We present a nonlinear optical cryptosystem with multi-dimensional keys including phase, polarization and diffraction distance. To make full use of the degrees of freedom that optical processing offers, an elaborately designed vector wave with both a space-variant phase and locally linear polarization is generated with a common-path interferometer for illumination. The joint transform correlator in the Fresnel domain, implemented with a double optical wedge, is utilized as the encryption framework which provides an additional key known as the Fresnel diffraction distance. Two nonlinear operations imposed on the recorded joint Fresnel power distribution (JFPD) by a charge coupled device (CCD) are adopted. The first one is the division of power distribution of the reference window random function which is previously proposed by researchers and can improve the quality of the decrypted image. The second one is the recording of a hybrid JFPD using a micro-polarizers array with orthogonal and random transmissive axes attached to the CCD. Then the hybrid JFPD is further scrambled by substituting random noise for partial power distribution. The two nonlinear operations break the linearity of this cryptosystem and provide ultra security. We verify our proposal using a quick response code for noise-free recovery.
We present a nonlinear optical cryptosystem with multi-dimensional keys including phase, polarization and diffraction distance. To make full use of the degrees of freedom that optical processing offers, an elaborately designed vector wave with both a space-variant phase and locally linear polarization is generated with a common-path interferometer for illumination. The joint transform correlator in the Fresnel domain, implemented with a double optical wedge, is utilized as the encryption framework which provides an additional key known as the Fresnel diffraction distance. Two nonlinear operations imposed on the recorded joint Fresnel power distribution (JFPD) by a charge coupled device (CCD) are adopted. The first one is the division of power distribution of the reference window random function which is previously proposed by researchers and can improve the quality of the decrypted image. The second one is the recording of a hybrid JFPD using a micro-polarizers array with orthogonal and random transmissive axes attached to the CCD. Then the hybrid JFPD is further scrambled by substituting random noise for partial power distribution. The two nonlinear operations break the linearity of this cryptosystem and provide ultra security. We verify our proposal using a quick response code for noise-free recovery.
A noiseless optical cryptosystem based on a joint Fresnel transform correlator (JFTC) with a Billet split lens (BSL) was designed. Benefitting from the adjustable structure of the BSL, we can control the size and recording position of the joint Fresnel transform power distribution by changing the split width of the BSL. To avoid the text being affected by noise, we converted the text into quick response (QR) code in advance, then used the QR code as the plaintext and utilized the noise tolerance ability of the QR code to realize noiseless recovery of the text. In this cryptosystem, we designed a complex secret key (CSK) to replace the secret key made from a random phase mask, and the CSK consists of a QR code filter and a spiral phase mask. Because the QR code and spiral phase can be determined by a few simple data, the transmission and preservation of the CSK is convenient. Finally, the validity and feasibility of the cryptosystem were demonstrated, and the sensitivity of the CSK was researched by simulation and experiment.
In this paper, we propose a new asymmetric cryptosystem for phase image encryption, using the physically unclonable functions (PUFs) as security keys. For encryption, the original amplitude image is first converted into a phase image and modulated with a PUF to obtain a complex image. This complex image is then illuminated with a plane wave, and the complex wavefront at a distance d is recorded. The real part of the complex wavefront is further processed to obtain the encrypted image and the imaginary part is kept as the private key. The polar decomposition approach is utilized to generate two more private security keys and to enable the multi-user capability in the cryptosystem. Numerical simulations confirm the feasibility of the proposed method.
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.
Abstract In this study, we propose a new nonlinear optical image encryption technique using spiral phase transform (SPT). First, the primary image is phase encoded and multiplied with a random amplitude mask (RAM), and using power function, the product is then powered to m . This powered output is Fresnel propagated with distance z 1 and then modulated with a random phase mask (RPM). The modulated image is further Fresnel propagated with distance z 2 . Similarly, a security image is also modulated with another RAM and then Fresnel propagated with distance z 3 . Next, the two modulated images after Fresnel propagations, are interfered and further Fresnel propagated with distance z 4 to get a complex image. Finally, this complex image is SPT with particular spiral phase function (SPF), to get the final encrypted image for transmission. In the proposed technique, the security keys are Fresnel propagation distances, the security image, RPM, RAMs, power order, m , and order of SPF, q . Numerical simulation results confirm the validity and effectiveness of the proposed technique. The proposed technique is robust against noise and brutal force attacks.
In this paper, a dual optics paths optical image cryptosystem based on tilt Fresnel diffraction and a phase modulation in extend fractional Fourier transform (eFrFT) domain is presented. The tilt Fresnel is designed by using a non-spherical mirror. A part of data from the original image is modulated by the mirror, while the other part is encoded by an expanded fractional Fourier transform. Besides, the random data of the dual channels is combined for forming the encrypted image. The structure parameters in designing the optical hardware system and the random phase can be regarded as decryption keys. Various potential attack experiments are implemented to check the validity of the proposed cryptographic system.
Joint-transform correlator (JTC) architecture presents some advantages, such as no requirement of interferometric recording of the phase distribution or complex conjugation of the key phase mask, in order to optically implement the well-known double random phase encryption (DRPE) method. In addition, a practical optical realization was proposed in a way that the whole information (primary image and two random phase masks) was easily introduced in the same input plane of the JTC system. However, poor image quality was obtained in the decryption stage. Cryptanalysis of JTC-based encryption systems demonstrated that they were vulnerable to certain intruder attacks, similarly to the original DRPE method. In this work, we review recent modifications of encryption algorithms based on JTC architecture that permit, on the one hand, to significantly increase the quality of the retrieved image after information decryption, and on the other hand, to achieve a high security level against a variety of system attacks. The modifications, which were firstly introduced in the Fourier-based JTC system, have been also adapted to be used in the Fresnel and Fractional Fourier domains as well as in the Gyrator domain. Nonlinear operations have been also introduced in multifactor encryption-authentication.