Optical image encryption based on the multiple-parameter fractional Fourier transform

A novel image encryption algorithm is proposed based on the multiple-parameter fractional Fourier transform, which is a generalized fractional Fourier transform, without the use of phase keys. The image is encrypted simply by performing a multiple-parameter fractional Fourier transform with four keys. Optical implementation is suggested. The method has been compared with existing methods and shows superior robustness to blind decryption.     

Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function

In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. In this paper, we propose a new approach for image encryption based on the multiple-parameter discrete fractional Fourier transform and chaotic logistic maps in order to meet the requirements of the secure image transmission. In the proposed image encryption scheme, the image is encrypted by juxtaposition of sections of the image in the multiple-parameter discrete fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. This method does not require the use of phase keys. The new method has been compared with several existing methods and shows comparable or superior robustness to blind decryption.     

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 reality-preserving multiple-parameter fractional Fourier transform

In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by using the fractional Fourier transform, but most of their encryptions are complex values and need digital hologram technique to record information, which is inconvenient for digital transmission. In this paper, we propose a new approach for image encryption based on the real-valuedness and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission. In the proposed scheme, the original and encrypted images are respectively in the spatial domain and the reality-preserving multiple-parameter fractional Fourier transformed domain determined by the encryption keys. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Phase image encryption of colored images using double random phase encoding technique in HSV color space

A double random phase encoding based digital phase encryption technique for colored images is proposed in the Fourier domain. The RGB input image is brought to HSV color space and then converted into phase, prior to the encryption. In the decryption process the HSV image is and converted back to the RGB format. The random phase codes used during encryption are prepared by stacking three two-dimensional random phase masks. These random phase codes serve as keys for encryption and decryption. The proposed technique carries all the advantages of phase encryption and is supposedly three-dimensional in nature. Robustness of the technique is analyzed against the variations in random phase codes and shuffling of the random phase masks of a given phase code. Performance of the scheme is also verified against occlusion of Fourier plane random phase code as well as the encrypted image. Effects of noise attacks and attacks using partial windows of correct random phase codes have also been checked. Digital simulations are presented to support the idea.     

双随机相位图像加密的实值编码研究

提出了一种基于双随机相位的图像实值编码方法,该方法可应用于光学图像加密.要编码的纯相位图像分别在空间域和频域加入随机相位掩膜,其中在频域将编码范围扩大4倍,经过光学系统的变换,将生成的图像取实部作为编码图像.实值编码的图像利用与编码过程类似的方法进行解码,可以准确地重建原图像.该编译码方法简单,编码图像是一个近似随机噪声的实值图像,便于数字图像的传输与输出.     

基于随机相位实值编码的光学图像加密

提出了一种用于图像加密的随机相位实值编码方法,待编码的纯相位图像与一个随机相位掩膜一起作傅里叶变换,取其实部作为编码图像.已编码的图像和随机相位掩膜的傅里叶变换相加作傅里叶反变换,反变换的光强可以准确地重建原图像.该编译码方法简单,编码图像是一个实值图像,便于计算机打印或显示输出.     

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 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.     

用于光学图象加密的分数傅里叶变换双相位编码

作者提出了一种用于图象加密的基于分数傅里叶变换的双相位编码技术.该方法由于密钥比传统的编码技术增加两重,因而其安全性有所改进.