Based on a fractional-order quantum cellular neural network (QCNN), we present a new image encryption method. This technique uses an anamorphic fractional Fourier transform and was designed to solve the current insufficiency of nonlinearities that exist in optical cryptosystems. The primary advantage of an anamorphic transform is the additional degree of freedom offered from the fractional order, which increases flexibility of the optical system. First and second chaos random phase masks were obtained through the fractional-order QCNN system with varying parameters which provide a complex key space. An input image was processed by the first chaos random phase mask and then transformed using an anamorphic fractional Fourier transform. An encrypted image was then produced using the second chaos random phase mask and the second anamorphic fractional Fourier transform. The cryptosystem exhibited powerful resistance against many sorts of potential attacks, such like noise and occlusion. The simulation experiments verify the security and effectiveness of scheme in this paper.
Based on a fractional-order quantum cellular neural network (QCNN), we present a new image encryption method. This technique uses an anamorphic fractional Fourier transform and was designed to solve the current insufficiency of nonlinearities that exist in optical cryptosystems. The primary advantage of an anamorphic transform is the additional degree of freedom offered from the fractional order, which increases flexibility of the optical system. First and second chaos random phase masks were obtained through the fractional-order QCNN system with varying parameters which provide a complex key space. An input image was processed by the first chaos random phase mask and then transformed using an anamorphic fractional Fourier transform. An encrypted image was then produced using the second chaos random phase mask and the second anamorphic fractional Fourier transform. The cryptosystem exhibited powerful resistance against many sorts of potential attacks, such like noise and occlusion. The simulation experiments verify the security and effectiveness of scheme in this paper.
We propose a new optical encryption technique using the fractional Fourier transform. In this method, the data are encrypted to a stationary white noise by two statistically independent random phase masks in fractional Fourier domains. To decrypt the data correctly, one needs to specify the fractional domains in which the input plane, encryption plane, and output planes exist, in addition to the key used for encryption. The use of an anamorphic fractional Fourier transform for the encryption of two-dimensional data is also discussed. We suggest an optical implementation of the proposed idea. Results of a numerical simulation to analyze the performance of the proposed method are presented.
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.
In the digital era, the security of image data has become increasingly important. This study aims to develop an image encryption scheme based on Quantum Key Distribution (QKD) and Fractional Fourier Transform (FRFT) to enhance the security of image data transmission and storage. The proposed scheme first utilizes QKD to generate and distribute secure encryption keys, ensuring the unconditional security of the key distribution process. Subsequently, FRFT is employed to perform complex transformations on the image data, using fractional order parameters to achieve multi-scale representation of the image in both time and frequency domains, thereby increasing the complexity and security of the encryption process. Experimental results demonstrate that this scheme exhibits significant advantages in terms of the quality of encrypted images and their resistance to attacks. Specifically, the encrypted images possess high Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), effectively resisting various attacks. Comparative analysis further verifies the superiority of this scheme in terms of security and efficiency. In summary, the proposed combination of QKD and FRFT for image encryption holds great potential and research value in the protection of image data.
Abstract We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.
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.
A number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.