Provably Secure Generative Steganography Based on Adjustable Orthogonal Mapping

Generative steganography employs generative models to synthesize stego images directly from secret information, avoiding cover image modifications required in traditional steganography, thereby evading detection by steganalytic tools. The latest advances in image generation technology have spurred significant progress in the field of generative steganography. Nevertheless, existing generative steganography still encounters significant challenges in terms of provable security, robustness, capacity, and visual quality. To this end, we construct an adjustable orthogonal mapping (AOM) framework, and based on it propose a provably secure generative steganographic method, named GSAOM. Specifically, the sender employs AOM to convert the secret information into the latent variable that follows the standard normal distribution and then inputs it into the diffusion model to generate a high-quality stego image. Correspondingly, the receiver converts the stego image back into the latent variable through the inversion of the diffusion model, and then extracts the secret information via the inverse mapping of the AOM. Since both the latent variable exported from AOM and the latent variable randomly generated during regular image generation follow the standard normal distribution, our proposed GSAOM can achieve provable security. Additionally, AOM allows for adjustable capacity and can maximize the distinguishability of the extracted secret information, endowing GSAOM with advantages in capacity and robustness. Extensive experiments demonstrate that GSAOM performs well in capacity, visual quality, security, robustness, and generalization.