“A Mathematical Model for Public Key Image Encryption Algorithm Using Higher Order Differential Equations"

Abstract

This paper introduces a novel public-key image encryption scheme grounded in higher-order ordinary differential equations (ODEs). A fourth-order nonlinear hyperchaotic system is proposed. The public key is constructed from discretized chaotic trajectories, while the private key consists of sensitive initial conditions and control parameters. The encryption combines pixel permutation and diffusion using sequences derived from the hyperchaotic system. Experimental results on standard test images (Lena, Baboon, Peppers, Boat) demonstrate outstanding performance with information entropy close to 8, near-zero correlation coefficients, NPCR > 99.61%, and UACI > 33.45%. Security analyses confirm strong resistance against statistical, differential, chosen-plaintext, and brute-force attacks. The proposed model offers a significant contribution to public-key cryptography using higher-order differential equations.