Phase-only Masks Research Articles

Hierarchical multiple-image encryption based on the cascaded interference structure and vector stochastic decomposition algorithm

A new kind of hierarchical multiple-image encryption method based on the cascaded interference structure and vector stochastic decomposition algorithm is proposed. In this method, by using the nonequal modulus decomposition and vector stochastic decomposition algorithm, the Kth-level secret image modulated by a random phase distribution is analytically encoded into a Kth-level phase-only mask (POM) key and the (K−1)th-level complex amplitude field whose real amplitude is the (K−1)th-level secret image. Then, served as the input condition, the generated complex amplitude field is further encoded into a (K−1)th-level POM key and the (K−2)th-level complex amplitude, and so on, until the 1st-level complex amplitude field is decomposed into two POMs: one is the 1st-level key, and the other is the ciphertext. When decryption occurs, only when the high-level users simultaneously obtain all the phase keys, the correct sequential orders of phase keys, and the correct geometrical parameters, all the secret images are retrieved successfully. Both theoretical analysis and numerical simulations verify the feasibility of this method.

Specific attack and security enhancement to optical image cryptosystem based on two random masks and interference

In this paper, we evaluate the security of an amplitude-phase retrieval attack free encryption scheme based on two random masks and interference. In the proposed cryptosystem, two phase-only masks (POMs) are generated from two random images using interference technique. The POMs are then used as encryption keys in a phase-truncated Fourier transform (PTFT) based encryption scheme. Compared to traditional PTFT-based cryptosystem, the security of the encryption scheme is improved by integrating the interference technique. Consequently, the scheme is immune to some attacks. We proposed a specific attack based on a phase retrieval algorithm with median filtering to break the cryptosystem. Numerical simulation results show that the cryptosystem is vulnerable to the proposed attack. Moreover, based on the proposed attack and the existing cryptosystem, full phase encoding technique is added to the previous cryptosystem to enhance the security.

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

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

Securing multiple information using chaotic spiral phase encoding with simultaneous interference and superposition methods

A new asymmetric multiple information cryptosystem based on chaotic spiral phase encoding with simultaneous interference and superposition methods is developed. In this method, the first and second sets of secret color images of multiple authorized users are asymmetrically self-encoded by interference and superposition methods, respectively. The three phase-only masks (POMs) of each channel of the first set of all the authorized users are obtained by interference method. The two phase masks (PMs) of corresponding channel of second set of all the authorized users are acquired by superposition method. The first and second POMs are individually multiplexed. The first PMs are also multiplexed. The first multiplexed POM is modulated with the first multiplexed PM and then gyrator transformed, which is phase and amplitude truncated to produce first encrypted image and first universal decryption key. The first encrypted image is multiplied with the second multiplexed POM and then gyrator transformed, which is phase and amplitude truncated to generate final encrypted image and second universal decryption key. The third POM and second PM are the same chaotic spiral phase function (CSPF) for the same authorized user exploited as special decryption key besides three individual decryption keys. The two sets of decrypted images are free from cross-talk noise effects. For decryption, an optoelectronic system has been suggested. Simulation results are presented to verify the feasibility and effectiveness of the proposed encryption scheme.

Secret shared multiple-image encryption based on row scanning compressive ghost imaging and phase retrieval in the Fresnel domain

A multiple-image encryption method is proposed that is based on row scanning compressive ghost imaging, (t, n) threshold secret sharing, and phase retrieval in the Fresnel domain. In the encryption process, after wavelet transform and Arnold transform of the target image, the ciphertext matrix can be first detected using a bucket detector. Based on a (t, n) threshold secret sharing algorithm, the measurement key used in the row scanning compressive ghost imaging can be decomposed and shared into two pairs of sub-keys, which are then reconstructed using two phase-only mask (POM) keys with fixed pixel values, placed in the input plane and transform plane 2 of the phase retrieval scheme, respectively; and the other POM key in the transform plane 1 can be generated and updated by the iterative encoding of each plaintext image. In each iteration, the target image acts as the input amplitude constraint in the input plane. During decryption, each plaintext image possessing all the correct keys can be successfully decrypted by measurement key regeneration, compression algorithm reconstruction, inverse wavelet transformation, and Fresnel transformation. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.

Information verification and encryption based on phase retrieval with sparsity constraints and optical inference

A novel optical information verification and encryption method is proposed based on inference principle and phase retrieval with sparsity constraints. In this method, a target image is encrypted into two phase-only masks (POMs), which comprise sparse phase data used for verification. Both of the two POMs need to be authenticated before being applied for decrypting. The target image can be optically reconstructed when the two authenticated POMs are Fourier transformed and convolved by the correct decryption key, which is also generated in encryption process. No holographic scheme is involved in the proposed optical verification and encryption system and there is also no problem of information disclosure in the two authenticable POMs. Numerical simulation results demonstrate the validity and good performance of this new proposed method.

Multiple color-image fusion and watermarking based on optical interference and wavelet transform

A novel multiple color-image fusion and watermarking using optical interference and wavelet transform is proposed. In this method, each secret color image is encoded into three phase-only masks (POMs). One POM is constructed as user identity key and the other two POMs are generated as user identity key modulated by corresponding secret color image in gyrator transform domain without using any time-consuming iterative computations or post-processing of the POMs to remove inherent silhouette problem. The R, G, and B channels of different user identity keys POM are then individually multiplied to get three multiplex POMs, which are exploited as encrypted images. Similarly the R, G, and B channels of other two POMs are independently multiplied to obtain two sets of three multiplex POMs. The encrypted images are fused with gray-level cover image to produce the final encrypted image as watermarked image. The secret color images are shielded by encrypted images (which have no information about secret images) as well as cover image (which reveals no information about encrypted images). These two remarkable features of the proposed system drastically reduce the probability of the encrypted images to be searched and attacked. Each individual user has an identity key and two phase-only keys as three decryption keys besides transformation angles regarded as additional keys. Theoretical analysis and numerical simulation results validate the feasibility of the proposed method.

Interference-based image encryption with silhouette removal by aid of compressive sensing

Compressive sensing (CS) offers the opportunity to reconstruct a signal from its sparse representation, either in the space domain or the transform domain. Exploiting this character, we propose a simple interference-based image encryption method. For encryption, a synthetic image, which contains sparse samples of the original image and the designated values, is analytically separated into two phase only masks (POMs). Consequently, only fragmentary data of the primary image can be directly collected in the traditional decryption scheme. However, the subsequent CS reconstruction will retrieve a high quality image from the fragmentary information. The proposed method has effectively suppressed the silhouette problem. Moreover, it has also some distinct advantages over the previous approaches.

Optically secured information retrieval using two authenticated phase-only masks.

We propose an algorithm for jointly designing two phase-only masks (POMs) that allow for the encryption and noise-free retrieval of triple images. The images required for optical retrieval are first stored in quick-response (QR) codes for noise-free retrieval and flexible readout. Two sparse POMs are respectively calculated from two different images used as references for authentication based on modified Gerchberg-Saxton algorithm (GSA) and pixel extraction, and are then used as support constraints in a modified double-phase retrieval algorithm (MPRA), together with the above-mentioned QR codes. No visible information about the target images or the reference images can be obtained from each of these authenticated POMs. This approach allows users to authenticate the two POMs used for image reconstruction without visual observation of the reference images. It also allows user to friendly access and readout with mobile devices.

Optical image encryption based on real-valued coding and subtracting with the help of QR code

A novel optical image encryption based on real-valued coding and subtracting is proposed with the help of quick response (QR) code. In the encryption process, the original image to be encoded is firstly transformed into the corresponding QR code, and then the corresponding QR code is encoded into two phase-only masks (POMs) by using basic vector operations. Finally, the absolute values of the real or imaginary parts of the two POMs are chosen as the ciphertexts. In decryption process, the QR code can be approximately restored by recording the intensity of the subtraction between the ciphertexts, and hence the original image can be retrieved without any quality loss by scanning the restored QR code with a smartphone. Simulation results and actual smartphone collected results show that the method is feasible and has strong tolerance to noise, phase difference and ratio between intensities of the two decryption light beams.

Phase-only asymmetric encryption based on coherent superposition and phase-truncated Fourier transforms

A phase-only asymmetric encryption (POAE) based on coherent superposition and phase-truncated Fourier transforms is proposed in this paper. An original image can be encrypted into a phase-only mask (POM) by using a random phase mask. Thereafter, the POM is encrypted into an amplitude image via a series of asymmetric operations based on phase-truncated Fourier transforms. Finally, the encrypted result is hidden in a public image. The encryption can be performed digitally, and the decryption can be performed optically or digitally. Simulation results are presented to demonstrate the validity and security of the proposed protocol.

Enhancement of optical image encryption based on radial shearing interference

We present a security enhanced method for optical image encryption based on a radial shearing interferometer (RSI). In the encryption process, an image (plaintext) is first encoded into a phase-only mask (POM) and then successively modulated by a random phase mask (RPM) and a random amplitude mask (RAM). As the input of the radial shearing interferometer, the modulated plaintext is illuminated by a coherent light and then divided into two beams, which will interference with each other leading to an interferogram (ciphertext) at the output plane. The decryption process could only be analytically accomplished with the help of a recursive algorithm. Numerical simulations are provided to demonstrate the validity of this scheme.

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.

Single-beam image encryption using spatially separated ciphertexts based on interference principle in the Fresnel domain

A new optical security system for image encryption based on optical interference principle and translation property of Fresnel transform (FrT) has been proposed in this article. The algorithm of this proposal is specially designed for single-beam optical decryption and can thoroughly resolve the silhouette problem existing in the previous interference-based scheme. Different from earlier schemes using interference of phase-only masks (POMs), the inverse FrT of primitive image is digitally decomposed into a random POM and a complex field distribution. Information associated with the primitive images can be completely smoothed away by the modulation of this random POM. Through the translation property of FrT, two linear phase-only terms are then used to modulate the obtained random POM and the complex distribution, respectively. Two complex ciphertexts are generated by performing digital inverse FrT again. One cannot recover any visible information of secret image using only one ciphertext. Moreover, to recover the primitive image correctly, the correct ciphertexts must be placed in the certain positions of input plane of decryption system, respectively. As additional keys, position center coordinates of ciphertexts can increase the security strength of this encryption system against brute force attacks greatly. Numerical simulations have been given to verify the performance and feasibility of this proposal. To further enhance the application value of this algorithm, an alternative approach based on Fourier transform has also been discussed briefly.

Interference-based multiple-image encryption by phase-only mask multiplexing with high quality retrieved images

We propose a novel interference-based method for multiple-image encryption by phase-only mask (POM) multiplexing. The information of multiple images can be encrypted into two POMs (i.e. ciphertexts) without any iterative process. For correct decryption, one should hold the ciphertexts as well as the private keys, which are also POMs obtained analytically. Moreover, the bothersome silhouette problem can also be thoroughly resolved during the generation procedure of these POMs. The retrieved images by this method are totally free from the cross-talk noise that puzzles previous interference-based multiple-image encryption methods. Numerical results are presented to verify the validity of the proposed approach.

Optical image-hiding method with false information disclosure based on the interference principle and partial-phase-truncation in the fractional Fourier domain

An image-hiding method based on the optical interference principle and partial-phase-truncation in the fractional Fourier domain is proposed. The primary image is converted into three phase-only masks (POMs) using an analytical algorithm involved partial-phase-truncation and a fast random pixel exchange process. A procedure of a fake silhouette for a decryption key is suggested to reinforce the encryption and give a hint of the position of the key. The fractional orders of FrFT effectively enhance the security of the system. In the decryption process, the POM with false information and the other two POMs are, respectively, placed in the input and fractional Fourier planes to recover the primary image. There are no unintended information disclosures and iterative computations involved in the proposed method. Simulation results are presented to verify the validity of the proposed approach.

Multiple-image encryption system using cascaded phase mask encoding and a modified Gerchberg–Saxton algorithm in gyrator domain

We present a novel method for multiple-image encryption by combining modified Gerchberg–Saxton algorithm (MGSA) with phase-only mask (POM) multiplexing in gyrator transform (GT) domains. In this proposal, the primitive images are firstly encoded into a single synthetic complex image by phase mutual encoding and MGSA based on GT. Then the complex encoded image is further converted into two computer-generated POMs by carrying out MGSA again in GT domains. The proposed scheme has not any capability limitation that is caused by crosstalk effect between multiplexing images. An optical cascaded GT architecture, in which two POM ciphertexts and decryption phase keys are displayed in the input planes of GTs, respectively, can be employed for decryption. Combined with the POMs as main keys, the transform angles and wavelength of GTs can further increase the security of this system by offering very sensitive additional keys. Moreover, one can adjust the transform angles of GT flexibly without using any axis movement. Numerical simulations have been carried out to verify the effectiveness and feasibility of the proposed 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.

Optical image encryption based on a radial shearing interferometer

We present a novel method for optical image encryption based on a modified radial shearing interferometer (MRSI), which is generally used for wavefront reconstruction. In this method, a plaintext image is first encoded into a phase-only mask (POM) and then modulated by a random phase mask (RPM), the result is regarded as the input of the radial shearing interferometer and is divided into two coherent lights, which interfere with each other, leading to an interferogram (ciphertext). The aforementioned encryption process can be achieved digitally or optically while the decryption process can only be analytically accomplished. Numerical simulation is provided to demonstrate the validity of this method.

Information authentication system using interference of two beams in gyrator transform domain

A novel information authentication system, i.e., an asymmetric optical interference of two beams in the gyrator transform (GT) domain, is proposed. In this algorithm, the input color image is divided into R, G, and B channels. The complex field of each channel is constructed by the inverse Fourier transform of the channel attached with a random phase function. The phase-only mask (POM) and amplitude-only mask (AOM) are analytically derived from the complex field. The POM and AOM are separately gyrator transformed. The two asymmetric phase keys and two encrypted images are obtained by the amplitude truncations and phase truncations of the transform images, respectively. Finally, the encoded image is produced by the interference of two encrypted images. The two asymmetric keys and two angle parameters of the GT are regarded as additional keys for each channel to enhance the security level of the cryptosystem. The noniterative authentication procedure is devoid of any silhouette problem. The proposed system can be implemented digitally or optically, and its architecture is free from optical misalignment problems. The theoretical analysis and numerical simulation results both validate the proposed technique.