An Algorithm of Image Encryption Using Logistic and Two-Dimensional Chaotic Economic Maps

Abstract

In the literature, there are many image encryption algorithms that have been constructed based on different chaotic maps. However, those algorithms do well in the cryptographic process, but still, some developments need to be made in order to enhance the security level supported by them. This paper introduces a new cryptographic algorithm that depends on a logistic and two-dimensional chaotic economic map. The robustness of the introduced algorithm is shown by implementing it on several types of images. The implementation of the algorithm and its security are partially analyzed using some statistical analyses such as sensitivity to the key space, pixels correlation, the entropy process, and contrast analysis. The results given in this paper and the comparisons performed have led us to decide that the introduced algorithm is characterized by a large space of key security, sensitivity to the secret key, few coefficients of correlation, a high contrast, and accepted information of entropy. In addition, the results obtained in experiments show that our proposed algorithm resists statistical, differential, brute-force, and noise attacks.

Image Encryption Algorithm Based on Logistic and Two-Dimensional Lorenz

“…In order to better understand the influence of the change of a single pixel in a cryptographic image on a cryptographic image, measurement methods such as NPCR (pixel number change rate) and UACI (uniform average change intensity) are used [7]:…”

“…Gray image can be analyzed by comparing the pixel difference between a pixel point in the image and its four surrounding pixels. Gray-scale analysis of the image is carried out by calculating equation 12, equation 13 and equation 14 [7].…”

“…Chaotic models include Arnold Cat map, Logistic map, Lorenz, Henon map, and some other models [6]. This complex nature of chaotic mapping can be reflected in the characteristics of certain encryption processes similar to ideal ciphers, such as diffusion, aliasing, balancing, and avalanche [7].…”

An Image Encryption Scheme Based on Block Scrambling, Modified Zigzag Transformation and Key Generation Using Enhanced Logistic—Tent Map

“…Previously, various encryption techniques that are dependent on chaos have been examined and broadly contemplated. Image encryption algorithms have been constructed based on a logistic and two-dimensional (2D) chaotic economic map [ 6 ], variable length codes that are based on Collatz conjecture [ 7 ], 2D discrete wavelet transform and Arnold mapping [ 8 ], logistic mapped convolution and cellular automata [ 9 ], cat map [ 10 ], 2D Chebyshev-sine map [ 11 ], 2D Sine Logistic modulation map [ 12 ], one-dimensional (1D) delay with linearly coupled Logistic chaotic map [ 13 ], a hyper-chaotic system that combines Dynamic Filtering, DNA computing, and Latin Cubes (DFDLC) [ 14 ], Arnold Transform followed by Qubit Random Rotation [ 15 ], 2D Baker’s map with diffusion process based on XORing [ 16 ], ant colony optimization [ 17 ], Chebyshev Map followed by Rotation Equation [ 18 ], an algorithm combining Julia fractal and Hilbert curve [ 19 ], four-dimensional (4D) hyper-chaotic nonlinear Rabinovich system [ 20 ], Josephus traversing and mixed chaotic map [ 21 ], 2D logistic-modulated-sine-coupling-logistic chaotic map [ 22 ], multiple permutation of pixels followed by the 2D Chebyshev function [ 23 ], chaos map with pixel permutation [ 24 ], improved hyperchaotic sequences [ 25 ], high-dimension Lorenz chaotic system with a perceptron model [ 26 ], rotation matrix bit-level permutation with block diffusion [ 27 ], and discrete Chirikov map with chaos-based fractional random transform [ 28 ].…”

Breaking an Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos

“…In the past three decades, many novel image encryption schemes based on various methodologies were proposed, such as chaos theory [ 6 ], DNA computing [ 7 ], cellular automaton [ 8 , 9 ], and quantum information [ 9 , 10 ]. Among them, chaos is the most popular one because it has the unique characteristics of sensitivity to initial values and parameters, ergodicity, and deterministic inherent randomness [ 11 , 12 , 13 , 14 , 15 , 16 ], which correspond to the confusion and diffusion properties of encryption [ 17 ]. Moreover, DNA computing has the characteristics of high parallelism, large storage capacity, and low energy consumption [ 7 ].…”