Nonlinear Dynamics in Cryptographic Systems for Image Encryption: A Mathematical Modeling Approach

Abstract

Strong image encryption techniques are vital in recent years given the exponential growth of digital media and the accompanying rise in cyberthreats. High-dimensional data such as images questions conventional cryptographic methods in handling. Nonlinear dynamics offer a good replacement by means of chaotic systems to attain high degrees of security and computational efficiency. This work proposes a novel nonlinear dynamic model image encryption technique using which cryptographic security is enhanced. The fundamental flaw of linear cryptographic methods to differential and linear cryptanalysis is mostly fixed here. Our method introduces considerable uncertainty and sensitivity to initial conditions by including nonlinear transformations and chaotic maps, so improving security. Using a two-dimensional logistic map to produce encryption keys collectively together with a diffusion and permutation process guarantees pixel-level obfuscation in the proposed model. Important sensitivity and entropy values show the success of our approach in experimental results. Our method particularly achieves an average entropy of 7.9992 and a correlation coefficient of -0.0013 between adjacent pixels, so indicating a considerable increase in randomness and security relative to present methods.