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

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.

Optical double-image cryptosystem based on generalized singular value decomposition and five-dimensional hyperchaotic maps

In this paper, we propose an asymmetric optical double-image cryptosystem based on generalized singular value decomposition (GSVD) and five-dimensional (5D) hyperchaotic maps. In the proposed cryptosystem, the two plain images are first decomposed into five components by the GSVD operation. The two unitary matrices obtained by GSVD are encoded as a complex function, which is then modulated by the chaotic random phase masks (CRPMs). The private key and the final encryption result are generated by phase-truncation and amplitude-truncation operations. The GSVD operation can decompose two images at the same time and is used to generate the private key that enables the encryption process to be asymmetric. Compared with the existing phase-truncated-based cryptosystems, our cryptosystem can improve security against a special attack. In addition, the CRPMs are generated by 5D hyperchaotic maps, which have a larger parameter space and better randomness. Numerical simulation results are shown to verify the feasibility and robustness of our cryptosystem. Furthermore, the proposed cryptosystem can be extended to encrypt multiple images conveniently.

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

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

Modified plaintext attacks in a session for an optical cryptosystem based on DRPE with PFS

In this paper, the security of an optical cryptosystem based on double random phase encoding (DRPE) with perfect forward secrecy (PFS) is analyzed for a particular session. In the cryptosystem, the PFS strategy is utilized to enhance the security and key management of the traditional DRPE scheme. Our analysis reveals that the use of PFS has certain advantages in the key management approach, but the method is still vulnerable against modified plaintext attacks when the attack is performed in the same session. Also, it is noted that the method is safe against conventional plaintext attacks, but it is vulnerable to the modified chosen and known plaintext attacks. The original plaintext can be easily retrieved with the proposed attack algorithms. Numerical simulation results are presented to validate the effectiveness of the proposed attack algorithms.

Lensless Optical Encryption of Multilevel Digital Data Containers Using Spatially Incoherent Illumination

The necessity of the correction of errors emerging during the optical encryption process led to the extensive use of data containers such as QR codes. However, due to specifics of optical encryption, QR codes are not very well suited for the task, which results in low error correction capabilities in optical experiments mainly due to easily breakable QR code’s service elements and byte data structure. In this paper, we present optical implementation of information optical encryption system utilizing new multilevel customizable digital data containers with high data density. The results of optical experiments demonstrate efficient error correction capabilities of the new data container.

Lensless optical encryption with speckle-noise suppression and QR codes

The majority of contemporary optical encryption techniques use coherent illumination and suffer from speckle-noise pollution, which severely limits their applicability even when information encoded into special "containers" such as a QR code. Spatially incoherent encryption does not have this drawback, but it suffers from reduced encryption strength due to formation of an unobscured image right on top of the encrypted one by undiffracted light from the encoding diffraction optical element (DOE) in axial configuration. We present a new lensless encryption scheme, experimentally implemented with two liquid crystal spatial light modulators, that does not have this disadvantage because of a special encoding DOE design, which forms desired light distribution in the photosensor plane under spherically diverging illumination without a converging lens. Results of optical experiments on encryption of QR codes and successful information retrieval from decoded images are presented. Conducted analysis of encryption strength demonstrates sufficiently high key sensitivity and large enough key space to resist any brute force attacks.

Asymmetric image encryption scheme based on the Quantum logistic map and cyclic modulo diffusion

In this study, a novel asymmetric image encryption scheme based on the Rivest-Shamir-Adleman (RSA) algorithm and Arnold transformation is proposed. First, the asymmetric public key RSA algorithm is used to generate the initial values for a quantum logistic map. Second, the parameters of the Arnold map are calculated. Then, Arnold scrambling operation is performed on the plain image to achieve the rough hiding of image information. Third, each row and each column of the image are taken as different units respectively and then exclusive-OR (XOR) diffusion is applied. Finally, the generated keystream is used to perform an end-to-start cyclic modulo diffusion operation for all rows and columns to produce the final cipher image. In addition, the keystream is related to the plain image, which can enhance the ability to resist chosen plaintext attack and known plaintext attack. The test results also show that the proposed encryption algorithm has strong plain sensitivity and key sensitivity.

Asymmetric multiple-image encryption system based on a chirp z-transform

An asymmetric multi-image encryption system based on the chirp z-transform (CZT) is demonstrated. The setup is a hybrid architecture that combines a double-random-phase encryption scheme in 4f configuration and a multiplexing procedure based on the CZT. The setup allows encodement of multiple images and their transmittal in a single multiplexed element. The decryption stage has a compact design that allows retrieval of several data without cross-talk noise. Since the system is asymmetric, the users' decryption keys are different from those used in the encryption process, resulting in an encoding scheme resistant to cryptanalysis attacks. It is demonstrated that multiplexing based on the CZT allows functionality expansion of the static encoding setups (optical, digital or hybrid) to a dynamic range, a fact that provides a versatile solution to handle large volumes of encrypted data efficiently and safely. The viability of this proposal is verified using virtual optical systems.

Multi-depth three-dimensional image encryption based on the phase retrieval algorithm in the Fresnel and fractional Fourier transform domains

We propose a multi-depth three-dimensional (3D) image cryptosystem by employing the phase retrieval algorithm in the Fresnel and fractional Fourier (Fr-FrF) domains. Encryption was realized by applying the phase retrieval algorithm based on the double-random-phase-encoding architecture in which two encryption keys will be incessantly updated in each iteration loop. The phase-only functions (POFs) are generated in two cascaded Fr-FrF transforms (Fr-FrFT), serving as decryption keys to efficiently reduce the speckle noise and crosstalk between encrypted 3D image depths. The use of Fr-FrFT position parameters and fractional order as decryption keys further extended the key space, enhancing the cryptosystem's security level. Numerical simulations demonstrated the feasibility and robustness of our proposed scheme.

Optical cryptography with biometrics for multi-depth objects

We propose an optical cryptosystem for encrypting images of multi-depth objects based on the combination of optical heterodyne technique and fingerprint keys. Optical heterodyning requires two optical beams to be mixed. For encryption, each optical beam is modulated by an optical mask containing either the fingerprint of the person who is sending, or receiving the image. The pair of optical masks are taken as the encryption keys. Subsequently, the two beams are used to scan over a multi-depth 3-D object to obtain an encrypted hologram. During the decryption process, each sectional image of the 3-D object is recovered by convolving its encrypted hologram (through numerical computation) with the encrypted hologram of a pinhole image that is positioned at the same depth as the sectional image. Our proposed method has three major advantages. First, the lost-key situation can be avoided with the use of fingerprints as the encryption keys. Second, the method can be applied to encrypt 3-D images for subsequent decrypted sectional images. Third, since optical heterodyning scanning is employed to encrypt a 3-D object, the optical system is incoherent, resulting in negligible amount of speckle noise upon decryption. To the best of our knowledge, this is the first time optical cryptography of 3-D object images has been demonstrated in an incoherent optical system with biometric keys.

Key-length analysis of double random phase encoding

Double random phase encoding (DRPE) is a classical optical symmetric-key encryption method. DRPE prevents the key length from being determined because of its redundancy between encryption and decryption, unlike digital symmetric-key cryptographies. In our study, we numerically analyzed the key length of DRPE based on key-space analysis. We estimated the key length of DRPE by calculating the inverse value of the cumulative probability of the normal distribution that was estimated from samples of DRPE and then discuss security against brute-force attacks.

Binary-tree encryption strategy for optical multiple-image encryption

In traditional optical multiple-image encryption schemes, different images typically have almost the same encryption or decryption process. Provided that an attacker manages to correctly decrypt some image, the conventional attacks upon other images are much easier to be made. In this paper, a binary-tree encryption strategy for multiple images is proposed to resist the attacks in this case. The encryption schemes produced by this strategy can not only increase the security of multiple-image encryption, but also realize an authority management with high security among the users sharing a cipher image. For a simulation test, we devise a basic binary-tree encryption scheme, whose encryption nodes are based on an asymmetric double random phase encoding in the gyrator domain. The favorable simulation results about the tested scheme can testify to the feasibility of the strategy.

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.

Optical compression and encryption system combining multiple measurement matrices with fractional Fourier transform

Optical cryptosystems combined with compressed sensing can achieve compression and encryption simultaneously. But they usually use the same measurement matrix to sample all blocks of an image, which makes it easy to estimate the measurement matrix in the chosen plaintext attack. In this paper, we propose a robust scheme adopting multiple measurement matrices to overcome this shortcoming. The matrices can be efficiently derived by applying random row exchanging to a basic one, which is also encoded into the fractional Fourier transform (FrFT) domain to improve the visual effect of wrongly decrypted images. Chaos-based pixel scrambling is added into our double FrFT cryptosystem to guarantee its nonlinearity. Simulation results have shown the security and effectiveness of our scheme.

Improved method of attack on an asymmetric cryptosystem based on phase-truncated Fourier transform

We propose an improved method of attack on an asymmetric cryptosystem based on a phase-truncated Fourier transform. With the proposed method of attack, an attacker is able to access the exact decryption keys and obtain precise attack results. The method is based on a novel median-filtering phase-retrieval algorithm. Compared with existing attacks, the proposed attack has the following advantages: (1) exact information of the original image can be obtained in gray-scale and binary forms; (2) better computing efficiency; (3) more robust against noise and occlusion contaminations. Numerical simulation results show the effectiveness and robustness of the proposed method. Based on the proposed method of attack, we further propose a new cryptosystem, which not only enhances the security of the system but also does not require truncated phases.

Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition

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

Double-image encryption without information disclosure using phase-truncation Fourier transforms and a random amplitude mask

We present a study about information disclosure in phase-truncation-based cryptosystems. The main information of the original image to be encoded can be obtained by using a decryption key in the worst case. The problem cannot be thoroughly solved by imaginary part truncating, keeping the encryption keys as private keys, or applying different phase keys for different plaintexts during each encryption process as well as the phase modulation in the frequency domain. In order to eliminate the risk of unintended information disclosure, we further propose a nonlinear spatial and spectral encoding technique using a random amplitude mask (RAM). The encryption process involving two security layers can be fully controlled by a RAM. The spatial encoding of the plaintext images and the simultaneous encryption of the plaintext images and the encryption key greatly enhance the security of system, avoiding several attacks that have cracked the phase-truncation-based cryptosystems. Besides, the hybrid encryption system retains the advantage of a trap door one-way function of phase truncation. Numerical results have demonstrated the feasibility and effectiveness of the proposed encryption algorithm.

Asymmetric information hiding and noise-free recovery based on rotating analyzer ellipsometry and quick-response code

We report an asymmetric optical information hiding method based on a rotating analyzer ellipsometry technique. This asymmetric hiding architecture not only avoids the interception of keys during transmission or distribution but also makes the cyphertext more inconspicuous for attackers. A new kind of one-way optical trapdoor function is constructed based on the fact that the state of polarization (SOP) of elliptical polarized light cannot be recovered with only the knowledge of intensity captured after passing through a linear polarizer. Meanwhile, the SOP of a polarization ellipse could be calculated by rotating the polarizer to record two scenes of intensity after it. Introduction of a quick response code as a container leads to noise-free recovery for original information and enhances practicality of the proposed cryptosystem with versatile key sensitivity and fault tolerance capability. Numerical simulation results that support theoretical analysis are presented. Analysis on the relationship between hiding effect or quality of decryption and parameters of the algorithm also is provided.

Optical asymmetric cryptography based on elliptical polarized light linear truncation and a numerical reconstruction technique

We demonstrate a novel optical asymmetric cryptosystem based on the principle of elliptical polarized light linear truncation and a numerical reconstruction technique. The device of an array of linear polarizers is introduced to achieve linear truncation on the spatially resolved elliptical polarization distribution during image encryption. This encoding process can be characterized as confusion-based optical cryptography that involves no Fourier lens and diffusion operation. Based on the Jones matrix formalism, the intensity transmittance for this truncation is deduced to perform elliptical polarized light reconstruction based on two intensity measurements. Use of a quick response code makes the proposed cryptosystem practical, with versatile key sensitivity and fault tolerance. Both simulation and preliminary experimental results that support theoretical analysis are presented. An analysis of the resistance of the proposed method on a known public key attack is also provided.

An optical encryption and authentication scheme using asymmetric keys

We propose a novel optical information encryption and authentication scheme that uses asymmetric keys generated by the phase-truncation approach and the phase-retrieval algorithm. Multiple images bonded with random phase masks are Fourier transformed, and obtained spectra are amplitude- and phase-truncated. The phase-truncated spectra are encoded into a single random intensity image using the phase-retrieval algorithm. Unlike most of the authentication schemes, in this study, only one encrypted reference image is required for verification of multiple secured images. The conventional double random phase encoding and correlation techniques are employed for authentication verification. Computer simulation results and theoretical explanation prove the effectiveness of the proposed scheme.

Image fusion using wavelet transform and its application to asymmetric cryptosystem and hiding

Image fusion is a popular method which provides better quality fused image for interpreting the image data. In this paper, color image fusion using wavelet transform is applied for securing data through asymmetric encryption scheme and image hiding. The components of a color image corresponding to different wavelengths (red, green, and blue) are fused together using discrete wavelet transform for obtaining a better quality retrieved color image. The fused color components are encrypted using amplitude- and phase-truncation approach in Fresnel transform domain. Also, the individual color components are transformed into different cover images in order to result disguising information of input image to an attacker. Asymmetric keys, Fresnel propagation parameters, weighing factor, and three cover images provide enlarged key space and hence enhanced security. Computer simulation results support the idea of the proposed fused color image encryption scheme.

Fresnel domain nonlinear optical image encryption scheme based on Gerchberg-Saxton phase-retrieval algorithm

We propose a novel nonlinear image-encryption scheme based on a Gerchberg-Saxton (G-S) phase-retrieval algorithm in the Fresnel transform domain. The decryption process can be performed using conventional double random phase encoding (DRPE) architecture. The encryption is realized by applying G-S phase-retrieval algorithm twice, which generates two asymmetric keys from intermediate phases. The asymmetric keys are generated in such a way that decryption is possible optically with a conventional DRPE method. Due to the asymmetric nature of the keys, the proposed encryption process is nonlinear and offers enhanced security. The cryptanalysis has been carried out, which proves the robustness of proposed scheme against known-plaintext, chosen-plaintext, and special attacks. A simple optical setup for decryption has also been suggested. Results of computer simulation support the idea of the proposed cryptosystem.

Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform

A discussion and a cryptanalysis of the optical phase-truncated Fourier-transform-based cryptosystem are presented in this paper. The concept of an optical asymmetric cryptosystem, which was introduced into the optical image encryption scheme based on phase-truncated Fourier transforms in 2010, is suggested to be retained in optical encryption. A new method of attack is also proposed to simultaneously obtain the main information of the original image, the two decryption keys from its cyphertext, and the public keys based on the modified amplitude-phase retrieval algorithm. The numerical results illustrate that the computing efficiency of the algorithm is improved and the number of iterations is much less than that by the specific attack, which has two iteration loops.

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

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

Simultaneous nonlinear encryption of grayscale and color images based on phase-truncated fractional Fourier transform and optical superposition principle

A nonlinear color and grayscale images cryptosystem based on phase-truncated fractional Fourier transform and optical superposition principle is proposed. In order to realize simultaneous encryption of color and grayscale images, each grayscale image is first converted into two phase masks by using an optical coherent superposition, one of which is treated as a part of input information that will be fractional Fourier transformed while the other in the form of a chaotic random phase mask (CRPM) is used as a decryption key. For the purpose of optical performance, all the processes are performed through three channels, i.e., red, green, and blue. Different from most asymmetric encryption methods, the decryption process is designed to be linear for the sake of effective decryption. The encryption level of a double random phase encryption based on phase-truncated Fourier transform is enhanced by extending it into fractional Fourier domain and the load of the keys management and transmission is lightened by using CRPMs. The security of the proposed cryptosystem is discussed and computer simulation results are presented to verify the validity of the proposed method.

Image encryption using polarized light encoding and amplitude and phase truncation in the Fresnel domain

In this paper, an image encryption scheme based on polarized light encoding and a phase-truncation approach in the Fresnel transform domain is proposed. The phase-truncated data obtained by an asymmetric cryptosystem is encrypted and decrypted by using the concept of the Stokes-Mueller formalism. Image encryption based on polarization of light using Stokes-Mueller formalism has the main advantage over Jones vector formalism that it manipulates only intensity information, which is measurable. Thus any intensity information can be encrypted and decrypted using this scheme. The proposed method offers several advantages: (1) a lens-free setup, (2) flexibility in the encryption key design, (3) use of asymmetric keys, and (4) immunity against special attack. We present numerical simulation results for gray-scale and color images in support of the proposed security scheme. The performance measurement parameters relative error and correlation coefficient have been calculated to check the effectiveness of the scheme.

Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform

In this paper, we propose a scheme for information security under the basic double random phase encoding framework but with enhanced complexity and immunity against the known-plaintext attack. Modified Gerchberg-Saxton algorithm is used to convert a primary image into a phase-only mask (POM). The POM is used as a Fresnel domain key for encrypting an arbitrary data, called random intensity mask (RIM) bonded with a random phase mask. With phase- and amplitude-truncation, asymmetric keys are generated from the RIM. For decryption, the main target is to get the POM, for which the concept of known-plaintext attack has been used. The conventional schemes for attack use known-plaintext for key generation, but in this study it refers to the asymmetric keys. Obtaining Fresnel transform with the same parameters of the POM gives the primary image. We present the computer simulation results of multiple gray-scale images without any cross talk and also for a color image. The decryption is simple and straightforward and can be done digitally or optically. An optical setup for decryption has been suggested.

Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask

A single channel asymmetric color image encryption scheme is proposed that uses an amplitude- and phase- truncation approach with interference of polarized wavefronts. Instead of commonly used random phase masks, wavelength-dependent structured phase masks (SPM) are used in the fractional Fourier transform domain for image encoding. The primary color components bonded with different SPMs are combined into one grayscale image using convolution. We then apply the amplitude and phase truncation to the fractional spectrum, which helps generate unique decryption keys. The encrypted image bonded with a different SPM is then encoded into a polarization selective diffractive optical element. The proposed scheme alleviates the alignment problem of interference and does not need iterative encoding and offers multiple levels of security. The effect of a special attack to the proposed asymmetric cryptosystem has been studied. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. The computer simulation results support the proposed idea.