A fast algorithm for matrix embedding steganography is proposed in this paper. Matrix embedding encodes the cover image and the secret message with an error correction code and modifies the cover image according to the coding result. The modification to the cover image is the coset leader of the error correction code, and it is computationally complex to find the coset leader. This paper proposes a fast algorithm to find the coset leader by using a lookup table algorithm. The proposed algorithm is suitable for matrix embedding steganography using Hamming code and random linear code. In our scheme, the syndrome of the coset is used to search for the coset leader in the standard array of the error correction code. For the Hamming code, we improved the parity check matrix of the code in order to make the syndrome indicate the coset leader by itself. Therefore, it is not necessary to search for the coset leader in a table. For the random linear code, this method is effective for most cosets, and we only memorize the coset leaders that cannot be identified by their syndromes. With this approach, the size of the table can be reduced significantly, and the computational complexity of embedding can be decreased. The proposed fast embedding algorithm has the same embedding efficiency as the conventional matrix embedding. Compared with the existing fast matrix embedding algorithms, the computational complexity of the proposed scheme is decreased significantly for the steganographic systems with low and medium embedding rates. 
A fast algorithm for matrix embedding steganography