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.     

Digital image watermarking using gyrator transform and chaotic maps

We propose a new method for digital image watermarking using gyrator transform and chaotic maps. Four chaotic maps have been used in the proposed technique. The four chaotic maps that have been used are the logistic map, the tent map, the Kaplan-Yorke map and the Ikeda map. These chaotic maps are used to generate the random phase masks and these random phase masks are known as chaotic random phase masks. A new technique has been proposed to generate the single chaotic random phase mask by using two chaotic maps together with different seed values. The watermark encoding method in the proposed technique is based on the double random phase encoding method. The gyrator transform and two chaotic random phase masks are used to encode the input image. The mean square error, the peak signal-to-noise ratio and the bit error rate have been calculated. Robustness of the proposed technique has been evaluated in terms of the chaotic maps, the number of the chaotic maps used to generate the CRPM, the rotation angle of the gyrator transform and the seed values of the chaotic random phase masks. Optical implementation of the technique has been proposed. The computer simulations are presented to verify the validity of the proposed technique.     

Gyrator transform-based optical image encryption,using chaos

We propose a new method for image encryption, using gyrator transform and chaos theory. Random phase masks are generated using chaos functions and are called as chaotic random phase masks. In the proposed technique, the image is encrypted using gyrator transform and two chaotic random phase masks. Three types of chaos functions have been used to generate the chaotic random phase masks. These chaos functions are the logistic map, the tent map and the Kaplan-Yorke map. The computer simulations are presented to verify the validity of the proposed technique. The mean square errors have been calculated. The robustness of the proposed technique to blind decryption in terms of rotation angle and the seed values of the chaotic random phase mask have been evaluated. The optical implementation of the encryption and the decryption technique has been proposed.     

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.     

Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

基于多混沌系统的双图像光学加密算法

为了扩展双图像光学加密算法的密钥空间,克服双随机相位加密系统中随机相位掩模作为密钥难于存储、传输和重构的问题,突破传统图像加密的研究思路,提出了一种基于多混沌系统的双图像加密算法,构造了光学加密系统。系统增加混沌系统参数作为密钥,利用混沌加密密钥空间大和图像置乱隐藏性好的特点,构建基于Logistic混沌映射的图像置乱算法,利用Kent混沌映射生成的伪随机序列构造出一对随机相位掩模,分别放置在分数傅里叶变换光学装置的两端,图像经加密系统变换后得到密文。数值仿真结果表明,算法的密钥敏感性极高,能够有效地对抗统计攻击,具有较高的安全性。     

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.     

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.     

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.     

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.     

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.     

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.     

Double image encryption based on linear blend operation and random phase encoding in fractional Fourier domain

A novel method for double image encryption is proposed by using linear blend operation and double-random phase encoding (DRPE) in the fractional Fourier domain. In the linear blend operation, a random orthogonal matrix is defined to linearly recombined pixel values of two original images. The resultant blended images are employed to constitute a complex-valued image, which is encrypted into an encrypted image with stationary white distribution by the DRPE in the fractional Fourier domain. The primitive images can be exactly recovered by applying correct keys with fractional orders, random phase masks and random angle function that is used in linear blend operation. Numerical simulations demonstrate that the proposed scheme has considerably high security level and certain robustness against data loss and noise disturbance.     

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.     

Optics based biometric encryption using log polar transform

We propose an optics based biometric encryption technique using log polar transform. In this method, the key of the encryption process has been linked to the fingerprint of the enrolled person. The order of fractional Fourier transform and the seed values of the chaotic random phase masks in combination act as the key for the encryption process. In order to link the combined key to the fingerprint, a lookup table has been formed by the key and the log polar transform of the fingerprint. The linking algorithm not only encrypts the image of the enrolled person but also authenticates the input image. The main advantage of this method is its capability to retrieve the same key in the decryption process by using the live fingerprint. The key is not required to be communicated to the receiver side. The retrieval of the image is possible only when the live fingerprint of the enrolled person is presented at the decryption side. The real life fingerprints have been used to demonstrate the proposed technique. Simulations have been performed on the Matlab platform to validate the proposed technique. The signal to noise ratio and mean square error has been calculated in order to support the proposed technique. The effect of the rotation and the scaling of the fingerprints have been studied to check the key retrieval from the live fingerprint of the enrolled person. The study of the different whorl types of fingerprint of different persons has also been done to check the efficacy of the key retrieval from the whorl types of the live fingerprints of different person.     

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.     

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.     

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.     

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.