2D Logistic-Modulated-Sine-Coupling-Logistic Chaotic Map for Image Encryption

Abstract

Due to the significant properties of unpredictability, ergodicity, and initial state sensitivity, chaotic system is widely used as a useful tool in image encryption. In this paper, we propose a 2-dimensional logistic-modulated-sine-coupling-logistic chaotic map (LSMCL), where we use the logistic map to modulate Sine map and couple the result of modulation and Sine map together. In terms of chaotic trajectory, Lyapunov exponent, and Kolmogorov entropy, comparing with other existing chaotic maps, we can observe that LSMCL has better chaotic performance. Furthermore, we propose an LSMCL-based image encryption algorithm with two rounds of permutation and diffusion operation. First, we provide a secret key generation procedure to generate the initial values and do permutation operation with the chaotic matrix by LSMCL. Furthermore, in diffusion procedure, we use two different chaotic matrices generated by LSMCL to change the pixel values in row and column. Finally, we provide some theoretical analyses and simulations to confirm the security and the validity of the proposed algorithm.

Image Encryption Algorithm Based on Tent Delay-Sine Cascade with Logistic Map

“…The circle symbol in Equation 4represents the composition of two functions. Compared to the 1D delay and linearly coupled logistic chaotic map (DLCL) [15] and a two-dimensional logistic-modulated sine-coupling logistic chaotic map (LSMCL) [1], the structure of TDSCL produces better chaotic performance. In the following section, we use the trajectory, Lyapunov exponent, and permutation entropy (PE) to analyze the characteristics of chaotic maps.…”

“…where C(i, j) and C'(i, j) are the cipher image generated by the original key and the changed key in the key sensitivity test, respectively. The ideal values of NPCR and UACI are 99.6094% and 33.4635% for an 8-bit grey scale image, respectively [1]. Table 2 lists the simulation results.…”

“…Their secure transmission plays a vital role in personal and military privacy. In recent years, many chaotic image encryption algorithms have been proposed [1][2][3][4][5][6][7][8][9][10] due to the excellent properties of chaotic maps, such as initial value sensitivity and intrinsic randomness.…”

A Tweakable Image Encryption Algorithm Using an Improved Logistic Chaotic Map

“…When the parameter r do not belong to this range, it cannot be considered to have a chaotic behavior and non-uniform distribution of the output chaotic sequences that affected the distributions of encrypted image data and the performance of encryption system. The Lyapunov exponent (LE) represents a quantitative measure of the sensitivity of the control parameters of chaotic maps [20]. Mathematically it can be represented as:…”

“…Chaotic maps with weak chaotic behaviors can make the cryptosystems vulnerable to attacks and can be easily broken. In recent years several works available in the literature have suggested to overcome the disadvantages of these chaotic maps by improving the properties of chaotic distribution for better performance and effectiveness of image encryption algorithms [19,20]. Hua et al [21] suggested a sine chaotic model (SCM) to improve the chaos complexity of existing chaotic range of (1-D) chaotic maps.…”