Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition

Attack on optical cryptosystems by skip connection networks

Optical encryption methods, due to their efficient operation speed and parallel processing capabilities, hold significant importance in securing multidimensional and large-volume data. Enhancing the security of optical cryptosystems from the perspective of cryptanalysis holds significant importance currently. Presently, attack methods against optical encryption are complex, and the effectiveness of these attacks is insufficient. Security analysis solutions face limitations in both breadth and depth. Therefore, this paper proposes an attack on optical cryptosystems based on a skip connection network, demonstrating the susceptibility of optical cryptosystems to attacks based on neural network algorithms. The network model is trained on plaintext-ciphertext pairs, fitting equivalent keys without various additional conditions. It approximates plaintext information in high-dimensional space, directly obtaining corresponding plaintext through ciphertext information, expanding the applicability and enhancing the effectiveness of the attack scheme. Finally, the feasibility and effectiveness of the attack scheme were verified through computer simulations. The experiments indicate that the method proposed in this paper has low computational complexity, wide applicability, produces high-quality decrypted images, and high decipherment accuracy. This provides a universal approach for analyzing the security of various optical cryptosystems from the perspective of chosen plaintext attacks.

Optical phase-truncation-based double-image encryption using equal modulus decomposition and random masks

This work reports an optical double-image crosstalk free encryption scheme that employs equal modulus decomposition and random masks. For the encryption, two plaintexts by a random amplitude mask and a random phase mask have been encrypted into a single ciphertext mask and two private key masks. Owing to the two random masks introduced, the functional relation between the plaintext pair and the ciphertext indirectly cause the paucity of constraints employed for the specific attack. Unlike the traditional phase-truncation-based techniques, this scheme is immune to the information leakage and different types of attacks. Furthermore, the three different diffraction distances and the illuminating wavelength also function as four additional keys to significantly reinforce the security. Simulation results demonstrate the feasibility and validity of the proposal.

Multiuser medical image encryption algorithm using phase-only CGH in the gyrator domain

In this paper, a multiuser medical image encryption algorithm is proposed. The proposed algorithm utilizes polar decomposition, which enables multiuser features in the proposed algorithm. A computer-generated hologram (CGH) improves the security of the proposed algorithm in the gyrator domain. The phase-only CGH-based multiuser algorithm offers advantages such as storing a large amount of information in a compact space, resistance to counterfeiting, and enhanced security. The proposed method is validated with various statistical metrics, such as information entropy, mean squared error, correlation coefficient, histogram, and mesh plots. Results confirm that the proposed algorithm is secure and robust against potential attacks, such as plaintext attacks, iterative attacks, and contamination attacks. The proposed method has a large keyspace, which makes it very difficult to be breached in real-time with existing computational power.

Optical asymmetric JTC cryptosystem based on binary phase modulation and image superposition-subtraction operation

The joint transform correlator (JTC) cryptosystem is a simple and practical optical cryptosystem. But its identical key in both encryption and decryption brings security risks in the key distribution and management. To overcome these drawbacks, we first create a trapdoor one-way function based on image superposition and subtraction operation. Then combined with the one-way binary phase modulation, an optical asymmetric JTC cryptosystem is proposed in this paper. These two kinds of trapdoor one-way functions are not only effective and implementable, but also can greatly enhance the ability of our proposal to resist various attacks. In addition, we select the structured spiral phase mask (SSPM) controlled by its structural parameters as the key mask of the JTC cryptosystem to facilitate the key transmission. When the structural parameters of the SSPM are protected by the RSA algorithm during encryption and decryption, not only the security of the proposed cryptosystem can be enhanced, but also the key distribution and management will be improved. This also makes our proposal conform more closely to the basic agreement of the public key cryptosystem. Simulation analysis and initial experimental results verified the correctness and feasibility of our proposal.

Parallel optical hash function based on the interaction between linearly polarized light and multiple-scattering media

A method is proposed for constructing a cryptographic hash function based on the interaction between linearly polarized light and multiple-scattering media in a parallel fashion. It is well known that an unpredictable noise-like speckle pattern will appear when a light beam passes through a scattering medium. By leveraging this natural optical-encoding mechanism, we developed a paralleled algorithm to construct an optical hash function. It was shown by numerical simulation to have a high security level. Furthermore, in the proposed conceptual optical-digital setup, a strategy for multiplexing linearly polarized light was introduced to accelerate data processing.

Cryptoanalysis on the optical image encryption scheme based on full phase encoding and equal modulus decomposition

In this paper, the security of a security-enhanced optical cryptosystem based on full phase encoding and equal modulus decomposition (EMD) is evaluated. Compared to the original EMD-based image scheme in which plaintext is the amplitude information of the spectrum to generate two complex-valued masks with equal moduli, phase-encoded plaintext is regarded as the input of EMD-based structure to generate masks in the full phase encoding and EMD combined cryptosystem. It seems that the security strength has been improved by decreasing the number of constraints in the iterative attack; however, it is found that this scheme is still under security risk. Thus, we propose two iterative attacks based on normalization operator and phase-retrieval techniques with different constraints to break the security-enhanced scheme. Numerical simulations are carried out to demonstrate the feasibility and effectiveness of the proposed attacks.

Asymmetric double-image encryption via wavelength multiplexing

In this paper, we propose an asymmetric double-image encryption via wavelength multiplexing. First, a novel iterative phase retrieval algorithm, to the best of our knowledge, is developed to encode two images into one complex-valued function via wavelength multiplexing. Then, the function is encoded by equal modulus decomposition (EMD). This cryptosystem not only retains the advantages of EMD but also reduces the number of public keys so as to enhance the resistance to the amplitude-phase retrieval algorithm (APRA). In the decryption, two high-quality decrypted images can be obtained with their corresponding wavelengths. To the best of our knowledge, this is the first time that wavelength multiplexing is used to achieve high-quality two-image encryption and decryption. Numerical simulation results show the effectiveness and robustness of this new method.

Asymmetric multiparameter encryption of hyperspectral images based on hybrid chaotic mapping and an equal modulus decomposition tree

We present an asymmetric encryption scheme for hyperspectral images using hybrid chaotic maps (HCMs) and an equal modulus decomposition tree (EMDT) structure in a discrete multiple-parameter fractional Fourier transform (dmpFrFT) domain. The original hyperspectral image was scrambled by an HCM and then encrypted into asymmetric ciphertext using the EMDT. In the EMDT, each pair of the band images of the scrambled hyperspectral image were regarded as leaf nodes, while the encryption modules using chaotic random phase mask, dmpFrFT, and improved equal modulus decomposition were regarded as branch nodes, and the encryption process was implemented along the paths from the leaf nodes to the topmost branch node. The EMDT structure could provide multiparameter encryption, real-valued output, and different pairs of band images with different secret keys and encryption/decryption paths. Compared with the previous optical encryption approaches for hyperspectral images, our asymmetric cryptosystem had larger key space, less data amount of storage and transmission, and stronger resistance to statistical attacks. Various numerical simulations verified the performance of our proposed asymmetric cryptosystem.

Polarization-Encoded Fully-Phase Encryption Using Transport-of-Intensity Equation

In this study, we propose a novel method to encrypt fully-phase information combining the concepts of the transport of intensity equation and spatially variant polarization encoding. The transport of intensity equation is a non-iterative and non-interferometric phase-retrieval method which recovers the phase information from defocused intensities. Spatially variant polarization encoding employs defocused intensity measurements. The proposed cryptosystem uses a two-step optical experimentation process—primarily, a simple set-up for defocused intensities recording for phase retrieval and then a set-up for encoding. Strong security, convenient intensity-based measurements, and noise-free decryption are the main features of the proposed method. The simulation results have been presented in support of the proposed idea. However, the TIE section of the cryptosystem, as of now, has been experimentally demonstrated for micro-lens.

Optical image encryption based on biometric keys and singular value decomposition

We propose an asymmetric optical image cryptosystem based on biometric keys and singular value decomposition (SVD) in the Fresnel transform domain. In the proposed cryptosystem, the biometric keys are palmprint phase mask generated by a palmprint, a chaotic phase mask, and an amplitude truncated Fourier transform, which can provide the cryptosystem with more data security due to the uniqueness of the palmprint. Two images are first encoded into a complex function, which then is modulated by the palmprint phase mask. A Fresnel transform and then an SVD operation are performed on the modulated result. The SVD operation is used to generate private secret keys, which makes the encryption secret keys and decryption secret keys different, and thus the encryption process and decryption process are different. In addition, multiple images are encrypted into a real-valued ciphertext, making it convenient to transport and record. Numerical simulation results have demonstrated that our proposed encryption system has robustness against statistical, occlusion, noise, and chosen-plaintext attacks.

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.

Linear space-variant optical cryptosystem via Fourier ptychography

An optical cryptosystem via Fourier ptychography with double random phase masks is proposed. The encryption process cannot be precisely simulated except by optical experiment due to vignetting, which is space variant and can act as a one-way function from the perspective of pure optics and improve the security of our system. In addition, the encryption for a high-resolution, large field-of-view, and complex-valued image is achievable. Optical experiments are presented to prove the validity and security of the proposed system. Our method will give more insight into separating optical cryptography from computer cryptography in nature.

Enhanced exclusive-OR and quick response code-based image encryption through incoherent illumination

For practical application of any optical cryptographic technique, good quality decryption is necessary. Exclusive-OR (XOR) operation is a well-known technique for image encryption but faces the problem of quality degradation, while optically implemented. One of the reasons for quality degradation is the presence of laser speckles. The other reason is the noise that induces around image pixels. In this study, we demonstrate an image encryption using XOR operation based on light-emitting diode (LED) and quick response code, which not only reduces the damage caused by speckles but also overcomes the noise problem. The results with green and white LEDs and laser sources have been compared. Overall, the proposed optical cryptosystem is simple, compact, and cost-effective.

Novel asymmetric cryptosystem based on distorted wavefront beam illumination and double-random phase encoding

Herein, we propose a new security enhancing method that employs wavefront aberrations as optical keys to improve the resistance capabilities of conventional double-random phase encoding (DRPE) optical cryptosystems. This study has two main innovations. First, we exploit a special beam-expander afocal-reflecting to produce different types of aberrations, and the wavefront distortion can be altered by changing the shape of the afocal-reflecting system using a deformable mirror. Then, we reconstruct the wavefront aberrations via the surface fitting of Zernike polynomials and use the reconstructed aberrations as novel asymmetric vector keys. The ideal wavefront and the distorted wavefront obtained by wavefront sensing can be regarded as a pair of private and public keys. The wavelength and focal length of the Fourier lens can be used as additional keys to increase the number of degrees of freedom. This novel cryptosystem can enhance the resistance to various attacks aimed at DRPE systems. Finally, we conduct ZEMAX and MATLAB simulations to demonstrate the superiority of this method.

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.

Cryptanalysis of an "asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition"

We analyze and present an attack scheme of the asymmetric optical cryptosystem proposed recently based on coherent superposition and equal modulus decomposition [Opt. Lett.40, 475 (2015)OPLEDP0146-959210.1364/OL.40.000475]. We prove that the attacker can recover the original image with the ciphertext and public keys through the amplitude-phase retrieval algorithm by using two constraints. One constraint of the amplitude-phase retrieval algorithm is the public key and the other is obtained through the analysis of the cryptosystem. The simulation results demonstrate the feasibility of the attack method.

Group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform

A novel method of group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform is presented. The proposed method employs three different groups of multiple images. The color images of each group are individually segregated into R, G, and B channels. Each channel is first permutated by using a sequence of chaotic pairs generated with a system of two symmetrically coupled identical logistic maps and then gyrator transformed. The gyrator spectrum of each channel is multiplied together and then modulated by a random phase function to obtain a corresponding multiplex channel. The encoded multiplex image is restituted through a concatenation of R, G, and B multiplex channels. The phase and amplitude functions of the first, second, and third groups of encoded multiplex images are generated. The host image is a single-level 2D discrete wavelet transformed to decompose into LL, HL, LH, and HH subbands. HL, LH, and HH subbands are then replaced with phase functions of the first, second, and third groups, respectively. Finally, the resultant image is an inverse single-level 2D discrete wavelet transformed to construct a watermarked image. The three groups of multiple images are protected not only by the encryption algorithm but also visually by the host image. Thus, a high level of security can be achieved. Each group includes group decryption keys, and each image of the group comprises individual decryption keys beside parameters of coupled logistic maps and gyrator transform. As a result, the key space is very large. The decryption system can be realized by using an optoelectronic device. The numerical simulation results confirm the validity and security of the proposed scheme.

Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition: comment

I comment on the recent Letter by Cai et al. [Opt. Lett.40, 475 (2015).], in which the authors claimed that the method can resist the special attack. However, I think their attack analysis and algorithm are ill-considered and worth discussing.