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.     

Fractional Fourier plane image encryption technique using radial hilbert-, and Jigsaw transform

A new method for image encryption using integral order radial Hilbert transform (RHT) filter in the fractional Fourier transform (FRT) domain has been proposed. The technique is implemented using the popular double random phase encoding method in the fractional Fourier domain. The random phase masks (RPMs), integral orders of the RHT, fractional orders of FRT, and indices of the Jigsaw transform (JT) have been used as keys for encryption and decryption. Simulation results have been presented and the schematic representation for optical implementation has been proposed. The mean-square-error and signal-to-noise ratio between the decrypted image and the input image have been calculated for the correct as well as incorrect orders of the RHT. Effect of occlusion and noise on the performance of the proposed scheme has also been studied. The robustness of the technique has been verified against attack using partial windows of the correct random phase masks. Similar investigations have also been carried out for the chosen-, and the known-plain-text attacks.     

Image encryption based on extended fractional Fourier transform and digital holography technique

We present a new optical image encryption algorithm that is based on extended fractional Fourier transform (FRT) and digital holography technique. We can perform the encryption and decryption with more parameters compared with earlier similar methods in FRT domain. In the extended FRT encryption system, the input data to be encrypted is extended fractional Fourier transformed two times and random phase mask is placed at the output plane of the first extended FRT. By use of an interference with a wave from another random phase mask, the encrypted data is stored as a digital hologram. The data retrieval is operated by all-digital means. Computer simulations are presented to verify its validity and efficiency.     

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.     

An asymmetric single-channel color image encryption based on Hartley transform and gyrator transform

A novel asymmetric single-channel color image encryption using Hartley transform and gyrator transform is proposed. A color image is segregated into R, G, and B channels and then each channel is independently Hartley transformed. The three transformed channels are multiplied and then phase- and amplitude truncated to obtain first encrypted image and first decryption key. The encoded image is modulated with a conjugate of random phase mask. The modulated image is gyrator transformed and then phase- and amplitude truncated to get second encrypted image and second decryption key. The asymmetric (decryption) keys, random phase mask, and transformation angle of gyrator transform serve as main keys. The optoelectronic encryption and decryption systems are suggested. Numerical simulation results have been demonstrated to verify the performance and security of the proposed security system.     

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.     

Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys

A digital technique for multiplexing and encryption of four RGB images has been proposed using the fractional Fourier transform (FRT). The four input RGB images are first converted into their indexed image formats and subsequently multiplexed into a single image through elementary mathematical steps prior to the encryption. The encryption algorithm uses two random phase masks in the input- and the FRT domain, respectively. These random phase masks are especially designed using the input images. As the encryption is carried out through a single channel, the technique is more compact and faster as compared to the multichannel techniques. Different fractional orders, the random masks in input-, and FRT domain are the keys for decryption as well as de-multiplexing. The algorithms to implement the proposed multiplexing-, and encryption scheme are discussed, and results of digital simulation are presented. Simulation results show that the technique is free from cross-talk. The performance of the proposed technique has also been analyzed against occlusion, noise, and attacks using partial windows of the correct random phase keys. The robustness of the technique against known-, and chosen plain-text attacks has also been explained.     

Optical image encryption based on multichannel fractional Fourier transform and double random phase encoding technique

The optical image encryption based on multichannel fractional Fourier transform (FRT) and double random phase encoding technique is proposed. Optical principles of encoding and decoding are analyzed in detail. With this method, one can encrypt different parts of input image, respectively. The system security can be improved to some extent, not only because fractional orders and random phase masks in every channel can be set with freedom, but also because the system parameters among all channels are independent. Numerical simulation results of optical image encryption based on four channel FRT and double random phase encoding are given to verify the feasibility of the method.     

Optical security system employing shifted phase-encoded joint transform correlation

A new optical security system is proposed using a shifted phase-encoded joint transform correlation (JTC) architecture. In the proposed technique, at first, the address code is fed into two channels where one channel is shifted by 180°. The output signals from both the channels are phase-masked and then added with the input image to be encrypted. The joint power spectrum (JPS) obtained from one channel is subtracted from the JPS of the other channel, and the modified JPS is inverse Fourier transformed to yield the encrypted image. For decryption, the received signal is Fourier transformed and multiplied by the phase mask and the address code, which is then inverse Fourier transformed to generate the output signal. The proposed technique does not require complex conjugate of the address code otherwise required in the classical double random phase encryption. Also the decryption result is much more enhanced when compared to the output generated by alternate JTC techniques. Computer simulation results verify that the encryption and decryption are very much secure and efficient in both noise-free and noisy conditions.     

Optical image encryption using Hartley transform and logistic map

We propose a new method for image encryption using Hartley transform with jigsaw transform and logistic map. Logistic map has been used to generate the random intensity mask which is known as chaotic random intensity mask. The problem of bare decryption with Hartley transform has been solved by using the jigsaw transform. In the proposed technique, the image is encrypted using two methods in which the second method is the extension of the first method. In the first method, the image is encrypted using Hartley transform and jigsaw transform. In the second method, the image is encrypted using Hartley transform, jigsaw transform and logistic map. The mean square errors and the signal to noise ratio have been calculated. Robustness of the technique in terms of blind decryption and the algorithmic complexity has been evaluated. The optical implementation has been proposed. The computer simulations are presented to verify the validity of the proposed technique.     

Image encryption based on double random amplitude coding in random Hartley transform domain

We propose an image encryption scheme based on double random amplitude coding technique by using random Hartley transform, which is defined according to the random Fourier transform. The significant feature of this algorithm is that the encrypted image is real and convenient for storage as well as transfer of the encrypted information. Moreover, the algorithm has enhanced security and the correct information of original image can be well protected under bare decryption, blind decryption and brute force attacks. Numerical simulation results are also presented in support of the proposed scheme.     

基于gyrator变换和矢量分解的非对称图像加密方法

本文结合矢量分解和gyrator变换的数学实现得到了一种新的非对称图像加密算法,它将待加密图像先通过矢量分解加密到两块纯相位板中,然后利用从gyrator变换的数学实现中推导出来的加密算法加密其中一块相位板,获得最终的实值密文.另一块相位板作为解密密钥.算法的解密密钥不同于加密密钥,实现了非对称加密,加密过程中产生的两个私钥增大了算法的安全性.数值模拟结果验证了该算法的可行性和有效性.     

Image encryption based on the multiple-order discrete fractional cosine transform

A novel scheme for image encryption based-on the multiple-order discrete fractional cosine transform (MODFrCT) is proposed. The DFrCT has a similar relationship with the discrete fractional Fourier transform (DFrFT). Not only has the DFrCT many useful properties similar to the conventional discrete cosine transform, but it also has another property, namely its fraction, or its transform order. The image to be encrypted is transformed with the multiple-order DFrCT using a random row cipher key vector and a random column key vector successively, and the corresponding cipher key vectors of decryption are also very sensitive. The transmission of the encrypted image with the algorithm of the multiple-order DFrCT is faster due to its reality. The digital simulation results proved the validity and safety of this algorithm.     

Multiple information encryption by user-image-based gyrator transform hologram

A novel multiple information encryption by user-image-based gyrator transform hologram is proposed. In encryption process, each channel of the user image is phase encoded, modulated by random phase function and then gyrator transformed to get the gyrator spectrum of user image. Subsequently, each channel of the secret image is normalized, phase encoded, multiplied by modulated user image, and then gyrator transformed to obtain the gyrator spectrum of secret image. The encrypted digital hologram is recorded by the interference between the gyrator spectrum of user image and the spherical wave function. Similarly, the digital hologram for decryption is recorded by the interference between the gyrator spectrum of secret image and the spherical wave function. The multiple encrypted digital holograms are multiplexed into a final encoded hologram and the corresponding digital holograms for decryption are multiplexed into a final hologram for decryption. The wavelength and radius of the spherical wave function, and angle of gyrator transform are all essential keys for decryption. The proposed system has two main features. First, the encrypted hologram has no information about secret image. Second, the hologram for decryption used as identification key. Consequently the two marked security layers of information protection are achieved. The proposal can be realized by optoelectronic system. Numerical simulation results demonstrate the feasibility and security of the proposed technique.     

Image encryption using fractional Mellin transform,structured phase filters,and phase retrieval

An image encryption scheme has been presented by using two structured phase masks in the fractional Mellin transform (FrMT) plane of a system, employing a phase retrieval technique. Since FrMT is a non-linear integral transform, its use enhances the system security. We also add further security features by carrying out spatial filtering in the frequency domain by using a combination of two phase masks: a toroidal zone plate (TZP) and a radial Hilbert mask (RHM). These masks together increase the key space making the system more secure. The phase key used in decryption has been obtained by applying an iterative phase retrieval algorithm based on the fractional Fourier transform. The algorithm uses amplitude constraints of secret target image and the ciphertext (encrypted image) obtained from multiplication of fractional Mellin transformed arbitrary input image and the two phase masks (TZP and RHM). The proposed encryption scheme has been validated for a few grayscale images, by numerical simulations. The efficacy of the scheme has been evaluated by computing mean-squared-error (MSE) between the secret target image and the decrypted image. The sensitivity analysis of the decryption process to variations in various encryption parameters has also been carried out.     

Double-image encryption based on discrete fractional random transform and chaotic maps

A novel double-image encryption algorithm is proposed, based on discrete fractional random transform and chaotic maps. The random matrices used in the discrete fractional random transform are generated by using a chaotic map. One of the two original images is scrambled by using another chaotic map, and then encoded into the phase of a complex matrix with the other original image as its amplitude. Then this complex matrix is encrypted by the discrete fractional random transform. By applying the correct keys which consist of initial values, control parameters, and truncated positions of the chaotic maps, and fractional orders, the two original images can be recovered without cross-talk. Numerical simulation has been performed to test the validity and the security of the proposed encryption algorithm. Encrypting two images together by this algorithm creates only one encrypted image, whereas other single-image encryption methods create two encrypted images. Furthermore, this algorithm requires neither the use of phase keys nor the use of matrix keys. In this sense, this algorithm can raise the efficiency when encrypting, storing or transmitting.     

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 image encryption using improper Hartley transforms and chaos

We propose a new method for image encryption using improper Hartley transform and chaos theory. Improper Hartley transform is a Hartley transform in which the phase between the two Fourier transforms is a fractional multiple of π/2. This fractional order is called fractional parameter and serves as a key in the image encryption and decryption process. Four types of chaos functions have been used. These functions are the logistic map, the tent map, the Kaplan-Yorke map and the Ikeda map. Random intensity masks have been generated using these chaotic functions and are called chaotic random intensity masks. The image is encrypted by using improper Hartley transform and two chaotic random intensity masks. The mean square error has been calculated. The robustness of the proposed technique in terms of blind decryption has been tested. The computer simulations are presented to verify the validity of the proposed technique.     

Asymmetric multiple-image encryption based on the cascaded fractional Fourier transform

A multiple-image cryptosystem is proposed based on the cascaded fractional Fourier transform. During an encryption procedure, each of the original images is directly separated into two phase masks. A portion of the masks is subsequently modulated into an interim mask, which is encrypted into the ciphertext image; the others are used as the encryption keys. Using phase truncation in the fractional Fourier domain, one can use an asymmetric cryptosystem to produce a real-valued noise-like ciphertext, while a legal user can reconstruct all of the original images using a different group of phase masks. The encryption key is an indivisible part of the corresponding original image and is still useful during decryption. The proposed system has high resistance to various potential attacks, including the chosen-plaintext attack. Numerical simulations also demonstrate the security and feasibility of the proposed scheme.     

Fully phase-encrypted memory using cascaded extended fractional Fourier transform

In this paper, we implement a fully phase-encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The full phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, the conjugate of the encrypted image. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the decrypted phase image, alleviating the need of alignment in the Fourier plane making the system rugged.