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Cryptographic Image Scrambling Techniques
Published in S. Ramakrishnan, Cryptographic and Information Security, 2018
In [6], a matrix based scrambling technique is used, based on Arnold’s cat map. Arnold’s cat map is a chaotic map named after Vladimir Arnold who proposed the algorithm. The scrambling using Arnold’s cat map is also known as Arnold’s Transformation. The matrix based scrambling may also be done based on Fibonacci transform [5]. Fibonacci transform [7] has a unique property of uniformity. The pixels that are at equal distance from each other in original image remain at equal distances in the encrypted image as well. The adjacent pixels are also spread as far as possible resulting very low correlation between the adjacent pixels. In [8,9] the authors claimed a comparison of six scrambling methods, But they have kept the scrambling procedure unchanged with six different random matrix generators. Two other permutation measures are presented in [8].
Hiding Media Data via Shaders: Enabling Private Sharing in the Clouds
Published in Kaikai Liu, Xiaolin Li, Mobile SmartLife via Sensing, Localization, and Cloud Ecosystems, 2017
Define the chaotic mapping as Γ $ \Gamma $ . Using Γ $ \Gamma $ for image encryption, it should be invertible. There are lots of chaotic maps available, e.g., Arnold’s cat map, Baker’s map, logistic map, tent map. Using the Arnold’s cat map as an example, the transform of Γ $ \Gamma $ could be written as Γ:(x,y)→(2x+y,x+y)modN $ \Gamma \, : \, (x,y) \rightarrow (2x+y,x+y) \;\@mod \;N $ , where N is the pixel dimension. The initial coefficient of the Arnold mapping is ar=[21;11] $ a_r=[2 \quad 1; 1 \quad 1] $ ; its higher order O-th could be written as arO $ a_r^O $ . We encrypt the image frame with different orders of Arnold transform. The encrypted images are shown in Fig. 11.2. It is clear to see that higher order contributes a better encryption property with higher randomization. However, higher orders show pixel blur due to the amplification of the round-off error as stated before.
Image Encryption Algorithm Based on Arnold Transform and Chaos Theory in the Multi-wavelet Domain
Published in International Journal of Computers and Applications, 2023
Ali Akram Abdul-Kareem, Waleed Ameen Mahmoud Al-Jawher
Arnold Transform (AT), also known as Arnold cat map, is a chaotic system utilized extensively in image encryption to transform pixels from position (x, y) to position (x1, y1) straightforwardly and efficiently [20]. AT can also be expressed as: Where N is the image size, although it can destroy the image structure and produce an incomprehensible image by scrambling the pixel positions, the traditional Arnold transform described in equation (5) has a high periodicity proportional to the size of the image and is easy for unauthorized individuals to decipher, resulting in Weak security. However, its speed and ease of use are unmatched [21–26]. In the proposed algorithm, the Arnold Transform was used instead of other methods to globally change the GHM coefficients and image energy dissipation due to its simplicity and speed in dealing with 2D images. In the final two stages of the algorithm, 3D chaotic systems are employed to rearrange the image position index and modify the element values, thereby destroying the intrinsic periodicity of the Arnold transform and enhancing the image’s security.
Advanced 5D logistic and DNA encoding for medical images
Published in The Imaging Science Journal, 2023
Bharti Ahuja, Rajesh Doriya, Sharad Salunke, Md. Farukh Hashmi, Aditya Gupta
Vladimir Arnold created the approach and demonstrated its results using a cat drawing in 1967. As shown in Figure 4, the Arnold Cat Map algorithm is an iterative series of stretching with the shear of a unit square and translation back to the unit square. The mapping retains and combines regions, and it is reversible. It is also often used in cryptography and may be described as: