Image Encryption Using Logistic Chaotic Map

This article explores an image encryption method based on the Logistic chaotic map, designed to protect images from unauthorized access and theft. The methodology employs chaotic mapping to scramble image pixels, significantly enhancing encryption security through pseudorandom sequence generation. In implementation, the Logistic map equation xₙ₊₁ = μxₙ(1-xₙ) is typically iterated to produce chaotic sequences, where μ represents the bifurcation parameter (usually 3.57<μ≤4) and x₀ the initial value. These sequences are then binarized or normalized to generate permutation keys for pixel position shuffling and substitution operations. Key algorithmic steps include: 1) Converting the input image to a pixel matrix; 2) Generating chaotic sequences using predefined parameters; 3) Applying XOR operations or modulo arithmetic for pixel value diffusion; 4) Implementing Arnold cat map or custom permutation for spatial confusion. The discussion covers advantages like high key sensitivity and resistance to statistical attacks, alongside limitations including computational overhead and parameter selection challenges. Future research directions involve hybrid chaotic systems integration and performance optimization for real-time applications. We believe this Logistic map-based encryption approach will play a vital role in privacy protection and holds promise for widespread adoption in secure multimedia communication systems.