Asymmetric multiple-image encryption based on coupled logistic maps in fractional Fourier transform domain

A multiple-image encryption scheme is proposed based on the asymmetric technique, in which the encryption keys are not identical to the decryption ones. First, each plain image is scrambled based on a sequence of chaotic pairs generated with a system of two symmetrically coupled identical logistic maps. Then, the phase-only function of each scrambled image is retrieved with an iterative phase retrieval process in the fractional Fourier transform domain. Second, all phase-only functions are modulated into an interim, which is encrypted into the ciphertext with stationary white noise distribution by using the fractional Fourier transform and chaotic diffusion. In the encryption process, three random phase functions are used as encryption keys to retrieve the phase-only functions of plain images. Simultaneously, three decryption keys are generated in the encryption process, which make the proposed encryption scheme has high security against various attacks, such as chosen plaintext attack. The peak signal-to-noise is used to evaluate the quality of the decrypted image, which shows that the encryption capacity of the proposed scheme is enhanced considerably. Numerical simulations demonstrate the validity and efficiency of the proposed method.     

Optical encryption scheme for multiple color images using complete trinary tree structure

We propose an optical encryption scheme for multiple color images based on the complete trinary tree structure. In the proposed encryption scheme, the encryption modules (EMs) are taken as branch nodes, and the color components of plain images are input as leaf nodes. In each EM which consists of phase truncated Fresnel transforms and random amplitude-phase masks, three input images are subsequently encoded into a complex function and finally encrypted to a real-value image. The proposed encryption scheme can encrypt multiple color images into a real-value grayscale cipher image, and make different color images have different encryption and decryption paths. By the proposed encryption scheme, we can realize an authority management with high security among multiple users. In addition, the proposed scheme possesses the advantages such as high robustness against various attacks and high encryption efficiency. Moreover, as the number of plain color images increases, high quality of the decrypted color images can still be maintained. Extensive simulation results have shown the performance of the proposed scheme. The proposed scheme can also be directly extended to encrypt multiple gray images.     

An algorithm for encryption of secret images into meaningful images

Image encryption algorithms typically transform a plain image into a noise-like cipher image, whose appearance is an indication of encrypted content. Bao and Zhou [Image encryption: Generating visually meaningful encrypted images, Information Sciences 324, 2015] propose encrypting the plain image into a visually meaningful cover image. This improves security by masking existence of encrypted content. Following their approach, we propose a lossless visually meaningful image encryption scheme which improves Bao and Zhou's algorithm by making the encrypted content, i.e. distortions to the cover image, more difficult to detect. Empirical results are presented to show high quality of the resulting images and high security of the proposed algorithm. Competence of the proposed scheme is further demonstrated by means of comparison with Bao and Zhou's scheme.     

Color-image encryption scheme based on channel fusion and spherical diffraction

A secure encryption scheme for color images based on channel fusion and spherical diffraction is proposed in this paper. In the proposed encryption scheme, a channel fusion technology based on the discrete wavelet transformation is used to transform color images into single-channel grayscale images, firstly. In the process of transformation, the hyperchaotic system is used to permutate and diffuse the information of red—green—blue (RGB) channels to reduce the correlation of channels. Then the fused image is encrypted by spherical diffraction transform. Finally, the complex-valued diffraction result is decomposed into two real parts by the improved equal module decomposition, which are the ciphertext and the private key. Compared with the traditional color image encryption schemes that encrypt RGB channels separately, the proposed scheme is highly secure and robust.     

Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence

The paper studies a recently developed evolutionary-based image encryption algorithm. A novel image encryption algorithm based on a hybrid model of deoxyribonucleic acid (DNA) masking, a genetic algorithm (GA) and a logistic map is proposed. This study uses DNA and logistic map functions to create the number of initial DNA masks and applies GA to determine the best mask for encryption. The significant advantage of this approach is improving the quality of DNA masks to obtain the best mask that is compatible with plain images. The experimental results and computer simulations both confirm that the proposed scheme not only demonstrates excellent encryption but also resists various typical attacks.     

A 3D image encryption technique using computer-generated integral imaging and cellular automata transform

A novel three-dimensional (3D) image encryption approach by using the computer-generated integral imaging and cellular automata transform (CAT) is proposed, in which, the two-dimensional (2D) elemental image array (EIA) digitally recorded by light rays coming from the 3D image is mapped inversely through the virtual pinhole array according to the ray-tracing theory. Next, the encrypted image is generated by using the 2D CAT scrambling transform for the 2D EIA. The reconstructed process is carried out by using the modified computational integral-imaging reconstruction (CIIR) technique; the depth-dependent plane images are reconstructed on the output plane. The reconstructed 3D image quality of the proposed scheme can be greatly improved, because the proposed encryption scheme carries out in a computer which can avoid the light diffraction caused by optical device CIIR, and solves blur problem caused by CIIR by using the pixel-averaging algorithm. Furthermore, the CAT-based encryption algorithm is an error-free encryption method; CAT as an orthogonal transformation offers considerable simplicity in the calculation of the transform coefficient, that is, it can improve the quality of the reconstructed image by reducing energy loss compared with the traditional complicated transform process. To show the effectiveness of the proposed scheme, we perform computational experiments. Experimental results show that the proposed scheme outperforms conventional encryption methods.     

A Novel Image Encryption Scheme Based on Elliptic Curves over Finite Rings

Image encryption based on elliptic curves (ECs) is emerging as a new trend in cryptography because it provides high security with a relatively smaller key size when compared with well-known cryptosystems. Recently, it has been shown that the cryptosystems based on ECs over finite rings may provide better security because they require the computational cost for solving the factorization problem and the discrete logarithm problem. Motivated by this fact, we proposed a novel image encryption scheme based on ECs over finite rings. There are three main steps in our scheme, where, in the first step, we mask the plain image using points of an EC over a finite ring. In step two, we create diffusion in the masked image with a mapping from the EC over the finite ring to the EC over the finite field. To create high confusion in the plain text, we generated a substitution box (S-box) based on the ordered EC, which is then used to permute the pixels of the diffused image to obtain a cipher image. With computational experiments, we showed that the proposed cryptosystem has higher security against linear, differential, and statistical attacks than the existing cryptosystems. Furthermore, the average encryption time for color images is lower than other existing schemes.     

Cryptographic Algorithm Using Newton-Raphson Method and General Bischi-Naimzadah Duopoly System

Image encryption is an excellent method for the protection of image content. Most authors used the permutation-substitution model to encrypt/decrypt the image. Chaos-based image encryption methods are used in this model to shuffle the rows/columns and change the pixel values. In parallel, authors proposed permutation using non-chaotic methods and have displayed good results in comparison to chaos-based methods. In the current article, a new image encryption algorithm is designed using combination of Newton-Raphson’s method (non-chaotic) and general Bischi-Naimzadah duopoly system as a hyperchaotic two-dimensional map. The plain image is first shuffled by using Newton-Raphson’s method. Next, a secret matrix with the same size of the plain image is created using general Bischi-Naimzadah duopoly system. Finally, the XOR between the secret matrix and the shuffled image is calculated and then the cipher image is obtained. Several security experiments are executed to measure the efficiency of the proposed algorithm, such as key space analysis, correlation coefficients analysis, histogram analysis, entropy analysis, differential attacks analysis, key sensitivity analysis, robustness analysis, chosen plaintext attack analysis, computational analysis, and NIST statistical Tests. Compared to many recent algorithms, the proposed algorithm has good security efficiency.     

A new cryptosystem based on spatial chaotic system

Encryption of images is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which is generally difficult to handle by traditional methods. This paper proposes a new spatial chaos system (SCS), which is investigated by conducting FIPS 140-1 statistic test, and is especially useful for encryption of digital images. It is shown how to adapt a two dimensional (2D) ergodic matrix obtained from SCS to permute the positions of image pixels and confuse the relationship between the cipher image and plain image simultaneously. Experimental results show that the performance and security of the proposed cryptographic system are better than those of existing lower dimensional chaotic cryptographic systems.     

Multi-Image Encryption Method via Computational Integral Imaging Algorithm

Under the framework of computational integral imaging, a multi-image encryption scheme based on the DNA-chaos algorithm is proposed. In this scheme, multiple images are merged to one image by a computational integral imaging algorithm, which significantly improves the efficiency of image encryption. Meanwhile, the computational integral imaging algorithm can merge images at different depth distances, thereby the different depth distances of multiple images can also be used as keys to increase the security of the encryption method. In addition, the high randomness of the chaos algorithm is combined to address the outline effect caused by the DNA encryption algorithm. We have experimentally verified the proposed multi-image encryption scheme. The entropy value of the encrypted image is 7.6227, whereas the entropy value of the merge image with two input images is 3.2886, which greatly reduces the relevance of the image. The simulation results also confirm that the proposed encryption scheme has high key security and can protect against various attacks.     

Joint Lossless Image Compression and Encryption Scheme Based on CALIC and Hyperchaotic System

For efficiency and security of image transmission and storage, the joint image compression and encryption method that performs compression and encryption in a single step is a promising solution due to better security. Moreover, on some important occasions, it is necessary to save images in high quality by lossless compression. Thus, a joint lossless image compression and encryption scheme based on a context-based adaptive lossless image codec (CALIC) and hyperchaotic system is proposed to achieve lossless image encryption and compression simultaneously. Making use of the characteristics of CALIC, four encryption locations are designed to realize joint image compression and encryption: encryption for the predicted values of pixels based on gradient-adjusted prediction (GAP), encryption for the final prediction error, encryption for two lines of pixel values needed by prediction mode and encryption for the entropy coding file. Moreover, a new four-dimensional hyperchaotic system and plaintext-related encryption based on table lookup are all used to enhance the security. The security tests show information entropy, correlation and key sensitivity of the proposed methods reach 7.997, 0.01 and 0.4998, respectively. This indicates that the proposed methods have good security. Meanwhile, compared to original CALIC without security, the proposed methods increase the security and reduce the compression ratio by only 6.3%. The test results indicate that the proposed methods have high security and good lossless compression performance.     

Triple image encryption scheme in fractional Fourier transform domains

We proposed a triple image encryption scheme by use of fractional Fourier transform. In this algorithm, an original image is encoded in amplitude part and other two images are encoded into phase information. The key of encryption algorithm is obtained from the difference between the third image and the output phase of transform. In general case, random phase encoding technology is not required in the proposed algorithm. Moreover, all information of images is preserved in theory when image are decrypted with correct key. The optical implementation of the algorithm is presented with an electro-optical hybrid structure. Numerical simulations have demonstrated the efficiency and the security of this algorithm. Based on this scheme a multiple image algorithm is expanded and designed.     

A bit-level image encryption algorithm based on spatiotemporal chaotic system and self-adaptive

This paper proposes a bit-level image encryption algorithm based on spatiotemporal chaotic system which is self-adaptive. We use a bit-level encryption scheme to reduce the volume of data during encryption and decryption in order to reduce the execution time. We also use the adaptive encryption scheme to make the ciphered image dependent on the plain image to improve performance. Simulation results show that the performance and security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.     

Visual Secure Image Encryption Scheme Based on Compressed Sensing and Regional Energy

The network security transmission of digital images needs to solve the dual security problems of content and appearance. In this paper, a visually secure image compression and encryption scheme is proposed by combining compressed sensing (CS) and regional energy. The plain image is compressed and encrypted into a secret image by CS and zigzag confusion. Then, according to the regional energy, the secret image is embedded into a carrier image to obtain the final visual secure cipher image. A method of hour hand printing (HHP) scrambling is proposed to increase the pixel irrelevance. Regional energy embedding reduce the damage to the visual quality of carrier image, and the different embedding positions between images greatly enhances the security of the encryption algorithm. Furthermore, the hyperchaotic multi-character system (MCS) is utilized to construct measurement matrix and control pixels. Simulation results and security analyses demonstrate the effectiveness, security and robustness of the propose algorithm.     

A self-cited pixel summation based image encryption algorithm

In this paper, a novel image encryption algorithm is presented based on self-cited pixel summation. With the classical mechanism of permutation plus diffusion, a pixel summation of the plain image is employed to make a gravity influence on the pixel positions in the permutation stage. Then, for each pixel in every step of the diffusion stage, the pixel summation calculated from the permuted image is updated. The values from a chaotic sequence generated by an intertwining logistic map are selected by this summation. Consequently, the keystreams generated in both stages are dependent on both the plain image and the permuted image. Because of the sensitivity of the chaotic map to its initial conditions and the plain-image-dependent keystreams, any tiny change in the secret key or the plain image would lead to a significantly different cipher image. As a result, the proposed encryption algorithm is immune to the known plaintext attack (KPA) and the chosen plaintext attack (CPA). Moreover, experimental simulations and security analyses show that the proposed permutation-diffusion encryption scheme can achieve a satisfactory level of security.     

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 novel chaotic image encryption algorithm based on water wave motion and water drop diffusion models

This paper will put forward a novel chaotic image encryption algorithm with confusion–diffusion architecture. First of all, secret keys will be processed by key generator before they can really be used in the encryption scheme, and in this stage this paper associates plain image with secret keys; Secondly, by imitating the trajectory of water wave movement, encryption algorithm will do scrambling operations to the image. Thirdly, this paper combines water drop motion and dynamic look up table to realize diffusion operations. For an 8 bits pixel, this algorithm will just dispose the higher 4 bits, which is because the higher 4 bits contain the vast majority of information of the image. At last, the experiment results and security analysis show that this proposed algorithm has a desirable encryption effect. Its key space is large enough, it is sensitive to keys and plain image, its encryption speed is fast and it can resist cryptanalysis such as brute attack, differential attack, etc.     

Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain

A novel method of the optical multiple-image encryption based on the modified Gerchberg–Saxton algorithm (MGSA) is presented. This proposed method with an architecture of two adjacent phase only functions (POFs) in the Fresnel transform (FrT) domain that can extremely increase capacity of system for completely avoiding the crosstalk between the decrypted images. Each encrypted target image is separately encoded into a POF by using the MGSA which is with constraining the encrypted target image. Each created POF is then added to a prescribed fixed POF composed of a proposed MGSA-based phase encoding algorithm. Not only the wavelength and multiple-position parameters in the FrT domain as keys to increase system security, the created POFs are also served mutually as the encryption keys to decrypt target image based on cascading two POFs scheme. Compared with prior methods [23], [24], the main advantages of this proposed encryption system is that it does not need any transformative lenses and that makes it very efficient and easy to implement optically. Simulation results show that this proposed encryption system can successfully achieve the multiple-image encryption with multiple-position keys, which is more advantageous in security than previous work [24] for its decryption process with only two POFs keys to accomplish this task.     

Double image encryption based on iterative fractional Fourier transform

We present an image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders. From the encrypted image we can get two original images independently by fractional Fourier transforms with two different fractional orders. This algorithm can be independent of additional random phases as the encryption/decryption keys. Numerical results are given to analyze the capability of this proposed method. A possible extension to multi-image encryption with a fractional order multiplexing scheme has also been given.     

A novel chaos-based image encryption algorithm using DNA sequence operations

An image encryption algorithm based on chaotic system and deoxyribonucleic acid (DNA) sequence operations is proposed in this paper. First, the plain image is encoded into a DNA matrix, and then a new wave-based permutation scheme is performed on it. The chaotic sequences produced by 2D Logistic chaotic map are employed for row circular permutation (RCP) and column circular permutation (CCP). Initial values and parameters of the chaotic system are calculated by the SHA 256 hash of the plain image and the given values. Then, a row-by-row image diffusion method at DNA level is applied. A key matrix generated from the chaotic map is used to fuse the confused DNA matrix; also the initial values and system parameters of the chaotic system are renewed by the hamming distance of the plain image. Finally, after decoding the diffused DNA matrix, we obtain the cipher image. The DNA encoding/decoding rules of the plain image and the key matrix are determined by the plain image. Experimental results and security analyses both confirm that the proposed algorithm has not only an excellent encryption result but also resists various typical attacks.