A Novel Color Image Encryption Scheme Based on Hyperchaos and Hopfield Chaotic Neural Network

Problems such as insufficient key space, lack of a one-time pad, and a simple encryption structure may emerge in existing encryption schemes. To solve these problems, and keep sensitive information safe, this paper proposes a plaintext-related color image encryption scheme. Firstly, a new five-dimensional hyperchaotic system is constructed in this paper, and its performance is analyzed. Secondly, this paper applies the Hopfield chaotic neural network together with the novel hyperchaotic system to propose a new encryption algorithm. The plaintext-related keys are generated by image chunking. The pseudo-random sequences iterated by the aforementioned systems are used as key streams. Therefore, the proposed pixel-level scrambling can be completed. Then the chaotic sequences are utilized to dynamically select the rules of DNA operations to complete the diffusion encryption. This paper also presents a series of security analyses of the proposed encryption scheme and compares it with other schemes to evaluate its performance. The results show that the key streams generated by the constructed hyperchaotic system and the Hopfield chaotic neural network improve the key space. The proposed encryption scheme provides a satisfying visual hiding result. Furthermore, it is resistant to a series of attacks and the problem of structural degradation caused by the simplicity of the encryption system’s structure.     

基于WT算法联合混沌理论的图像加密研究

图像加密作为信息加密领域的重要一支,其对于信息安全的重要性显得愈发重要,能够有效地对目标图像信息进行加解密逐步成为了人们的研究热点。为了提高图像加密的安全性,以混沌系统所具有的初值敏感性以及类似随机为基础,提出了采用“混沌变换”方法对图像进行置乱操作的算法,随后以此为基础结合小波理论设计一种图像加密算法。在图像的预处理阶段首先对图像采用小波变换得到四幅小波子图;随后基于混沌置换将四幅子图置乱处理;最后通过小波逆变换恢复出目标加密图像。通过数值仿真实验表明通过该方法解密获得的图像具有与原图像非常高的一致性,并且获得了较高的安全性。     

A Novel Image Encryption Algorithm Based on Improved Arnold Transform and Chaotic Pulse-Coupled Neural Network

Information security has become a focal topic in the information and digital age. How to realize secure transmission and the secure storage of image data is a major research focus of information security. Aiming at this hot topic, in order to improve the security of image data transmission, this paper proposes an image encryption algorithm based on improved Arnold transform and a chaotic pulse-coupled neural network. Firstly, the oscillatory reset voltage is introduced into the uncoupled impulse neural network, which makes the uncoupled impulse neural network exhibit chaotic characteristics. The chaotic sequence is generated by multiple iterations of the chaotic pulse-coupled neural network, and then the image is pre-encrypted by XOR operation with the generated chaotic sequence. Secondly, using the improved Arnold transform, the pre-encrypted image is scrambled to further improve the scrambling degree and encryption effect of the pre-encrypted image so as to obtain the final ciphertext image. Finally, the security analysis and experimental simulation of the encrypted image are carried out. The results of quantitative evaluation show that the proposed algorithm has a better encryption effect than the partial encryption algorithm. The algorithm is highly sensitive to keys and plaintexts, has a large key space, and can effectively resist differential attacks and attacks such as noise and clipping.     

A New Hyperchaotic 4D-FDHNN System with Four Positive Lyapunov Exponents and Its Application in Image Encryption

In this paper, a hyperchaotic four-dimensional fractional discrete Hopfield neural network system (4D-FDHNN) with four positive Lyapunov exponents is proposed. Firstly, the chaotic dynamics’ characteristics of the system are verified by analyzing and comparing the iterative trajectory diagram, phase diagram, attractor diagram, 0-1 test, sample entropy, and Lyapunov exponent. Furthermore, a novel image encryption scheme is designed to use the chaotic system as a pseudo-random number generator. In the scenario, the confusion phase using the fractal idea proposes a fractal-like model scrambling method, effectively enhancing the complexity and security of the confusion. For the advanced diffusion phase, we proposed a kind of Hilbert dynamic random diffusion method, synchronously changing the size and location of the pixel values, which improves the efficiency of the encryption algorithm. Finally, simulation results and security analysis experiments show that the proposed encryption algorithm has good efficiency and high security, and can resist common types of attacks.     

基于多混沌系统的双图像光学加密算法

为了扩展双图像光学加密算法的密钥空间,克服双随机相位加密系统中随机相位掩模作为密钥难于存储、传输和重构的问题,突破传统图像加密的研究思路,提出了一种基于多混沌系统的双图像加密算法,构造了光学加密系统。系统增加混沌系统参数作为密钥,利用混沌加密密钥空间大和图像置乱隐藏性好的特点,构建基于Logistic混沌映射的图像置乱算法,利用Kent混沌映射生成的伪随机序列构造出一对随机相位掩模,分别放置在分数傅里叶变换光学装置的两端,图像经加密系统变换后得到密文。数值仿真结果表明,算法的密钥敏感性极高,能够有效地对抗统计攻击,具有较高的安全性。     

Single Neuronal Dynamical System in Self-Feedbacked Hopfield Networks and Its Application in Image Encryption

Image encryption is a confidential strategy to keep the information in digital images from being leaked. Due to excellent chaotic dynamic behavior, self-feedbacked Hopfield networks have been used to design image ciphers. However, Self-feedbacked Hopfield networks have complex structures, large computational amount and fixed parameters; these properties limit the application of them. In this paper, a single neuronal dynamical system in self-feedbacked Hopfield network is unveiled. The discrete form of single neuronal dynamical system is derived from a self-feedbacked Hopfield network. Chaotic performance evaluation indicates that the system has good complexity, high sensitivity, and a large chaotic parameter range. The system is also incorporated into a framework to improve its chaotic performance. The result shows the system is well adapted to this type of framework, which means that there is a lot of room for improvement in the system. To investigate its applications in image encryption, an image encryption scheme is then designed. Simulation results and security analysis indicate that the proposed scheme is highly resistant to various attacks and competitive with some exiting schemes.     

Efficient Entropic Security with Joint Compression and Encryption Approach Based on Compressed Sensing with Multiple Chaotic Systems

This paper puts forward a new algorithm that utilizes compressed sensing and two chaotic systems to complete image compression and encryption concurrently. First, the hash function was utilized to obtain the initial parameters of two chaotic maps, which were the 2D-SLIM and 2D-SCLMS maps, respectively. Second, a sparse coefficient matrix was transformed from the plain image through discrete wavelet transform. In addition, one of the chaotic sequences created by 2D-SCLMS system performed pixel transformation on the sparse coefficient matrix. The other chaotic sequences created by 2D-SLIM were utilized to generate a measurement matrix and perform compressed sensing operations. Subsequently, the matrix rotation was combined with row scrambling and column scrambling, respectively. Finally, the bit-cycle operation and the matrix double XOR were implemented to acquire the ciphertext image. Simulation experiment analysis showed that the compressed encryption scheme has advantages in compression performance, key space, and sensitivity, and is resistant to statistical attacks, violent attacks, and noise attacks.     

FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient

A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and dynamically analyzed,and implemented on FPGA.Then,a new pseudo-random number generator(PRNG)based on MHNN is proposed.The post-processing unit of the PRNG is composed of nonlinear post-processor and XOR calculator,which effectively ensures the randomness of PRNG.The experiments in this paper comply with the IEEE 754-1985 high precision32-bit floating point standard and are done on the Vivado design tool using a Xilinx XC7 Z020 CLG400-2 FPGA chip and the Verilog-HDL hardware programming language.The random sequence generated by the PRNG proposed in this paper has passed the NIST SP800-22 test suite and security analysis,proving its randomness and high performance.Finally,an image encryption system based on PRNG is proposed and implemented on FPGA,which proves the value of the image encryption system in the field of data encryption connected to the Internet of Things(Io T).     

离散分数阶随机变换与加权直方图交叉置乱的双图像加密算法

为了实现对两幅图像进行同步加密,降低传输负载并提高密文的抗明文攻击能力,提出了离散分数阶随机变换与加权像素混沌置乱的双图像加密算法。将2个分阶参数引入到Tent映射中,设计了新的Tent映射;根据明文像素值,构建加权像素直方图模型,联合位外部密钥,生成改进的Tent映射的初值;再利用初值对分数阶Tent映射进行迭代,输出2组随机序列,对2幅明文进行位置交叉混淆,获取2个置乱密文;基于DWT(discrete wavelet transform)技术,对2个置乱密文进行稀疏表示;根据混沌序列,定义随机循环矩阵,联合稀疏表示,获取2个置乱密文对应的测量矩阵。根据随机掩码与调制相位掩码,建立数据融合模型,将2个测量矩阵组合为复合矩阵;基于离散分数阶随机变换,对复合图像进行扩散,获取密文。测试数据显示:与已有的多图像加密方案相比,该算法的抗明文攻击能力与用户响应值更理想,密文的NPCR、UACI值分别达到了99.83%、34.57%。该算法具有较高的加密安全性,能够有效抵御网络中的外来攻击,确保图像安全传输。     

A Hybrid Domain Image Encryption Algorithm Based on Improved Henon Map

A hybrid domain image encryption algorithm is developed by integrating with improved Henon map, integer wavelet transform (IWT), bit-plane decomposition, and deoxyribonucleic acid (DNA) sequence operations. First, we improve the classical two-dimensional Henon map. The improved Henon map is called 2D-ICHM, and its chaotic performance is analyzed. Compared with some existing chaotic maps, 2D-ICHM has larger parameter space, continuous chaotic range, and more complex dynamic behavior. Second, an image encryption structure based on diffusion–scrambling–diffusion and spatial domain–frequency domain–spatial domain is proposed, which we call the double sandwich structure. In the encryption process, the diffusion and scrambling operations are performed in the spatial and frequency domains, respectively. In addition, initial values and system parameters of the 2D-ICHM are obtained by the secure hash algorithm-512 (SHA-512) hash value of the plain image and the given parameters. Consequently, the proposed algorithm is highly sensitive to plain images. Finally, simulation experiments and security analysis show that the proposed algorithm has a high level of security and strong robustness to various cryptanalytic attacks.     

An image encryption algorithm based on improved baker transformation and chaotic S-box

The algorithm is an image encryption algorithm based on the improved baker transformation and chaotic substitution box(S-box). It mainly uses the initial values and parameters of a one-dimensional logistic chaotic system as an encryption key. Specifically, in the image scrambling stage, the algorithm primarily uses an improved baker transform method to process the image. In the image diffusion stage, the algorithm first uses the chaotic S-box method to process the encryption key. Secondly, an exclusive OR(XOR) operation is performed on the image and the encryption key to initially diffuse the image. Finally, the image is again diffused using the method of ortho XOR. Simulation analysis shows that the algorithm can achieve good encryption effect, simple and easy implementation, and good security. In the digital image communication transmission, it has good practical value.     

An Encryption Algorithm for Region of Interest in Medical DICOM Based on One-Dimensional eλ-cos-cot Map

Today, with the rapid development of the Internet, improving image security becomes more and more important. To improve image encryption efficiency, a novel region of interest (ROI) encryption algorithm based on a chaotic system was proposed. First, a new 1D eλ-cos-cot (1D-ECC) with better chaotic performance than the traditional chaotic system is proposed. Second, the chaotic system is used to generate a plaintext-relate keystream based on the label information of a medical image DICOM (Digital Imaging and Communications in Medicine) file, the medical image is segmented using an adaptive threshold, and the segmented region of interest is encrypted. The encryption process is divided into two stages: scrambling and diffusion. In the scrambling stage, helical scanning and index scrambling are combined to scramble. In the diffusion stage, two-dimensional bi-directional diffusion is adopted, that is, the image is bi-directionally diffused row by column to make image security better. The algorithm offers good encryption speed and security performance, according to simulation results and security analysis.     

Scaling Analysis of an Image Encryption Scheme Based on Chaotic Dynamical Systems

Despite that many image encryption systems based on chaotic or hyperchaotic systems have been proposed to protect different kinds of information, it has been crucial to achieve as much security as possible in such systems. In this sense, we numerically implement a known image encryption system with some variants, making special emphasis when two operations are considered in the scrambling stage. The variants of such an encryption system are based on some hyperchaotic systems, which generated some substitution boxes and the keys of the system. With the aim to have a more complete evaluation, some internal stages of the image encryption scheme have been evaluated by using common statistical tests, and also the scaling behavior of the encrypted images has been calculated by means of a two-dimensional detrended fluctuation analysis (2D-DFA). Our results show that the image encryption systems that include two operations or transformations in the scrambling stage present a better performance than those encryption systems that consider just one operation. In fact, the 2D-DFA approach was more sensitive than some common statistical tests to determine more clearly the impact of multiple operations in the scrambling process, confirming that this scaling method can be used as a perceptual security metric, and it may contribute to having better image encryption systems.     

A Bit Shift Image Encryption Algorithm Based on Double Chaotic Systems

A chaotic system refers to a deterministic system with seemingly random irregular motion, and its behavior is uncertain, unrepeatable, and unpredictable. In recent years, researchers have proposed various image encryption schemes based on a single low-dimensional or high-dimensional chaotic system, but many algorithms have problems such as low security. Therefore, designing a good chaotic system and encryption scheme is very important for encryption algorithms. This paper constructs a new double chaotic system based on tent mapping and logistic mapping. In order to verify the practicability and feasibility of the new chaotic system, a displacement image encryption algorithm based on the new chaotic system was subsequently proposed. This paper proposes a displacement image encryption algorithm based on the new chaotic system. The algorithm uses an improved new nonlinear feedback function to generate two random sequences, one of which is used to generate the index sequence, the other is used to generate the encryption matrix, and the index sequence is used to control the generation of the encryption matrix required for encryption. Then, the encryption matrix and the scrambling matrix are XORed to obtain the first encryption image. Finally, a bit-shift encryption method is adopted to prevent the harm caused by key leakage and to improve the security of the algorithm. Numerical experiments show that the key space of the algorithm is not only large, but also the key sensitivity is relatively high, and it has good resistance to various attacks. The analysis shows that this algorithm has certain competitive advantages compared with other encryption algorithms.     

Image feature extraction by dynamic neural filtering and phase-only joint transform correlation

Neural network-based image processing algorithms present numerous advantages due to their supervised adjustable properties. Among various neural network architectures, dynamic neural networks, Hopfield and Cellular networks, have been found inherently suitable for filtering applications. Combining supervised and filtering features of dynamic neural networks, this paper presents dynamic neural filtering technique based on Hopfield neural network architecture. The filtering technique has also been implemented by using phase-only joint transform correlation (POJTC) for optical image processing applications. Filtering structure is basically similar to the Hopfield neural network structure except for the adjustable filter mask and 2D convolution operation instead of weight matrix operations. The dynamic neural filtering architecture has learnable properties by back-propagation learning algorithm. POJTC presents significant advantages to achieve the operation of summing the cross-correlation of bipolar data by phase-encoding bipolar data in parallel. The image feature extraction performance of the proposed optical system is reported for various image processing applications using a simulation program.     

Multi-Image Compression–Encryption Algorithm Based on Compressed Sensing and Optical Encryption

In order to achieve large-capacity, fast and secure image transmission, a multi-image compression–encryption algorithm based on two-dimensional compressed sensing (2D CS) and optical encryption is proposed in this paper. Firstly, the paper uses compressed sensing to compress and encrypt multiple images simultaneously, and design a new structured measurement matrix. Subsequently, double random phase encoding based on the multi-parameter fractional quaternion Fourier transform is used to encrypt the multiple images for secondary encryption, which improves the security performance of the images. Moreover, a fractional-order chaotic system with more complex chaotic behavior is constructed for image compression and encryption. Experimental results show that the algorithm has strong robustness and security.     

基于组合混沌和位运算的图像加密算法

为了有效改进图像加密效果及其安全性,在对基于混沌系统及位运算的图像加密算法进行研究的基础上,提出基于组合混沌和位运算的图像加密算法,算法先对灰度图像进行位平面分解,考虑到图像的高四位含有较大的信息量,对高四位分别进行置乱变换,再与低四位构成一个整体进行置乱变换,然后组合置乱后的位平面,并与二值矩阵进行异或运算得到密文图像。实验结果表明,与像素位置置换算法和二维数据加密算法比较,改进算法具有更好的加密效率,密钥空间接近2192,具有较好的安全性,且能较好地抵御椒盐噪声和高斯噪声攻击,有效恢复出原始图像。     

Multi-Image Encryption Algorithm Based on Cascaded Modulation Chaotic System and Block-Scrambling-Diffusion

To address the problem of a poor security image encryption algorithm based on a single chaotic map, this paper proposes a cascade modulation chaotic system (CMCS) that can generate multiple chaotic maps. On this basis, a multi-image encryption algorithm with block-scrambling-diffusion is proposed using CMCS. The algorithm makes full use of the features of CMCS to achieve the effect of one encryption at a time for images. Firstly, the key-value associated with the plaintexts is generated using a secure hash algorithm-512 (SHA-512) operation and random sequence, and the three images are fully confused by the double scrambling mechanism. Secondly, the scrambled image is converted into a bit-level matrix, and the pixel values are evenly distributed using the bit-group diffusion. Finally, the non-sequence diffusion of hexadecimal addition and subtraction rules is used to improve the security of the encryption algorithm. Experimental results demonstrate that the encryption algorithm proposed in this paper has a good encryption effect and can resist various attacks.     

An Image Encryption Algorithm Based on Complex Network Scrambling and Multi-Directional Diffusion

Various security threats are encountered when keys are transmitted in public channels. In this paper, we propose an image encryption algorithm based on complex network scrambling and multi-directional diffusion. Combining the idea of public key cryptography, the RSA algorithm is used to encrypt the key related to plaintext. The algorithm consists of three stages: key generation stage, complex network scrambling stage, and multi-directional diffusion stage. Firstly, during the key generation phase, SHA-512 and the original image are used to generate plaintext-related information, which is then converted to plaintext-related key through transformation mapping. Secondly, in the complex network scrambling stage, the chaotic random matrix establishes the node relationships in the complex network, which is then used to construct an image model based on the complex network, and then combines pixel-level and block-level methods to scramble images. Finally, in the multi-directional diffusion stage, the multi-directional diffusion method is used to perform forward diffusion, middle spiral diffusion, and backward diffusion on the image in turn to obtain the final ciphertext image. The experimental results show that our encryption algorithm has a large keyspace, the encrypted image has strong randomness and robustness, and can effectively resist brute force attack, statistical attack, and differential attack.     

Image encryption with fractional wavelet packet method

We introduce a new method called fractional wavelet packet transform to encrypt images in this paper, in which fractional orders and wavelet packet filter are its two series of keys. Fractional orders are additional keys in this method compared to wavelet packet encryptions. Selected image encryption is also proposed in this paper, and it is quite more flexible and effective than wavelet, fractional wavelet or wavelet packet encryptions. The possible optical implementation and digital computation are proposed. Computer simulations prove its feasibility.