Angular-Multiplexing Optical Multiple-Image Encryption Based on Digital Holography and Random Amplitude Mask

We propose an improved optical image encryption scheme. By illuminating original images positioned in the input plane of the 4-f correlator and introducing reference waves with different incident angles in the output plane, we accomplish multiple-image encryption. To enhance the feasibility of the system and decrease the coding compliance for random phase mask, we apply the random amplitude masks and some digital manipulations in the encryption and decryption procedure. We also analyze the encryption and decryption quality of the method proposed together with the influence of different random number generators. Numerical simulation has proved the validity of the architecture suggested.     

Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain

The classical double random phase encoding technique (DRPE) is vulnerable to chosen ciphertext attacks, known-plaintext attacks and chosen-plaintext attacks for its linearity. In order to avoid the disadvantages originated from the linearity and symmetric, an improved method for multiple-image encryption based on nonlinear operations in Fourier domain is proposed. The random phase masks (RPMs) for encryption and additive keys which are determined by the original images and generated by the nonlinear operations in encryption process, are necessary for image decoding. As a result of the nonlinear operations, the increase in the number of keys, removal of linearity and high robustness could be achieved in this cryptosystem. Computer simulations are presented to demonstrate its good performance, and the security is analyzed as well.     

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.     

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.     

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.     

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.     

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.     

Securing multiplexed information by in-plane rotation of random phase diffusers constituting a sandwich diffuser placed in the Fourier plane of a double random phase encoding system

We propose the encryption and multiplexing of two-dimensional input images by rotating the constituent diffusers of a sandwich random phase diffuser kept in the Fourier plane of a double random phase encoding system. Successive recording of encrypted images is done by taking the input images one by one. The results of multiplexing in encryption and decryption due to different sets of rotation of one or both of the random constituent phase masks have been presented. The use of an aperture system in addition to the rotation of one or both of the random phase masks enhances the multiplexing capability and security of the system avoiding the generation of cross-talk images at the time of decryption. Simulation results are presented in support of the proposed techniques. The decrypted images obtained from a multiplexed encrypted image have been recorded successfully. Mean square-error (MSE) and signal-to-noise ratio (SNR) values as a function of the number of multiplexed images have been calculated.     

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.     

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.     

Multiple-image parallel optical encryption

A novel technique for multiple-image optical encryption is proposed, in which a set of parallel plaintexts can be extracted from the same designed ciphertext respectively. In the process of encryption, the principle of random phase encoding is utilized, and the phase keys corresponding to different plaintexts are achieved independently from the same designed ciphertext by cascade phase retrieval algorithm (CPRA). The advantages of the approach could be concluded as implementing decryption without cross-talk, infinite encrypted capacity and simple architecture. And the plaintexts extracted mode is extended from peer-to-peer to peer-to-multipeer. Numerical simulation verifies the validity.     

Image encoding based on coherent superposition and basic vector operations

A new method for image encryption based on optical coherent superposition and basic vector operations is proposed in this paper. In this encryption, the original image can be directly separated into two phase masks (PMs). One is a random phase mask (RPM) and the other is a modulation of the RPM by the original image. The mathematical calculation for obtaining the two PMs is quite simple and direct resulting from the simple principle of optical coherent superposition. The arbitrarily selected RPM can be treated as the encrypted result while the PM can be taken as the key for decryption. With this technique, the same encrypted result can be obtained for different images with the same size while the keys for decryption are different. The encryption can be performed digitally and the decryption can be performed optically or digitally. The security of the proposed method is discussed and computer simulation results are presented to verify the validity of proposed method.     

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 technique based on compressed sensing and Arnold transformation

A new optical image encryption method based on compressed sensing and Arnold transformation is proposed. First, dimensional reduction and random projection, the characteristics of compressed sensing, are utilized to compress and encrypt a digital image. Second, Arnold transformation is used to scramble the encryption image followed by compressed sensing with low data volume. Then, the encryption image is encrypted again by double random phase encoding optical encryption technique; two random phase masks generated by sequences of irrational number are been used as secret keys. In the end, the multi-encrypted information is embedded into the host image and transmitted. At the receiver, original image information is reconstructed approximately via orthogonal matching pursuit algorithm. The peak signal-to-noise ratio and the normalized cross-correlation between the original image and the decrypted one are used to calculate the quality of the decryption image. The experimental results demonstrate that our method is secure and robust.     

用多重菲涅耳衍射变换和相位密码板实现图像加密的技术

基于多重菲涅耳衍射变换和相位密码板,设计了一种新的图像加密计算方法.待加密的明文图像在多重离散菲涅耳衍射变换和相位密码板的共同作用下,变换为一个具有随机码特征的密文矩阵;衍射距离和相位密码板是主要的密钥.只有当所有密钥都正确时,才能成功地解密密文.结果表明,该加密算法能抵抗JPEG有损压缩、图像剪切、重度噪音污染和重采样等攻击,因此该法具有较强的鲁棒性;由于很难破解多重密钥,所以该算法具有极高的安全性.     

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.     

Image encryption using exclusive-OR with DNA complementary rules and double random phase encoding

We propose an optical image encryption scheme based on the Deoxyribonucleic Acid (DNA) theory and the double random phase encoding (DRPE) technique. The piecewise linear chaotic map (PWLCM) is used to generate key images and random phase masks, and to determine DNA encoding rules. In order to achieve ultra-fast DNA encryption, we propose using an optical exclusive-OR (XOR) gate to achieve XOR operation in DNA encryption. Different plaintexts use different initial values of PWLCM, which are generated by Message Digest Algorithm 5 (MD5). The plaintext is encrypted by two rounds of DNA and then by DRPE to form a ciphertext. Numerical simulation and the analysis of attacks on encrypted image are implemented to demonstrate the security and validity of the proposed approach.     

Fully phase multiple-image encryption based on superposition principle and the digital holographic technique

We propose an optoelectronic image encryption and decryption technique based on coherent superposition principle and digital holography. With the help of a chaotic random phase mask (CRPM) that is generated by using logistic map, a real-valued primary image is encoded into a phase-only version and then recorded as an encoded hologram. As for multiple-image encryption, only one digital hologram is to be transmitted as the encrypted result by using the multiplexing technique changing the reference wave angle. The bifurcation parameters, the initial values for the logistic maps, the number of the removed elements and the reference wave parameters are kept and transmitted as private keys. Both the encryption and decryption processes can be implemented in opto-digital manner or fully digital manner. Simulation results are given for testing the feasibility of the proposed approach.     

Image encryption based on pure intensity random coding and digital holography technique

We propose a novel image encryption method that combines the pure intensity random encoding and the digital holography technique. A phase-shifting interferometer records both phase and amplitude information of a complex object with a CCD sensor array. The encryption is performed by placing two pure intensity random masks between the image to be encrypted and an intensity recording device. Electronic decryption can be performed with fast Fresnel reconstruction procedure. Numerical simulation results show the validity of the algorithm and an optoelectronic implementation setup is also presented.     

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.