Secure color image encryption using a fractional-order chaotic PRNG and DNA-level operations

Color image encryption is challenging due to large data volumes, strong inter-pixel correlations, and high redundancy, limiting the use of conventional text-oriented encryption. While chaos-based methods have been studied extensively, many schemes struggle with unjustified key spaces, plaintext-dependent keystreams, insufficient evaluation of keystream randomness, and inadequate support for DNA rule design. This work proposes a secure color image cryptosystem by integrating a fractional-order chaotic pseudo-random number generator (FCPRNG) with a DNA-level encryption framework. The proposed FCPRNG is built on a three-dimensional fractional-order Lü system under a non-uniform-grid numerical scheme, and its admissible parameter-order joint space is systematically identified to restrict keystream generation to regions of sustained bounded chaos. Based on this generator, a plaintext-independent encryption framework is constructed, decoupling keystream generation from plaintext processing. In addition, a purely DNA-level encryption architecture is designed, in which the plain image undergoes joint RGB-channel permutation and pixel-value transformation through an inter-layer pixel-value-dependent DNA encoding mechanism, followed by DNA-domain confusion and diffusion operations. Experimental results show statistically suitable keystreams, strong ciphertext randomness, high sensitivity to the key and plaintext, and moderate robustness against noise and cropping. These results indicate that the scheme provides a structurally improved and empirically effective approach to secure color image encryption.