Sudheesh K. Rajput

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

We propose an image encryption technique based on the interference principle and phase-truncation approach in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys and is free from the silhouette problem. Multiple input images bonded with random phase masks are independently fractional Fourier transformed. Amplitude truncation of obtained spectrum helps generate individual and universal keys while phase truncation generates two phase-only masks analytically. For decryption, these two phase-only masks optically interfere, and this results in the phase-truncated function in the output. After using the correct random phase mask, universal key, individual key, and fractional orders, the original image is retrieved successfully. Computer simulation results with four gray-scale images validate the proposed method. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and decryption keys formation are complicated and should be realized digitally. For decryption, an optoelectronic scheme has been suggested.

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.

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.

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.

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.

Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification

Abstract. Collision is a phenomenon in which two distinct inputs produce an identical output, so if an attacker finds the encryption keys in such a way that when it is applied to an encrypted image, it produces an arbitrary image instead of original one. We propose collision in an asymmetric cryptosystem based on a phase-truncated Fresnel transform. For encryption, instead of using conventional random-phase masks, structured phase masks with desired construction parameters are used. The decryption keys are generated using the amplitude and phase truncation. An attacker generates an arbitrary (collision) image from the encrypted image using a modified Gerchberg-Saxton phase retrieval algorithm. Two different users, authorized and unauthorized user (attacker), can claim the retrieved image as the original data. The authorized user uses the correct decryption keys and retrieves the original image, while an unauthorized user uses the generated keys and retrieves the collision image. In order to verify the authenticity of the retrieved data, a joint transform correlator is used. A sharp auto-correlation peak is obtained when an image retrieved by authorized user is matched with the encrypted image. However, cross-correlation is obtained when an encrypted image is matched with the collision image. Results of computer simulation support the idea of the proposed collision.

Photon counting imaging and polarized light encoding for secure image verification and hologam watermarking

We propose an optical image security scheme based on polarized light encoding and the photon counting technique. An input image is encoded using the concept of polarized light, which is parameterized using Stokes–Mueller formalism. The encoded image is further encrypted by applying the photon counting imaging technique to obtain a photon limited image. For decryption, the photon limited decrypted image is obtained by using a polarized light decoding scheme with the help of appropriate keys. The decrypted image has sparse representation, which contains sufficient information for verification. This photon counted decrypted image can be verified using correlation filters. The proposed encryption technique offers benefits over the double random phase encoding in that it does not require active elements such as a lens and provides flexibility in the design of encryption keys. The proposed encryption scheme has also been used for hologram watermarking. The computer simulation results for secure image verification and the hologram watermarking scheme have been presented.

Photon counting imaging and phase mask multiplexing for multiple images authentication and digital hologram security

We propose an image encryption system based on phase mask multiplexing and photon counting imaging (PCI) technique for multiple image authentications and digital hologram security. Multiple images to be authenticated are converted into phase-only images using a phase-retrieval algorithm in fractional Fourier transform domain. The multiple phase-only images are multiplexed into a single phase-only mask and it is further encrypted into a complex-valued function. The photon-limited image is generated by applying the PCI technique to a complex-valued function. For decryption, the photon-limited decrypted images are obtained after applying the appropriate keys. The photon-limited decrypted image contains sufficient information for verification because this image has sparse representation. To verify the photon-limited decrypted image, the optical correlation filters can be used. The proposed system has also been used for hologram security. For hologram security, the system provides multiple layers of security by hiding multiple encrypted images. The computer simulation results have been presented. The authentication scheme has been tested for securing three-dimensional information through experimentally recorded Fresnel digital hologram.

Known plain-text Attack on Asymmetric Cryptosystem

It is believed that asymmetric cryptosystem based on phase-truncated Fourier transform has immunity against knownplaintext attack. However, generation of two asymmetric keys is possible, if plaintext-ciphertext pair is known. In this paper, we show that amplitude- and phase-truncation-based asymmetric cryptosystem is vulnerable to known-plaintext attack. The decryption keys are generated with the help of modified Gerchberg-Saxton phase retrieval algorithm from known-plaintext and cipher-text. The first key is generated from known-plaintext and the second key is generated from the cipher-text. With the help of the generated keys, the encrypted image in one domain is decrypted successfully in another domain. The domains used for this study are Fourier, Fresnel, fractional Fourier or gyrator domain. The vulnerability is proved through the results of computer simulation.