Optical image encryption using password key based on phase retrieval algorithm

The optical image encryption has attracted more and more researchers’ attention, and the various encryption schemes have been proposed. In existing optical cryptosystem, the phase functions or images are usually used as the encryption keys, and it is difficult that the traditional public-key algorithm (such as RSA, ECC, etc.) is used to complete large numerical key transfer. In this paper, we propose a key distribution scheme based on the phase retrieval algorithm and the RSA public-key algorithm, which solves the problem for the key distribution in optical image encryption system. Furthermore, we also propose a novel image encryption system based on the key distribution principle. In the system, the different keys can be used in every encryption process, which greatly improves the security of the system.

With the rapid development of computer network technology, information security has attracted increasing attention. Due to the characteristics of multi-dimensional operation and parallel processing capability, optical image encryption techniques have been receiving more and more attention. Since the well-known double random phase encoding technique was proposed, many other methods based on optical information processing means such as the use of optical transform, interference, and polarized light encoding, have been proposed for optical image encryption. However, recent researches have demonstrated that traditional optical encryption techniques are symmetric cryptosystems, in which decryption keys are identical to encryption keys and they have been found to be vulnerable to different types of attacks, such as known plaintext and chosen plaintext attacks. To overcome this shortcoming, asymmetric cryptosystems based on nonlinear phase-truncation techniques and phase retrieval algorithm have been proposed. Asymmetric cryptosystem is a cryptographic system in which encryption keys are different from decryption keys. The encryption keys are used as public keys which are disseminated widely, and the decryption keys are used as private keys which are known only to the authorized users. So, asymmetric cryptosystem can offer a higher-level security than symmetric cryptosystem. However, asymmetric cryptosystems based on phase retrieval algorithms require a lot of computational time, and asymmetric cryptosystems based on phase-truncated Fourier transforms have been found to be vulnerable to special attack. Therefore, in this paper, a novel asymmetric image encryption method is proposed by using the gyrator transform and vector operation. The original image is encrypted into two phase masks with vector operation. One is a random phase mask and the other is a phase mask related to the original image. In the encryption process, the random phase mask is used as a phase key and the other phase mask is transformed by gyrator transform. The transform result is performed by Fourier transform after being modulated by a phase distribution. The ciphertext is the amplitude of the above result. Compared with previous encryption schemes, the suggested method has two advantages. Firstly, we have proposed a new asymmetric encryption method based on the gyrator transform and vector operation. The decryption process is different from the encryption process. The gyrator transform and Fourier transform are used in the encryption process, while only the inverse operation of Fourier transform is employed in the decryption process. In addition, the decryption keys produced in the encryption process are different from the encryption keys. Therefore, the proposed scheme has high resistance against the conventional attacks. Secondly, the encrypted result is real-valued, which is convenient for display, transmission and storage.Numerical simulations illustrate the feasibility and effectiveness of the proposed encryption scheme.

In conventional symmetric encryption, it is common for the encryption/decryption key to be reused for multiple plaintexts. This gives rise to the concept of a known-plaintext attack. In optical image encryption systems, such as double random phase encoding (DRPE), this is also the case. With optical encryption, if one knows a plaintext-ciphertext pair, one can carry out a known-plaintext attack more efficiently than a bruteforce attack, using heuristics based on phase retrieval or simulated annealing. However, it is more likely that an attacker will find an imperfect encryption/decryption key using such heuristics. Such an imperfect key will work for the known plaintext-ciphertext pair, but not an arbitrary unseen plaintext-ciphertext pair using the original key. In this paper, we illustrate the problem and attempt to characterise the increase in security it affords optical encryption.

BackgroundOptical information encryption technology has received extensive attention from researchers in recent years because of its advantages of parallel and high-speed processing capability, as well as the controllability of phase components.MethodsAn encryption method for grayscale images with a pair of random phase masks based on gamma distribution in the gyrator domain is proposed. In this scheme, two random distribution phase-images using random parameters according to the definition of the gamma probability distribution function are generated. They are loaded onto spatial light modulators as random phase masks used in the encryption process. The input grayscale image transmitted through the first random phase mask. And then they are encoded by the first gyrator transform. The resulting information is again encrypted by a second gamma distribution random phase mask at the gyrator frequency plane. The final results are encoded by the second gyrator transform.ResultsNumerical simulations are presented to confirm the security, validity, and flexibility of the proposed idea. The gyrator transform rotation angle sensitivity test is also simulated. The occlusion and noise attacks analysis establish the scheme’s robustness.ConclusionsIn gyrator transform-based optical image encryption cipher system, encrypting the input image with different parameters of gamma distribution RPMs will significantly change the statistical distribution of phase in the ciphertext. It means that the phase distribution in the ciphertext will not obey the law of random scattering medium. Therefore, it has potential to resist the attack based on the phase retrieval algorithm. Therefore, the security and flexibility of encryption can be improved by using gamma distribution RPMs.

Based on the chaos and phase retrieval algorithm, a hierarchical multiple binary image encryption is proposed. In the encryption process, each plaintext is encrypted into a diffraction intensity pattern by two chaos-generated random phase masks (RPMs). Thereafter, the captured diffraction intensity patterns are partially selected by different binary masks and then combined together to form a single intensity pattern. The combined intensity pattern is saved as ciphertext. For decryption, an iterative phase retrieval algorithm is performed, in which a support constraint in the output plane and a median filtering operation are utilized to achieve a rapid convergence rate without a stagnation problem. The proposed scheme has a simple optical setup and large encryption capacity. In particular, it is well suited for constructing a hierarchical security system. The security and robustness of the proposal are also investigated.

The technique of the multiple phase encoding for optical security and verification systems is presented in this paper. This technique is based on a 4-f optical correlator that is a common architecture for optical image encryption and verification systems. However, two or more phase masks are iteratively retrieved by use of the proposed multiple phases retrieval algorithm (MPRA) to obtain the target image. The convergent speed of the iteration process in the MPRA is significantly increased and the recovered image is much more similar to the target image than those in previous approaches. In addition, the quantization effects due to the finite resolution of the phase levels in practical implementation are discussed. The relationships between the number of phase masks and the quantized phase levels are also investigated. According to the simulation results, two and three phase masks are enough to design an efficient security verification system with 64 and 32 phase levels, respectively.

Most of existing optical color image encryption schemes have born security risks due to the adoption of linear transform, and data redundancy for the generation of complex image. To settle these problems effectively, a self-adaptive scheme for double color-image encryption is proposed in this paper. In this scheme, each RGB color component of two secret color images is first compressed and encrypted by 2D compressive sensing (CS) in which measurement matrices are generated by compound chaotic systems. Then, the two measured images are regarded as the real part and imaginary part, constituting a complex image to reduce data redundancy caused by following optical encryption. In the end, the complex image is reencrypted by self-adaptive random phase encoding and discrete fractional random transform (DFrRT) to obtain the final encrypted data. In the process of DFrRT and random phase encoding, the correlations between R, G, B components are adequately utilized. The production of key streams not only depends on the initial value but also on plain-text, and the three color components affect each other to enhance the ability against the known plaintext attack. The projection neural network algorithm is adopted to obtain the decryption images. Simulation results also verify the validity and security of the proposed method.

Optical image encryption is one of the most promising technologies being investigated in the field of data communication and information technology. In this paper, a novel image encryption system based on virtual optical technique, Fourier transform phase retrieval algorithm and RSA public key exchange is proposed. In this strategy, a gray-level image is captured using a digital camera and encrypted using a linear grating superposed on the reflected intensity map of the object. A speckle mask is simulated and used as a secret key in both transmission and reception ends so that the receiver can identify the authenticity of the ciphertext by using the speckle pattern in the decryption process. The decryption method is performed to recover the phase of the deformed grating pattern. Towards this, Fourier transform based phase retrieval and sequential line scan phase unwrapping algorithm is utilized. The simulation results demonstrate the validity of the encryption method and the high robustness against potential attacks. To determines the accuracy of the information retrieved by the proposed technique, root mean square error is calculated between the original image and retrieved image. The proposed technique is also applicable for the information authentication.

Optica Applicata, Vol. 46, 2016, nr 1, s. 57-69

Optical encryption methods attract a lot of attention owing to their high encryption speed and bandwidth. Recently, neural networks (NNs) have been used for cryptanalysis of optical encryption techniques. In this paper, we for the first time to our knowledge applied a NN for ciphertext only attack on an optical encryption system with spatially incoherent illumination. A NN was used to extract encryption keys from ciphertexts, which can be used to decrypt the plaintext QR codes. Additionally, an optically encrypted QR code was successfully decoded after using the key extracted by the trained NN, that has been processed to account for discrepancies between the numerical model and the optical setup. The results show the vulnerability of the existing optical encryption system with incoherent light to attacks of this type, which indicates the need for improved optical encryption security.

In this paper, a virtual optical encryption open source software system for image security is proposed. Our system makes it possible to encrypt and decrypt images based on the optical theorem, which includes the virtual optical image encryption technique (VOIET), the data hiding technique (DHT), the data extraction technique (DET), and the virtual optical image decryption technique (VOIDT). The optical theorem is based the digitized double-random-phase algorithm, which is called the virtual optical theorem. In the system, secret data can be embedded into the encrypted image data without distortion. The comparison of data hiding capacity and reconstructed image quality is performed in the experiment. Our system is designed and implemented by the open source software, which is called the Virtual Optical Image Encryption System (VOIES) and released on the Open Source Software Foundry (OSSF).

A new optical encryption system is presented in this paper.By replacing the random phase plates by random amplitude plates in the double random phase encoding system, a novel optical encryption system is formed.The Statistical characteristics of the autocorrelation function of the encoded image are investigated; we found that the original image had been changed into a complex-amplitude stationary white noise.As a result, this approach proved to be robustness against brute force attack.Computer simulations are performed and the results are consistent with theoretical analysis.Moreover, some properties of this method prior to double random phase encoding system are discussed.

We present a simple and robust technique for measuring the nonlinear refractive index. The principle is based on an iterative phase retrieval algorithm with a pump-probe system. Different strong phase modulations are intentionally introduced into the probe beam, and corresponding diffraction intensity patterns are recorded. The recordings are used in the phase retrieval algorithm to reconstruct the pump-induced phase on the probe beam. The nonlinear refractive index is then extracted from the reconstructed phase. The reconstruction method offers a straightforward procedure and a simple lensless setup. Simulations validate the proposed method. The effects of different characteristics of the pump and probe beams on the quality of reconstructions are investigated. The obtained results demonstrate that the reconstructions are accurate even for the probe beams with complex-valued fields and non-Gaussian pump beams; it removes the requirement for smooth fields of the pump and probe beams. The validity of the method in noisy conditions is also shown.

The most biological samples are transparent and have no amplitude modulation for the incident wave. It is hard to observe the sample without dyeing in traditional microscope. Phase retrieval algorithm can reconstruct complex-valued sample with several diffraction intensity patterns. In this paper, a lensless imaging method is designed by diffuser 1-D moving, which decreases acquisition dada time, simplifies the experimental equipment and reduces experiment cost compared to typical ptychography based on 2-D shifting. A diffuser is placed into imaging system to improve resolution, which brought higher frequency information into the captured patterns via scattering effect. In field reconstruction, the additional amplitude constraint is added into the iterative phase retrieval algorithm. The proposed algorithm achieved faster convergence and reconstructed high-quality images. For the biological sample image, a wide field of view was realized with 20 diffraction patterns.

Intensive studies have been done to get robust encryption algorithms. Due to the importance of image information, optical encryption has played a vital role in information security. Many optical encryption schemes have been proposed but most of them suffer from poor robustness. In this paper six proposed algorithms will be presented for optical encryption to be robust to severe attacks: composite attack. Three of these approaches are based on one level Discrete Wavelet Transform (DWT) and the others are based on Wavelet Packet (WP). Not only will new techniques be presented but also a new proposed chaotic map has been developed as random keys for all algorithms. After extensive comparative study with some traditional techniques, it has been found that the novel algorithms have achieved better performance versus conventional ones. Also it has been found that WP based algorithms have achieved better performance than DWT based ones against severe composite attacks.