Article Preview
Top1. Introduction
With the development of the Internet, smartphones and cellular networks, the transmitting of secure information has been becoming vital. Since images carry sensitive information and transmit in public environments universally, data protection such as image encryption represents a significant portion of the research undertaken nowadays (Artiles et al., 2019; Chen et al., 2018; Ding et al., 2018; Chen et al., 2018). Optical systems with transforms are of growing interest for image encryption because of their distinct advantages of processing two-dimensional data in parallel and at high speed (Javidi et al., 1995; Chen et al., 2006; Huang et al., 2016). Among them, double random phase encryption (DRPE) proposed by Refregier and Javidi is the most widely used encryption scheme (Liu et al., 2001). This method uses two random phase masks to encrypt the original image, one in the input plane and the other in the Fourier plane. Afterwards, to increase the security of the classical DRPE, some transforms have been used to instead of the Fourier transform such as the fractional Fourier transform (Unnikrishnan et al., 2000; Annaby et al., 2016).
These improved algorithms have shown their advantages in image security. However, because they are independent of plaintext, the encryption techniques based on transforms have been proven to be vulnerable to chosen-ciphertext, known-plaintext, chosen-plaintext attacks (Wu et al., 2015; Rajput et al., 2013; Peng et al., 2006; Carnicer et al., 2005). Although several enhancement strategies have been proposed to avoid this vulnerability (Alfalou et al., 2013; Kumar et al., 2009; Dong et al., 2008), the security of transforms themselves have been threatened by a ciphertext-only attack with the phase retrieval algorithm (Liao et al., 2017; Guo et al., 2016). Relating the transform with plaintext and its relevant information is efficient to enhance security under cryptographic attacks.
As an efficient model, the graph Fourier transform (GFT) (Sandryhaila et al., 2013; Shuman et al., 2013) enables us to analyze the structural data sets described by graphs. Recently, the graph spectral interpretation of traditional 2D images has been researched and demonstrated advancement in some digital image processing areas, such as image compression (Shen et al., 2010), restoration (Liu et al., 2015) and filtering (Chen et al., 2015). Since the underlying graphs reveal signal structures and the signal samples at vertexes are analyzed for their correlation and similarity, the graph transforms are naturally related with plaintexts and can enhance the security under plaintext attack and ciphertext attack. So far, there are only a few methods using graph signal processing methods for gray-level image encryption (Fracastoro et al., 2017; Sharm et al., 2018; Gondim et al., 2019), and color image encryption is even not researched. When the GFT is used for encryption, the problem appears that the parameters are fixed for the whole image, which can not provide large parameter space. Meanwhile, the energy of encrypted images is still assembled in particular intervals, which makes the transformed signal non-uniform and vulnerable for different attacks.
In this paper, an angular graph Fourier transform (AGFT) is introduced to encrypt color images with their intrinsic structures. To enlarge parameter space, the GFT is extended to the AGFT which has the desired multiple-parameter property of angular transform and the structural-related property of graph transform. Then, an image encryption method based on the AGFT is proposed to encrypt images with their intrinsic structures for better security. In the proposed encryption method, color images are encoded by DNA sequences, and the DNA encoded diffused image is confused under the control of the spatiotemporal chaotic key streams firstly. Then, a color image is decomposed into several sparse sub-images. Since these sub-images comprise random walk paths reflecting pixels correlation of image, this step improves the randomness of spatial distribution. Afterwards, the Laplacian matrix is used to indicate the underlying graph structure, which makes the encryption process not only related to the transform operator but also related to the intrinsic image structure. Thus, the security of the proposed algorithm under plaintext attacks is enhanced. Then, the signals are transformed into the AGFT domains with different angular parameters, which determine the energy distribution of the original signal on eigenvectors and control the uniformity of signal energy distribution. Finally, the experimental results demonstrate that the proposed algorithm significantly enhances data security and achieves better performance than state-of-art algorithms.