In the current research field of digital image encryption technology, there are some key challenges, including insufficient key space, the weak sensitivity of key parameters, and low complexity of the encryption process. To address these issues, this study proposes a double image encryption framework to enhance the security of image encryption algorithms. In the first encryption, this study proposes an improved generative adversarial network incorporating unsupervised learning properties, adaptive layer instance normalization, multi-level attention enhanced residual network structure, and feature distribution fidelity module. This study also proposes a comprehensive loss function for the network, which consists of an encryption loss function, a decryption loss function, an image space smoothness improvement loss function, a generator veracity enhancement loss function, and an identity loss function. In the second encryption, this study proposes a six-dimensional hyperchaotic system possessing four positive Lyapunov exponents for the first scrambling operation, and combines the Fibonacci Q-matrix and classical shuffling algorithms for the diffusion and second scrambling operations. By combining deep learning techniques with chaotic systems, the key space and the quality of the encrypted images are effectively improved, as well as the ability of resistance to the burst attack, salt-and-pepper noise attack and cropping attack. This study provides new perspectives and technical routes for solving the challenges faced in digital image encryption.