Single-channel color image encryption using phase retrieve algorithm in fractional Fourier domain

A single-channel color image encryption is proposed based on a phase retrieve algorithm and a two-coupled logistic map. Firstly, a gray scale image is constituted with three channels of the color image, and then permuted by a sequence of chaotic pairs generated by the two-coupled logistic map. Secondly, the permutation image is decomposed into three new components, where each component is encoded into a phase-only function in the fractional Fourier domain with a phase retrieve algorithm that is proposed based on the iterative fractional Fourier transform. Finally, an interim image is formed by the combination of these phase-only functions and encrypted into the final gray scale ciphertext with stationary white noise distribution by using chaotic diffusion, which has camouflage property to some extent. In the process of encryption and decryption, chaotic permutation and diffusion makes the resultant image nonlinear and disorder both in spatial domain and frequency domain, and the proposed phase iterative algorithm has faster convergent speed. Additionally, the encryption scheme enlarges the key space of the cryptosystem. Simulation results and security analysis verify the feasibility and effectiveness of this method.     

Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain

The classical double random phase encoding technique (DRPE) is vulnerable to chosen ciphertext attacks, known-plaintext attacks and chosen-plaintext attacks for its linearity. In order to avoid the disadvantages originated from the linearity and symmetric, an improved method for multiple-image encryption based on nonlinear operations in Fourier domain is proposed. The random phase masks (RPMs) for encryption and additive keys which are determined by the original images and generated by the nonlinear operations in encryption process, are necessary for image decoding. As a result of the nonlinear operations, the increase in the number of keys, removal of linearity and high robustness could be achieved in this cryptosystem. Computer simulations are presented to demonstrate its good performance, and the security is analyzed as well.     

Multiple-image encryption algorithm based on mixed image element and permutation

To improve encryption efficiency and facilitate the secure transmission of multiple digital images, by defining the pure image element and mixed image element, this paper presents a new multiple-image encryption (MIE) algorithm based on the mixed image element and permutation, which can simultaneously encrypt any number of images. Firstly, segment the original images into pure image elements; secondly, scramble all the pure image elements with the permutation generated by the piecewise linear chaotic map (PWLCM) system; thirdly, combine mixed image elements into scrambled images; finally, diffuse the content of mixed image elements by performing the exclusive OR (XOR) operation among scrambled images and the chaotic image generated by another PWLCM system. The comparison with two similar algorithms is made. Experimental results and algorithm analyses show that the proposed MIE algorithm is very simple and efficient, which is suitable for practical image encryption.     

Optical encryption by double-random phase encoding in the fractional Fourier domain

We propose an optical architecture that encodes a primary image to stationary white noise by using two statistically independent random phase codes. The encoding is done in the fractional Fourier domain. The optical distribution in any two planes of a quadratic phase system (QPS) are related by fractional Fourier transform of the appropriately scaled distribution in the two input planes. Thus a QPS offers a continuum of planes in which encoding can be done. The six parameters that characterize the QPS in addition to the random phase codes form the key to the encrypted image. The proposed method has an enhanced security value compared with earlier methods. Experimental results in support of the proposed idea are presented.     

Double image encryption based on linear blend operation and random phase encoding in fractional Fourier domain

A novel method for double image encryption is proposed by using linear blend operation and double-random phase encoding (DRPE) in the fractional Fourier domain. In the linear blend operation, a random orthogonal matrix is defined to linearly recombined pixel values of two original images. The resultant blended images are employed to constitute a complex-valued image, which is encrypted into an encrypted image with stationary white distribution by the DRPE in the fractional Fourier domain. The primitive images can be exactly recovered by applying correct keys with fractional orders, random phase masks and random angle function that is used in linear blend operation. Numerical simulations demonstrate that the proposed scheme has considerably high security level and certain robustness against data loss and noise disturbance.     

Multiple-image encryption with bit-plane decomposition and chaotic maps

Image encryption is an efficient technique of image content protection. In this work, we propose a useful image encryption algorithm for multiple grayscale images. The proposed algorithm decomposes input images into bit-planes, randomly swaps bit-blocks among different bit-planes, and conducts XOR operation between the scrambled images and secret matrix controlled by chaotic map. Finally, an encrypted PNG image is obtained by viewing four scrambled grayscale images as its red, green, blue and alpha components. Many simulations are done to illustrate efficiency of our algorithm.     

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.     

Image encryption by using local random phase encoding in fractional Fourier transform domains

Based on fractional Fourier transform, an image encryption algorithm is proposed and researched. A local random phase encoding is introduced into this algorithm. The data at the local area of complex function is converted by fractional Fourier transform. The local random phase encoding is performed many times. Moreover only one set of random phase data is used in image encryption process. Compare to double random phase encoding, the parameter defining local area can be regarded as the additional key to increase the security of the encryption scheme. Some numerical simulations are achieved to demonstrate the performance of the image encryption scheme.     

Multiple-image hiding in the Fresnel domain

To avoid additive cross-talk among multiple images, they are separated from each other and even from the host image in the hiding and the extraction process by locating them independently in the Fresnel domain with computer-generated double phase-only masks. Gray images and white-ground and black-ground binary images can be hidden in the system at the same time. The hiding capacity of the system as to these three types of multiple image has also been investigated using a cascaded iterative algorithm. The security and the multiplexing parameters of the system are analyzed as well.     

Color image encryption and decryption for twin images in fractional Fourier domain

We propose a method for the encryption of twin color images using fractional Fourier transform (FRT). The color images to be encrypted are converted into the indexed image formats before being processed through twin image encryption algorithm based on the FRT. The proposed algorithm uses one random code in the image domain and one random phase code in the FRT domain to perform double image encryption. The conversion of both the input RGB images into their indexed formats facilitates single-channel processing for each image, and is more compact and robust as compared to multichannel techniques. Different fractional orders, the random masks in image- and FRT domain are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption schemes are discussed, and results of digital simulation are presented. We examine sensitivity of the proposed scheme against the use of unauthorized keys (e.g. incorrect fractional orders, incorrect random phase mask etc.). Robustness of the method against occlusion and noise has also been discussed.     

Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

Color image encryption and decryption using fractional Fourier transform

We propose the encryption of color images using fractional Fourier transform (FRT). The image to be encrypted is first segregated into three color channels: red, green, and blue. Each of these channels is encrypted independently using double random phase encoding in the FRT domain. The different fractional orders and random phase masks used during the process of encryption and decryption are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption scheme are discussed, and results of digital simulation are presented. The technique is shown to be a powerful one for colored text encryption. We also outline the implementation of the algorithm and examine its sensitiveness to changes in the fractional order during decryption.     

分数傅里叶域中二维复图像相位恢复的混合输入输出算法

通过推广经典傅里叶域内的混合输入输出算法,研究分数傅里叶域内二维复图像的相位恢复问题。给出算法的具体实施过程,并进行了数值模拟。结果表明：对于级次在0与2之间的分数傅里叶变换,当级次在1/2与3/2之间时,该算法较好;对于其余的级次,该算法的效果不能令人满意。     

Nonlinear image encryption using a fully phase nonzero-order joint transform correlator in the Gyrator domain

A novel nonlinear image encryption scheme based on a fully phase nonzero-order joint transform correlator architecture (JTC) in the Gyrator domain (GD) is proposed. In this encryption scheme, the two non-overlapping data distributions of the input plane of the JTC are fully encoded in phase and this input plane is transformed using the Gyrator transform (GT); the intensity distribution captured in the GD represents a new definition of the joint Gyrator power distribution (JGPD). The JGPD is modified by two nonlinear operations with the purpose of retrieving the encrypted image, with enhancement of the decrypted signal quality and improvement of the overall security. There are three keys used in the encryption scheme, two random phase masks and the rotation angle of the GT, which are all necessary for a proper decryption. Decryption is highly sensitivity to changes of the rotation angle of the GT as well as to little changes in other parameters or keys. The proposed encryption scheme in the GD still preserves the shift-invariance properties originated in the JTC-based encryption in the Fourier domain. The proposed encryption scheme is more resistant to brute force attacks, chosen-plaintext attacks, known-plaintext attacks, and ciphertext-only attacks, as they have been introduced in the cryptanalysis of the JTC-based encryption system. Numerical results are presented and discussed in order to verify and analyze the feasibility and validity of the novel encryption–decryption scheme.     

Image watermarking by using phase retrieval algorithm in gyrator transform domain

We propose an image watermarking scheme based on the phase retrieval algorithm in gyrator domain. The watermark is converted into a noise-like image by Arnold transform. The scrambled image is regarded as the amplitude of gyrator spectrum. The Gerchberg-Saxton algorithm is employed to obtain the unknown phase function in gyrator pair, in which the host image is the amplitude of input function. The phase information and the parameters of the two transforms serve as the key of watermarking algorithm. The numerical simulation has demonstrated the performance of the proposed algorithm.     

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.     

Logarithms-based RGB image encryption in the fractional Fourier domain: A non-linear approach

We propose a non-linear image encryption scheme for RGB images, using natural logarithms and fractional Fourier transform (FRT). The RGB image is first segregated into the component color channels and each of these components is hidden inside a random mask (RM) using base changing rule of logarithms. Subsequently, these channels are encrypted independently using random phase masks (RPMs) and the FRT. The fractional orders of the FRT, input random masks and random phase masks used in each channel serve as the keys for encryption and decryption. The algorithms to implement the proposed scheme are discussed, and results of digital simulation are presented. The robustness of the technique is analyzed against the variation in fractional orders of the FRT, change of RMs and RPMs, and occlusion of the encrypted data, respectively. Performance of the scheme has also been studied against the attacks using noise and partial windows of the correct RPMs. The proposed technique is shown to perform better against some attacks in comparison to the conventional linear methods.     

Asymmetric multiple-image hiding using phase retrieval technique based on amplitude- and phase-truncation in fractional Fourier domain

We propose a multiple-image hiding scheme based on the amplitude- and phase-truncation approach, and phase retrieval iterative algorithm in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys. Multiple input images multiplied with random phase masks are independently fractional Fourier transformed with different orders. The individual keys and common keys are generated by using phase and amplitude truncation of fractional spectrum. After using two fractional Fourier transform, the resultant encrypted image is hided in a host image with phase retrieval iterative algorithm. Using the correct universal keys, individual keys, and fractional orders, one can recover the original image successfully. Computer simulation results with four gray-scale images support the proposed method. To measure the validity of the scheme, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and generation of decryption keys are complicated and should be realized using computer. For decryption, an optoelectronic setup has been suggested.     

Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane

In the present paper, we describe multiplexing in optical encryption of two-dimensional images, by using apertures and rotation of one of the constituent phase diffusers of a sandwich phase diffuser in the Fourier plane. The sandwich phase diffuser is made with two random constituent phase-diffusing surfaces sandwiched together. The apertures of different sizes and shapes are made with the help of ‘paint brush’ software. Simulation results are presented showing the effects of size, shape, and orientation of the apertures on the decrypted images obtained via multiplexing techniques. In addition to the results of using aperture systems in encryption and decryption, the results of rotation of one of the constituent phase diffusers in decryption are analyzed and used in multiplexing. Due to the use of aperture systems and the rotation of the constituent phase diffuser, the multiplexing capability of the system in encryption is enhanced along with the enhanced security due to using a sandwich diffuser. To evaluate the reliability of the technique, mean square error between the decrypted and the original image has been calculated.