A dual-protection approach to enhance optical image encryption using QZ decomposition and generalized Reed–Muller codes

On monomial codes in modular group algebras

Codes C 1 ,…,C M of length n over ? q and an M × N matrix A over ? q define a matrix-product code C = [C 1 …C M ] ·A consisting of all matrix products [c 1 … c M ] ·A. This generalizes the (u|u+v)-, (u+v+w|2u+v|u)-, (a+x|b+x|a+b+x)-, (u+v|u-v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of |C|, d(C), the minimum Hamming distance of C, and C ⊥. It also reveals an interesting connection with MDS codes. We determine |C| when A is non-singular. To underbound d(C), we need A to be `non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary `Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C ⊥ can be described using C 1 ⊥, …,C M ⊥ and a transformation of A. This yields d(C ⊥). Finally we show that an NSC matrix-product code is a generalized concatenated code.

Intensive studies have been done to get robust encryption algorithms. Due to the importance of image information, optical encryption has played a vital role in information security. Many optical encryption schemes have been proposed but most of them suffer from poor robustness. In this paper six proposed algorithms will be presented for optical encryption to be robust to severe attacks: composite attack. Three of these approaches are based on one level Discrete Wavelet Transform (DWT) and the others are based on Wavelet Packet (WP). Not only will new techniques be presented but also a new proposed chaotic map has been developed as random keys for all algorithms. After extensive comparative study with some traditional techniques, it has been found that the novel algorithms have achieved better performance versus conventional ones. Also it has been found that WP based algorithms have achieved better performance than DWT based ones against severe composite attacks.

Extendable Steiner designs from finite geometries

Most of existing optical color image encryption schemes have born security risks due to the adoption of linear transform, and data redundancy for the generation of complex image. To settle these problems effectively, a self-adaptive scheme for double color-image encryption is proposed in this paper. In this scheme, each RGB color component of two secret color images is first compressed and encrypted by 2D compressive sensing (CS) in which measurement matrices are generated by compound chaotic systems. Then, the two measured images are regarded as the real part and imaginary part, constituting a complex image to reduce data redundancy caused by following optical encryption. In the end, the complex image is reencrypted by self-adaptive random phase encoding and discrete fractional random transform (DFrRT) to obtain the final encrypted data. In the process of DFrRT and random phase encoding, the correlations between R, G, B components are adequately utilized. The production of key streams not only depends on the initial value but also on plain-text, and the three color components affect each other to enhance the ability against the known plaintext attack. The projection neural network algorithm is adopted to obtain the decryption images. Simulation results also verify the validity and security of the proposed method.

With the rapid development of computer network technology, information security has attracted increasing attention. Due to the characteristics of multi-dimensional operation and parallel processing capability, optical image encryption techniques have been receiving more and more attention. Since the well-known double random phase encoding technique was proposed, many other methods based on optical information processing means such as the use of optical transform, interference, and polarized light encoding, have been proposed for optical image encryption. However, recent researches have demonstrated that traditional optical encryption techniques are symmetric cryptosystems, in which decryption keys are identical to encryption keys and they have been found to be vulnerable to different types of attacks, such as known plaintext and chosen plaintext attacks. To overcome this shortcoming, asymmetric cryptosystems based on nonlinear phase-truncation techniques and phase retrieval algorithm have been proposed. Asymmetric cryptosystem is a cryptographic system in which encryption keys are different from decryption keys. The encryption keys are used as public keys which are disseminated widely, and the decryption keys are used as private keys which are known only to the authorized users. So, asymmetric cryptosystem can offer a higher-level security than symmetric cryptosystem. However, asymmetric cryptosystems based on phase retrieval algorithms require a lot of computational time, and asymmetric cryptosystems based on phase-truncated Fourier transforms have been found to be vulnerable to special attack. Therefore, in this paper, a novel asymmetric image encryption method is proposed by using the gyrator transform and vector operation. The original image is encrypted into two phase masks with vector operation. One is a random phase mask and the other is a phase mask related to the original image. In the encryption process, the random phase mask is used as a phase key and the other phase mask is transformed by gyrator transform. The transform result is performed by Fourier transform after being modulated by a phase distribution. The ciphertext is the amplitude of the above result. Compared with previous encryption schemes, the suggested method has two advantages. Firstly, we have proposed a new asymmetric encryption method based on the gyrator transform and vector operation. The decryption process is different from the encryption process. The gyrator transform and Fourier transform are used in the encryption process, while only the inverse operation of Fourier transform is employed in the decryption process. In addition, the decryption keys produced in the encryption process are different from the encryption keys. Therefore, the proposed scheme has high resistance against the conventional attacks. Secondly, the encrypted result is real-valued, which is convenient for display, transmission and storage.Numerical simulations illustrate the feasibility and effectiveness of the proposed encryption scheme.

A visually meaningful image encryption scheme with an asymmetric structure based on the discrete wavelet transform (DWT) and Schur decomposition is proposed in this study. First, the RSA algorithm is used to generate the initial values for the chaotic system to produce the random sequence. Then, both scrambling and diffusion operations are performed on the plain image to obtain the preencrypted image. Moreover, the Schur decomposition is applied on the preencrypted plain image to obtain the upper triangular and orthogonal matrices. Second, the cover image is scrambled followed by a DWT operation. Four subbands are then formed, namely, LL, HL, LH, and HH. Finally, the former upper triangular matrix and orthogonal matrix are embedded into subbands LH and HH produced by the cover image. After the application of the inverse DWT and inverse scrambling operation, the final visually meaningful cover image embedded with a secret plain image can be obtained. No one can identify any useful information about the plain image from the final embedded cover image, nor can anybody know that there is any hidden secret image. Experimental simulations show that the normalized correlation values between the original cover image and the final visually meaningful cover image are approximately 0.9997. Therefore, the proposed encryption scheme is imperceptible for secret image communications.

Optical color image encryption based on computer generated hologram and chaotic theory

Full Poincaré beams, which cover all polarization states on the Poincaré sphere, provide a unique and complete degree of freedom for polarization manipulation in optical encryption. This paper introduces a novel optical image encryption method based on double random phase encoding (DRPE) system with multi-dimensional keys of full Poincaré beam. The encryption process begins by preprocessing the full Poincaré beam with a polarizer, followed by loading the image to be encrypted along this polarization direction, and finally performing encryption via the DRPE system. The scheme integrates conventional optical keys, such as wavelength, topological charge, amplitude, and phase, with the complete polarization dimension afforded by the full Poincaré beam, as well as the spatial loading dimension of the image placed behind the lens. By synergistically combining these multi-dimensional keys, the encryption system significantly expands the key space. Additionally, the dual random phase modulation capability of the DRPE system further enhances information security. This work establishes a new paradigm for high-security optical encryption.

In conventional symmetric encryption, it is common for the encryption/decryption key to be reused for multiple plaintexts. This gives rise to the concept of a known-plaintext attack. In optical image encryption systems, such as double random phase encoding (DRPE), this is also the case. With optical encryption, if one knows a plaintext-ciphertext pair, one can carry out a known-plaintext attack more efficiently than a bruteforce attack, using heuristics based on phase retrieval or simulated annealing. However, it is more likely that an attacker will find an imperfect encryption/decryption key using such heuristics. Such an imperfect key will work for the known plaintext-ciphertext pair, but not an arbitrary unseen plaintext-ciphertext pair using the original key. In this paper, we illustrate the problem and attempt to characterise the increase in security it affords optical encryption.

A new method of three-dimensional (3D) image optical encryption based on phase-shifting compressive Fresnel holography (PSCFH) is presented. In the optical encryption step, the 3D object is encrypted with random phase masks using phase-shifting interferometry to record three intensity images with different phase-shifting. In the decryption step, the three-step phase-shifting technique is first used to extract the complex optical field at the recording plane. Finally, the 3D object is reconstructed from the recovered complex optical field using compressive Fresnel holography with the correct key. Numerical experiments demonstrate the feasibility and robustness of our proposed PSCFH method.

We investigate the effects on rotation angle arrangement in the proposed angle multiplexing method for optical image encryption using the phase-only function in the Fresnel transform domain. The computer simulation results show that the images reconstructed with the asymmetric rotation angles can be more secure than that with symmetric arrangements.

A novel chaos based optical image encryption using fractional Fourier transform and DNA sequence operation

The optical image encryption has attracted more and more researchers’ attention, and the various encryption schemes have been proposed. In existing optical cryptosystem, the phase functions or images are usually used as the encryption keys, and it is difficult that the traditional public-key algorithm (such as RSA, ECC, etc.) is used to complete large numerical key transfer. In this paper, we propose a key distribution scheme based on the phase retrieval algorithm and the RSA public-key algorithm, which solves the problem for the key distribution in optical image encryption system. Furthermore, we also propose a novel image encryption system based on the key distribution principle. In the system, the different keys can be used in every encryption process, which greatly improves the security of the system.

High-efficiency optical image authentication scheme based on ghost imaging and block processing