基于随机分数傅里叶变换的双图像加密算法

利用光学随机分数傅里叶变换设计了一种双图像加密算法,并给出了相应的光学实现.加密算法中,将两幅原始图像分别作为加密系统输入复函数的振幅和位相分布函数,利用随机分数傅里叶变换进行加密,所得复函数的振幅即为加密图像,而位相部分是变换的输出相位,随机位相作为加密算法的密码.在数值模拟中,二值文本图像和灰度图像分别被作为原始图像用于加密结果分析和加密安全测试,结果表明该加密算法具有很好的安全性.     

Triple image encryption scheme in fractional Fourier transform domains

We proposed a triple image encryption scheme by use of fractional Fourier transform. In this algorithm, an original image is encoded in amplitude part and other two images are encoded into phase information. The key of encryption algorithm is obtained from the difference between the third image and the output phase of transform. In general case, random phase encoding technology is not required in the proposed algorithm. Moreover, all information of images is preserved in theory when image are decrypted with correct key. The optical implementation of the algorithm is presented with an electro-optical hybrid structure. Numerical simulations have demonstrated the efficiency and the security of this algorithm. Based on this scheme a multiple image algorithm is expanded and designed.     

Random fractional Fourier transform

We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers.     

Double image encryption based on discrete multiple-parameter fractional Fourier transform and chaotic maps

A double image encryption method is proposed by utilizing discrete multiple-parameter fractional Fourier transform and chaotic maps. One of the two original images scrambled by one chaotic map is encoded into the amplitude of a complex signal with the other original image as its phase. The complex signal multiplied by another chaotic random phase mask is then encrypted by discrete multiple-parameter fractional Fourier transform. The parameters in chaotic map and discrete multiple-parameter fractional Fourier transform serve as the keys of this encryption scheme. Numerical simulations have been done to demonstrate the performance of this algorithm.     

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.     

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.     

相位编码光学加密算法的扩散及混淆特性分析

为了阐明相位编码光学加密算法的扩散及混淆特性,基于傅里叶变换位移定理,从分组密码设计准则出发,以双随机相位光学加密算法为研究对象,分析了采用单个随机相位模板的2 f系统的扩散和混淆特性。将单随机相位加密过程分解为2个相互关联的过程,结果表明,傅里叶变换在加密算法中引入了混淆操作,而傅里叶变换结合随机相位模板实现了扩散操作。通过数值模拟对上述理论分析进行了验证,引入信息熵来评价加密图像的统计分布特性,进一步分析了菲涅尔域及分数阶傅里叶变换域随机相位加密算法的扩散混淆特性。研究表明,单随机相位加密和双随机相位加密图像的信息熵分布为7.038和7.157,而随机振幅加密图像信息熵为4.521。因而,随机相位加密算法比随机振幅加密算法能实现对信息更好地扩散。     

Novel optical image encryption scheme based on fractional Mellin transform

A novel nonlinear image encryption scheme is proposed by introducing the fractional Mellin transform (FrMT) into the field of image security. As a nonlinear transform, FrMT is employed to get rid of the potential insecurity of the optical image encryption system caused by the intrinsic object-image relationship between the plaintext and the ciphertext. Different annular domains of the original image are transformed by FrMTs of different orders, and then the outputs are further encrypted by comprehensively using fractional Fourier transform (FrFT), amplitude encoding and phase encoding. The keys of the encryption algorithm include the orders of the FrMTs, the radii of the FrMT domains, the order of the FrFT and the phases generated in the further encryption process, thus the key space is extremely large. An optoelectronic hybrid structure for the proposed scheme is also introduced. Numerical simulations demonstrate that the proposed algorithm is robust with noise immunity, sensitive to the keys, and outperforms the conventional linear encryption methods to counteract some attacks.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Implementing compressive fractional Fourier transformation with iterative kernel steering regression in double random phase encoding

This paper proposes a novel approach in double random phase encryption based on compressive fractional Fourier transform along with the kernel steering regression. The method increases the complexity of the image by using fractional Fourier transform and taking fewer measurements from the image data. Numerical results are given to analyze the validity of this technique. Considering natural images to be sparse in some domain, we apply a compressive sensing (CS) approach by using a TwIST algorithm. The encryption process has kernel steering regression algorithm for denoising and compressive sensing technique for image compression along with the fractional Fourier transform that makes the image in more complex form.     

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.     

Double image encryption by using Arnold transform and discrete fractional angular transform

Based on Arnold transform and discrete fractional angular transform, a double image encryption algorithm is designed. Two original images are regarded as the amplitude and phase of a complex function. Arnold transform is introduced for scrambling the pixels at a local area of the complex function. Subsequently the changed complex function is converted by discrete fractional angular transform. The operations mentioned will be performed many times. The amplitude of final output complex function is the encrypted image and its phase is regarded as the key of encryption algorithm. The parameters of the two transforms serve as the additional keys for enhancing the security. Some numerical simulations have been done to validate the performance of this encryption scheme.     

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.