Optical image encryption with redefined fractional Hartley transform

A new method for optical image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform. We encrypt the image by two fractional orders and random phase codes. It has an advantage over Hartley transform, for its fractional orders can also be used as additional keys, and that, of course, strengthens image security. Only when all of these keys are correct, can the image be well decrypted. The optical realization is then proposed and computer simulations are also performed to confirm the possibility of the proposed method.     

Color image encoding in dual fractional Fourier-wavelet domain with random phases

A new cryptology in dual fractional Fourier-wavelet domain is proposed in this paper, which is calculated by discrete fractional Fourier transform and wavelet decomposition. Different random phases are used in different wavelet subbands in encryption. A new color image encoding method is also presented with basic color decomposition and encryption respectively. All the keys, including random phases and fractional orders in R, G and B three channels, should be correctly used in decryption, otherwise people cannot obtain the totally correct information. Some numerical simulations are presented to demonstrate the possibility of the method. It would have widely potential applications in digital color image processing and protection.     

A half-blind color image hiding and encryption method in fractional Fourier domains

We have proposed a new technique for digital image encryption and hiding based on fractional Fourier transforms with double random phases. An original hidden image is encrypted two times and the keys are increased to strengthen information protection. Color image hiding and encryption with wavelength multiplexing is proposed by embedding and encryption in R, G and B three channels. The robustness against occlusion attacks and noise attacks are analyzed. And computer simulations are presented with the corresponding results.     

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.     

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.     

Novel color image encryption algorithm based on the reality preserving fractional Mellin transform

A nonlinear color image encryption algorithm based on reality preserving fractional Mellin transform (RPFrMT) is proposed. So far as image encryption is concerned, RPFrMT has two fascinating advantages: (1) the real-valued output of the transform ensures that the ciphertext is real which is convenient for display, transmission and storage; (2) as a nonlinear transform, RPFrMT gets rid of the potential insecurity which exists in the conventional linear encryption schemes. The original color image is first transformed from RGB color space to R′G′B′ color space by rotating the color cube. The three components of the output are then transformed by RPFrMT of different fractional orders. To further enhance the security of the encryption system, the result of the former step is scrambled by three dimensional scrambling. Numerical simulations demonstrate that the proposed algorithm is feasible, secure, sensitive to keys and robust to noise attack and occlusion. The proposed color image encryption can also be applied to encrypt three gray images by transforming the gray images into three color components of a specially constructed color image.     

An optical image cryptosystem based on Hartley transform in the Fresnel transform domain

A novel method for image encryption and decryption based on Hartley transform in the Fresnel transform domain is presented. Different from the conventional method which requires lens to perform the Fourier transform for achieving Hartley transform, the proposed new optical architecture of Hartley transform is based on the Fresnel diffraction which requires no Fourier transform lenses. The position coordinate as well as the wavelength in the Fresnel transform is used as encoding keys that can ensure the sufficient information security. The main advantages of this proposed image security system are that it uses fewer optical devices and the decryption scheme is straightforward and more secure than the previous works.     

A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains

Based on 1-D fractional Fourier transform, we proposed an image encryption algorithm in order to hide two images simultaneously. When the fractional order is closed to 1, most energy in frequency domain is centralized in the center part of spectrum. The image can be recovered acceptable by using a half of spectrum, which locates in the middle part at x-direction or y-direction. Cutting operation is employed in order to combine two spectra. Double random phase encoding is employed for image encryption. The corresponding numerical simulations are performed to demonstrate the validity and efficiency of the algorithm.     

Optical Image Encryption with Simplified Fractional Hartley Transform

We present a new method for image encryption on the basis of simplifed fractional Hartley transform （SFRHT）. SFRHT is a real transform as Hartley transform （HT） and furthermore, superior to HT in virtue of the advantage that it can also append fractional orders as additional keys for the purpose of improving the system security to some extent. With this method, one can encrypt an image with an intensity-only medium such as a photographic film or a CCD camera by spatially incoherent or coherent illumination. The optical realization is then proposed and computer simulations are also performed to verify the feasibility of this method.     

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.     

基于变形分数傅里叶变换的六重密钥图像加密

提出一种利用变形分数傅里叶变换和双随机相位编码对图像加密的方法.对要加密的图像分别进行两次变形分数傅里叶变换和两次随机相位函数调制,使加密图像的密钥由原来两重增加到六重.利用全息元件,可以用光学系统实现这种加密和解密变换.计算机模拟结果表明,只有当六重密钥都完全正确时,才能准确地重建原图像,这种六重密钥加密方法提高了图像信息的安全保密性.     

Application of Cosine Zone Plates to Image Encryption

We analyse the diffraction result of optical field after Cosine zone plate, and theoretically deduce its transform matrix. Under some conditions, its diffraction distribution is a mixture of fractional Fourier spectra. Then we use Cosine zone plate and its diffraction result to image encryption. Possible optical image encryption and decryption implementations are proposed, and some numerical simulation results are also provided.     

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.     

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.     

Color image encryption by using the rotation of color vector in Hartley transform domains

We propose an algorithm to encrypt color image by using the rotation of color vector based on discrete Hartley transform. The three component images (red, green and blue) of color image are regarded as the axes of Cartesian coordinates. Two random angle shifts are introduced to rotate the color vectors composed by the three color components in discrete Hartley transform domains in image encryption process. The corresponding rotation shifts of the two angles can serve as the key of the scheme. Moreover the encrypted image is encoded with real number. Some numerical simulations have demonstrated the possibility of the proposed scheme.     

Novel image encryption algorithm based on multiple-parameter discrete fractional random transform

A new method of digital image encryption is presented by utilizing a new multiple-parameter discrete fractional random transform. Image encryption and decryption are performed based on the index additivity and multiple parameters of the multiple-parameter fractional random transform. The plaintext and ciphertext are respectively in the spatial domain and in the fractional domain determined by the encryption keys. The proposed algorithm can resist statistic analyses effectively. The computer simulation results show that the proposed encryption algorithm is sensitive to the multiple keys, and that it has considerable robustness, noise immunity and security.     

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.     

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.     

Triple color images encryption algorithm based on scrambling and the reality-preserving fractional discrete cosine transform

An image encryption algorithm to secure three color images simultaneously by combining scrambling with the reality-preserving fractional discrete cosine transform (RPFrDCT) is proposed. The three color images to be encrypted are converted to their indexed formats by extracting their color maps, which can be considered as the three components of a color image. These three components are affected each other by scrambling the interims obtained from vertically and horizontally combining the three indexed formats with the help of the chaos-based cyclic shift. The three scrambled components are separately transformed with the RPFrDCT, in which the generating sequences are determined by the Chirikov standard chaotic map. Arnold transform is used to further enhance the security. Due to the inherent properties of the chaotic maps, the cipher keys are highly sensitive. Additionally, the cipher image is a single color image instead of three color ones, and is convenient for display, storage and transmission due to the reality property of RPFrDCT. Numerical simulations are performed to show the validity of the proposed algorithm.     

基于分频域和菲涅耳域的光学图像加密方法

结合分数傅里叶变换及菲涅耳变换,在光学图像加密系统中分别具有多密钥性和无透镜性的优点,提出了基于分频域和菲涅耳域的光学图像加密方法。基于分数傅里叶变换的光学加密系统,引入菲涅耳变换及全息技术,使原有的加密系统在不增加光学元件的基础上提高了系统的安全性。理论分析和计算机仿真模拟证明了这种方法的可行性。