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.     

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.     

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.     

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.     

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。     

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.     

基于分数阶傅里叶变换的光学加密影片

随着通信与网络的快速发展,能够包含大容量信息的影片得到了广泛应用。利用分数阶傅里叶变换的特点,提出了一种全光学加密解密影片的方法。将现有的影片加密密钥从二重变为了四重,显著增加了影片的安全性。通过改变振幅型正弦光栅的作用位置,将影片的加密解密次数由现有的每帧各一次减小为总共一次,优化了算法。仿真结果验证了该方法的有效性。     

Single phase encoding method based on the fractional Fourier transform

We propose a single phase encoding scheme for encrypting image by using fractional Fourier transform. Single phase mask is designed in order to be symmetrical about certain direction, which can be used in the process of both encryption and decryption. A conjugate mask is not required in the image decryption process, which is very convenient for the practical application in optics. Moreover, the optical implementation of the image encryption and decryption is given. The implementing structure is composed of lens and spherical mirror. Numerical simulations have demonstrated the validity and security of the encryption algorithm.     

Optical color image encryption with redefined fractional Hartley transform

We propose a new method for color image encryption by wavelength multiplexing 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. A color image can be considered as three monochromatic images and then divided into three components and each component is encrypted independently with different wavelength corresponding to red, green or blue light. The system parameters of fractional Hartley transform and random phase masks are keys in the color image encryption and decryption. 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.     

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.     

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.     

Ghost imaging-based optical cryptosystem for multiple images using integral property of the Fourier transform

A novel ghost imaging-based optical cryptosystem for multiple images using the integral property of the Fourier transform is proposed. Different from other multiple-image encryption schemes, we mainly construct the modulation patterns related to the plaintext images to realize the encrypted transmission of multiple images. In encryption process, the first image is encrypted by the ghost imaging encryption scheme, and the intensity sequence obtained by the bucket detector is used as the ciphertext. Then modulation patterns of other images are constructed by using the integral property of the Fourier transform and used as the keys. Finally, the ciphertext and keys are transmitted to the receiver to complete the encryption process. During decryption, the receiver uses different keys to decrypt the ciphertext and gets different plaintext images, and decrypted images have no image aliasing problem. Experiments and simulations verify the feasibility, security, and robustness of the proposed scheme. This scheme has high scalability and broad application prospect, which provides a new idea for optical information encryption.     

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.     

基于不对称非标准傅里叶变换的光学图像加密

针对以往光学图像加密系统中输入面和频谱面对称性的缺点，在不增加系统元件的基础上，利用球面波照射不对称非标准傅里叶变换系统进行图像加密。通过把相位掩模置于该系统的傅里叶变换平面，利用不对称非标准傅里叶变换系统的输入面和频谱面的不对称性以及频谱面对于点光源相关参数的依赖性，克服了以前光学加密系统中输入面和频谱面的对称性所带来的安全隐患，并且获得了除相位掩模以外的另外四重密匙。理论分析和模拟实验表明：该方法不仅可行，而且多增加了几重密匙，增强了系统的安全性能。     

Compressive optical image watermarking using joint Fresnel transform correlator architecture

A new optical image watermarking technique based on compressive sensing using joint Fresnel transform correlator architecture has been presented. A secret scene or image is first embedded into a host image to perform optical image watermarking by use of joint Fresnel transform correlator architecture. Then, the watermarked image is compressed to much smaller signal data using single-pixel compressive holographic imaging in optical domain. At the received terminal, the watermarked image is reconstructed well via compressive sensing theory and a specified holographic reconstruction algorithm. The preliminary numerical simulations show that it is effective and suitable for optical image security transmission in the coming absolutely optical network for the reason of the completely optical implementation and largely decreased holograms data volume.     

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.     

不对称离散分数傅里叶变换实现数字图像的加密变换

利用不对称分数傅里叶变换的特性,提出了一种图像加密变换的新方法。对图像的x,y方向分别实施不同级次的一维分数傅里叶变换,得到加密图像。解密方法就是对变换后的图像实施对应级次的分数傅里叶逆变换,只有当x,y方向的逆变换级次分别与原变换级次都相同或者满足周期条件时,才能恢复原图像。加密变换有效地提高了图像加密和防伪力度。数值计算验证了方法的正确性和可行性。     

Image encryption and decryption using fractional Fourier transform and radial Hilbert transform

A technique for image encryption using fractional Fourier transform (FRT) and radial Hilbert transform (RHT) is proposed. The spatial frequency spectrum of the image to be encrypted is first segregated into two parts/channels using RHT, and image subtraction technique. 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.     

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.