Enhancement of image hiding by exchanging two phase masks

Security analysis on an interference-based optical image encryption scheme

In this paper, the security strength of the improved optical cryptosystem based on interference has been evaluated. Compared to the previous interference-based cryptosystems in which the plaintext is encoded into two phase-only masks (POMs), here the plaintext is encoded into a POM and an amplitude mask (AM). Since the information of the plaintext cannot be recovered directly when one of the masks is released in the decryption process of the improved cryptosystem, it seems that it is free from the silhouette problem. However, we found that the random phase mask (RPM) serving as the encryption key is not related to the plaintext. Thus, it is possible to recover the RPM first by using the known-plaintext attack (KPA). Moreover, the POM and the AM generated in the encryption path only contains the phase and amplitude information, respectively. Thus, these can be utilized as additional constraints in the proposed iterative process. Based on these findings, two kinds of hybrid attacks, including a KPA and the iterative processes with different constraints, are proposed to crack the improved cryptosystem. In the designed KPA with a pair of the known plaintext and its corresponding masks, the RPM is recovered first. With the aid of the recovered RPM, two iterative processes with different released masks are proposed to recover the information of the plaintext without any knowledge of another mask. To the best of our knowledge, this is the first time that the existence of the silhouette problem in the cryptosystem under study has been reported. Numerical simulation has been carried out to validate the feasibility and effectiveness of the proposed hybrid attacks.

Improved multiple-image authentication based on optical interference by wavelength multiplexing

In this paper, an improved multiple-image authentication based on optical interference by wavelength multiplexing is proposed, which has high security and easy optical implementation. The Fresnel spectra of original images are diffracted from the same axial position but by different wavelengths, which makes the optical implementation easy and stable without any mechanical translation. Then, the Fresnel spectra are sparsely sampled by predesigned binary amplitude masks and diffracted again, and all spectra are multiplexed into one synthetized spectrum. Finally, the synthetized spectrum is analytically decomposed into one phase-only mask and one amplitude-only mask by an improved interference-based encryption (IBE) scheme. Benefiting from the wavelength multiplexing, the encryption capacity is enlarged, and the optical implementation for decryption becomes easy. With the aid of the sparse sampling, every decrypted image could be entirely unrecognizable but authenticated by nonlinear correlation. Moreover, instead of a conventional IBE, an improved IBE is used in this scheme, which can attenuate the information leakage and further enhance the security. Various numerical simulation results are presented to demonstrate the feasibility and effectiveness of this scheme.

Cryptoanalysis and enhancement of a binary image encryption system based on interference

In this paper, cryptoanalysis on a binary image encryption system based on interference is conducted. In the cryptosystem under study, the binary plaintext image modulated by a random phase mask (RPM) is separated directly into two phase-only masks (POMs) as private keys. Phase wrapping operation is applied to modulate two separated POMs further for silhouette removal. The plaintext image can be reconstructed by compositing two phase-wrapped POMs. However, since the RPM used in the encryption process is irrelative to the plaintexts, it is possible to retrieve the RPM by a known-plaintext attack (KPA). And then with the help of the retrieved RPM, the information encoded in the arbitrarily given ciphertext can be reconstructed by a ciphertext-only attack (COA). Based on our analysis, a hybrid attack including a KPA and a COA with different constraints is proposed in this study. Besides, the cryptosystem under study can only be used to encode binary plaintexts, which would limit the application of this scheme in the information security. Consequently, an improved cryptosystem in which both binary and gray-scale plaintext images can be encoded is proposed. In addition, the RPM to generate two private keys in the enhanced system is dependent on the plaintexts, which makes the proposed encryption scheme immune to the proposed hybrid attack. The feasibility and effectiveness of the security-enhanced cryptosystem have been validated by numerical simulations.

Cryptoanalysis on optical image encryption systems based on the vector decomposition technique in the Fourier domain

In this paper, the security of optical cryptosystems based on the vector decomposition technique in the Fourier domain is analyzed. Compared to the conventional cryptosystem based on the equal modulus decomposition (EMD) technique, an additional EMD structure is introduced in the cascaded EMD-based cryptosystem; hence, the mask including the phase information of the Fourier spectrum is further encoded in the second EMD structure to enhance the security level. However, it is shown that the number of the private keys has not been increased in the cascaded EMD-based cryptosystem, which makes it possible to crack the cascaded EMD-based cryptosystem. Therefore, a chosen-plaintext attack (CPA) and a special attack with an arbitrarily given private key are proposed to retrieve information from encoded images obtained by the cascaded EMD-based cryptosystem. In addition, the security of the cryptosystem based on the random modulus decomposition (RMD) technique is also analyzed. Compared to the EMD-based cryptosystem in which the Fourier spectrum is decomposed into two vectors with equal moduli, the security level of the cryptosystem has been improved by using the RMD technique to decompose the spectrum into vectors with unequal moduli to decrease the number of the amplitude constraints. However, it is found that the arbitrarily given ciphertext provides the attackers enough information to retrieve the precise information of the plaintext without any knowledge of the private keys. A special attack is proposed to crack the RMD-based cryptosystem. This is the first time to report that these two cryptosystems based on the vector decomposition technique are attacked successfully. Numerical simulation is conducted to validate the feasibility and effectiveness of the proposed attacks.

Security validation based on orthogonal polarization multiplexing in three-dimensional space

To enhance the security and practicality of the optical validation technique, a multiple-level security validation method is proposed based on orthogonal polarization multiplexing in a three-dimensional (3D) space. First, the original image is partitioned into two complementary images. Each image is divided into several subblocks. Then, two phase-only masks are generated by adopting the multiple diffractive planes and multiple signal windows phase-retrieval algorithm to reproduce a 3D diffraction field with all of the subblocks randomly distributed in specific locations. One of the phase masks is taken as the fixed system lock. The other one is preserved to act as the validation key. At last, the two diffraction beams of two phase-only masks are converted into orthogonal polarization states when illuminated by a collimated wave. As a result, the simultaneous control of both intensity and polarization distributions in desired longitudinal planes and transversal positions is achieved. A 3D polarization mapping protocol is established to generate the 3D polarization key. During validation, both the validation key and the 3d polarization key must be correct for a person to receive access permission. Experimental results show that the method is easy to implement and offers multiple-level validation functionality.

Silhouette-free image encryption using interference in the multiple-parameter fractional Fourier transform domain

A novel approach for silhouette-free image encryption based on interference is proposed using discrete multiple-parameter fractional Fourier transform (DMPFrFT), which generalizes from fractional Fourier transform. An original image is firstly applied by chaotic pixel scrambling (CPS) and then encoded into the real part of a complex signal. Using interference principle, the complex signal generates three phase-only masks in DMPFrFT domain. The silhouette of the original image cannot be extracted using one or two of the three phase-only masks. The parameters of both CPS and DMPFrFT can also serve as encryption keys to extend the key space, which further enhance the level of cryptosystem security. Numerical simulations are demonstrated to show the feasibility and validity of this approach.

New method of attack and security enhancement on an asymmetric cryptosystem based on equal modulus decomposition

A recently proposed asymmetric cryptosystem based on coherent superposition and equal modulus decomposition has shown to be robust against a specific attack. In this paper, we have shown that it is vulnerable to a newly designed attack. With this attack, an intruder is able to access the exact private key and obtain precise attack results using a phase retrieval algorithm. In addition, we have also proposed a security-enhanced asymmetric cryptosystem using a random decomposition technique and a 4f optical system. In the proposed system, random decomposition is employed to create an effective trapdoor one-way function. As a result, it is able to avoid various types of attacks and maintain the asymmetric characteristics of the cryptosystem. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed method.

Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition

A novel asymmetric cryptosystem based on coherent superposition, which is free from silhouette problem, is proposed. Being different from the phase-truncated Fourier transform-based cryptosystem, the encryption process uses equal modulus decomposition (EMD) to create an effective trapdoor one-way function. As a result, the proposed method achieves high robustness against the special attack based on iterative Fourier transform. Simulation results are presented to prove the validity of the proposed system.

Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding

We present a novel image hiding method based on phase retrieval algorithm under the framework of nonlinear double random phase encoding in fractional Fourier domain. Two phase-only masks (POMs) are efficiently determined by using the phase retrieval algorithm, in which two cascaded phase-truncated fractional Fourier transforms (FrFTs) are involved. No undesired information disclosure, post-processing of the POMs or digital inverse computation appears in our proposed method. In order to achieve the reduction in key transmission, a modified image hiding method based on the modified phase retrieval algorithm and logistic map is further proposed in this paper, in which the fractional orders and the parameters with respect to the logistic map are regarded as encryption keys. Numerical results have demonstrated the feasibility and effectiveness of the proposed algorithms.

A multispectral photon-counting double random phase encoding scheme for image authentication

In this paper, we propose a new method for color image-based authentication that combines multispectral photon-counting imaging (MPCI) and double random phase encoding (DRPE) schemes. The sparsely distributed information from MPCI and the stationary white noise signal from DRPE make intruder attacks difficult. In this authentication method, the original multispectral RGB color image is down-sampled into a Bayer image. The three types of color samples (red, green and blue color) in the Bayer image are encrypted with DRPE and the amplitude part of the resulting image is photon counted. The corresponding phase information that has nonzero amplitude after photon counting is then kept for decryption. Experimental results show that the retrieved images from the proposed method do not visually resemble their original counterparts. Nevertheless, the original color image can be efficiently verified with statistical nonlinear correlations. Our experimental results also show that different interpolation algorithms applied to Bayer images result in different verification effects for multispectral RGB color images.

Multiple-image encryption using polarized light encoding and the optical interference principle in the Fresnel-transform domain

We propose a multiple-image encryption scheme, based on polarized light encoding and the interference principle of phase-only masks (POMs), in the Fresnel-transform (FrT) domain. In this scheme, each secret image is converted into an intensity image by polarized light encoding, where a random key image and a pixilated polarizer with random angles are employed as keys. The intensity encrypted images produced by different secret images are convolved together and then inverse Fresnel-transformed. Phase and amplitude truncations are used to generate the asymmetric decryption keys. The phase-truncated inverse FrT spectrum is sent into an interference-based encryption (IBE) system to analytically obtain two POMs. To reduce the transmission and storage load on the keys, the chaotic mapping method is employed to generate random distributions of keys for encryption and decryption. One can recover all secret images successfully only if the corresponding decryption keys, the mechanism of FrTs, and correct chaotic conditions are known. The inherent silhouette problem can be thoroughly resolved by polarized light encoding in this proposal, without using any time-consuming iterative methods. The entire encryption and decryption process can be realized digitally, or in combination with optical means. Numerical simulation results are presented to verify the effectiveness and performance of the proposed scheme.

Ciphertext-only attack on a joint transform correlator encryption system

A ciphertext-only attack (COA) on a joint transform correlator (JTC) encryption system is proposed. From the perspective view of optical cryptanalysis, we find out that the issue to be solved in the COA scheme could be transferred into a phase retrieval problem with single intensity measurement. And in this paper, the hybrid input-output (HIO) algorithm is employed to handle this issue with the help of an inartificial signal domain support and a given frequency domain constraint. Meanwhile, we provide a set of numerical simulations to demonstrate the validity and feasibility of the presented method.

Multiple-image encryption based on interference principle and phase-only mask multiplexing in Fresnel transform domain

In this article, a multiple-image encryption method based on the optical interference principle and phase-only mask (POM) multiplexing is proposed. During the encryption process, each secret image is encoded into two analytically obtained POMs and one computer-generated random POM, in which no iterative computation is required. The analytically obtained POMs taken from different secret images are then synthesized by POM multiplexing and further encoded into two complex ciphertext images. The silhouette problem that exists in the earlier interference principle-based encryption approaches is totally resolved by the proposal. Both digital and optical means can be used for decryption. The crosstalk effect between the secret images will not appear in the decrypted results by using the proposed system. Numerical simulations have been given to verify the performance and feasibility of the proposal. We also discuss briefly the influence of information compression on the quality of decrypted images.

Interference-based multiple-image encryption with silhouette removal by position multiplexing

An approach for multiple-image encryption based on interference and position multiplexing is proposed. In the encryption process, multiple images are analytically hidden into three phase-only masks (POMs). The encryption algorithm for this method is quite simple and does not need iterative encoding. For decryption, both the digital method and optical method could be employed. Also, we analyze the multiplexing capacity through the correlation coefficient. In addition, the silhouette problem that exists in previous interference-based encryption methods with two POMs can be eliminated during the generation procedure of POMs based on the interference principle. Simulation results are presented to verify the validity of the proposed approach.

Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding

A color information cryptosystem based on optical interference principle and spiral phase encoding is proposed. A spiral phase mask (SPM) is used instead of a conventional random phase mask because it contains multiple storing keys in a single phase mask. The color image is decomposed into RGB channels. The decomposed three RGB channels can avoid the interference of crosstalks efficiently. Each channel is encoded into an SPM and analytically generates two spiral phase-only masks (SPOMs). The two SPOMs are then phase-truncated to get two encrypted images and amplitude-truncated to produce two asymmetric phase keys. The two SPOMs and the two asymmetric phase keys can be allocated to four different authorized users. The order, the wavelength, the focal length, and the radius are construction parameters of the SPM (or third SPOM) that can also be assigned to the four other different authorized users. The proposed technique can be used for a highly secure verification system, so an unauthorized user cannot retrieve the original image if only one key out of eight keys is missing. The proposed method does not require iterative encoding or postprocessing of SPOMs to overcome inherent silhouette problems, and its optical setup alleviates stringent alignment of SOPMs. The validity and feasibility of the proposed method are supported by numerical simulation results.

Interference-based optical image encryption using three-dimensional phase retrieval

In recent years, optical image encryption has attracted more and more attention in information security due to its unique advantages, such as parallel processing and multiple-parameter characteristics. In this paper, we propose a new method using three-dimensional (3D) processing strategy for interference-based optical image encryption. The plaintext is considered as a series of particles distributed in 3D space, and any one sectional extraction cannot render information about the plaintext during image decryption. In addition, the silhouette problem in the conventional interference-based optical encryption method is effectively suppressed, and the proposed optical cryptosystem can achieve higher security compared with the previous work. A numerical experiment is conducted to demonstrate the feasibility and effectiveness of the proposed method.

Binary image encryption based on interference of two phase-only masks

Optical image encryption based on interference has attracted a lot of attention recently. The technique employs two pure phase masks derived from the complex field of the image in the Fresnel diffraction domain. The image decryption procedure can be carried out by inverse Fresnel transformation of the summation of two pure phase masks. However, the silhouette of the original image, which is recovered by either of the two phase-only masks, impedes the application of this technique. In this paper, a very simple method for binary image encryption based on interference of two phase-only masks is proposed without any silhouette problem. The binary image in combination with a random phase mask is separated into two phase-only masks directly, and the decryption by summation of the two masks can be performed digitally or optically. In this paper, the encryption and decryption processes are analyzed, after which both the optical simulation and the experimental results based on single-beam holography are given to demonstrate the feasibility of the encryption method. As information nowadays is mainly digitized into binary codes, the proposed encryption method may find applications in the information processing field.

Image encryption based on interference that uses fractional Fourier domain asymmetric keys

We propose an image encryption technique based on the interference principle and phase-truncation approach in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys and is free from the silhouette problem. Multiple input images bonded with random phase masks are independently fractional Fourier transformed. Amplitude truncation of obtained spectrum helps generate individual and universal keys while phase truncation generates two phase-only masks analytically. For decryption, these two phase-only masks optically interfere, and this results in the phase-truncated function in the output. After using the correct random phase mask, universal key, individual key, and fractional orders, the original image is retrieved successfully. Computer simulation results with four gray-scale images validate the proposed method. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and decryption keys formation are complicated and should be realized digitally. For decryption, an optoelectronic scheme has been suggested.

Optical image hiding with silhouette removal based on the optical interference principle

The earlier proposed interference-based encryption method with two phase-only masks (POMs), which actually is a special case of our method, is quite simple and does not need iterative encoding. However, it has been found recently that the encryption method has security problems and cannot be directly applied to image encryption due to the inherent silhouette problem. Several methods based on chaotic encryption algorithms have been proposed to remove the problem by postprocessing of the POMs, which increased the computation time or led to digital inverse computation in decryption. Here we propose a new method for image encryption based on optical interference and analytical algorithm that can be directly used for image encryption. The information of the target image is hidden into three POMs, and the silhouette problem that exists in the method with two POMs can be resolved during the generation procedure of POMs based on the interference principle. Simulation results are presented to verify the validity of the proposed approach.

Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator

Interference-based optical encryption schemes have an inherent silhouette problem due to the equipollent nature of the phase-only masks (POMs) generated using an analytical method. One of the earlier methods suggested that removing the problem by use of exchanging process between two masks increases the computational load. This shortcoming is overcome with a noniterative method using the jigsaw transformation (JT) in a single step, with improved security because the inverse JT of these masks, along with correct permutation keys that are necessary to decrypt the original image. The stringent alignment requirement of the POMs in two different arms during the experiment is removed with an alternative method using a single spatial light modulator. Experimental results are provided to demonstrate the decryption process with the proposed method.