Image encryption using the random FrDCT and the chaos-based game of life

A novel image encryption algorithm using the random fractional DCT (RFrDCT) and the chaos-based Game of Life (GoL) is presented here. Firstly the plaintext image is transformed by the reality-preserving RFrDCT into the RFrDCT domain, and a preliminary encryption output is obtained. And then a combination of the confusion and diffusion (C&D) processes is performed in the transform domain, where the confusion process is carried out by GoL, and the diffusion process is carried out by an XOR operation. Therefore a more random-like encryption result can be obtained after further encryption by the C&D. Both the GoL and XOR operation are based on chaos whose control parameters serve as cipher keys in order to enlarge cipher space and enhance key sensitivity. Theoretical analysis and simulation experiments for the proposed algorithm are described, the desirable encryption performance is obtained, and it is secure against various common attacks.     

Image encryption combining multiple generating sequences controlled fractional DCT with dependent scrambling and diffusion

Based on the fractional discrete cosine transform with multiple generating sequences (MGSFrDCT) and the dependent scrambling and diffusion (DSD), an image encryption algorithm is proposed, in which the multiple-generating sequences greatly enlarge the key space of the encryption system. The real-valued output of MGSFrDCT is beneficial to storage, display and transmission of the cipher-text. During the stage of confusion and diffusion, the locations and values of all MGSFrDCT transformed coefficients change due to DSD, and the initial values and fractional orders of encryption system depend not only on the cipher keys but also on the plain-image due to introduction of a disturbance factor, which allows the encryption system to resist the known-plaintext and chosen-plaintext attacks. Experimental results demonstrate that the proposed encryption algorithm is feasible, effective and secure and able to resist common classical attacks.     

Asymmetric encryption algorithm for colour images based on fractional Hartley transform

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 special attack.     

基于双向相关扩散与非线性混沌S盒的图像加密算法

目的 当前混沌加密方案主要采用存在迭代周期性的序列与单向扩散机制来实现像素的混淆,设计一种加密算法以解决其抗破译性能较弱的问题。方法 设计了基于双向相关扩散与非线性S盒的图像加密算法。借助哈希方案,形成一个与初始图像内容相关的密钥;基于2D混合混沌函数,利用子密钥来设计位置交叉规则,实现明文的像素置乱;基于线性分阶变换,联合混沌随机数组,构建一个16×16的非线性S盒;定义S盒的循环向前移位机制和向前扩散机制,对置乱图像完成正向加密;再更新混合混沌系统的初始条件,构建逆向扩散机制,对正向密文完成反向加密。结果 测试数据显示,与已有混沌加密方案相比,在安全性和效率方面,所提方案的优势更大,其时耗时仅为0.59 s,且稳定的NPCR和UACI值分别达到了99.74%,33.69%。结论 所提加密方案可以抵御网络中外来攻击,可充分保证图像内容的真实性。     

Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain

We propose a novel image encryption algorithm based on compressive sensing (CS) and chaos in the fractional Fourier domain. The original image is dimensionality reduction measured using CS. The measured values are then encrypted using chaotic-based double-random-phase encoding technique in the fractional Fourier transform domain. The measurement matrix and the random-phase masks used in the encryption process are formed from pseudo-random sequences generated by the chaotic map. In this proposed algorithm, the final result is compressed and encrypted. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys for distribution simultaneously. Numerical experiments verify the validity and security of the proposed algorithm.     

Flexible multiple-image encryption algorithm based on log-polar transform and double random phase encoding technique

We present a novel multiple-image encryption algorithm by combining log-polar transform with double random phase encoding in the fractional Fourier domain. In this algorithm, the original images are transformed to annular domains by inverse log-polar transform and then the annular domains are merged into one image. The composite image is encrypted by the classical double random phase encoding method. The proposed multiple-image encryption algorithm takes advantage of the data compression characteristic of log-polar transform to obtain high encryption efficiency and avoids cross-talk in the meantime. Optical implementation of the proposed algorithm is demonstrated and numerical simulation results verify the feasibility and the validity of the proposed algorithm.     

基于加权直方图位混淆与分阶混沌异扩散的快速图像加密算法

目的为了解决当前图像加密技术因在置乱和扩散过程忽略了明文像素特性,导致其抗明文攻击能力较弱,并且整个像素扩散均采用相同的加密机制来实现,存在安全性不理想问题,文中设计基于加权直方图位混淆和分阶混沌异扩散的快速图像加密算法。方法该算法充分利用整个明文的像素值,将其嵌入到整个置乱与扩散阶段,且在扩散过程中,利用不同的加密函数对不同的像素进行扩散。首先,联合Logistic与Tent映射,利用非线性组合思想构建新的低维混沌系统,并分析其混沌性能;考虑输入明文的像素值,建立像素加权直方图,借助外部密钥,生成复合混沌系统的初值,通过迭代输出随机序列;再将明文的每个像素在位水平上进行扩展,利用离散化的随机序列在位水平上实现明文混淆;随后,将分数阶理论嵌入Logistic映射中,构建分阶Logistic混沌映射,利用像素的加权直方图对其迭代,输出混沌数组;对混淆密文的像素进行分类,结合混沌数组,设计异扩散模型,对三类像素进行不同的加密。结果测试结果显示,与当前混沌加密算法相比,所提加密机制具有更强的抗明文攻击能力,其输出密文的像素分布更为均匀。结论所提加密技术兼顾了较高的安全性与效率,能够较好地保护图像在网络中安全传输。     

Asymmetric hybrid encryption scheme based on modified equal modulus decomposition in hybrid multi-resolution wavelet domain

In this paper, an asymmetric hybrid encryption scheme, using coherent superposition and modified equal modulus decomposition in a hybrid multi-resolution wavelet, is proposed. The hybrid multi-resolution wavelet is generated using fractional Fourier transform of multiple orders and Walsh transform. The fractional orders of the fractional Fourier transform increase the key space and hence provide additional strength to the cryptosystem. The designed scheme has a large key space to avoid brute-force attack and is non-linear in nature. The scheme is validated on grey-scale images. Computer-based simulations have been performed to verify the validity and performance of the proposed scheme against various attacks. Scheme's robustness to the special attack is also checked. Results show that single equal modulus decomposition with fractional Fourier transform and hybrid transform are vulnerable to the special attack, whereas the proposed scheme endures the special attack.     

Image encryption based on interference that uses fractional Fourier domain asymmetric keys

We propose an image encryption technique based on the interference principle and phase-truncation approach in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys and is free from the silhouette problem. Multiple input images bonded with random phase masks are independently fractional Fourier transformed. Amplitude truncation of obtained spectrum helps generate individual and universal keys while phase truncation generates two phase-only masks analytically. For decryption, these two phase-only masks optically interfere, and this results in the phase-truncated function in the output. After using the correct random phase mask, universal key, individual key, and fractional orders, the original image is retrieved successfully. Computer simulation results with four gray-scale images validate the proposed method. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and decryption keys formation are complicated and should be realized digitally. For decryption, an optoelectronic scheme has been suggested.     

Image encryption based on a reality-preserving fractional discrete cosine transform and a chaos-based generating sequence

A novel image encryption technique based on a reality-preserving fractional discrete cosine transform (FrDCT) and a chaos-based generating sequence is proposed. The FrDCT is a generalization of the discrete cosine transform (DCT). This reality-preserving FrDCT inherits the virtues of both the DCT and fractional transform, providing improved security and flexibility by employing the generating sequence as an extra key in addition to the fractional orders. The most fascinating advantage of the FrDCT is its reality-preserving property, which ensures real ciphertext for real plaintext, which is conducive to display, storage, and transmission. Performance and security analysis demonstrates that this algorithm is valid, secure, sensitive to keys, and robust to noise and occlusion attacks.     

Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask

A single channel asymmetric color image encryption scheme is proposed that uses an amplitude- and phase- truncation approach with interference of polarized wavefronts. Instead of commonly used random phase masks, wavelength-dependent structured phase masks (SPM) are used in the fractional Fourier transform domain for image encoding. The primary color components bonded with different SPMs are combined into one grayscale image using convolution. We then apply the amplitude and phase truncation to the fractional spectrum, which helps generate unique decryption keys. The encrypted image bonded with a different SPM is then encoded into a polarization selective diffractive optical element. The proposed scheme alleviates the alignment problem of interference and does not need iterative encoding and offers multiple levels of security. The effect of a special attack to the proposed asymmetric cryptosystem has been studied. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. The computer simulation results support the proposed idea.     

Double-image encryption by iterative phase retrieval algorithm in fractional Fourier domain

A novel double-image encryption algorithm is proposed, which can simultaneously encrypt two images into a single one as the amplitude of a fractional Fourier transform with two different groups of fractional orders. The two original images can be retrieved independently by fractional Fourier transforms with two different groups of fractional orders, one public phase mask, and two different private phase masks. The proposed approach can enlarge the key space, achieve faster convergence in the iterative process, and avoid cross-talk between the two images in reconstruction. Numerical simulations are presented to verify its validity and efficiency.     

Joint image compression–encryption using discrete fractional transforms

Exchange of data in the form of text and image on internet is in fast progression and it is spawning new compression and encryption algorithms for bandwidth and security respectively. We have proposed a new kind of joint algorithm using discrete fractional transforms for compression–encryption of image. In this algorithm, the discrete fractional Fourier transform which is discrete version of fractional Fourier transform, is used to compress the images with variation of its parameter ‘α’ (order of transform). The compressed image is encrypted using discrete fractional cosine transform to provide security. The advantage of this method is its feasible implementation in practice, superior, robustness, security and sensitivity of keys, which has a good prospect and practicability in information security field. Results of computer simulations are presented to verify the validity of the proposed method such as mean square error (MSE) and peak signal to noise ratio between the original image and decrypted image. Sensitivity for right decryption key is proved with respect to MSE.     

一种新的基于可逆矩阵的具有完整性检验能力的图像加密方案

为了保护图像信息的安全,论文利用组合理论知识,提出一种新的基于可逆整数矩阵的、具有完整性检验能力的图像加密方案。应用该方案将一个灰度图像加密生成一个脆弱的噪声密图,解密过程是加密的简单逆过程。密图的完整性可以凭借人类视觉系统进行检验,不需要任何复杂的计算。当密图遭受恶意篡改时,解密得到一个噪声图,无法得到原始图像的任何信息。论文加密方案的密钥简单,且密钥空间足够大。理论分析和实验结果证明了,该方案为图像加密提供了一种高安全性和有效的机制。     

A New Multi Chaos-Based Compression Sensing Image Encryption

The advancements in technology have substantially grown the size of image data. Traditional image encryption algorithms have limited capabilities to deal with the emerging challenges in big data, including compression and noise toleration. An image encryption method that is based on chaotic maps and orthogonal matrix is proposed in this study. The proposed scheme is built on the intriguing characteristics of an orthogonal matrix. Gram Schmidt disperses the values of pixels in a plaintext image by generating a random orthogonal matrix using logistic chaotic map. Following the diffusion process, a block-wise random permutation of the data is performed using multi-chaos. The proposed scheme provides sufficient security and resilience to JPEG compression and channel noise through a series of experiments and security evaluations. It enables Partial Encryption (PE) for faster processing as well as complete encryption for increased security. The higher values of the number of pixels change rates and unified average change intensity confirm the security of the encryption scheme. In contrast to other schemes, the proposed approach can perform full and partial encryption depending on security requirements.     

Selective and adaptive signal hiding technique for security of JPEG2000

In this article, we proposed a selective partial image encryption scheme of Secure JPEG2000 (JPSEC) for digital cinema or any other JPEG2000‐based applications. It makes a scalable encryption scheme possible on the basis of a trade‐off relationship between the encryption effect and the encryption cost. The encryption scheme was designed to activate during the image compression process, which is between quantization and entropy coding. Three data selection schemes were involved to select the parts of data to be encrypted: subband selection, data bit selection, and random selection of coefficients. The experimental results with over 3000 test images revealed that the PSNRs were between about 9.5 to 7.5 dB when the portion of the encrypted data by this scheme was between 1/4096 and 1/256. As the encryption effect is reasonably high with very low cost, the proposed scheme has high potential to provide secure communications in a variety of wired/wireless scenarios. © 2010 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 20, 277‐284, 2010     

Image compression and encryption scheme with hyper-chaotic system and mean error control

Based on a hyper-chaotic system, an image compression and encryption scheme is presented by adopting mean error control to improve the quantization compression performance of the discrete cosine transform (DCT) coefficients. The transform coefficients of DCT forming a structure similar to the sub-band can be classified and encoded. Then the image is scanned with Zigzag operation in different directions to achieve sufficiently scrambled effects. The cyclic shift matrix for image encryption is generated by the hyper-chaotic system. The four initial inputs for generating the cyclic shift matrix serve as the key. Simulation results demonstrate the security and the effectiveness of the proposed image compression and encryption scheme.     

A Secure and Lightweight Chaos Based Image Encryption Scheme

In this paper, we present an image encryption scheme based on the multi-stage chaos-based image encryption algorithm. The method works on the principle of confusion and diffusion. The proposed scheme containing both confusion and diffusion modules are highly secure and effective as compared to the existing schemes. Initially, an image (red, green, and blue components) is partitioned into blocks with an equal number of pixels. Each block is then processed with Tinkerbell Chaotic Map (TBCM) to get shuffled pixels and shuffled blocks. Composite Fractal Function (CFF) change the value of pixels of each color component (layer) to obtain a random sequence. Through the obtained random sequence, three layers of plain image are encrypted. Finally, with each encrypted layer, Brownian Particles (BP) are XORed that added an extra layer of security. The experimental tests including a number of statistical tests validated the security of the presented scheme. The results reported in the paper show that the proposed scheme has higher security and is lightweight as compared to state-of-the-art methods proposed in the literature.     

Optical watermark scheme based on singular value decomposition ghost imaging and particle swarm optimization algorithm

An optical image watermarking algorithm, based on singular value decomposition (SVD) ghost imaging and multiple transforms, is designed. The watermark image is first encrypted by applying an SVD ghost imaging system, then the encrypted watermark is embedded into the cover image with the help of multiple transforms, including lifting wavelet transform (LWT), discrete cosine transform (DCT), discrete fractional angular transform (DFAT) and SVD. Four sub-band images are produced from the host image by LWT and DCT. The improved DFAT, whose scaling factors and parameter are optimized by particle swarm optimization algorithm, is operated in the new matrix. Afterwards, SVD is executed in the two-part image and the encrypted watermark is embedded in the host image by mutual operation of different matrices. Simulation results validate that the proposed watermark scheme is superior in the aspects of security, robustness and imperceptibility.     

A Highly Secured Image Encryption Scheme using Quantum Walk and Chaos

The use of multimedia data sharing has drastically increased in the past few decades due to the revolutionary improvements in communication technologies such as the 4th generation (4G) and 5th generation (5G) etc. Researchers have proposed many image encryption algorithms based on the classical random walk and chaos theory for sharing an image in a secure way. Instead of the classical random walk, this paper proposes the quantum walk to achieve high image security. Classical random walk exhibits randomness due to the stochastic transitions between states, on the other hand, the quantum walk is more random and achieve randomness due to the superposition, and the interference of the wave functions. The proposed image encryption scheme is evaluated using extensive security metrics such as correlation coefficient, entropy, histogram, time complexity, number of pixels change rate and unified average intensity etc. All experimental results validate the proposed scheme, and it is concluded that the proposed scheme is highly secured, lightweight and computationally efficient. In the proposed scheme, the values of the correlation coefficient, entropy, mean square error (MSE), number of pixels change rate (NPCR), unified average change intensity (UACI) and contrast are 0.0069, 7.9970, 40.39, 99.60%, 33.47 and 10.4542 respectively.