We propose a joint scrambling and diffusion image encryption algorithm based on RNA theory and row–column–level operation (JSDRR), encompassing the following procedures: initially, pseudo-random sequences are generated utilizing a six-dimensional hyper-chaotic system, which serves to augment the randomization in the image encryption process. Subsequently, the theory of RNA is integrated with the row–column–level cryptographic approach for combined scrambling and diffusion, thereby augmenting the efficacy of the proposed algorithm. Finally, we elucidate a cutting-edge joint scrambling and diffusion image encryption algorithm, designed to withstand a multiplicity of attacks. Employing simulation and comparative analytical methodologies, it is demonstrated that the JSDRR exhibits robustness against a varied spectrum of attacks with commendable efficiency.