Reversible steganography in cipher domain for JPEG images using polynomial homomorphism

Reversible steganography in the cipher domain enables secret communication while preserving the privacy of the cover media. In this paper, we present a novel reversible steganographic method for JPEG images in cipher domain. The direct current (DC) coefficients are encrypted in a manner that maintains both the JPEG format and file size. The alternating current (AC) coefficients and the secret data are first encoded into codewords over a Galois field using Hamming code. The resulting codewords are then independently encrypted via polynomial-based secret sharing. Subsequently, the shares of secret data are embedded into the shares of AC coefficients using polynomial homomorphism. To ensuring reliability of image reconstruction and secret extraction, a cheating detection code is employed to authenticate the marked shares. Experimental findings demonstrate that our scheme outperforms the state-of-the-art methods in terms of embedding capacity while preserving the file size and format.