A new hybrid dyadic-tent chaotic function for secure digital image encryption

Abstract

Image encryption is significant for protecting visual data in modern digital communication systems. The sensitivity of chaotic functions to initial conditions and strong pseudo-randomness has led to their usefulness as cryptography techniques. This study developed a new hybrid chaotic function which combines the Dyadic Transformation Map and the Tent Map to create a stronger and more secure mechanism for image encryption. To further enhance keystream unpredictability, SHA-256 hashing was used as a whitening layer. The chaotic characteristics of the proposed function were evaluated using the Lyapunov exponent, confirming its usefulness in cryptography. The hybrid function was tested on both grayscale and color images to evaluate its performance in entropy, histogram uniformity, pixel decorrelation, and resistance to statistical attacks, and the effect of SHA-whitening. Results show that the hybrid function provides strong pixel diffusion and confusion while maintaining low computational cost, making it a lightweight yet highly secure encryption method. Thus, the proposed approach offers an effective and reliable solution for image protection in resource-constrained environments.