systems e.g. smartphones. In this article, we present a comparison of the implementations of the phase correlation function using FFT and FHT. Particular attention is given to the analytical steps necessary to implement the POC by means of the Hartley transform.

Known-Plaintext Attack on Cryptosystem Based on Fractional Hartley Transform Using Particle Swarm Optimization Algorithm

Abstract: Known-plaintext attack based on particle swarm optimization algorithm is mounted successfully on an image encryption scheme that uses single-fractional Hartley transform. The results point out that the proposed algorithm successfully retrieved the fractional orders of the transform, which forms the secret keys. Robustness of the algorithm is tested on noisy and missing data encrypted images. The secret keys are successfully retrieved in the presence of Gaussian noise of considerable strength. This study brings out the success of particle swarm optimization algorithm in mounting known-plaintext attack on an optical image encryption scheme in fractional Hartley domain.

Security enrichment of optical image cryptosystem based on superposition technique using fractional Hartley and gyrator transform domains deploying equal modulus decomposition

Abstract: In this paper, a symmetric cryptosystem has been suggested to increase security of double random phase encoding using superposition technique in fractional Hartley transform (FrHT) and gyrator transform (GT) domains. It uses structured phase mask (SPM) and hybrid mask (HM) deploying equal modulus decomposition (EMD). Related to original phase truncated Fourier transform (PTFT) based cryptosystem, the security of encoding and decoding is upgraded by using the superposition technique. With the usage of SPM we can increase the key space while encoding and can also overcome the axis alignment difficulty. Decoding is just the reversal of the encoding method. The proposed scheme has robustness against common attacks like: noise and occlusion attacks. With the help of numerical simulation results we also show that our cryptosystem is vulnerable to various attacks. Performance of the suggested method is calculated in terms of Mean Square Error (MSE) between original and decoded image and also the sensitivity of the SPM parameters and rotational angles of GT is investigated. The competence of the suggested method includes analysis on EMD, histogram and correlation coefficient. The suggested cryptosystem is also open to the occlusion attack and noise attack to analyze its performance and evenness.

Asymmetric watermarking scheme in fractional Hartley domain using modified equal modulus decomposition

Abstract: Motivated by the endurance of special attack on asymmetric cryptosystems by modified equal modulus decomposition, a new watermarking scheme for grayscale images in fractional Hartley domain is proposed in this paper. The input grayscale images, bonded with random phase mask, are transformed according to fractional Hartley transform, followed by equal modulus decomposition. One of the two images obtained by equal modulus decomposition serves as a private key, whereas the other image is further transformed with another fractional Hartley transform followed by equal modulus decomposition. Again, one of the resulting images acts as a second private key, whereas the other image is phase truncate…

Multiple Image Encryption with Fractional Hartley Transform and Robust Chaotic Mapping

Abstract: In this paper, we present a simple yet highly robust mechanism for multiple image encryption with optical transformation. A fractional order Hartley transform framework along with secret reversible integer transform (RIT) is used to decorrelate the images. The selection of fractional orders is based on a robust chaotic mapping. Optical transforms support fast and parallel processing but have limitation in digital implementation due to complex coefficients. We present a paradigm where complexity is completely eliminated at each security level to overcome the need of time consuming phase retrieval algorithms. The amalgamation of chaos further make it a highly sensitive and secure technique. This method gives optimum results with almost uniform histogram and lossless recovery of data which is otherwise limitation of optical transforms whose energy is concentrated at the center.

Discrete Orthogonal Multi-transform on Chip (DOMoC)

Abstract: The modern real time applications such as orthogonal frequency division multiplexing, data/image/video compression, speech processing, and etc., demand high performance discrete orthogonal transform designs with lesser area/power and delay. This paper proposes two kinds of architectures to perform multiple N-point 1D-discrete orthogonal transforms on single chip. They are FFT parallel architecture based and matrix-vector multiplier based. The proposed architectures have the feasibility to perform N or $\frac {N}{2}$ or $\frac {N}{4}$ or $\frac {N}{8}$ -point discrete forward/reverse orthogonal transforms, where FFT, discrete Cosine, Sine, Haar, Hartley, Slant, and Walsh-Hadamard transforms are considered. The novelty with proposed architectures is the provision of multiple transforms using the single hardware. The frequency of the proposed 16-point FFT parallel architecture based and matrix-vector multiplier based 1D-discrete orthogonal transform architectures are 110.9 MHz and 26.65 MHz using 45 nm technology respectively.

Quantum chaos optical image encryption and decryption method based on Kronecker product

Abstract: The present invention provides a quantum chaos optical image encryption and decryption method based on Kronecker product, and relates to the technical field of optical information safety The safety defect is solved that a current optical image encryption technology is not enough in nonlinearity The optical image encryption and decryption method based on four-dimensional quantum Dicke chaos system and fractional order Hartley transform makes up the safety defect that the traditional optical image encryption technology is not enough in linearity due to the non-linear feature of the quantum chaos system The fractional order quantum cellular neural network hyperchaos system is taken as a key generator to allow secret keys to have a larger space so as to safely resist to violent attacks Thequantized Dicke model is very sensitive to the initial state, and a quantum chaos random phase template generated by the four-dimensional quantum Dicke chaos system and composite chaotic mapping hasgood randomness The employed fractional order Hartley optical transform provides more selected control parameters compared to the integer order transform The used Kronecker product template in the encryption process enhances the non-linear safety features of the optical encryption method