Incorporating Zero-Knowledge Proofs into Chaos-Based Steganography for Image Verification

Abstract

Conventional steganographic systems primarily aim at imperceptible data hiding but lack a formal mechanism to verify that an embedding procedure has been executed correctly without revealing the hidden content. This paper proposes a fragile verifiable steganographic framework that integrates chaos-based Least-Significant-Bit (LSB) embedding with a zero-knowledge proof system. A secret message is embedded into the LSBs of image pixels whose locations are permuted using a combination of Arnold's Cat Map and the Logistic Map, with chaos seeds derived from image-dependent features. In parallel, a zk-SNARK (Groth16) proof is generated to attest, in a zero-knowledge proof technique, that a valid LSB embedding consistent with the prescribed chaotic transformations and system parameters has been performed. Verification properties, including chaos parameters, hash commitments, proof length, and the serialized Groth16 proof, reside entirely in pixel LSBs, with the public verification header placed at positions derived from a publicly known proof key. This allows a verifier, given only a single received image and a pre-installed system configuration, to extract the required verification parameters directly from the LSBs of the image and validate the proof without accessing the embedded message. Consequently, any post-embedding modification, including lossy transformations, is treated as an integrity violation that invalidates verification. Experimental results show that the proposed scheme preserves high visual fidelity, achieving favorable PSNR, SSIM, and MSE values while maintaining a Groth16 proof in raw binary of 256 Bytes and a compact proof size of 739 Bytes in the JSON serialization used by the implementation. These properties make the system suitable for deployment in resource-constrained environments, including IoT networks and embedded communication settings such as CAN-based systems, where verifiable embedding integrity is required.