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Workshop on Information Optics

Image quality and security through nonlinear joint transform encryption

Juan M. Vilardy, Elisabet Pérez–Cabré, María Sagrario Millán

Published Jul 1, 2016• 1 citation
Publisher

Abstract

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.

DOI
10.1109/wio.2016.7745591

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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.
Opticalinformation processing systems have shown great potential for security applications. Optical encryption and authentication techniques use the parallel processing capabilities, high computing speed and also, the wide range of controllable physical parameters provided by the optical processing systems. All these features permit to obtain highly secure systems. The research here contained focuses on the design and development of opto-digital security systems based on the architecture of the joint transform correlator (JTC). The security systems presented in this thesis correspond to encryption and authentication systems. The proposed encryption systems are simple and nonlinear opto-digital systems with a twofold purpose: first, an improved quality of decrypted images in comparison with other encryption systems of similar technology, and second, a high degree of security due to the use of several keys and an improved resistance against various security attacks. All these features are achieved for all the designed encryption systems based on a JTC in the Fourier, Fresnel and fractional Fourier optical processing domains, respectively. In this work, an experimental validation of the most basic aspects of the proposed encryption system is also included. Finally, we present the integration of the photon-counting technique with the nonlinear encryption system based on a JTC in order to authenticate and verify a primary image (for instance, an image of a fingerprint) and a random phase code, respectively, in a secure and simultaneous manner. The integration of the photon-counting technique in the information processing system increases the security of the encryption system and also, makes the authentication system more robust against unauthorized attacks.
A new optical security system for image encryption based on a fractional joint transform correlator and nonlinear filtering is proposed.The position of the lens in the proposed optical encryption setup can be chosen, so that an additional key is introduced in the security system.The distributions at the input and output planes of the encryption system are related by a fractional Fourier transform (FrFT) at a given fractional order that is defined, among other parameters, by the focal length and the position of the lens in the setup; this fractional order acts as an additional key of the security system.The optical intensity of the complex distribution in the fractional Fourier domain (output plane) is captured by a CCD camera.The nonlinearity introduced in the last step of the encryption process, maintains the encrypted function as a real-valued function.The security system proposed in this work is an generalization of the encryption system based on a conventional joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain.Additional advantages of the proposed system are: new degrees of freedom for the optical setup, alleviated alignment requirement, and the introduction of an additional key (the fractional order of the FrFT) that improves security.Numerical simulations verify the validity of this new optical security system.
An image encryption method combining the joint transform correlator (JTC) architecture with phase-shifting interferometry to realize double random-phase encoding is proposed. The encrypted field and the decrypting key are registered as holograms by phase-shifting interferometry. This method can encrypt two images simultaneously to improve the encryption efficiency of the methods based on JTC architecture, and eliminate the system alignment constraint of the methods based on Mach-Zehnder interferometer (MZI) architecture. Its feasibility and validity are verified by computer simulations. Moreover, image encryption and decryption can be achieved at high speed optically or digitally. The encrypted data are suitable for Internet transmission.
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.
In this paper, we analyze the security of the classical double random phase encoding (DRPE) technique in Fourier domain, as well as its extended schemes in Fresnel and fractional Fourier domains. These schemes are resistant to bruteforce attacks, for their large key spaces. However, due to the linearity property of their encryption transformations, they are vulnerable to other attacks, such as chosen-plaintext attack and known-plaintext attack. We successfully break each of the three encryption schemes with the help of a certain quantity of plaintext-ciphertext pairs. Each attack is validated by computer simulations. The cryptanalysis indicates that, to minimize the risks, it is recommendable to introduce nonlinear operations to optical encryption systems.
The double random phase encoding (DRPE) image encryption method has garnered significant attention in color image processing and optical encryption thanks to its R, G, and B parallel encryption. However, DRPE-based color image encryption faces two challenges. Firstly, it disregards the correlation of R, G, and B, compromising the encrypted image’s robustness. Secondly, DRPE schemes relying on Discrete Fourier Transform (DFT) and Discrete Fractional Fourier Transform (DFRFT) are vulnerable to linear attacks, such as Known Plaintext Attack (KPA) and Chosen Plaintext Attack (CPA). Quantum walk is a powerful tool for modern cryptography, offering robust resistance to classical and quantum attacks. Therefore, this study presents an optical color image encryption algorithm that combines two-dimensional quantum walking (TDQW) with 24-bit plane permutation, dubbed OCT. This approach employs pseudo-random numbers generated by TDQW for phase modulation in DRPE and scrambles the encrypted image’s real and imaginary parts using the generalized Arnold transform. The 24-bit plane permutation helps reduce the R, G, and B correlation, while the generalized Arnold transform bolsters DRPE’s resistance to linear attacks. By incorporating TDQW, the key space is significantly expanded. The experimental results validate the effectiveness and security of the proposed method.