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.

Keywords

• chaotic image encryption
• enhanced confusion-diffusion
• image cryptography
• mixed chaotic maps
• multi-level image encryption