An Image Encryption Scheme Combining 2D Cascaded Logistic Map and Permutation-Substitution Operations

Abstract

Confusion, diffusion, and encryption keys affect the quality of image encryption. This research proposes combining bit- and pixel-level permutation and substitution methods based on three advanced chaotic logistic map methods. The three chaotic methods are the 2D Logistic-adjusted-Sine map (2D-LASM), the 2D Logistic-sine-coupling map (2D-LSCM), and the 2D Logistic ICMIC cascade map (2D-LICM). The encryption method’s design consists of six stages of encryption, involving permutation operations based on chaotic order, substitution based on modulus and bitXOR, and hash functions. Hash functions are employed to enhance key space and key sensitivity quality. Several testing tools are utilized to assess encryption performance, including histogram and chi-square analysis, information entropy, correlation of adjacent pixels, differential analysis, key sensitivity and key space analysis, data loss and noise attacks, NIST randomness tests, and TestU01. Compared to using a single 2D logistic map, the amalgamation of bit-level and pixel-level encryption and the utilization of three 2D cascade logistic maps has improved encryption security performance. This method successfully passes the NIST, TestU01, and chi-square tests. Furthermore, it outperforms the previous method regarding correlation, information entropy, NPCR, and UACI tests.

Can There Be a Two Way Hash Function?

“…Confusion refers to making it difficult to estimate the statistical relationship between the original data and encrypted data. Diffusion is the homogeneous distribution of the original data to encrypted data [15]. The strength of encryption is directly proportional to the success of the confusion-diffusion complexity and randomness of the keys.…”

Fractal-Based Hybrid Cryptosystem: Enhancing Image Encryption with RSA, Homomorphic Encryption, and Chaotic Maps

“…Proposed Lena −0.0041 0.0062 0.0091 Hue et al [48] 0.0004 0.0012 0.0009 Zhang et al [47] −0.00058 0.01091 −0.012076 Setiadi et al [49] −0.0011 0.0005 0.0007 Proposed Pepper 0.0021 0.0006 0.0018 Hue et al [48] 0.0027 0.0020 −0.0042 Alexian et al [50] −0.00021 0.00027 0.00128 Proposed Baboon −0.0003 −0.0011 0.0008 Hue et al [48] −0.0070 0.0021 −0.0077…”