Discrete Fractional Random Transform Research Articles

Secure Selective Image Encryption Based on Wavelet Domain, 3D-Chaotic Map, and Discrete Fractional Random Transform

Secure Selective Image Encryption Based on Wavelet Domain, 3D-Chaotic Map, and Discrete Fractional Random Transform

An Efficient Cryptosystem for Video Surveillance in the Internet of Things Environment

Surveillance systems paradigm envisions the pervasive interconnection and cooperation of interactive devices over the Internet infrastructure. Nevertheless, dissemination and processing of surveillance video amid the Internet of Things (IoT) applications become a susceptible issue due to the large volume and the significant information of these data. Moreover, surveillance devices on IoT have very limited resources such as memory and storage. The actual security methods are not quite appropriate for surveillance IoT systems. Thus, a particular cryptosystem technique is required for surveillance data security. In this paper, we propose an efficient cryptosystem to secure IoT-based surveillance systems. The proposed cryptosystem framework contains three parts. First, a lightweight automatic summarization technique based on a fast histogram-clustering approach is used to extract the keyframes from the surveillance video. Then, we employ a discrete cosine transform (DCT) technique to compress the extracted data size. Finally, the proposed framework performs an efficient image encryption algorithm by employing a discrete fractional random transform (DFRT). The testing results and analysis confirm the features of the proposed cryptosystem on surveillance systems. The proposed framework is fast and ensures secure and efficient real-time processing by minimizing the transmission cost and storage.

Asymmetric color cryptosystem based on compressed sensing and equal modulus decomposition in discrete fractional random transform domain

In this paper, we propose an asymmetric encryption and compression method for a color image based on compressed sensing and equal modulus decomposition in the discrete fractional random transform (DFrRT) domain. In this scheme, a color image is firstly encrypted into a single channel image, which is divided into low-frequency image and high-frequency image by the discrete wavelet transform. Subsequently, the high-frequency image is compressed into two matrices by compressed sensing. One of the matrices is combined with the low-frequency image into one input of DFrRT. The other acts as another input of DFrRT. Finally, the output result of DFrRT is encrypted by the equal modulus decomposition in DFrRT domain to create an effective trapdoor one-way function. Compared to the other transformations, the private key of DFrRT is the high-frequency component related to the plaintext in this paper. Thus, the proposed cryptosystem is able to resist various types of attacks and maintain the asymmetric characteristics of the cryptosystem. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed method.

A novel approach to encrypt multiple images using multiple chaotic maps and chaotic discrete fractional random transform

Due to recent advances in network technology, it has become easier to send multiple images together. Hence, image encryption using multiple images is an emerging area of interest amidst researchers. The paper proposes a multiple-image encryption technique based on the chaotic confusion-diffusion strategy and chaotic Discrete Fractional Random Transform (DFRNT). Initially, odd and even bits of three input images (M × N) are separated and a composite image (3M × 2N) is derived by combining the even and odd bits of every image. Secondly, chaotic confusion-diffusion strategy using four chaotic maps Arnold Cat Map (ACM), Logistic-Tent Map (LTM), Logistic-Sine Map (LSM) and Tent-Sine Map (TSM) is applied to scramble and diffuse the pixel values of the composite image. Thereafter, three diffused images are extracted from the diffused composite image. Finally, chaotic DFRNT uses Tent-Sine Map (TSM) to generate the random kernel transform matrix for itself and encrypt the extracted images into a single image. The parameters Histogram, Correlation distribution (CD), Correlation Coefficient (CC), Entropy, Number of Pixel Change Rate (NPCR) and Unified Averaged Changed Intensity (UACI) have been computed to show the potential of the proposed encryption technique.

Imperceptible digital watermarking scheme in multiple transform domains

A novel imperceptible digital watermarking scheme in multiple transform domains is presented, where the cover image is dealt with by discrete wavelet transform (DWT), discrete cosine transform (DCT) and discrete fractional random transform (DFRNT), while the watermark image is scrambled by Arnold transform and logistic map. First the watermark is scrambled by the Arnold transform, then the row and the column of the resulting watermark are scrambled by the Logistic map, respectively. In addition, four sub-band images are generated from the host image by the two-dimensional discrete wavelet transform. The low-frequency sub-band images are divided into 8 × 8 small matrices, and a coefficient matrix is produced by performing the discrete cosine transform on each matrix. An intermediate matrix with the same size as the watermark image is constructed by the intermediate frequency coefficients. Then the discrete fractional random transformation is performed on the intermediate frequency coefficient matrix and the scrambled watermark is embedded into the discrete fractional random transformation domain. Compared with the previous schemes, the proposed digital watermarking scheme has stronger imperceptibility and robustness.

Quaternion discrete fractional random transform for color image adaptive watermarking

As for the fractional transforms, to date only fractional Fourier transform (FrFT) has been applicable to color images in a holistic manner by using the quaternion algebra, yet, discrete fractional random transform (DFRNT) with the useful intrinsic randomness is still to be explored. This paper first defines quaternion DFRNT (QDFRNT) which generalizes DFRNT to efficiently process quaternion signals, and then applies QDFRNT to color image adaptive watermarking. For the QDFRNT, this paper also derives the relationship between QDFRNT of a quaternion signal and DFRNT of four components for this signal to efficiently compute QDFRNT. For the color image adaptive watermarking based on QDFRNT and SVM, in order to efficiently utilize the color information in the adaptive process, this paper also exploits the human vision system’s (HVS) masking properties of texture, edge and color tone directly from the color host image to adaptively adjust the watermark strength for each block. In addition, the constraints in watermark embedding are discussed to preserve the watermarking energy. Experimental results show that: (a) the proposed efficient computation method takes only half the computational time of the direct method; (b) the comparison of five color models (RGB, YUV, YIQ, CIEL*a*b* and YCbCr) shows that the proposed QDFRNT-based watermarking scheme using YCbCr color model has the overall best performance and can achieve a good balance between invisibility and robustness to the Checkmark attacks; (c) The proposed scheme is superior to the existing schemes respectively using DCT, DFRNT, discrete quaternion Fourier transform (DQFT), discrete fractional quaternion Fourier transform (DFrQFT), and quaternion radial moments (QRMs). Moreover, the fractional order and the random matrix of QDFRNT enhance the security of the proposed scheme.

A hybrid scheme for self-adaptive double color-image encryption

Most of existing optical color image encryption schemes have born security risks due to the adoption of linear transform, and data redundancy for the generation of complex image. To settle these problems effectively, a hybrid scheme for self-adaptive double color-image encryption is proposed in this paper. In this scheme, each RGB color component of two secret color images is first compressed and encrypted by 2-D compressive sensing (CS) in which measurement matrices are generated by 1-D compound chaotic systems and further are optimized by steepest descent algorithm to improve image reconstruction effect. Then, the two measured images are regarded as the real part and imaginary part to constitute a complex image, respectively. In the end, the complex image is reencrypted by self-adaptive random phase encoding and discrete fractional random transform (DFrRT) to obtain the final encrypted data. In the process of DFrRT and random phase encoding, the correlations between R, G, B components are adequately utilized. The production of key streams not only depends on the initial values of chaotic systems but also on plaintexts, and the three color components affect each other to enhance the ability against the known plaintext attack. The projection neural network algorithm is adopted to obtain the decryption images. Simulation results also verify the validity and security of the proposed method.

Image compression-encryption scheme combining 2D compressive sensing with discrete fractional random transform

Most of the existing image encryption algorithms based on compressive sensing are too complex to operate. An image compression-encryption scheme with simple operation is presented based on 2D compressive sensing and discrete fractional random transform (DFrRT). To accomplish compression and encryption simultaneously, the original image is expressed in a 2D discrete cosine domain and measured by the measurement matrices in two orthogonal directions during the encryption process, where the matrices are constructed with Logistic chaos map to control the row vectors of Hadamard matrix. Then the intermediate resulting image is re-encrypted by taking discrete fractional random transform. Decryption process includes the inverse operation of the DFrRT and the reconstruction process with the Newton Smoothed l0 Norm (NSL0) algorithm in sequence. Simulation results verify the security and the effectiveness of this scheme by taking advantages of both compressive sensing and DFrRT.

Multispectral and panchromatic image fusion using a joint spatial domain and transform domain for improved DFRNT

The use of traditional spatial domain fusion methods such as intensity-hue-saturation (IHS) and principal component analysis (PCA) achieve good spatial quality but often lead to spectral distortion. Use of discrete fractional random transform (DFRNT) fusion, which is a transform domain method proposed by the authors before, can maintain the high spectral information. Hence, in this paper we propose using the respective advantages of DFRNT and IHS or PCA, via combined IHS-DFRNT and PCA-DFRNT approaches to obtain good spectral quality and high spatial quality, which is also for improved DFRNT method. At the same time, instead of fusion in the spatial domain or the transform domain, respectively, as in the conventional methods, the proposed IHS-DFRNT and PCA-DFRNT approaches are fused in a kind of joint spatial domain and transform domain. Moreover, different random distributions of DFRNT produce different fusion results which can meet different application demands. The fused images are found to preserve both the spectral information of the multispectral image and the high spatial information of the panchromatic image. Especially, the proposed combined methods are much faster and keep better comprehensive information than DFRNT. Objective quantitative evaluation indexes are also used to illustrate the effectiveness of the proposed methods.

A Robust Digital Watermarking Technique for Image Contents based on DWT-DFRNT Multiple Transform Method

Copyright protection of digital content has become one of important issues in digital content marketplace. Digital watermarking may be used as an effective method for identifying the copyright ownership of digital content against unauthorized use and distribution. In this paper, we propose a robust digital image watermarking algorithm based on the multiple transform method, discrete wavelet transform (DWT) and discrete fractional random transform (DFRNT). We adopt a two-dimensional (2D) barcode for hiding information and apply the block code encoding and generate a watermark through them. The generated watermark image is embedded into DWT-DFRNT using quantization technique in order to ensure robustness and imperceptibility of the watermark. Experimental results present that our proposed algorithm has improved the extraction performance by accurately extracting the hidden information in the 2D barcode from the detected watermark. Also, combining the dual transform method, DWT and DFRNT, has improved the imperceptibility and robustness of the watermark against basic image signal processing attacks.

Remote Sensing Image Fusion Based on Discrete Fractional Random Transform for Modified IHS

Abstract. The traditional IHS fusion, as a spatial domain method, mostly achieves the good spatial quality but the spectral distortion. The discrete fractional random transform (DFRNT) fusion, as a transform domain method, can maintain the high spectral information. Thus, in this paper, we propose a combined DFRNT-IHS approach to obtain good spectral quality and high spatial quality. Moreover, instead of fusion in spatial domain or transform domain respectively as in the conventional way, the proposed DFRNT-IHS approach is for joint spatial and transform domain. Real multi-spectral and panchromatic images are used to evaluate the effectiveness of the proposed method. The fused images are found to preserve both the spectral information of the multi-spectral image and the high spatial resolution information of the panchromatic image more effectively than several existing image fusion techniques. Spectrum distribution of DFRNT is random and dispersive, which guarantees low spectral distortion and certain robustness.

Double-color Image Encryption Based on Discrete Fractional Random Transform

该文基于离散分数随机变换和线性同余理论，提出一种单通道双彩色图像加密算法。输入的两幅RGB图像转换成相应的索引图像格式，其中一幅2维索引图像被编码为振幅部分，另一幅则被编码为空域相位掩模。分数域相位掩模由线性同余发生器 (LCG) 生成，并将彩色映射矩阵嵌入其中。引入光学幅相调制技术，在不增加光学元件的基础上实现了双彩色图像加密。离散分数随机变换的分数阶和线性同余函数的4个参数作为密钥提高了算法的安全性，对应所有密钥计算了输入图像和解密图像的均方误差。针对唯密文攻击，噪声叠加和抗裁剪性能分别进行了数值模拟，验证了该算法的可行性和有效性。

Color image encryption by using Arnold and discrete fractional random transforms in IHS space

In this paper, we propose a novel color image encryption method using discrete fractional random transform (DFRNT) and Arnold transform (AT) in the intensity-hue-saturation (IHS) color space. A color image is converted into IHS space from the standard red–green–blue (RGB) space. The intensity component is encrypted by DFRNT, which is a kind of encryption with the secrecy of pixel value and pixel position simultaneously. The hue and saturation components are encrypted using Arnold transform, which is a kind of position scrambling. Comparing to the classical double-random-phase encoding, DFRNT encryption method can save storage space of the encryption keys required to be stored for decryption, meanwhile with the similar security. The fractional order of DFRNT, the random matrix of DFRNT and the iteration numbers of Arnold transform are the encryption keys to enhance the security of the proposed scheme. The performance of the proposed scheme is analyzed against the variation in fractional order, the change of Arnold transform iteration number, known-plaintext attack, noise addition and occlusion of the encrypted image, respectively. Numerical simulation results have demonstrated the feasibility and effectiveness of the proposed method.

Shadow Size Reduction and Multiple Image Secret Sharing Based on Discrete Fractional Random Transform

Shadow Size Reduction and Multiple Image Secret Sharing Based on Discrete Fractional Random Transform

Novel image fusion method based on discrete fractional random transform

We introduce a new spectrum transform into the image fusion field and propose a novel fusion method based on discrete fractional random transform (DFRNT). In DFRNT domain, high amplitude spectrum (HAS) and low amplitude spectrum (LAS) components carry different information of original images. For different fusion goals, different fusion rules can be adopted in HAS and LAS components, respectively. The proposed method is applied to fuse real multi-spectral (MS) and panchromatic (Pan) images. The fused image is observed to preserve both spectral information of MS and spatial information of Pan. Spectrum distribution of DFRNT is random and uniform, which guarantees that good information is reserved.

Image sharing scheme based on discrete fractional random transform

We present a novel image sharing algorithm based on the discrete fractional random transform (DFRNT). The secret image is shared into several shadow images in the DFRNT domain together with some noise images as the encryption keys to increase the security. The decryption only requires a part of shadow images and therefore is independent of those noise images. The ( t , n ) threshold sharing scheme can be implemented completely by the proposed algorithm. The numerical simulations have demonstrated the effectiveness of this image sharing scheme.