In the digital era, the significance of cryptographic algorithms has grown significantly within the realm of cybersecurity. This research presents an innovative approach to image encryption that eliminates the security limitations of the conventional one-dimensional logistic mapping. This approach relies on an enhanced two-dimensional logistic-fraction hybrid chaotic mapping (2D-LFHCM) and deoxyribonucleic acid (DNA) computing. Initially, the improved 2D-LFHCM is utilized to effectively scramble the image by incorporating chaotic sequences. Then, two novel algebraic DNA computing rules are introduced to enhance diffusion encryption. Experimental findings show that this approach offers superior security performance, even with renowned attacks.