Single-channel color image encryption using a modified Gerchberg-Saxton algorithm and mutual encoding in the Fresnel domain

A single-channel color image encryption is proposed based on the modified Gerchberg-Saxton algorithm (MGSA) and mutual encoding in the Fresnel domain. Similar to the double random phase encoding (DRPE), this encryption scheme also employs a pair of phase-only functions (POFs) as encryption keys. But the two POFs are generated by the use of the MGSA rather than a random function generator. In the encryption process, only one color component is needed to be encrypted when these POFs are mutually served as the second encryption keys. As a result, a more compact and simple color encryption system based on one-time-pad, enabling only one gray cipheretext to be recorded and transmitted when holographic recording is used, is obtained. Moreover, the optical setup is lensless, thus easy to be implemented and the system parameters and wavelength can be served as additional keys to further enhance the security of the system. The feasibility and effectiveness of the proposed method are demonstrated by numerical results.     

Flexible multiple-image encryption algorithm based on log-polar transform and double random phase encoding technique

We present a novel multiple-image encryption algorithm by combining log-polar transform with double random phase encoding in the fractional Fourier domain. In this algorithm, the original images are transformed to annular domains by inverse log-polar transform and then the annular domains are merged into one image. The composite image is encrypted by the classical double random phase encoding method. The proposed multiple-image encryption algorithm takes advantage of the data compression characteristic of log-polar transform to obtain high encryption efficiency and avoids cross-talk in the meantime. Optical implementation of the proposed algorithm is demonstrated and numerical simulation results verify the feasibility and the validity of the proposed algorithm.     

Multiple-image encryption scheme via compressive sensing and orthogonal encoding based on double random phase encoding

We propose an optical multiple-image encryption scheme based on compressive sensing and double random phase encoding. The orthogonal encoding method is used for integrating and extracting multiple-image compressed sampling data. In the encryption process, each plain image is sampled by compressive sensing and the sampled data of all the images are integrated into a synthesized ciphertext by orthogonal encoding method. The synthesized ciphertext is re-encrypted through the double random phase encoding technique to form final ciphertext. In order to reduce the data of keys, chaotic matrix, of which only the initial value should be memorized, is employed in the compressive sampling process and double random phase encoding process. Numerical simulation and the analysis of attacks on encrypted image are implemented to demonstrate the security and validity of the proposed approach.     

Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain

We propose a novel image encryption algorithm based on compressive sensing (CS) and chaos in the fractional Fourier domain. The original image is dimensionality reduction measured using CS. The measured values are then encrypted using chaotic-based double-random-phase encoding technique in the fractional Fourier transform domain. The measurement matrix and the random-phase masks used in the encryption process are formed from pseudo-random sequences generated by the chaotic map. In this proposed algorithm, the final result is compressed and encrypted. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys for distribution simultaneously. Numerical experiments verify the validity and security of the proposed algorithm.     

Multiple images encryption method via spiral phase mask rotations under a JTC system

A method of multiple-image encryption via spiral phase mask rotations based on the joint transform correlator encryption system was proposed. Multiple images can be encrypted into one ciphertext through this approach. When decrypted the ciphertext, we have no need to produce too many key masks, only need rotate the key mask to the angle corresponding to the plaintext. The system also has good resistance to occlusion attack and differential attack. Computer simulations initially verified the correctness of this method, and the experimental results also confirmed its validity further.     

Color image security system using double random-structured phase encoding in gyrator transform domain

A novel method for encoding color information based on a double random phase mask and a double structured phase mask in a gyrator transform domain is proposed. The amplitude transmittance of the Fresnel zone plate is used as structured phase-mask encoding. A color image is first segregated into red, green, and blue component images. Each of these component images are then independently encrypted using first a random phase mask placed at the image plane and transmitted through the first structured phase mask. They are then encoded by the first gyrator transform. The resulting information is again encrypted by a second random phase mask placed at the gyrator transform plane and transmitted through the second structured phase mask, and then encoded by the second gyrator transform. The system parameters of the structured phase mask and gyrator transform in each channel serve as additional encryption keys and enlarge the key space. The encryption process can be realized with an electro-optical hybrid system. The proposed system avoids problems arising from misalignment and benefits of a higher space-bandwidth product. Numerical simulations are presented to confirm the security, validity, and possibility of the proposed idea.     

Color image hiding based on the phase retrieval technique and Arnold transform

A new (to our knowledge) method is proposed in this paper for color image hiding and extracting using the phase retrieval algorithm in the fractional Fourier transform (FRFT) domain and Arnold transform (ART). Based on a cascaded phase iterative FRFT algorithm, the three channels (R, G, and B) of the secret color image permuted by ART are encrypted. Then the encoded information is embedded in the blue channel (B channel) of the enlarged color host image. Using the security enhanced encryption method, not only the random phase mask and the wavelength but also the transform parameters of ART and FRFT are provided as additional keys for decryption. It is shown that the security of information hiding will be enhanced. Computer simulations are performed to show the hiding capacity of the proposed system. Numerical results are presented to verify the validity and efficiency of the proposed method.     

Key-space analysis of double random phase encryption technique

We perform a numerical analysis on the double random phase encryption/decryption technique. The key-space of an encryption technique is the set of possible keys that can be used to encode data using that technique. In the case of a strong encryption scheme, many keys must be tried in any brute-force attack on that technique. Traditionally, designers of optical image encryption systems demonstrate only how a small number of arbitrary keys cannot decrypt a chosen encrypted image in their system. However, this type of demonstration does not discuss the properties of the key-space nor refute the feasibility of an efficient brute-force attack. To clarify these issues we present a key-space analysis of the technique. For a range of problem instances we plot the distribution of decryption errors in the key-space indicating the lack of feasibility of a simple brute-force attack.     

A kind of multilevel authentication system for multiple-image by modulated real part synthesis and iterative phase multiplexing

A kind of multilevel authentication system for multiple-image based on modulated real part synthesis and iterative phase multiplexing in the Fresnel domain is proposed. In the design process of the low-level authentication system, a series of normalized real part information are iteratively generated by phase retrieval algorithm in the Fresnel domain, and the final private keys for different individual low-level certification images can be fabricated by binary amplitude modulation, superposition, synthesis, and sampling; while in the design process of the high-level authentication system, the final private keys for different individual high-level certification images can be generated by iterative phase information encoding and multiplexing. During the high-level authentication, the meaningful certification image can be reconstructed by the inverse Fresnel transform with the corresponding correct private keys, meanwhile, the correlation coefficient is utilized as judgment criterion; while in the low-level authentication, with the help of correct keys, the noise-like image with meaningless information can be recovered, but a remarkable peak output in the nonlinear correlation coefficient can be generated, which is adopted as the criterion to judge whether the low-level authentication is successful or not. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.     

Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain

This paper proposes a method of double image encryption based on hybrid structured phase mask (HSPM) in the gyrator transform (GT) domain. The scheme becomes more secure by parameters used in the HSPM. These HSPMs are generated by using the combination of the optical vortex phase masks and secondary images after taking Fourier transform (FT). The input images are encrypted and recovered with correct values of HSPMs, rotation angles of GT and their keys used during the encryption. The use of an HSPM-based phase mask increases the security and key space for encryption. It can also be implemented opto-electronically. The mean square error calculated between the input and retrieved images shows the efficacy of scheme. The proposed method has also been investigated for its sensitivity to encryption parameters and its security against occlusion and noise attacks under a number of iterations. A set of numerical simulation results support the feasibility and security of the proposed scheme.     

Optical scanning cryptography for secure wireless transmission

We propose a method for secure wireless transmission of encrypted information. By use of an encryption key, an image or document is optically encrypted by optical heterodyne scanning and hence encryption is performed on the fly. We call this technique optical scanning cryptography. The output of the heterodyne encrypted signal is at radio frequency and can be directly sent through an antenna to a secure site for digital storage to be prepared for decryption. In the secure site, an identical optical scanning system to that used for encryption is used, together with a decryption key, to generate an electrical signal. The electrical signal is then processed and sent to a computer to be used for decryption. Utilizing the stored information received from the encryption stage and the electrical information from the secure site, a digital decryption unit performs a decryption algorithm. If the encryption key and the decryption key are matched, the decryption unit will decrypt the image or document faithfully. The overall cryptosystem can perform the incoherent optical processing counterpart of the well-known coherent double-random phase-encoding technique. We present computer simulations of the idea.     

Optical image encryption scheme with multiple light paths based on compressive ghost imaging

An optical image encryption method with multiple light paths is proposed based on compressive ghost imaging. In the encryption process, M random phase-only masks (POMs) are generated by means of logistic map algorithm, and these masks are then uploaded to the spatial light modulator (SLM). The collimated laser light is divided into several beams by beam splitters as it passes through the SLM, and the light beams illuminate the secret images, which are converted into sparse images by discrete wavelet transform beforehand. Thus, the secret images are simultaneously encrypted into intensity vectors by ghost imaging. The distances between the SLM and secret images vary and can be used as the main keys with original POM and the logistic map algorithm coefficient in the decryption process. In the proposed method, the storage space can be significantly decreased and the security of the system can be improved. The feasibility, security and robustness of the method are further analysed through computer simulations.     

Simultaneous transmission for an encrypted image and a double random-phase encryption key

We propose a method to simultaneously transmit double random-phase encryption key and an encrypted image by making use of the fact that an acceptable decryption result can be obtained when only partial data of the encrypted image have been taken in the decryption process. First, the original image data are encoded as an encrypted image by a double random-phase encryption technique. Second, a double random-phase encryption key is encoded as an encoded key by the Rivest-Shamir-Adelman (RSA) public-key encryption algorithm. Then the amplitude of the encrypted image is modulated by the encoded key to form what we call an encoded image. Finally, the encoded image that carries both the encrypted image and the encoded key is delivered to the receiver. Based on such a method, the receiver can have an acceptable result and secure transmission can be guaranteed by the RSA cipher system.     

Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask

A single channel asymmetric color image encryption scheme is proposed that uses an amplitude- and phase- truncation approach with interference of polarized wavefronts. Instead of commonly used random phase masks, wavelength-dependent structured phase masks (SPM) are used in the fractional Fourier transform domain for image encoding. The primary color components bonded with different SPMs are combined into one grayscale image using convolution. We then apply the amplitude and phase truncation to the fractional spectrum, which helps generate unique decryption keys. The encrypted image bonded with a different SPM is then encoded into a polarization selective diffractive optical element. The proposed scheme alleviates the alignment problem of interference and does not need iterative encoding and offers multiple levels of security. The effect of a special attack to the proposed asymmetric cryptosystem has been studied. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. The computer simulation results support the proposed idea.     

Multiple-image encryption scheme with a single-pixel detector

Abstract

A multiple-image encryption (MIE) scheme with a single-pixel detector has been proposed according to the principle of ghost imaging. In this scheme, each of the spatially coherent laser beams is modified by a set of phase-mask keys and illuminates on a secret image. All of the transmitted lights are recorded together by a single-pixel (bucket) detector to obtain a ciphertext, but anyone of the secret images can be decrypted from the ciphertext independently without any mutually overlapped despite some noise in them. The MIE scheme will bring convenience for data storage and transmission, especially in the case that different secret images need to be distributed to different authorized users, because the ciphertext is a real-valued function and this scheme can effectively avoid the secret images being extracted mutually. The basic principle of the MIE scheme is described theoretically and verified by computer simulations. Finally, the feasibility, robustness and encryption capacity are also tested numerically.     

Joint image compression–encryption using discrete fractional transforms

Exchange of data in the form of text and image on internet is in fast progression and it is spawning new compression and encryption algorithms for bandwidth and security respectively. We have proposed a new kind of joint algorithm using discrete fractional transforms for compression–encryption of image. In this algorithm, the discrete fractional Fourier transform which is discrete version of fractional Fourier transform, is used to compress the images with variation of its parameter ‘α’ (order of transform). The compressed image is encrypted using discrete fractional cosine transform to provide security. The advantage of this method is its feasible implementation in practice, superior, robustness, security and sensitivity of keys, which has a good prospect and practicability in information security field. Results of computer simulations are presented to verify the validity of the proposed method such as mean square error (MSE) and peak signal to noise ratio between the original image and decrypted image. Sensitivity for right decryption key is proved with respect to MSE.     

A new color image encryption scheme based on chaos synchronization of time-delay Lorenz system

In this paper, a new image encryption scheme is presented based on time-delay chaos synchronization. Compared with existing methods, a new method is proposed and a lot of coupled items can be taken as zero items to simplify the whole system. A simple linear controller is introduced to realize time-delay chaos synchronization and image encryption. The positions of the image pixels are firstly shuffled and then be hidden in the carrier image. The address codes of the chaotic sequences are adopted to avoid the disturbances induced by the initial value and computer accuracy error. Simulation results for color image are provided to illustrate the effectiveness of the proposed method. It can be seen clearly that the system can converge quickly and the image can be encrypted rapidly.     

Reversible Data Hiding in Encrypted Images Based on Prediction and Adaptive Classification Scrambling

Reversible data hiding in encrypted images (RDH-EI) technology is widely used in cloud storage for image privacy protection. In order to improve the embedding capacity of the RDH-EI algorithm and the security of the encrypted images, we proposed a reversible data hiding algorithm for encrypted images based on prediction and adaptive classification scrambling. First, the prediction error image is obtained by a novel prediction method before encryption. Then, the image pixel values are divided into two categories by the threshold range, which is selected adaptively according to the image content. Multiple high-significant bits of pixels within the threshold range are used for embedding data and pixel values outside the threshold range remain unchanged. The optimal threshold selected adaptively ensures the maximum embedding capacity of the algorithm. Moreover, the security of encrypted images can be improved by the combination of XOR encryption and classification scrambling encryption since the embedded data is independent of the pixel position. Experiment results demonstrate that the proposed method has higher embedding capacity compared with the current state-ofthe-art methods for images with different texture complexity.     

Reversible Data Hiding in Encrypted Image Based on Block Classification Permutation

Recently, reversible data hiding in encrypted image (RDHEI) has attracted extensive attention, which can be used in secure cloud computing and privacy protection effectively. In this paper, a novel RDHEI scheme based on block classification and permutation is proposed. Content owner first divides original image into non-overlapping blocks and then set a threshold to classify these blocks into smooth and non-smooth blocks respectively. After block classification, content owner utilizes a specific encryption method, including stream cipher encryption and block permutation to protect image content securely. For the encrypted image, data hider embeds additional secret information in the most significant bits (MSB) of the encrypted pixels in smooth blocks and the final marked image can be obtained. At the receiver side, secret data will be extracted correctly with data-hiding key. When receiver only has encryption key, after stream cipher decryption, block scrambling decryption and MSB error prediction with threshold, decrypted image will be achieved. When data hiding key and encryption key are both obtained, receiver can find the smooth and non-smooth blocks correctly and MSB in smooth blocks will be predicted correctly, hence, receiver can recover marked image losslessly. Experimental results demonstrate that our scheme can achieve better rate-distortion performance than some of state-of-the-art schemes.     

Reversible Data Hiding in Classification-Scrambling Encrypted-Image Based on Iterative Recovery

To improve the security and quality of decrypted images, this work proposes a reversible data hiding in encrypted image based on iterative recovery. The encrypted image is firstly generated by the pixel classification scrambling and bit-wise exclusive-OR (XOR), which improves the security of encrypted images. And then, a pixel-type-mark generation method based on block-compression is designed to reduce the extra burden of key management and transfer. At last, an iterative recovery strategy is proposed to optimize the marked decrypted image, which allows the original image to be obtained only using the encryption key. The proposed reversible data hiding scheme in encrypted image is not vulnerable to the ciphertext-only attack due to the fact that the XOR-encrypted pixels are scrambled in the corresponding encrypted image. Experimental results demonstrate that the decrypted images obtained by the proposed method are the same as the original ones, and the maximum embedding rate of proposed method is higher than the previously reported reversible data hiding methods in encrypted image.