Security and encryption optical systems based on a correlator with significant output images

Broadband decoupling of intensity and polarization with vectorial Fourier metasurfaces

Intensity and polarization are two fundamental components of light. Independent control of them is of tremendous interest in many applications. In this paper, we propose a general vectorial encryption method, which enables arbitrary far-field light distribution with the local polarization, including orientations and ellipticities, decoupling intensity from polarization across a broad bandwidth using geometric phase metasurfaces. By revamping the well-known iterative Fourier transform algorithm, we propose "à la carte" design of far-field intensity and polarization distribution with vectorial Fourier metasurfaces. A series of non-conventional vectorial field distribution, mimicking cylindrical vector beams in the sense that they share the same intensity profile but with different polarization distribution and a speckled phase distribution, is demonstrated. Vectorial Fourier optical metasurfaces may enable important applications in the area of complex light beam generation, secure optical data storage, steganography and optical communications.

Optical secret sharing with cascaded metasurface holography

Secret sharing is a well-established cryptographic primitive for storing highly sensitive information like encryption keys for encoded data. It describes the problem of splitting a secret into different shares, without revealing any information to its shareholders. Here, we demonstrate an all-optical solution for secret sharing based on metasurface holography. In our concept, metasurface holograms are used as spatially separable shares that carry encrypted messages in the form of holographic images. Two of these shares can be recombined by bringing them close together. Light passing through this stack of metasurfaces accumulates the phase shift of both holograms and optically reconstructs the secret with high fidelity. In addition, the hologram generated by each single metasurface can uniquely identify its shareholder. Furthermore, we demonstrate that the inherent translational alignment sensitivity between two stacked metasurface holograms can be used for spatial multiplexing, which can be further extended to realize optical rulers.

Modified Gerchberg-Saxton (G-S) Algorithm and Its Application

The Gerchberg-Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which n plaintexts can be recovered from n ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm.

Computer-generated hologram marked by correlated photon imaging

The computer-generated hologram (CGH) has been studied for many applications. In this paper, CGH is watermarked by correlated photon imaging. An input image is encoded into two cascaded phase-only masks by using the CGH principle. Subsequently, two different marks are independently encoded into one-dimensional (1D) intensity points by using correlated photon imaging (or ghost imaging), and the recorded 1D intensity points are embedded into the extracted phase masks for optical watermarking. During the decoding, the input is recovered by using two watermarked phase masks. To verify copyright of the recovered input image, information embedded in two phase-only masks is retrieved and used to decode the hidden marks. The decoded marks do not visually render clear information due to only a few measurements and, instead, are authenticated. It is illustrated that the quality of the recovered input image is high, and a different imaging approach can be applied in the CGH system for optical watermarking. The proposed approach provides a promising strategy for optical information security.

Fast non-interferometric iterative phase retrieval for holographic data storage

Fast non-interferometric phase retrieval is a very important technique for phase-encoded holographic data storage and other phase based applications due to its advantage of easy implementation, simple system setup, and robust noise tolerance. Here we present an iterative non-interferometric phase retrieval for 4-level phase encoded holographic data storage based on an iterative Fourier transform algorithm and known portion of the encoded data, which increases the storage code rate to two-times that of an amplitude based method. Only a single image at the Fourier plane of the beam is captured for the iterative reconstruction. Since beam intensity at the Fourier plane of the reconstructed beam is more concentrated than the reconstructed beam itself, the requirement of diffractive efficiency of the recording media is reduced, which will improve the dynamic range of recording media significantly. The phase retrieval only requires 10 iterations to achieve a less than 5% phase data error rate, which is successfully demonstrated by recording and reconstructing a test image data experimentally. We believe our method will further advance the holographic data storage technique in the era of big data.

Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses

We present a lensless, interferenceless incoherent digital holography technique based on the principle of coded aperture correlation holography. The acquired digital hologram by this technique contains a three-dimensional image of some observed scene. Light diffracted by a point object (pinhole) is modulated using a random-like coded phase mask (CPM) and the intensity pattern is recorded and composed as a point spread hologram (PSH). A library of PSHs is created using the same CPM by moving the pinhole to all possible axial locations. Intensity diffracted through the same CPM from an object placed within the axial limits of the PSH library is recorded by a digital camera. The recorded intensity this time is composed as the object hologram. The image of the object at any axial plane is reconstructed by cross-correlating the object hologram with the corresponding component of the PSH library. The reconstruction noise attached to the image is suppressed by various methods. The reconstruction results of multiplane and thick objects by this technique are compared with regular lens-based imaging.

Double-random-phase encryption with photon counting for image authentication using only the amplitude of the encrypted image

We present a photon-counting double-random-phase encryption technique that only requires the photon-limited amplitude of the encrypted image for decryption. The double-random-phase encryption is used to encrypt an image, generating a complex image. Photon counting is applied to the amplitude of the encrypted image, generating a sparse noise-like image; however, the phase information is not retained. By not using the phase information, the encryption process is simplified, allowing for intensity detection and also less information to be recorded. Using a phase numerically generated from the correct encryption keys together with the photon-limited amplitude of the encrypted image, we are able to decrypt the image. Moreover, nonlinear correlation algorithms can be used to authenticate the decrypted image. Both amplitude-based and full-phase encryption using the proposed method are investigated. Preliminary computational results and performance evaluation are presented.

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.

Triple-image encryption based on phase-truncated Fresnel transform and basic vector operation

A triple-image encryption method is proposed that is based on phase-truncated Fresnel transform (PTFT), basic vector composition, and XOR operation. In the encryption process, two random phase masks, with one each placed at the input plane and the transform plane, are generated by basic vector resolution operations over the first and the second plaintext images, and then a ciphered image in the input plane is fabricated by XOR encoding for the third plaintext image. When the cryptosystem is illuminated by an on-axis plane, assisted by PTFT, the ciphered image is finally encrypted into an amplitude-only noise-like image in the output plane. During decryption, possessing the correct private key, decryption keys, and the assistant geometrical parameter keys, and placing them at the corresponding correct positions, the original three plaintext images can be successfully decrypted by inverse PTFT, basic vector composition, and XOR decoding. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.

Manipulative attack using the phase retrieval algorithm for double random phase encoding

A novel attack scheme is proposed based on a phase retrieval algorithm. In the scheme, the attacker interferes with the user's normal communication through wiretapping the channel and falsifying the ciphertext and quickly cracks the system by gathering information. The difference of this attack scheme from previous schemes is the dispensability of certain assumptions, which results in a higher value of practical application and further significance of the research. In this paper, the double random phase encoding is taken as an example to verify the validity of the scheme. The results show that our proposed scheme is feasible and efficient.

Phase retrieval encryption in an enhanced optical interference by key phase constraint

In this paper, we demonstrate a security system by using optical interference and phase retrieval algorithm (PRA) techniques. The modified PRA is proposed to encode the target image into random phase distribution. Optical and digital methods can be used for decryption. By using this method, silhouette elimination is realized. In addition, due to this simplified system design, the iterative rate is improved and the optical decryption realization is easier. Validity and performance of the proposed system are demonstrated by means of numerical simulations. The system encryption capacity as to both binary and gray images is numerically investigated. Then, the decryption procedure is demonstrated by optical experiment means and the decryption result is given.

Multiple-image authentication with a cascaded multilevel architecture based on amplitude field random sampling and phase information multiplexing

A multiple-image authentication method with a cascaded multilevel architecture in the Fresnel domain is proposed, in which a synthetic encoded complex amplitude is first fabricated, and its real amplitude component is generated by iterative amplitude encoding, random sampling, and space multiplexing for the low-level certification images, while the phase component of the synthetic encoded complex amplitude is constructed by iterative phase information encoding and multiplexing for the high-level certification images. Then the synthetic encoded complex amplitude is iteratively encoded into two phase-type ciphertexts located in two different transform planes. During high-level authentication, when the two phase-type ciphertexts and the high-level decryption key are presented to the system and then the Fresnel transform is carried out, a meaningful image with good quality and a high correlation coefficient with the original certification image can be recovered in the output plane. Similar to the procedure of high-level authentication, in the case of low-level authentication with the aid of a low-level decryption key, no significant or meaningful information is retrieved, but it can result in a remarkable peak output in the nonlinear correlation coefficient of the output image and the corresponding original certification image. Therefore, the method realizes different levels of accessibility to the original certification image for different authority levels with the same cascaded multilevel architecture.

Optical encryption using photon-counting polarimetric imaging

We present a polarimetric-based optical encoder for image encryption and verification. A system for generating random polarized vector keys based on a Mach-Zehnder configuration combined with translucent liquid crystal displays in each path of the interferometer is developed. Polarization information of the encrypted signal is retrieved by taking advantage of the information provided by the Stokes parameters. Moreover, photon-counting model is used in the encryption process which provides data sparseness and nonlinear transformation to enhance security. An authorized user with access to the polarization keys and the optical design variables can retrieve and validate the photon-counting plain-text. Optical experimental results demonstrate the feasibility of the encryption method.

Security authentication using phase-encoded nanoparticle structures and polarized light

Phase-encoded nanostructures such as quick response (QR) codes made of metallic nanoparticles are suggested to be used in security and authentication applications. We present a polarimetric optical method able to authenticate random phase-encoded QR codes. The system is illuminated using polarized light, and the QR code is encoded using a phase-only random mask. Using classification algorithms, it is possible to validate the QR code from the examination of the polarimetric signature of the speckle pattern. We used Kolmogorov-Smirnov statistical test and Support Vector Machine algorithms to authenticate the phase-encoded QR codes using polarimetric signatures.

Full-phase photon-counting double-random-phase encryption

We investigate a full-phase-based photon-counting double-random-phase encryption (PC-DRPE) method. A PC technique is applied during the encryption process, creating sparse images. The statistical distribution of the PC decrypted data for full-phase encoding and amplitude-phase encoding are derived, and their statistical parameters are used for authentication. The performance of the full-phase PC-DRPE is compared with the amplitude-based PC-DRPE method. The PC decrypted images make it difficult to visually authenticate the input image; however, advanced correlation filters can be used to authenticate the decrypted images given the correct keys. Initial computational simulations show that the full-phase PC-DRPE has the potential to require fewer photons for authentication than the amplitude-based PC-DRPE.

Optical identity authentication scheme based on elliptic curve digital signature algorithm and phase retrieval algorithm

An optical identity authentication scheme based on the elliptic curve digital signature algorithm (ECDSA) and phase retrieval algorithm (PRA) is proposed. In this scheme, a user's certification image and the quick response code of the user identity's keyed-hash message authentication code (HMAC) with added noise, serving as the amplitude and phase restriction, respectively, are digitally encoded into two phase keys using a PRA in the Fresnel domain. During the authentication process, when the two phase keys are presented to the system and illuminated by a plane wave of correct wavelength, an output image is generated in the output plane. By identifying whether there is a match between the amplitude of the output image and all the certification images pre-stored in the database, the system can thus accomplish a first-level verification. After the confirmation of first-level verification, the ECDSA signature is decoded from the phase part of the output image and verified to allege whether the user's identity is legal or not. Moreover, the introduction of HMAC makes it almost impossible to forge the signature and hence the phase keys thanks to the HMAC's irreversible property. Theoretical analysis and numerical simulations both validate the feasibility of our proposed scheme.

Lensless optical data hiding system based on phase encoding algorithm in the Fresnel domain

A novel and efficient algorithm based on a modified Gerchberg-Saxton algorithm (MGSA) in the Fresnel domain is presented, together with mathematical derivation, and two pure phase-only masks (POMs) are generated. The algorithm's application to data hiding is demonstrated by a simulation procedure, in which a hidden image/logo is encoded into phase forms. A hidden image/logo can be extracted by the proposed high-performance lensless optical data-hiding system. The reconstructed image shows good quality and the errors are close to zero. In addition, the robustness of our data-hiding technique is illustrated by simulation results. The position coordinates of the POMs as well as the wavelength are used as secure keys that can ensure sufficient information security and robustness. The main advantages of this proposed watermarking system are that it uses fewer iterative processes to produce the masks, and the image-hiding scheme is straightforward.

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.

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.

Lensless multiple-image optical encryption based on improved phase retrieval algorithm

A novel architecture of the optical multiple-image encryption based on the modified Gerchberg-Saxton algorithm (MGSA) by using cascading phase only functions (POFs) in the Fresnel transform (FrT) domain is presented. This proposed method can greatly increase the capacity of the system by avoiding the crosstalk, completely, between the encrypted target images. Each present stage encrypted target image is encoded as to a complex function by using the MGSA with constraining the encrypted target image of the previous stage. Not only the wavelength and position parameters in the FrT domain can be keys to increase system security, the created POFs are also served mutually as the encryption keys to decrypt target image from present stage into next stage in the cascaded scheme. Compared with a prior method [Appl. Opt.48, 2686-2692 (2009)], the main advantages of this proposed encryption system is that it does not need any transformative lenses and this makes it very efficient and easy to implement optically. Simulation results show that this proposed encryption system can successfully achieve the multiple-image encryption via fewer POFs, which is more advantageous in simpler implementation and efficiency than a prior method where each decryption stage requires two POFs to accomplish this task.

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.

Optical double-image cryptography based on diffractive imaging with a laterally-translated phase grating

In this paper, we propose a method using structured-illumination-based diffractive imaging with a laterally-translated phase grating for optical double-image cryptography. An optical cryptosystem is designed, and multiple random phase-only masks are placed in the optical path. When a phase grating is laterally translated just before the plaintexts, several diffraction intensity patterns (i.e., ciphertexts) can be correspondingly obtained. During image decryption, an iterative retrieval algorithm is developed to extract plaintexts from the ciphertexts. In addition, security and advantages of the proposed method are analyzed. Feasibility and effectiveness of the proposed method are demonstrated by numerical simulation results.

Lensless optical data embedding system using concealogram and cascaded digital Fresnel hologram

A robust lensless optical data embedding system using both the computer-generated concealogram and the digital Fresnel hologram (DFH) is proposed. The concealogram and the DFH are cascaded as the input and filter planes, respectively. When the concealogram is illuminated by a plane wave, the hidden data can be extracted at the output plane without using any lenses. The longitudinal positions of the filter and the output planes, as well as the wavelength, can be used as the secret keys to enhance system security. Furthermore, the robustness of the proposed system against noise and distortion is also demonstrated.

Vulnerability to chosen-plaintext attack of optoelectronic information encryption with phase-shifting interferometry

The optical cryptosystem based on phase-shifting interferometry (PSI) is one of the most interesting optical cryptographic schemes in recent years. However, we find that the PSI technique provides an attractive method to record the ciphertext, but contributes little to the security level of the cryptosystem. From the cryptanalysis point of view, in a certain simplified case, an attacker is only required to crack two equivalent decryption keys instead of the original random phase keys and geometric key. Moreover, a chosen-plaintext attack method is proposed, in which an impulse function is chosen as a known plaintext. By using this attack, the attacker can effectively recover any plaintext from the corresponding ciphertext. The validity of the attack is verified by computer simulations.

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.

Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain

We propose a method of wavelength multiplexing based on a modified Gerchberg-Saxton algorithm (MGSA) and a cascaded phase modulation scheme in the Fresnel transform domain to reduce the cross talk in the multiple-image-encryption framework. First, each plain image is encoded to a complex function by using the MGSA. Next, the phase components of the created complex functions are multiplexed with different wavelength parameters, and then they are modulated before being combined together as a phase-only function, which is recorded in the first phase-only mask (POM). Finally, the second POM is generated by applying the MGSA again on the amplitude derived from the summation of the total created complex functions. Simulation results show that the cross talk between multiplexed images has been significantly reduced compared with an existing similar method. Therefore, the multiplexing capacity in encrypting multiple gray-scale images can be increased accordingly.

An encryption method with multiple encrypted keys based on interference principle

An encryption and verification method with multiple encrypted keys based on interference principle is proposed. The encryption process is realized on computer digitally and the verification process can be completed optically or digitally. Two different images are encoded into three diffractive phase elements (DPEs) by using two different incident wavelengths. Three DPEs have different distances from output plane. The two wavelength parameters and three distance parameters can be used as encryption keys, which will boost security degree of this system. Numerical simulation proves that the proposed encryption method is valid and has high secrecy level.

Asymmetric cryptosystem based on phase-truncated Fourier transforms

We propose an asymmetric cryptosystem based on a phase-truncated Fourier transform. With phase truncation in Fourier transform, one is able to produce an asymmetric ciphertext as real-valued and stationary white noise by using two random phase keys as public keys, while a legal user can retrieve the plaintext using another two different private phase keys in the decryption process. Owing to the nonlinear operation of phase truncation, high robustness against existing attacks could be achieved. A set of simulation results shows the validity of proposed asymmetric cryptosystem.

Fast double-phase retrieval in Fresnel domain using modified Gerchberg-Saxton algorithm for lensless optical security systems

A novel fast double-phase retrieval algorithm for lensless optical security systems based on the Fresnel domain is presented in this paper. Two phase-only masks are efficiently determined by using a modified Gerchberg-Saxton algorithm, in which two cascaded Fresnel transforms are replaced by one Fourier transform with compensations to reduce the consumed computations. Simulation results show that the proposed algorithm substantially speeds up the iterative process, while keeping the reconstructed image highly correlated with the original one.

Multiple-image optical encryption: an improved encoding approach

An improved encoding approach to multiple-image optical encryption based on a cascaded phase retrieval algorithm (CPRA) is proposed. The system consists of several stages of a standard 4-f correlator, in which the keys are not only the phase mask pairs produced by CPRA but also the phase distribution of the output plane of the front stage. The security and the capacity of the system are also discussed. Results indicate that the system can resist known-plaintext attack to some extent, and the encrypted capacity is considerably enhanced. Computer simulations have proved the validity of the proposed idea. The system can be implemented using a pure optical architecture.

Optical image encryption based on interference

We proposed a novel architecture for optical image encryption based on interference. The encryption algorithm for this new method is quite simple and does not need iterative encoding. The parameters of the configuration can also serve as additional keys for encryption. Numerical simulation results demonstrate the flexibility of this new proposed method.

Cryptanalysis of optical security systems with significant output images

The security of the encryption and verification techniques with significant output images is examined by a known-plaintext attack. We introduce an iterative phase-retrieval algorithm based on multiple intensity measurements to heuristically estimate the phase key in the Fourier domain by several plaintext-cyphertext pairs. We obtain correlation output images with very low error by correlating the estimated key with corresponding random phase masks. Our studies show that the convergence behavior of this algorithm sensitively depends on the starting point. We also demonstrate that this algorithm can be used to attack the double random phase encoding technique.

Fast algorithm of phase masks for image encryption in the Fresnel domain

A high performance lensless optical security system based on the discrete Fresnel transform is presented. Two phase-only masks are generated with what we believe to be a novel and efficient algorithm. Their position coordinates and the wavelength are used as encoding parameters in the encryption process. Compared with previous studies, the main advantage of this proposed encryption system is that it does not need any iterative algorithms to produce the masks, and that makes it very efficient and easy to implement without losing the encryption security.

Two-step phase-shifting interferometry and its application in image encryption

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.

Information security system by iterative multiple-phase retrieval and pixel random permutation

A novel information security system based on multiple-phase retrieval by an iterative Fresnel-transform algorithm and pixel random permutation (PRP) technique is proposed. In this method a series of phase masks cascaded in free space are employed and the phase distributions of all the masks are adjusted simultaneously in each iteration. It can achieve faster convergence and better quality of the recovered image compared with double-phase encoding and a similar approach in the spatial-frequency domain with the same number of phase masks and can provide a higher degree of freedom in key space with more geometric parameters as supplementary keys. Furthermore, the security level of this method is greatly improved by the introduction of the PRP technique. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. The performance of this technique for different numbers of phase masks and quantized phase levels is investigated systematically with the correlation coefficient and mean square error as convergence criterions.

Design of cascaded phase keys for a hierarchical security system

An image cryptosystem based on multiple phase-only masks is proposed. The proposed cryptosystem is a hierarchical security system that can use multiple phase keys to retrieve different amounts of data. In addition to the sequential order of the phase keys, the distance parameters among the phase keys are introduced to increase the system security. Even when an illegal user steals all the phase keys, the system cannot be broken without the correct sequential order and the distance parameters. However, the proposed system can verify the identities of the persons by the cascaded structure for the phase keys to generate different verification images. Simulation results are further demonstrated to verify the proposed method.

Multiple-phase retrieval for optical security systems by use of random-phase encoding

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.

Hidden images in halftone pictures

A method of concealing an image in a different halftone image is proposed. Continuous-tone levels of the visible images are represented by the area of the halftone dots. However, the hidden image is encoded by the dots' positions inside their cells. Only a spatial correlator with a unique filter function can reveal the hidden image from the halftone picture. The technique and its robustness to noise and distortions are demonstrated.